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Outline of experiment under discussion.
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We investigate the theory of the process in which an idler photon emitted spontaneously from a nonlinear crystal in the process of parametric downconversion serves as idler input to a second downconverter. The signal photon from this second crystal is then detected in coincidence with the signal photon from the first crystal, which provides the tim...
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Citations
... The nonlinear optical process of parametric downconversion (PDC) has been extensively employed to generate quantum states of light structured in the transverse spatial degrees of freedom [1]. In the classical regime, the same process can be operated in the stimulated emission mode (StimPDC) [2,3], providing a convenient platform for the design of quantum optical schemes [4][5][6], and for the study of the interplay between the spatial structures of the interacting light fields in the parametric process [7][8][9][10][11]. In the same way, parametric upconversion plays an important role in a wide variety of applications in quantum and classical optical schemes, as, for instance, frequency conversion of squeezed light fields [12,13] and imaging with visible and invisible light [14,15]. ...
Preparation, control, and measurement of optical vortices are increasingly important, as they play essential roles in both fundamental science and optical technology applications. Spatial light modulation is the main approach behind the control strategies, although there are limitations concerning the controllable wavelength. It is therefore crucial to develop approaches that expand the spectral range of light modulation. Here, we demonstrate the modulation of light by light in nonlinear optical interactions to demonstrate the identification of the topological charge of optical vortices. A triangular-lattice pattern is observed in light beams resulting from the spatial cross modulation between an optical vortex and a triangular shaped beam undergoing parametric interaction. Both up- and downconversion processes are investigated, and the far-field image of the converted beam exhibits a triangular lattice. The number of sites and the lattice orientation are determined by the topological charge of the vortex beam. In the downconversion process, the lattice orientation can also be affected by phase conjugation. The observed cross modulation works for a large variety of spatial field structures. Our results show that modulation of light by light can be used at wavelengths for which solid-state devices are not yet available.
... The nonlinear optical process of parametric down-conversion has been extensively employed to generate quantum states of light structured in the transverse spatial degrees of freedom [1]. In the classical regime, the same process can be operated in the stimulated emission mode (StimPDC) [2,3], providing a convenient platform for the design of quantum optical schemes [4][5][6], and for the study of the interplay between the spatial structures of the interacting light fields in the parametric process [7][8][9][10][11]. In the same way, parametric up-conversion plays an important role in a wide variety of applications in quantum and classical optical schemes, as for instance frequency conversion of squeezed light fields [12,13] and imaging with visible and invisible light [14,15]. ...
A triangular-lattice pattern is observed in light beams resulting from the spatial cross modulation between an optical vortex and a triangular shaped beam undergoing parametric interaction. Both up- and down-conversion processes are investigated, and the far-field image of the converted beam exhibits a triangular lattice. The number of sites and the lattice orientation are determined by the topological charge of the vortex beam. In the down-conversion process, the lattice orientation can also be affected by phase conjugation. The observed cross modulation works for a large variety of spatial field structures, and could replace solid-state devices at wavelengths where they are not yet available.
... There have been a number of both theoretical analyses and experimental implementations involving parametric down-conversion (e.g., Refs. [64,65,66,67,68,69]) which have been interpreted in terms of stimulated emission and/or amplification. In all of these cases, coincidence counts involving both signal and idler modes are measured when a single-photon or a weak coherent probe pulse is sent into a crystal, so that it propagates collinearly with the signal mode. ...
... In conclusion, the interaction between the incident probe field with the atoms experiments such as ours and in Refs. [64,65,66,67,68,69] can be treated in a weak coupling approximation. In that limit the increase in coincidence counts can be fully described by HBT-type interference between the incident field and the field radiated by the medium. ...
A principal goal of distributed quantum processing is the ability to generate, manipulate, and transfer quantum states between distant nodes of a quantum network. These protocols generally require connecting photonic and material carriers of quantum information. In this thesis, I present investigations of two experimental realizations of light-matter interfaces that allow for engineered atom-photon interactions in free-space settings. First, we utilize reconfigurable arrays of trapped single atoms to study light scattering in lowdimensional systems. We observe noncollinear phase-matching geometries that have suppressed sensitivity to particle localization. We show that the scattered radiation can be controllably enhanced or diminished as a result of Bragg interference. Such scattering can be used for mapping collective states within an array of neutral atoms onto propagating light fields and for establishing quantum links between separated arrays. Second, we utilize ensembles of trapped Rydberg atoms to study collective many-body phenomena that arise due to strong dipole-dipole interactions. To do so, we employ a magic-wavelength optical lattice that allows for the simultaneous trapping of both ground and Rydberg levels. Using the enhanced coherence times enabled by this trapping scheme, we measure the so-called magic lattice detunings and use them to extract the 6P3/2 − nS1/2 reduced electric dipole matrix elements. Furthermore, we perform precision measurements of differential nuclear-spin dependent light shifts in the Paschen-Back regime in order to determine the hyperfine splitting of Rydberg levels. We create a quasi-two-level system in a regime of Rydberg excitation blockade for a mesoscopic ensemble of several hundred atoms. Using this system, we study Hanbury Brown-Twiss interference between the field radiated by the atoms and an input probe field with a controllable relative phase. Finally, we demonstrate coherent driving and Ramsey interference measurements of light shifts, with timescales on the order of ≃ 10 µs. Whereas the coupling producing the Rabi oscillations is enhanced, there is no corresponding enhancement for the lightshifts. These results may prove useful in applying collective qubits with Rydberg interactions to scalable quantum networking architectures.
... Solid curves in a and b are obtained from theory described in the text and the supplemental material of reference [46]. . . 52 4.1 (a) A cold sample of 87 Rb gas is trapped in a 0.5-µm-period one-dimensional optical lattice formed by a retro-reflected beam E L . Two nearly counter-propagating beams, E 1 and E 2 excite a spin wave between the |5s 1/2 , F = 2 and |ns 1/2 levels. ...
... There have been a number of both theoretical analyses and experimental implementations involving parametric down-conversion (e.g., Refs. [52,48,49,50,51,53]) which have been interpreted in terms of stimulated emission and/or amplification. In all of these cases, coincidence counts involving both signal and idler modes are measured when a single-photon or a weak coherent probe pulse is sent into a crystal, so that it propagates collinearly with the signal mode. ...
... In conclusion, the interaction between the incident probe field with the atoms in experiments such as ours and in Refs. [52,48,49,50,51,53] can be treated in a weak coupling approximation. In that limit the increase in coincidence counts can be fully described by HBT-type interference between the incident field and the field radiated by the medium. ...
Rydberg ensembles have many diverse and important applications for quantum information and quantum optics. For example, Rydberg ensembles can generate non-classical states of light which would be useful in a quantum network, and they could be used as qubits in a future quantum computer. For this reason, this thesis will present investigations of light-matter interactions in Rydberg ensembles. Non-classical states of light, such as single-photon states, are important for many quantum communication protocols. We have performed an experiment that demonstrates the generation of single-photon states from a Rydberg ensemble. We then studied the second-order correlations between this single-photon state of light and an incident coherent field. Under these conditions, we observed Hanbury Brown Twiss interference between the emission from a driven super-atom and a coherent field in the absence of stimulated emission. For a universal quantum computing architecture, coherence times must be much longer than gate operations. We observe ground-Rydberg coherence times in excess of 20 microseconds by using a "magic-wavelength" optical lattice to confine the atoms. Using this coherence time, we measured the differential nuclear-spin-dependent light shifts for principal quantum numbers, n, between n = 30 and n = 65, which is relevant for future high-fidelity Rydberg qubits in optical potentials. Also, we measured the hyperfine constant for atomic Rb to be 35.71 GHz with an uncertainty of 0.18 GHz.
... There have been a number of both theoretical analyses and experimental implementations involving parametric down-conversion (e.g., Refs. [2][3][4][5][6][7]), which have been interpreted in terms of stimulated emission and/or amplification. In all of these cases, coincidence counts involving both signal and idler modes are measured when a single-photon or a weak coherent probe pulse is sent into a crystal, so that it propagates collinearly with the signal mode. ...
... In conclusion, the interaction between the incident probe field with the atoms experiments such as ours and in Refs. [2][3][4][5][6][7] can be treated in a weak coupling approximation. In that limit, the increase in coincidence counts can be fully described by HBT-type interference between the incident field and the field radiated by the medium. ...
Hanbury Brown–Twiss interference and stimulated emission, two fundamental processes in atomic physics, have been studied in a wide range of applications in science and technology. We study interference effects that occur when a weak probe is sent through a gas of two-level atoms that are prepared in a singly excited collective (Dicke or “superatom”) state and for atoms prepared in a factorized state. We measure the time-integrated second-order correlation function g(2) of the output field as a function of the delay τ between the input probe field and radiation emitted by the atoms and find that, for the Dicke state, g(2) is twice as large for τ=0 as it is for γeτ≫1 (γe is an excited state decay rate), while for the product state, this ratio is equal to 3/2. The results agree with those of a theoretical model in which any effects related to stimulated emission are totally neglected—the coincidence counts measured in our experiment arise from Hanbury Brown–Twiss interference between the input field and the field radiated by the atoms.
... Optical parametric amplifiers and oscillators are being extensively used in fabrication of tunable coherent radiation source with considerably high gain and high conversion efficiency [1]. Parametric interactions are also employed successfully to study the photon amplifiers [2,3] and to generate high peak power subpicosecond optical pulse [4]. The choice of a nonlinear medium and operating wavelength are crucial aspects in design and fabrication of parametric amplifiers and oscillators. ...
The effect of doping concentrations and a transverse external magnetostatic field on operational characteristics of parametric amplification of backward Stokes signal has been studied, using hydrodynamic model of semiconductors, in the far infrared regime. The model suggests three achievable resonance conditions: (i) lattice frequency and plasma frequency (ii) stokes frequency and electron-cyclotron frequency (iii) stokes frequency and hybrid (plasma and electron-cyclotron) frequency and these conditions have been utilised, on one hand, to substantially reduce the value of threshold intensity for onset of the parametric amplification and on the other hand, for switching of parametric large positive and negative gain coefficient (i.e. amplification and absorption). For example a strong transverse magnetostatic field 10.0 T with free carrier concentration 1.5 x 1019m-3 enhances the gain by a factor of 103 as in its absence. Results also suggest that a weakly piezoelectric III–V semiconductor duly illuminated by slightly off-resonant not-too-high-power pulsed lasers with pulse duration sufficiently larger than the acoustic phonon lifetime is one of promising hosts for parametric amplifier/frequency converter.
... [9][10][11] From a quantum-mechanical point of view such nonlinear processes have led to the prediction and observation of many quantum phenomena, e.g., squeezing of vacuum fluctuations and photon antibunching. [12][13][14][15][16][17][18] On the other hand, one can see the atom-field interaction, which is usually described by the Jaynes-Cummings model for the case of a single two-level atom or by the Tavis-Cummings model for the case of a single multilevel atom. [19][20][21][22] In these cases the energy exchange occurs between the atom and the electromagnetic field, whereas in the frequency conversion the energy exchange is realized among the field modes themselves. ...
... To discuss squeezing we have to use the result obtained in Section 3, more precisely, Eqs. (18) and (19). For this reason let us consider the coherent states ...
... As the solutions [Eqs. (18)] are linear in the initial annihilation and creation operators, the quantum characteristic functions are Gaussian, as given in Section 5, and we obtain consequently for the quantities ...
We investigate the quantum statistics of three time-dependent coupled oscillators in the presence of multiphoton processes. The system is connected with the two-atom multiphoton Tavis–Cummings model. The solution of the Heisenberg equations of the motion is obtained in a compact form. We assume that the modes are initially prepared in coherent states, and we discuss nonclassical phenomena (squeezing and sub-Poissonian behavior). Further, we examine the joint quasi-distribution functions as well as photon-number distribution and its factorial moments. The system has shown that the nonclassical effect is apparent in compound modes ( 1 , 3 ) and ( 2 , 3 ) . Moreover, the superstructure phenomenon is observed when the photon transition is increased.
Preparation, control and measurement of optical vortices is increasingly important as they play an essential role in new applications to fundamental science and optical technologies. Spatial light modulation is the main approach behind the control strategies. Here, we demonstrate the modulation of light by light to observe the triangular-lattice pattern resulting from the spatial cross modulation between an optical vortex and a triangular shaped beam undergoing parametric interaction. Both up- and down-conversion processes are investigated.
An attempt has been made to study the effects of stationary nano-sized ion grains (NSGs) on the nonlinear parametric interaction (PI) of laser with an n-type piezoelectric semiconductor plasmas in presence of a transverse magnetic field. It is assumed that the streaming electrons collide with the NSGs and stick onto them, which results into net negative charge on NSGs and depletion of electron density of the plasma. In the present paper, we have investigated the effect of charge depletion on the threshold pump field for the onset of parametric interaction and spatial gain coefficient of the scattered mode. It is found that as the number of electrons sticking onto the NSGs increases, the threshold pump field reduces in relatively lightly and moderately doped semiconductor but increases in the heavily doped. With increase in doping concentration, the scattered mode shows attenuation in the region ωp < ω0. At the resonance condition ωp ≈ ω0, the amplification of the scattered mode sharply increases to maximum and falls thereafter with increase in doping level.
