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Vacuum effects on interference in two-photon down conversion
Abstract
A proposed experiment is analyzed theoretically. In the proposed experiment two coherent pump waves fall on two identical nonlinear crystals, down-converted signal and idler beams from the two crystals are mixed by two beam splitters, and the coincidence counting rate for photons leaving the beam splitters is measured. We show that this counting rate depends on the phase difference between the two coherent pump waves, and results from the interference of the vacuum with the down-converted photons. The experiment could be used to look for locality violations along the lines recently proposed by Grangier, Potasek, and Yurke [Phys. Rev. A 38, 3132 (1988)], but without the need for a coherent reference beam for homodyning.
... In this paper we revisit SPDC from a perspective somewhat different from much of the previous work on the subject. For this purpose, we investigated the interference of two biphotons generated in two parallel, pumped down-conversion crystals as in [7], but with no further coupling, as in [8,9]. Our experimental results are in agreement with the earlier work (but with much greater interference visibility), but it seems worthwhile to describe and analyze them from the perspectives taken in our recently-reported work [7,10] and to formulate in more detail the analyses outlined in that work. ...
... The factor K need not be specified, nor will it be necessary to normalize |ψ(t) for our purposes. As discussed in [8], the "entanglement with the vacuum" described by the state (9) implies the observed two-photon coincidence rate. In terms of interfering probability amplitudes as discussed above, the amplitude to count (annihilate) a signal photon s1 at Detector A in coincidence with an idler photon i1 at Detector B, including the phase delay φ 1 , is proportional to vac|a s1 e iφ 1 a i1 |ψ = C 1 e iφ 1 , where the vacuum state of the field is denoted by ...
... The generalization to non-identical crystals or pump fields is straightforward and of course reproduces the complementarity relation (8). ...
Using two crystals for spontaneous parametric down-conversion in a parallel setup, we observe two-photon interference with high visibility. The high visibility is consistent with complementarity and the absence of which-path information. The observations are explained as the effects of entanglement or equivalently in terms of interfering probability amplitudes and also by the calculation of a second-order field correlation function in the Heisenberg picture. The latter approach brings out explicitly the role of the vacuum fields in the down-conversion at the crystals and in the photon coincidence counting. For comparison, we show that the Hong–Ou–Mandel dip can be explained by the same approach in which the role of the vacuum signal and idler fields, as opposed to entanglement involving vacuum states, is emphasized. We discuss the fundamental limitations of a theory in which these vacuum fields are treated as classical, stochastic fields.
... In this paper we revisit SPDC from a perspective somewhat different from much of the previous work on the subject. For this purpose, we investigated the interference of two biphotons generated in two parallel, pumped down-conversion crystals as in [7], but with no further coupling, as in [8,9]. Our experimental results are in agreement with the earlier work (but with much greater interference visibility), but it seems worthwhile to describe and analyze them from the perspectives taken in our recently-reported work [7,10] and to formulate in more detail the analyses outlined in that work. ...
... The factor K need not be specified, nor will it be necessary to normalize |ψ(t) for our purposes. As discussed in [8], the "entanglement with the vacuum" described by the state (9) implies the observed two-photon coincidence rate. In terms of interfering probability amplitudes as discussed above, the amplitude to count (annihilate) a signal photon s1 at Detector A in coincidence with an idler photon i1 at Detector B, including the phase delay φ 1 , is proportional to vac|a s1 e iφ 1 a i1 |ψ = C 1 e iφ 1 , where the vacuum state of the field is denoted by ...
... The generalization to non-identical crystals or pump fields is straightforward and of course reproduces the complementarity relation (8). ...
Using two crystals for spontaneous parametric down-conversion in a parallel setup, we observe two-photon interference with high visibility. The high visibility is consistent with complementarity and the absence of which-path information. The observations are explained as the effects of entanglement or equivalently in terms of interfering probability amplitudes and also by the calculation of a second-order field correlation function in the Heisenberg picture. The latter approach brings out explicitly the role of the vacuum fields in the down-conversion at the crystals and in the photon coincidence counting. For comparison, we show that the Hong–Ou–Mandel dip can be explained by the same approach in which the role of the vacuum signal and idler fields, as opposed to entanglement involving vacuum states, is emphasized. We discuss the fundamental limitations of a theory in which these vacuum fields are treated as classical, stochastic fields.
... In the 1980's and 1990's, Mandel's group proposed and performed ground-breaking experiments involving two non-linear crystals. In such an experiment [14,15], "phase memory" of the pump beam implied an "induced coherence" between the two crystals: although the process of SPDC is random, coherence can be induced [16]. A follow-up proposal by Ou [17] showed how this type of experiment can be extended into a quantum eraser [18,19]. ...
... The maximally entangled state from equation (7) can be obtained with the experimental setup from Fig. 3. It is the experimenal setup propozed by Ou, Wang, Zhou and Mandel (OWZM) [14,15]. It is noteworthy that although in this experimental setup a single pair of photons is created, this pair is in a coherent superposition of originating from the first and second non-linear crystal. ...
... It is noteworthy that although in this experimental setup a single pair of photons is created, this pair is in a coherent superposition of originating from the first and second non-linear crystal. Coherence is induced by the pumping laser [14,15,16]. ...
Entangled states are notoriously non-separable, their sub-ensembles being only statistical mixtures yielding no coherences and no quantum interference phenomena. The interesting features of entangled states can be revealed only by coincidence counts over the (typically) two sub-ensembles of the system. In this paper we show that this feature extends to properties thought to be local, for example the transmissivity coefficient of a beam splitter. We discuss a well-known experimental setup and propose modifications, so that delayed-choice can be added and this new feature of entanglement tested.
... The non-linear optical process of spontaneous parametric down-conversion (SPDC) [1,2,3] creates pairs of highly entangled single photon pairs [4,5]. Its use became ubiquitous in quantum optics (QO), where numerous experiments rely on this process [6,7,8,9,10,11,12,13]. ...
... SPDC is a process that happens randomly, somehow in the spirit of spontaneous emission of an excited atom. However, in an experiment by Ou, Wang, Zou and Mandel [9,10], two non-linear crystals fed by the same pump laser show a phenomenon of "phase memory". A landmark experiment using two non-linear crystals was performed by Zou, Wang and Mandel [11]. ...
... The quantum state (1) also implies that no two down-conversions happen at the same moment. This is consistent with the low down-conversion efficiency [9,11,13] of the non-linear crystals. ...
In this paper we propose and analyse a Gedankenexperiment involving three non-linear crystals and two objects inserted in the idler beams. We show that, besides the behaviour that can be extrapolated from previous experiments involving two crystals and one object, we are able to predict a new effect: under certain circumstances, one of the objects can be rendered undetectable to any single detection rate on the signal photons with discarded idler photons. This effect could find applications in future developments of quantum imaging techniques.
Graphical abstract
... Refs. [85][86][87][88][89][90][91]). ...
... The overlap of the resulting state with the two-photon output state is then computed. This can either be performed directly via perturbation theory [86,87,101] or, equivalently, using a Fermi's Golden Rule approach [91]. The probability of achieving the desired final state can be converted to a count rate by multiplying the photon flux of the pump beam. ...
... Given a quantum state, |ψ , the count rate as seen by coincidence detectors located at r ds and r di is given by [86,87,101] ...
... In the spatial degree of freedom, a very general spatially partially coherent field was considered and it was shown that the spatial coherence properties of the pump field get entirely transferred to that of the down-converted two-photon field [19]. However, in the temporal degree of freedom, the effects due to the temporal correlations of the pump field have only been studied in two limiting situations: one, in which the constituent frequency components are completely correlated (fully-coherent pulsed field) [15,[32][33][34][35][36] and the other, in which the constituent frequency components are completely uncorrelated (continuous-wave field) [7][8][9][10][11][12][13][14][37][38][39][40][41][42][43]. In this article, we study the coherence transfer in PDC for a general temporally partially coherent pump field and explicitly quantify this correlation trans- * akjha9@gmail.com; ...
... The parameters defined above are identical to those defined in Ref. [11], except for τ ′ 1 , τ ′ 2 and ∆τ ′ , which have been scaled down by a factor of 2. It is found that this rescaling imparts the equations in this paper a neat and symmetric form. The two-photon state |ψ 1 produced in alternative 1 in the weak-downconversion limit is given by [32,37,45]: ...
We show that in parametric down-conversion the coherence properties of a temporally partially coherent pump field get entirely transferred to the down-converted entangled two-photon field. Under the assumption that the frequency-bandwidth of the down-converted signal-idler photons is much larger than that of the pump, we derive the temporal coherence functions for the down-converted field, for both infinitely-fast and time-averaged detection schemes. We show that in each scheme the coherence function factorizes into two separate coherence functions with one of them carrying the entire statistical information of the pump field. In situations in which the pump is a Gaussian Schell-model field, we derive explicit expressions for the coherence functions. Finally, we show that the concurrence of time-energy-entangled two-qubit states is bounded by the degree of temporal coherence of the pump field. This study can have important implications for understanding how correlations of the pump field manifest as two-particle entanglement as well as for harnessing energy-time entanglement for long-distance quantum communication protocols.
... However, we are interested only in the nonlinear optical process of parametric down-conversion. So, using equation (8), we write H I (t) as [89,90] ...
... The interaction time t 0 is assumed to be much longer than the time scale over which down-conversion takes place. Therefore, the limits of time integration can be extended to −∞ and ∞ [90,95] such that the time integration yieldŝ ...
Spontaneous parametric down-conversion (SPDC) is the most widely used process for generating photon pairs entangled in various degrees of freedom such as polarization, time-energy, position-transverse momentum, and angle-orbital angular momentum (OAM). In SPDC, a pump photon interacts with a non-linear optical crystal and splits into two entangled photons called the signal and the idler photons. The SPDC process has been studied extensively in the last few decades for various pump and crystal configurations, and the entangled photon pairs produced by SPDC have been used in numerous experimental studies on quantum entanglement and entanglement-based real-world quantum-information applications. In this tutorial article, we present a thorough study of phase matching in BBO crystals for spontaneous parametric down-conversion and thereby also investigate the generation of entangled photons in such crystals. First, we present a theoretical derivation of two-photon wavefunction produced by SPDC in the frequency and transverse momentum bases. We then discuss in detail the effects due to various crystal and pump parameters including the length of the crystal, the angle between the optic axis and the pump propagation direction, the pump incidence angle on the crystal surface, the refraction at the crystal surfaces, and the pump propagation direction inside the crystal. These effects are extremely relevant in experimental situations. We then present our numerical and experimental results in order to illustrate how various experimental parameters affect the phase matching and thus the generation of entangled photons. Finally, using the two-photon wavefunction in the transverse wave-vector basis, we show how to derive the two-photon wavefunction in the OAM basis and thereby calculate the two-photon angular Schmidt spectrum. We expect this article to be useful for researchers working in various capacities with entangled photons generated by SPDC in BBO crystals.
... However, we are interested only in the nonlinear optical process of parametric down-conversion. So, using equation (8), we write H I (t) as [89,90] H ...
... The interaction time t 0 is assumed to be much longer than the time scale over which down-conversion takes place. Therefore, the limits of time integration can be extended to −∞ and ∞ [90,95] such that the time integration yields ...
Spontaneous parametric down-conversion (SPDC) is the most widely used process for generating photon pairs entangled in various degrees of freedom such as polarization, time-energy, position-transverse momentum, and angle-orbital angular momentum (OAM). In SPDC, a pump photon interacts with a nonlinear optical crystal and splits into two entangled photons called the signal and the idler photons. The SPDC process has been studied extensively in the last few decades for various pump and crystal configurations, and the entangled photon
pairs produced by SPDC have been used in numerous experimental studies on quantum entanglement and entanglement-based real-world quantum-information applications. In this tutorial article, we present a thorough study of phase matching in β-barium borate (BBO) crystals for spontaneous parametric downconversion and thereby also investigate the generation of entangled photons in such crystals. First, we present a theoretical derivation of two-photon wavefunction produced by SPDC in the frequency and transverse momentum
bases. We then discuss in detail the effects due to various crystal and pump parameters including the length of the crystal, the angle between the optic axis and the pump propagation direction, the pump incidence angle on the crystal surface, the refraction at the crystal surfaces, and the pump propagation direction inside the crystal. These effects are extremely relevant in experimental situations. We then present our numerical and experimental results in order to illustrate
how various experimental parameters affect the phase matching and thus the generation of entangled photons. Finally, using the two-photon wavefunction in the transverse wave-vector basis, we show how to derive the two-photon wavefunction in the OAM basis and thereby calculate the two-photon angular Schmidt spectrum. We expect this article to be useful for researchers working in various capacities with entangled photons generated by SPDC in BBO crystals.
... Following Burnham and Weinberg's [16] introduction of non-linear crystals featuring SPDC, Mandel's group set a string of experiments that revolutionized the field of quantum optics [17][18][19]. Ou, Wang, Zou and Mandel (OWZM) proposed [20] an experimental setup with two non-linear crystals. What they suggested, and then experimentally confirmed [18], was a 'phase memory' if two crystals are pumped by the same laser. ...
... The situation gets worse for two or more non-linear crystals. Using a complete Hamiltonian approach rapidly evolves into painfully long calculations [20]. Authors typically use the monochromatic approximation and some arguments to cut down on the computational complexity. ...
In this paper we describe in detail a graphical method allowing the computation of field operator transformations in quantum optics (QO). Its applications include beam splitters (BS), Mach-Zehnder interferometers (MZI), optical resonators (Fabry–Perot etc) as well as non-linear crystals featuring the process of spontaneous parametric down-conversion (SPDC). Its main advantage compared to the traditional computation step-by-step method is its visual and intuitive approach, somehow similar to Feynman’s diagrammatic approach in Quantum Field Theory. It also seems adapted to computer-based implementations since calculations mainly consist on complex additions and multiplications, not matrix operations.
... In the spatial degree of freedom, a very general spatially partially coherent field was considered and it was shown that the spatial coherence properties of the pump field get entirely transferred to that of the down-converted twophoton field [19]. However, in the temporal degree of freedom, the effects due to the temporal correlations of the pump field have only been studied in two limiting situations: one, in which the constituent frequency components are completely correlated (fully coherent pulsed field) [15,[32][33][34][35][36] and the other, in which the constituent frequency components are completely uncorrelated (continuous-wave field) [7][8][9][10][11][12][13][14][37][38][39][40][41][42][43]. In this paper, we study the coherence transfer in PDC for a general temporally partially coherent pump field, and explicitly quantify this correlation transfer for the special case of a partially coherent Gaussian Schell-model field [44] in which the correlations between the constituent frequency components have a Gaussian distribution. ...
... The parameters defined above are identical to those defined in Ref. [11], except for τ 0 1 ; τ 0 2 , and Δτ 0 , which have been scaled down by a factor of 2. It is found that this rescaling imparts the equations in this paper a neat and symmetric form. The two-photon state jψi 1 produced in alternative 1 in the weak down-conversion limit is given by [32,37,45] ...
We show that in parametric down-conversion the coherence properties of a temporally partially coherent pump field get entirely transferred to the down-converted entangled two-photon field. Under the assumption that the frequency bandwidth of the down-converted signal-idler photons is much larger than that of the pump, we derive the temporal coherence functions for the down-converted field, for both infinitely fast and time-averaged detection schemes. We show that in each scheme the coherence function factorizes into two separate coherence functions with one of them carrying the entire statistical information of the pump field. In situations in which the pump is a Gaussian Schell-model field, we derive explicit expressions for the coherence functions. Finally, we show that the concurrence of time-energy-entangled two-qubit states is bounded by the degree of temporal coherence of the pump field. This study can have important implications for understanding how correlations of the pump field manifest as two-particle entanglement as well as for harnessing energy-time entanglement for long-distance quantum communication protocols.
... k 0 , ω 0 são, o vetor de onda e a frequência da onda de bombeamento respectivamente, tal campoé considerada ter amplitude E p , ser monocromática e tratada como um campo de radiação clássica, por isso,â k 0 s 0 foi incorporado na amplitude E p . Assim, k', k", ω ′ , ω ′′ são os vetores de onda e as frequências de onda dos feixes convertidos, χé a suscetibilidade magnética não-linear [28]. ...
... pode ter uma distribuição de frequência finita em torno de ω 1 e ω 2 , e ser bem diferente de monocromática. Faremos aqui uma expansão do vetor campo e expressaremos o Hamiltoniano de interaçãoĤ I[28] na formâ ...
... The following treatment of the theory of down-conversion is due to Refs. [69,116,63,130,65] and some of the simplifications made therein 5 . The interaction Hamiltonian of a non-linear optical crystal is usually derived by starting from the classical electric field energy density for a non-linear medium and then quantizing the electric field in the usual manner producing the following equation ...
... For a more complete treatment of SPDC please refer to Refs.[69,116,63,130,65] and the references therein. ...
... The non-linear process of spontaneous parametric downconversion (SPDC) [8] provides pairs of highly entangled photons [9,10,11,12]. It had been used hitherto in many experiments in quantum optics [1,2,3,13,14,15,16,17,18,19]. One could emphasize the fundamental experiments demonstrating the non-locality of quantum mechanics [13,14]. ...
... In an experiment by Ou, Wang, Zou and Mandel (proposed in [15] and reported in [16]), two non-linear crystals fed by the same pump laser through a beam splitter perform down-conversions. By slightly varying the position of the beam splitter (and therefore the relative phase of the pump field between the crystals), an interference pattern is recovered. ...
In this paper we describe and thoroughly discuss three reported experiments
in quantum optics (QO) involving interferometers and non-linear crystals. We
show that by using a graphical method and an over-simplified model of the
parametric down-conversion process, we arrive to explain all the important
results reported in the respective papers. Indistinguishability and
partial/total system knowledge are discussed in the case of
separable/non-separable (i.e. entangled) quantum systems and our interpretation
is sometimes at variance with the one given by the authors reporting the
experiments.
... r are the detector locations, and t 1 and t 2 are the detection times. The pump beam is taken to be a laser with a transverse Gaussian profile of The crystal is embedded in a passive medium whose linear refractive index is the same as that of the crystal[23]the frequencies of the signal and idler photons, respectively.The idler photon is phase-modulated using a spectral phase filter with a symmetric spectral phase distribution of the form ...
We present a general theoretical description of the temporal shaping of narrowband noncollinear type-I down-converted photons using a spectral phase filter with a symmetric phase distribution. By manipulating the spectral phase of the signal or idler photon, we demonstrate control of the correlation time and shape of the two-photon wave function with modulation frequency and modulation depth of the phase distribution.
... These signals and idlers are phase-correlated, as is typical in spontaneous parametric down-conversion (SPDC) processes. In the SPDC, the sum of the phases of the signal and idler photons is determined by the phase of the pump laser 36,37 . In this scheme, we assumed that the sum of the phases of the signal and idler photons remained constant across all modes within the same trial. ...
Quantum repeaters are pivotal in the physical layer of the quantum internet, and quantum repeaters capable of efficient entanglement distribution are necessary for its development. Quantum repeater schemes based on single-photon interference are promising because of their potential efficiency. However, schemes involving first-order interference with photon sources at distant nodes require stringent phase stability of the components, which pose challenges for long-distance implementation. In this paper, we present a quantum repeater scheme that leverages single-photon interference and reduces the difficulty of achieving phase stabilization. Additionally, under specific conditions, our scheme achieves a higher entanglement distribution rate between end nodes compared with the existing schemes. Thus, the proposed approach could lead to improved rates with technologies that are currently unavailable but possible in the future and will ultimately facilitate the development of multimode quantum repeaters.
... A detection scheme analogous to the above signal was used in Refs. [37,38]. ...
In classical macroscopic ultrafast optical four-wave mixing signals, phase matching selects three classes of light–matter interaction pathways: double quantum coherence; non-rephasing; and photon-echo. Multiple pathways contribute to each of these signals. We show that a coincidence-double-heterodyne detection scheme that employs two classical and two vacuum fields can isolate a single pathway contribution to each of these signals. We further demonstrate the advantage of the proposed technique by comparing it with the classical photon-echo signal for a model Frenkel-exciton dimer.
... In the case of a TEM 00 pump, this means that L k p w 2 0 . Following a standard perturbative approach [32], with the assumption that the interaction of the three waves is restricted only to the direction of propagation x , it can be shown that the time evolution operator related to the nonlinear interaction is given bŷ ...
We report a scheme for generating ultrabroadband two-photon states by spontaneous parametric downconversion (SPDC) using randomly aperiodically poled crystals designed with an optimization algorithm based on the Monte Carlo–Metropolis method with simulated annealing. A particular SPDC source is discussed, showing results of the spectral and temporal properties of the emitted two-photon states, obtaining almost transform-limited SPDC biphoton wave packets. We also analyze the effect of fabrication errors on the SPDC.
... evolve [148]), similarly to the first theorical studies on the quantum properties of the biphoton states carried out by Mandel, Ou and coworkers [149,150]. More particularly, we follow the analysis proposed by Guillaume Boucher, a previous PhD student of our group, in his manuscript [151]. ...
This thesis is devoted to the development of novel integrated semiconductor devices and methods for the generation and manipulation of high-dimensional states of light. We report on the study of an AlGaAs waveguide implementing type-II spontaneous parametric down conversion process in a monochromatic pump regime, with a focus on the joint spectral amplitude of the emitted biphoton state. The source works at room temperature, emits photon pairs in the telecom range and is compliant with electrical injection. The generation of broadband biphoton states is experimentally demonstrated via the reconstruction of the joint spectral intensity and via a Hong-Ou-Mandel experiment indicating that signal and idler photons are emitted over a large bandwidth (170nm) and with a high degree of indistinguishability (V=0.86). Moreover, we show that the cavity effect due to waveguide facets reflectivity leads to the production of biphoton frequency-comb states. This platform is used to demonstrate an original method to generate and control the symmetry of biphoton frequency combs exploiting cavity effects and a delay between the two photons of each pair. More specifically, we show that a fine tuning of the pump frequency enables the generation of resonant and anti-resonant comb states allowing to manipulate the wavefunction symmetry. The method can be adapted and applied to a large variety of systems, either bulk or integrated, thus increasing their flexibility and the richness of the generated states in view of implementation of new quantum information protocols.In addition, we demonstrate the realization of an AlGaAs ridge waveguide for the generation of light beams with tailored phase and polarization distributions, carrying spin angular momentum, and present the design of a device for the generation of a twisted light beam, carrying first order orbital angular momentum.
... Fig. 10). As a result, there are additional interference effects arising due to coherences with the vacuum components of each state [32,33]. This was also noted in [34] where a similar method was used to generate four photons; they applied a Pancharatnam (Berry) phase using waveplates on one of the modes to remove these coherences. ...
One of the central principles of quantum mechanics is that if there are multiple paths that lead to the same event, and there is no way to distinguish between them, interference occurs. It is usually assumed that distinguishing information in the preparation, evolution or measurement of a system is sufficient to destroy interference. For example, determining which slit a particle takes in Young's double slit experiment or using distinguishable photons in the two-photon Hong-Ou-Mandel effect allow discrimination of the paths leading to detection events, so in both cases interference vanishes. Remarkably for more than three independent quantum particles, distinguishability of the prepared states is not a sufficient condition for multiparticle interference to disappear. Here we experimentally demonstrate this for four photons prepared in pairwise distinguishable states, thus fundamentally challenging intuition of multiparticle interference.
... In these experiments, lights in two-photon states that are correlated with each other similar to parametric fluorescence are used as incident light. Mandel et al. conducted a series of experiments, such as 100% visibility in a two-photon simultaneous measurement [5][6][7][8], vacuum effects on interference in a two-photon down conversion [9], and violation of Bell's inequality and classical probability [10] by a two-photon interference using parametric down-conversion photons. Many related studies subsequently began to be published [11][12][13][14][15]. ...
Many experiments to verify nonlocal interaction and non-classical phenomena using entangled lights were conducted in the 1980s, and many physicists were interested in their unrecognizable correlation. These quantum mechanical effects were used in Aspect's experiments and Bell tests and had a great influence on the interpretation of quantum mechanics. However, their essence, including their "spooky" interaction, is unknown. In this study, we show that entangled light can be expressed by the product of electric fields and that the same result as quantum mechanics can be obtained using the product form.
... Second-order nonlinearity provides us with numerous frequency conversion processes like sum-frequency generation, difference-frequency generation, second-harmonic generation, and spontaneous parametric down conversion [1,2]. These processes have been widely studied in bulk crystals, channel waveguides, ridge waveguides, and planar waveguides [3][4][5][6][7][8][9] for different applications. ...
In this paper, we analyze second-harmonic (SH) generation and sum-frequency (SF) generation in a planar waveguide configuration using 2D quasi-phase-matching (QPM) gratings and show possibility of simultaneous generation of sum frequency and second harmonic. It is shown that it is possible for the two generated frequencies to be noncollinear with respect to the incident pump waves with the SF and SH frequencies exiting at different angles along the planar waveguide, leading to ease of collection. Numerical simulations are performed in a potassium titanyl phosphate planar waveguide, and it is shown that the proposed planar waveguide configuration provides wavelength tunability and has greater conversion efficiencies than bulk configuration and larger bandwidth than channel waveguide configuration.
... Following Ou et al. [51], we describe the two-photon state produced by the SPDC process using a perturbation expansion in the interaction picture. The canonical quantization of the electromagnetic field is performed by substituting the amplitudes of the electric fields with the corresponding non-commuting creation and annihilation quantum operators: ...
One of the main issues in the domain of quantum information and communication is the generation, manipulation and detection of several qubits on a single chip. Several approaches are currently investigated for the implementation of qubits on different types of physical supports and a variety of quantum information technologies are under development: for quantum memories, spectacular advances have been done on trapped atoms and ions, while to transmit information, photons are the ideal support thanks to their high speed of propagation and their almost immunity against decoherence. My thesis work has been focused on the conception, fabrication and characterization of a miniaturized semiconductor source of entangled photons, working at room temperature and telecom wavelengths. First the theoretical concepts relevant to understand the work are described (chapter 1). Then the conception and fabrication procedures are given (chapter 2). Chapter 3 presents the optoelectronics characterization of the device under electrical pumping, and chapter 4 the results on the optical losses measurements and the nonlinear optical characterization (second harmonic generation, spontaneous parametric down conversion and joint spectral intensity reconstruction). Chapters 5 and 6 focus on the characterization of the quantum state generated by a passive sample (demonstration of indistinguishability and energy-time entanglement) and its utilization in a multi- user quantum key distribution protocol (polarization entanglement). Finally the work on the first electrically driven photon pairs source emitting in the telecom range and working at room temperature is presented (chapter 7).
... Here, c.c and h.c represent the complex conjugate and the hermitian conjugate respectively. The Hamiltonian governing the interaction of pump with the nonlinear crystal is given by [29] ( ...
... Ces nouveaux photons se comportent alors plus comme des petits paquets d'ondes que comme une onde monochromatique. Ainsi, an de décrire correctement l'interaction paramétrique, il est utile d'appliquer, à l'instar de Ou et ses collaborateurs [77], une méthode perturbative de type multimode et de procéder à une décomposition en ondes planes de l'HamiltonienĤ int Il permet notamment, via l'équation du mouvement de Heisenberg, de calculer la forme des champs signal et idler ainsi que les statistiques photoniques associées. correspondant sur tous les modes possibles du champ. ...
This work reports the realization of energy-time and time-bin entangled photon-pair sources based on a periodically poled lithium niobate (PPLN) waveguide. Degenerate twin photons around 1314 nm wavelength are created by spontaneous parametric down-conversion and coupled into standard telecom fibers.
The PPLN waveguide produces a conversion efficiency of more than 10-6, roughly 4 orders of magnitude more than that obtained employing bulk crystals. Even if using low power laser diodes, this engenders a significant probability for creating two pairs at a time which is an important advantage for some quantum communication protocols. We point out two simple means to characterize the pair creation probability per pump photon (CW) and for the case of a pulsed pump.
To investigate the quality of the entangled states, we perform photon-pair interference experiments, leading to visibilities of 97 % for the case of energy-time entanglement and of 84 % for the case of time-bin entanglement. Although the last figure must still be improved, these results demonstrate the potential of PPLN waveguide based sources for future quantum communication schemes.
... A monochromatic polarized beam described by the scalar function E(r, t) = W b (ρ, z) e −i ω 0 t pumps the first crystal and the signal and idler beams produced in a SPDC, filtered out from the pump, are sent to the second crystal. The interaction between these beams and the second crystal give rise to a field which is described by the quantum state [4,5,6,7] ...
Using light produced in a spontaneous parametric down conversion process as the fundamental field, we show that second harmonic generation is sensitive to spatial transverse correlations between signal and idler fields. Particularly, if the fundamental beam exhibites spatial anti-bunching, the intensity of the second harmonic field may be zero, independent of the intensity of the fundamental beam.
... It can be derived by starting with the classical electric field energy density for a nonlinear medium, and then quantizing the electric field [29]. The resulting Hamiltonian is [30]: ...
... Experiments have shown that the phase information of the pump is not lost during downconversion [143] [144], and that, even though the phase of one of the downconverted beams is random, the phase of both together must sum to the phase of the pump. We use downconversion as the source of photon pairs for the two IFMs ...
... The situation is similar to the one of the conclusion of the previous section; the twoparticle interference may affect the single-particle visibility. (The coincidence rate for simultaneous detections of signal and idler photons was measured in [75,76].) Again, this can be examined using the approach of the next section (the results will likely depend on the difference of phases). ...
We suggest a few experiments using Young's interference, Fraunhofer diffraction, and parametric down conversion to be able to manifest considerable quantum nonlo-calities of a new type. Their most characteristic feature is the usage of merely one detector. An inequality defining Einsteinian locality and suitable for violating via a statistical procedure is formulated. It should be pointed out that our method is entirely distinct and independent of Bell inequalities. We demonstrate that proposed devices can be used to transfer information with superluminal velocities, even over very large distances. It is clearly shown that this is not at odds with quantum mechanics and Lorentz transformations provided a postulate, termed 'signal encapsulation', is added to special relativity. Finally, we consider possible momentous applications in computer technology (usable in various types of computers, the Internet, and even during a voyage to Mars) and astrobiology.
... The visibility of ghost interference has also been derived earlier by Barbosa [20], calculating a fourth-order correlation function in the theory of Mandel et al. [21][22][23][24]. However, a connection of the visibility of ghost interference to the which-path information for photon 1 has not been studied before. ...
We propose and analyse a modified ghost-interference experiment, and show that revealing the particle nature of a particle passing through a double-slit hides the wave nature of a spatially separated particle which it is entangled with. We derive a {\em nonlocal duality relation}, , which connects the path distinguishability of one particle to the interference visibility of the other. It extends Bohr’s principle of complementarity to a nonlocal scenario. We also propose a {\em ghost quantum eraser} in which, erasing the which-path information of one particle brings back the interference fringes of the other.
We propose a time-frequency resolved spectroscopic technique which employs nonlinear interferometers to study exciton-exciton scattering in molecular aggregates. A higher degree of control over the contributing Liouville pathways is obtained as compared to classical light. We show how the nonlinear response can be isolated from the orders-of-magnitude stronger linear background by either phase matching or polarization filtering. Both arise due to averaging the signal over a large number of noninteracting, randomly oriented molecules. We apply our technique to the Frenkel exciton model which excludes charge separation for the photosystem II reaction center. We show how the sum of the entangled photon frequencies can be used to select two-exciton resonances, while their delay times reveal the single-exciton levels involved in the optical process.
Optical nonlinear conversion processes are ubiquitously applied to scientific as well as industrial tasks. In particular, nonlinear processes are employed to generate radiation in many frequency ranges. In plenty of these nonlinear processes, the generation of paired photons occurs — the so‐called signal and idler photons. Although this type of generation has undergone a tremendous development over the last decades, either the generated signal or the idler radiation has been used experimentally. In contrast, novel quantum‐based measurement principles enable the usage of both partners of the generated photon pairs based on their correlation. These measurement approaches have an enormous potential for future applications, as they allow to transfer information from one spectral range to another. In particular, spectral ranges where photon generation and detection is particularly challenging can benefit from this principle. Above all, these include the extreme frequency ranges, such as on the low‐frequency side the mid to far infrared or even the terahertz spectral range, but also on the high‐frequency side the ultraviolet or X‐ray spectral range. In this review article, theoretical and experimental developments based on correlated biphotons are described specifically for the extreme spectral regions.
One of the central principles of quantum mechanics is that if there are multiple paths that lead to the same event and there is no way to distinguish between them, interference occurs. It is often assumed that distinguishing information in the preparation, evolution, or measurement of a system is sufficient to destroy interference. However, it is still possible for photons in distinguishable, separable states to interfere due to the indistinguishability of paths corresponding to possible exchange processes. Here we experimentally measure an interference signal that depends only on the multiparticle interference of four photons in a four-port interferometer despite pairs of them occupying distinguishable states.
In theoretical and experimental work, we consider the process in which an entangled photon pair recombines into a single photon in a nonlinear crystal, with particular interest in the amplitude distribution and coherence properties of the up-converted light. It is found that the up-converted state has perfect mutual coherence with the pump that originally produced the photon pair in another nonlinear crystal and that the amplitude has the spatiotemporal structure of the original pump mode, filtered by a linear transfer function. These conclusions are drawn from leading-order calculations performed in the interaction picture, with the multimodal nature of all fields being fully accounted for. In our experimental results, we observe the spatial similarity between the up-converted light and the original pump mode; their mutual coherence is demonstrated through observation of fringes with near-unit visibility. The effects studied here have potential applications in quantum information processing and also confirm that the principle of path indistinguishability holds even under unusually extreme conditions.
The fluorescence of an atomic transition can generate the elementary particle of light: a single photon. Conversely, the illumination of an atom with a single photon provides a tool to systematically study light-matter interactions on a fundamental level. Furthermore, single photons are a resource for tap-proof quantum communication. The efficient coupling of a single photon to a single atom is at the core of many quantum repeater protocols. Quantum repeaters are required for long-distance quantum communication. Efficient photon-atom interaction requires a matching of the photon and the atom in every spatial, spectral, temporal, and polarization degree of freedom. Widely-used sources of single photons are trapped atoms, rare earth ions in a host crystal, single molecules, vacancy centers in diamond, cadmium selenide nanocrystals, indium gallium arsenide quantum dots, four-wave mixing in either an atomic vapor or a noble-gas-filled photonic crystal fiber, or parametric down-conversion in a nonlinear optical medium. In parametric down conversion, single pump photons can split up into a pair of photons, namely the signal and the idler photon. Parametric frequencies can typically by generated between the near-ultraviolet and the far-infrared part of the electromagnetic spectrum, which may allow for a coupling to a huge variety of atomic transitions. The spectral bandwidth of the photons in single-pass parametric down-conversion, however, is typically at the terahertz scale. This leads to extremely low coupling rates to atomic transitions, when an atomic linewidth at the megahertz scale is given. A small photon bandwidth can be achieved in an optical parametric oscillator, in which the nonlinear effects are enhanced by placing the nonlinear medium in an optical resonator. In our experiments, we combine the nonlinear medium and the optical resonator in one monolithic device: a whispering-gallery mode resonators made of lithium niobate. Light is guided via the effect of total internal reflection around the circumference of these highly transparent microdiscs. One degree of freedom not fixed for our parametric converter is the manifold of eigenmodes, which typically comprises different longitudinal and transversal modes. Therefore, we developed a novel method to identify the different eigenmodes of whispering-gallery mode resonators based on their relative resonance frequencies and spatial emission patterns. In a next step, we could demonstrate the operation of our single photon source in a single parametric mode. This was based on the very low absorption in lithium niobate and the monolithic design of the resonator with the triply resonance for pump, signal, and idler. By selecting specific mode triplets for parametric down-conversion, we demonstrated temperature tuning of the parametric wavelengths from single 790-1630 nm in steps of approximately 8.2 GHz, as well as continuous tuning with megahertz resolution. The latter was achieved by placing a movable dielectric substrate within the evanescent field of the resonator. We then showed the compatibility of our system to an arbitrary atomic transitions by tuning the signal frequency to the D1 lines of rubidium and cesium at a wavelength of 795 nm and 895 nm, respectively. These two alkaline transitions are widely-used in quantum optics, and especially quantum information, due to their strong dipole interactions and favorable structures of the energy levels. In a subsequent experiment, we showed complete absorption of resonant signal photons in cesium and rubidium vapor. The correlation measurement between the fluorescent photons from the cesium D1 line and the idler photons directly gives information on the natural linewidth of this transition. This demonstration of frequency and bandwidth matching is one major step towards practical quantum repeaters. Parametric down-conversion in whispering-gallery mode resonators provides an efficient, low-cost, robust, and non-cryogenic source of tunable single photons and bright squeezed light, when optical parametric oscillator is driven above the oscillation threshold. Narrowband single photons are especially interesting for an investigation of semiconductor or crystalline quantum dots, single atoms, atomic clouds, or optomechanical resonators. The high efficiency of single photon generation reduces respective measurement times and allows to access multiphoton transitions.
The existence of quantum entanglement is what makes quantum physics different from classical physics. First introduced by Schrödinger in his discussion of the famous cat paradox [1], the amazing effects of quantum entanglement are very counter-intuitive and sometimes mind-boggling. As a pioneer and an expert in both classical and quantum coherence theory, Mandel is the right person to use light for the exploration of quantum entanglement. Among many of Mandel’s contributions, the pioneering work and subsequent development on parametric down-conversion (PDC) opened up a whole field of research to experimentally observe the phenomena of quantum entanglement. Today, in the newly established field of quantum information science, quantum entanglement has become an essential ingredient in basically all the discussions. Schrödinger may have been the first person to mention the word of “Entanglement”, but it was Mandel who first demonstrated it experimentally and created further a variety of different entangled states, which include entangled states of polarization, of frequency, and of phase variables. Besides quantum entanglement, Mandel also exploited PDC in the study of fundamental physics as well as practical applications in optical communication.
We study quantum statistics of the multimode radiation from two coherently pumped down-conversion crystals with aligned idler beams and confirm that induced coherence need not be accompanied by induced emission.
According to QED single photons carry no phase information about the optical field, yet it is possible for a superposition of states, including the vacuum, to carry phase memory. We have demonstrated this principle by showing experimentally that the photon pairs generated in the process of parametric down-conversion,1 through their entanglement with the vacuum state, contain information about the phase of the pump field, as was recently pointed out by Grangier et al.2 However, our experimental technique is different from the one they proposed.
We have studied the effect of the spectral distribution of parametrically down-converted photons on a quantum optical test of Bell's theorem. As a testing criterion, we consider Bell's inequality via fourth-order interferences in parametric down-conversion systems. In dealing with Bell's theorem, the effect of the choice of spectral distribution and the coincidence time delay are considered. Then, the visibility is analyzed as a function of the coincidence time delay under the condition that Bell's inequality is violated.
Dealing with a quantum optical test of Bell's theorem, we have studied the effects of the spectral distribution of the parametric down-converted photons and the quantum optical complementarity principle. As a testing criterion of the complementarity principle, we consider Bell's inequality via interferences in parametric down-conversion systems. In studying Bell's theorem, the effect of the coincidence time delay, the choice of the transmission filter function, and the differences between two parametric down conversion sources are considered. Then, the visibility is analyzed as a function of distinguishability and compared with the condition for the violation of Bell's inequality.
The fourth-order quantum interference of squeezed fields generated by two independent optical parametric oscillators(OPOs) is discussed based on the semi-classical theory. It is shown that at the oscillation threshold of OPOs the squeezing of two output fields is the highest but the fringe visibility of fourth-order interference is the lowest(33.3%). When the pump power is away from the threshold, the squeezing decreases while the correlation between them increases.
We studied a situation where coherence between the signal and the idler fields is induced by a laser field. It is predicted that, in the weak-field limit, interference between the idler field and another local oscillator field can be observed in a homodyne measurement when there is one photon in the signal field. It is found that indistinguishability of the photon path is directly related to this interference.
Multi-Photon Quantum Interference covers the phenomena of quantum interference through the multi-photon effects of photon correlation. The author's focus is on the temporal correlation among photons and how it influences the interference effect. Included is discussion of some of the well known multi-photon interference schemes, such as Hong-Ou-Mandel interferometer and Franson Interferometer for two-photon system, quantum state teleportation and swapping for four-photon system, and quantum state reconstruction for multi-photon system. A unique feature of the book is its quantitative characterization of photon indistinguishability and its connection to interference effects. © 2007 Springer Science+Business Media, LLC. All rights reserved.
This chapter discusses the quantum fluctuations in optical systems. Quantum fluctuations are present in every measurement. In the measurement device, quantum fluctuations have an effect similar to that of the instrumental noise or thermal fluctuations. The chapter describes the principal experiments that have generated light with reduced quantum fluctuations, and the applications of such light. Straightforward calculations involving squeezed fields help to explain the experimental results. The squeezed fields are treated in the framework of the semiclassical linear input output theory, which models the quantum fluctuations by classical random fields. The standard representations of quantum optics are used to treat the quantum fluctuations and properties of the squeezed states, and to study the ideal parametric interaction Hamiltonian in detail. The chapter also discusses the quantum properties of the parametric generation in an optical cavity, including the two regimes below and above the oscillation threshold.
Coherence can be induced or stimulated in parametric down-conversion using
two or three crystals when, for example, the idler modes of the crystals are
aligned. Previous experiments with induced coherence [Phys. Rev. Lett. 114,
053601 (2015)] focused on which-path information and the role of vacuum fields
in realizing complementarity via reduced visibility in single-photon
interference. Here we describe experiments comparing induced and stimulated
coherence. Different single-photon interference experiments were performed by
blocking one of the pump beams in a three-crystal setup. Each counted photon is
emitted from one of two crystals and which-way information may or not be
available, depending on the setup. Distinctly different results are obtained in
the induced and stimulated cases, especially when a variable transmission
filter is inserted between the crystals. A simplified theoretical model
accounts for all the experimental results and is also used to address the
question of whether the phases of the signal and idler fields in parametric
down-conversion are correlated.
We demonstrate a parametric downconversion source with an exceptionally large bandwidth (1080nm full-width half-maximum about the 1885nm degenerate wavelength), as a step towards the generation of photon pairs with high dimensional entanglement.
Two signal beams emitted from two simultaneously pumped parametric down converters show first order interference if the two idler beams were aligned. Due to the effect of phase memory it is found that the first order interference of the signal beams can be controlled by the phase delay between the pump beams.
Measurements of the Young interference pattern for down-converted light
in the two-photon state are performed. Light in the two-photon state is
generated at the output of a Hong-Ou-Mandel balanced interferometer.
Two-photon interference patterns with visibilities up to 100% are
obtained. Visibilities of the two-photon interference patterns as a
function of the double-slit separation are obtained and show that the
transverse coherence length of the two-photon light is much larger than
the one-photon beam for the distances considered in the experiment.
We report on the observation of strong Zeeman beats in the temporal correlation between the two photons emitted in the 4p2 1 S0 --> 4s 4p 1 P1 --> 4s2 1 S0 cascade in calcium. These beats result from a quantum interference between the various decaying channels. Unlike usual quantum beats, they are observed with a continuous excitation of the upper level.
Squeezed states of the electromagnetic field are generated by degenerate parametric down conversion in an optical cavity. Noise reductions greater than 50% relative to the vacuum noise level are observed in a balanced homodyne detector. A quantitative comparison with theory suggests that the observed squeezing results from a field that in the absence of linear attenuation would be squeezed by greater then tenfold.
It is shown that the two-photon phase coherence of parametrically generated photon pairs, which is at the origin of squeezed-light generation, can be directly probed using an intensity-correlation measurement. The resulting intensity correlation leads to a new violation of Bell's inequalities, which could be experimentally tested.
The amplification of electromagnetic fields is analyzed in a quantum-mechanical context by discussing the behavior of a simple theoretical model of the parametric amplifier. The statistical properties of the amplifier fields are described by means of the time-dependent density operator for the system. In doing this, extensive use is made of the coherent states and the P representation of the density operator, which provide a quantum-mechanical description of the fields closely resembling their classical description. Explicit solutions are obtained for the density operator for either of the two field modes for a variety of initial states of the modes. Initial states considered include combinations of coherent states, chaotic mixtures, and n-quantum states. Particular attention is given the behavior of the amplifier fields in the limit of large amplification. The conditions are established under which the amplification process leads in this limit to the existence of a non-negative P representation for the density operator for a single mode of oscillation.
A new connection between autocorrelation and cross correlation functions of the intensities of signal and idler in parametric oscillators is derived, with the same origin and generality as the Manley-Rowe relations and with inserting experimental implications in the quantum domain.
The problem of nonlinear optical sum-frequency generation and second harmonic generation is solved by a method neglecting changes of statistics of generating radiations. It is shown here that the increase of fluctuation levels in subfrequency radiations reduces the total efficiency of the sum-frequency generation, whilst in the degenerate case the second harmonic generation is accelerated with an increasing fluctuation level in the fundamental radiation. Total efficiencies of real nonlinear processes are estimated at the end of the paper.
If two initially coherent light fields with the frequencies omega and 2 omegas, which have been produced by a second harmonic generator, pass a degenerate parametric amplifier, photon-anticorrelation effects can develop. The time-development of the photon distribution for the signal wave is calculated by treating both fields quantum mechanically.
I discuss the photon antibunching effect and point out that there exist many states which exhibit the effect and demonstrate a simple procedure for generating them mathematically. I also suggest here a possible approach to the experimental observation of the effect.
The effect of phase and amplitude fluctuations of the pump mode on the quantum-statistical properties of the signal mode is considered. It is shown that these fluctuations in the laser field tend to decrease the squeezing of the signal field.
We present a quantum-statistical analysis of the steady-state light fields in driven parametric oscillation in a cavity. Using the solution of a Fokker-Planck equation for the generalized P representation of the signal and idler modes, we calculate the mean photon numbers, second-order correlation functions, and intermode correlation function as functions of the driving field. The generalized P distribution describes the signal and idler modes' statistics over the whole range of driving-field strengths except in the region far below the oscillation threshold. The second-order correlation functions are found to violate the Cauchy-Schwartz inequality, a violation allowed because the P distribution is complex. Squeezing is also found in a linear combination of the signal and idler fields.
A two-step nonlinear optical interaction consisting of (i) a spontaneous frequency down-conversion process coupled with (ii) a frequency up-conversion process is treated quantum mechanically in the experimentally observed case of simultaneous collinear phase matching of both processes. The temporal behavior of the output signals is found to depend on which process, (i) or (ii), predominates. The nature of the photon statistics for each of the output modes is found to be "super-Poisson," regardless of which process, (i) or (ii), is dominant, and the zero-point fluctuations characteristic of parametric amplification are exhibited.
Correlation effects in parametric photon-pair production are studied within the framework of a physically realistic model. The analysis, which is fully quantum mechanical, takes into account the finite sizes of the target and the beam cross section, and allows for dispersion and anisotropy in the linear susceptibility. The correlations in position and time at which the two members of a parametrically generated pair may be detected are carefully evaluated. These correlations, which have been measured experimentally, are intrinsically quantum mechanical; i.e., they can be explained by no theory in which the subharmonic fields are described purely by c-number functions. A complete solution, from which field correlation functions of arbitrarily high order may be evaluated, is obtained by a method which at the same time allows for an arbitrary degree of parametric gain. The solution is expressed entirely in terms of a particular two-point field-correlation-function, as evaluated in lowest order in the incident field strength, at points distant from the target. The function in question is found by directly examining the fluctuating currents in the material medium, rather than by eliminating the matter variables at the outset through the introduction of a nonlinear electomagnetic susceptibility.
The relationship between the squeezing and photon-number fluctuations in
the output of a degenerate parametric oscillator is investigated. The
addition of a second driving field at the idler frequency allows the
direction of the squeezing to be changed. The squeezing may appear in
the amplified quadrature. Photon antibunching or bunching may occur
depending on whether the quadrature carrying the coherent excitation is
squeezed.
The influence of intermodal correlations upon the efficiencies of nonlinear quadratic optical processes is treated for special cases of three-mode non-degenerate and degenerate optical processes, when the amplitude of at least one mode is equal to zero at the beginning of the process.
The nonlinear optical sum-frequency generation and the second harmonic generation with coherent and chaotic input radiations are treated in this paper. The short-time (-length) approximation method including the small parameter up to the eighth order is used. Effects of spectral widths of radiations as well as dispersion effects are neglected. Mean photon numbers, intermodal correlations and autocorrelations are calculated in the course of the nonlinear process. The obtained results are discussed from the point of view of the effect of intermodal correlations on nonlinear optical processes.
We report the first observation of sub-poissonian photon statistics for light generated by the use of a detection triggered optical shutter in parametric downconversion. A normalised second factorial moment of the photon counting distribution of 0.42 has been achieved with a pre-detection Fano factor of 0.984.
A violation of Bell's inequality is predicted in the system of correlated electromagnetic field modes present in an optical 8-port homodyne detector. In this system all of the field modes are of the same polarization, and the correlated field modes are analyzed with phase sensitive homodyne detectors.
An analysis of the degenerate parametric amplifier including the quantisation of pump and signal modes is presented. It is shown that the fluctuations in one quadrature of the signal mode may be reduced at most by a factor of two. This is in contradistinction to analyses where the pump field is treated classically which overestimate the reduction in fluctuations possible.
We analyse the nonlinear interaction between a fundamental and second harmonic wave inside a Fabry-Pérot cavity where both modes are driven by a coherent driving field with a definite phase. We find that under certain experimentally accessible conditions bistable operation is possible. In addition it is shown that photon antibunching in the steady state may occur.
Resonance fluorescence is treated as a collision process where incident laser photons are scattered by an atom. Correlation signals are extracted from an expansion to the second order of the post collision field state. Photon antibunching effect appears as a quantum interference between all the possible scattering amplitudes. When Rayleigh photons are rejected, some amplitudes vanish, leading to a bunching behaviour. La fluorescence de résonance est considérée ici comme une collision où des photons laser incidents sont diffusés par un atome. Les signaux de corrélation de photons sont calculés à partir du vecteur d'état décrivant le champ diffusé au second ordre. L'effet de dégroupement de photons provient d'une interférence quantique entre toutes les amplitudes de diffusion possibles. Quand les photons Rayleigh sont éliminés, certaines amplitudes disparaissent ce qui conduit à un groupement des photons détectés.
Simultaneity in optical photon pairs parametric production, verifying quantum mechanical description of fluorescence
Lande g factors measurement of excited electronic states in Ne 20 II and III, using alignment of radiating particles in beam foil light source
Homodyne detection has been proposed as a means of detecting squeezed coherent radiation. Here the response of a balanced homodyne detector to wideband squeezed coherent states is presented. In order to carry out the analysis the theory of wideband photodetection is reviewed and in order to determine the ultimate performance limits of photoemissive detectors small terms of order Deltaomega/omega0 that are usually neglected, where omega0 is the optical carrier frequency and Deltaomega is the electronics bandwidth, have been kept. It is shown that the ultimate noise reduction that can be achieved in the noise-power spectrum of a homodyne detector, detecting squeezed coherent radiation, is a factor of 2 worse when photoemissive detectors are used instead of power flux detectors.
Wideband calculations of the response of a homodyne detector to the outputs of various four-wave-mixer configurations are presented. It is shown that the noise-power spectrum of the homodyne detector output can exhibit regions where the noise is greatly reduced below the shot-noise level even at frequencies far from dc. Hence, in the detection of noise squeezing via homodyne detectors, 1/f noise and other low-frequency noise sources may be avoided by observing the homodyne detector’s noise power at frequencies far from dc.
A theoretical study is made of the process in which incident pump photons that interact with a nonlinear medium (such as a crystal lacking inversion symmetry) are spontaneously split into lower-frequency signal and idler photons. The down-converted fields are quantized and described by a continuum of modes, a subset of which interacts with each photodetector. It is shown that when two ideal photodetectors are appropriately located so that they receive the conjugate signal and idler photons, then the joint probability of two-photon detection by the two detectors can equal the single-photon detection probability. The time correlation between the two detected photons is shown to be limited either by the resolving time of the detectors, or by the bandwidth of the down-converted light, and to be independent of the coherence time of the pump field or of the length of the nonlinear medium. These conclusions are compared with the results of recent experiments.
A theoretical treatment is given of the process in which the two photons produced simultaneously in the parametric frequency splitting of light are allowed to interfere. It is shown that, while there is no interference in the usual sense involving quantities that are of the second order in the field, fourth-order interference effects are present. These may be revealed by measuring the joint probability of detecting two photons at two points in the interference plane with photoelectric detectors as a function of the separation of the points. The probability exhibits a cosine modulation with the separation of the points, with visibility that can approach 100 percent, even though the integration time in the experiment may greatly exceed the reciprocal bandwidth of the photons. The interference effect has a nonclassical origin and implies a violation of local realism in the highly correlated two-photon state.
The spread in time intervals between the two photons produced in the process of spontaneous parametric down-conversion in a potassium dihydrogen phosphate crystal have been measured with a time resolution of the order of 100 psec. The correlation time is found to be independent of the coherence time of the pump photons or of the propagation time through the crystal, consistent with recent theoretical predictions.
In the process of spontaneous parametric down-conversion a signal and an idler photon are created simultaneously. By use of the photoelectric detection of the signal photon as a gate, a good approximation to the ideal localized one-photon state can be achieved. This has been confirmed by direct photon-counting measurements.
A fourth-order interference technique has been used to measure the time intervals between two photons, and by implication the length of the photon wave packet, produced in the process of parametric down-conversion. The width of the time-interval distribution, which is largely determined by an interference filter, is found to be about 100 fs, with an accuracy that could, in principle, be less than 1 fs.
By measuring the joint probability for the detection of two photons at two points as a function of the separation between the points, the existence of nonclassical effects has been demonstrated in the interference of signal and idler photons in parametric down-conversion. In principle, the detection of one photon at one point rules out certain positions where the other photon can appear.
An improvement in precision beyond the limit set by the vacuum-state or zero-point fluctuations of the electromagnetic field is reported for the measurement of phase modulation in an optical interferometer. The experiment makes use of squeezed light to reduce the level of fluctuations below the shot-noise limit. An increase in the signal-to-noise ratio of 3.0 dB relative to the shot-noise limit is demonstrated, with the improvement currently limited by losses in propagation and detection and not by the degree of available squeezing.
When signal and idler photons produced in the process of parametric down-conversion are mixed together and directed to two photodetectors that respond to nonoverlapping optical frequencies centered at omega1 and omega2, it is found that the joint probability of two-photon detection exhibits a modulation of the form cos(omega1-omega2)tau, where c(tau) is the path difference. The experimental results are well described by a simple quantum-mechanical analysis.
Correlation measurements of mixed signal and idler photons produced in the process of parametric down-conversion have been performed as a function of two linear polarizer settings. It is found that the Bell inequality for two separated particles is violated by about 6 standard deviations, and that classical probability for light waves is violated substantially also.
It is demonstrated in a photon coincidence experiment with two photodetectors, in which signal and idler photons produced by parametric down-conversion are allowed to interfere, that the visibility of the interference pattern is well above 50% and remains unchanged when one of the two light beams is attenuated ninefold compared with the other. These results violate classical probability for light waves.
An exposition is given of the fundamental ideas of the recently opened field of two-particle interferometry, which employs spatially separated, quantum mechanically entangled two-particle states. These ideas are illustrated by a realizable arrangement, in which four beams are selected from the output of a laser-pumped down-converting crystal, with two beams interferometrically combined at one locus and two at another. When phase shifters are placed in these beams, the coincident count rates at the two loci will oscillate as the phases are varied, but the single count rates will not.
- B. R. Mollow