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Generation of Squeezed States by Parametric Down Conversion
Abstract
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.
... On the other hand, in quantum optics applications it is more important to solve the initial value problem, whereas the eigenstates of the full Hamiltonian do not correspond to the optical energy (given by the free propagation part of the Hamiltonian, see below). The most important example is the work-horse of all quantum optics -the twophoton parametric down conversion process in a nonlinear medium with the second-order nonlinearity [17,18] (see also the reviews [19][20][21]). The recent experimental realization of the long sought three-photon spontaneous parametric down-conversion [22] adds another integrable model to applications in quantum optics. ...
... In the second term in Eq. (17) the summation over s ′ 2 has the upper limit s ′ 1 +1 ≡ s 0 +1, with s 0 = m−2l−1 = (m+ 1) − 2l ′ i.e., exactly the index in the extra (the first from the left to the right) β-factor. Precisely this value of s 1 is missing in the first term on the right hand side of Eq. (17) in order to reproduce the sum over s 1 ≤ (m + 1) − 2l for l ≤ p, as suggested by Eq. (14) applied to m+ 1, whereas for l = p + 1 the respective sum contains just β m+1−2l ′ coming from the second term in Eq. (17). Hence, the two terms in Eq. (17) indeed combine to reproduce the respective sum over 2 ≤ l ≤ [ m+1 2 ], to coincide with Eq. (14) for m + 1. ...
... In the second term in Eq. (17) the summation over s ′ 2 has the upper limit s ′ 1 +1 ≡ s 0 +1, with s 0 = m−2l−1 = (m+ 1) − 2l ′ i.e., exactly the index in the extra (the first from the left to the right) β-factor. Precisely this value of s 1 is missing in the first term on the right hand side of Eq. (17) in order to reproduce the sum over s 1 ≤ (m + 1) − 2l for l ≤ p, as suggested by Eq. (14) applied to m+ 1, whereas for l = p + 1 the respective sum contains just β m+1−2l ′ coming from the second term in Eq. (17). Hence, the two terms in Eq. (17) indeed combine to reproduce the respective sum over 2 ≤ l ≤ [ m+1 2 ], to coincide with Eq. (14) for m + 1. ...
Quantum models of interacting bosons have wide range of applications, among them the propagation of optical modes in nonlinear media, such as the k-photon down conversion. Many of such models are related to nonlinear deformations of finite group algebras, thus, in this sense, they are exactly solvable. Whereas the advanced group-theoretic methods have been developed to study the eigenvalue spectrum of exactly solvable Hamiltonians, in quantum optics the prime interest is not the spectrum of the Hamiltonian, but the evolution of an initial state, such as the generation of optical signal modes by a strong pump mode propagating in a nonlinear medium. I propose a simple and general method of derivation of the solution to such a state evolution problem, applicable to a wide class of quantum models of interacting bosons. For the k-photon down conversion model and its generalizations, the solution to the state evolution problem is given in the form of an infinite series expansion in the powers of propagation time with the coefficients defined by a recursion relation with a single polynomial function, unique for each nonlinear model. As an application, I compare the exact solution to the parametric down conversion process with the semiclassical parametric approximation.
... Squeezed light was first produced in 1985 by Slusher et al. using four-wave-mixing in Na atoms in an optical cavity [54]. Shortly after, squeezed light was also generated by fourwave-mixing in an optical fibre [76] and by parametric downconversion in an optical cavity containing a second order nonlinear material [77]. In these early day experiments, squeezing of a few percent to 2 to 3 dB were routinely observed (For an overview of earlier experiments and squeezed light generation in the continuous-wave as well as pulsed regime please refer to Ref. [78]). Figure 7: Generation of squeezed light (a) A continuous-wave laser beam at the GW detector wavelength is first spatially filtered and then up-converted to a field at half the wavelength (second harmonic generation, SHG). ...
... High-power lasers for GW astronomy are based on optically pumped solid-state crystals in resonators [38], suggestive of a similar configuration for a "squeezed light resonator". Fig. 7 (a) shows a schematic setup for generation of squeezed light that is built upon one of the very first squeezing experiments [77], a setup that has been used in many experiments thereafter [72,73,79,80]. The setup uses a solid state laser similar to those used as master lasers in high-power systems. ...
... Although squeezed light was demonstrated in the 1980s shortly after the first applications were proposed [54,76,77], several important challenges pertaining to the application of squeezed states to GW detectors remained unsolved until recently. ...
Einstein's General Theory of Relativity predicts that accelerating mass distributions produce gravitational radiation, analogous to electromagnetic radiation from accelerating charges. These gravitational waves have not been directly detected to date, but are expected to open a new window to the Universe in the near future. Suitable telescopes are kilometre-scale laser interferometers measuring the distance between quasi free-falling mirrors. Recent advances in quantum metrology may now provide the required sensitivity boost. So-called squeezed light is able to quantum entangle the high-power laser fields in the interferometer arms, and could play a key role in the realization of gravitational wave astronomy.
... that model the squeezing of quantum fluctuations for the single field modes [84,85]. The final solutions arê ...
The Einstein-Podolsky-Rosen (EPR) paradox was presented as an argument that quantum mechanics is an incomplete description of physical reality. However, the premises on which the argument is based are falsifiable by Bell experiments. In this paper, we examine the EPR paradox from the perspective of Schrodinger's reply to EPR. Schrodinger pointed out that the correlated states of the paradox enable the simultaneous measurement of and , one by direct, the other by indirect measurement. Schrodinger's analysis takes on a timely importance because a recent experiment realizes these correlations for macroscopic atomic systems. Different to the original argument, Schrodinger's analysis applies to the experiment at the time when the measurement settings have been fixed. In this context, a subset of local realistic assumptions (not negated by Bell's theorem) implies that x and p are simultaneously precisely defined. Hence, an alternative EPR argument can be presented that quantum mechanics is incomplete, based on a set of (arguably) nonfalsifiable premises. As systems are amplified, macroscopic realism can be invoked, and the premises are referred to as weak macroscopic realism (wMR). In this paper, we propose a realization of Schrodinger's gedanken experiment where field quadrature phase amplitudes and replace position and momentum. Assuming wMR, we derive a criterion for the incompleteness of quantum mechanics, showing that the criterion is feasible for current experiments. Questions raised by Schrodinger are resolved. By performing simulations based on an objective-field (Q-based) model for quantum mechanics, we illustrate the emergence on amplification of simultaneous predetermined values for and . The values can be regarded as weak elements of reality, along the lines of Bell's macroscopic beables.
... Starting in O3, the LIGO detectors also began to inject non-classical states of light, known as "squeezed vacuum," at the anti-symmetric port to reduce quantum noise [36][37][38][39] during astrophysical observing [40][41][42][43][44] to reduce the noise variance in one quadrature of the squeezed state at the expense of increased noise in the conjugate quadrature, e.g, reducing fluctuations in phase at the cost of increasing fluctuations in amplitude [36,45]. For O4, a filter cavity was added to the squeezing system to prepare frequency-dependent squeezed vacuum states of light for broadband quantum noise reduction [16,46]. ...
On May 24th, 2023, the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO), joined by the Advanced Virgo and KAGRA detectors, began the fourth observing run for a two-year-long dedicated search for gravitational waves. The LIGO Hanford and Livingston detectors have achieved an unprecedented sensitivity to gravitational waves, with an angle-averaged median range to binary neutron star mergers of 152 Mpc and 160 Mpc, and duty cycles of 65.0% and 71.2%, respectively, with a coincident duty cycle of 52.6%. The maximum range achieved by the LIGO Hanford detector is 165 Mpc and the LIGO Livingston detector 177 Mpc, both achieved during the second part of the fourth observing run. For the fourth run, the quantum-limited sensitivity of the detectors was increased significantly due to the higher intracavity power from laser system upgrades and replacement of core optics, and from the addition of a 300 m filter cavity to provide the squeezed light with a frequency-dependent squeezing angle, part of the A+ upgrade program. Altogether, the A+ upgrades led to reduced detector-wide losses for the squeezed vacuum states of light which, alongside the filter cavity, enabled broadband quantum noise reduction of up to 5.2 dB at the Hanford observatory and 6.1 dB at the Livingston observatory. Improvements to sensors and actuators as well as significant controls commissioning increased low frequency sensitivity. This paper details these instrumental upgrades, analyzes the noise sources that limit detector sensitivity, and describes the commissioning challenges of the fourth observing run.
... In the classical regime, optical fields at new frequencies are generated with χ (2) nonlinear processes such as second-harmonic generation (SHG) [1][2][3], difference frequency generation (DFG) [4], and optical parametric oscillation (OPO) [5,6]. In the quantum regime, χ (2) nonlinearity is used to generate heralded single photons [7][8][9], entangled photons [10][11][12], and squeezed light [13][14][15]. ...
Second-harmonic generation (SHG) plays a significant role in modern photonic technology. Integrated photonic resonators fabricated with thin-film lithium niobate can achieve ultrahigh efficiencies by combining small mode volumes with high material nonlinearity. Cavity-enhanced SHG requires accurate phase and frequency matching conditions, where fundamental and second-harmonic wavelengths are both on resonance. However, this double-resonance condition can typically be realized only at a fixed random wavelength due to the high sensitivity of photonic resonances to the device geometry and fabrication variations. Here, we propose a novel method that can achieve the double-resonance condition over a large wavelength range. We combine thermal-optic and electro-optic (EO) effects to realize the separate tuning of fundamental and second-harmonic resonances. We demonstrated that the optimum SHG efficiency can be maintained over a wavelength range that exceeds the limit achievable with only thermal tuning. With this flexible tuning capability, we further show the precise alignment of SHG wavelengths of two separate thin-film lithium niobate resonators without sacrificing efficiencies.
... No obstante, en 1986 se demostró la generación de estados comprimidos basados fibra óptica que explotaba la no linealidad de tipo Kerr de tercer orden del SiO2 (Shelby et al., 1986), logrando un squeezing de 0.6 dB por debajo del ruido de vacío, así como el enfoque basado en la no linealidad de segundo orden de un cristal ferroeléctrico (Wu et al., 1986), donde la compresión fue de aproximadamente 3.5 dB debajo del ruido de vacío. Unos meses después, se presentó otra tecnología para la generación de luz comprimida. ...
The overall objective of this work is the comparative study of optical parametric amplification (OPA) in
microstructured solid-core fused silica fibers and hollow-core fibers filled with acetylene (C2H2). Both
media exhibit third-order nonlinearity, enabling the OPA process in collinear configurations with a high
spatial concentration of light power. An experiment was implemented to measure the quadratures of
a bimodal quantum state using parametric amplification via four-wave mixing (FWM) with a
degenerate pump by picosecond laser pulses centered at a wavelength of 737 nm. This process
ensured the generation of correlated signal/idler photon pairs that could be parametrically amplified
in a similar nonlinear microstructured fiber. Experiments were implemented to characterize phasesensitive parametric amplification in an acetylene cell. An experimental evaluation of the OPA gain in
a degenerate collinear FWM at 1530 nm near the P9 acetylene absorption line is presented.
Specifically, the transformation of amplitude modulation in the quasi-continuous W-scale input pump
wave to output phase modulation and vice versa was studied. This research compares OPA efficiencies
and the potential to generate squeezed and entangled light states in fiber-based media with resonant
and non-resonant nonlinearities.
This paper studies the effects of the postselected von Neumann measurement on the nonclassicality of the single-photon-subtracted squeezed vacuum (SPSSV) state. Specifically, we calculated the squeezing effect, Mandel factor, Wigner function, signal-to-noise ratio (SNR), and state distance function. We found that the postselected von Neumann measurement positively affects the SPSSV state optimization. Precisely, correctly choosing the anomalous weak value allows for optimizing the nonclassical inherent features of the SPSSV state, such as squeezing, photon statistics, and phase space distribution. Additionally, this study confirms the advantages of postselected WM in improving the SNR compared to non-postselected measurement schemes. Furthermore, a possible implementation method is proposed using optics setups. The superiority of the SPSSVS-based postselected WM in quantum state optimization can support various applications in the associated quantum information processing.
Quantum-mechanical calculations of the mean-square fluctuation spectra in optical homodyning and heterodyning are made for arbitrary input and local-oscillator quantum states. In addition to the unavoidable quantum fluctuations, it is shown that excess noise from the local oscillator always affects homodyning and, when it is broadband, also heterodyning. Both the quantum and the excess noise of the local oscillator can be eliminated by coherent subtraction of the two outputs of a 50–50 beam splitter. This result also demonstrates the fact that the basic quantum noise in homodyning and heterodyning is signal quantum fluctuation, not local-oscillator shot noise.
We show that all the minimum uncertainty packets are unitarily equivalent to the coherent states and that coherence is in fact stationary minimality.
The problem of detecting a coherent light beam in the presence of unwanted background radiation by the heterodyne method is examined. For a sufficiently strong local-oscillator field, the detectability of the signal is unaffected by the presence of the background radiation. It is shown that, in general, there exists an optimum receiver size that maximizes the signal-to-noise ratio. This result is illustrated by several examples. A procedure for the detection of a light signal of unknown direction is suggested.
In a previous paper we have shown that all minimum-uncertainty packets are unitarily equivalent to the coherent states and that coherence may be viewed as stationary minimality. In this note we give some additional information relating to the nature of the unitary-equivalence structure. We also give a new calculation of some matrix elements of the operator that implements the unitary equivalence which is not subject to the shortcoming inherent in the original calculation.
We describe a new and highly effective optical frequency discriminator and laser stabilization system based on signals reflected from a stable Fabry-Perot reference interferometer. High sensitivity for detection of resonance information is achieved by optical heterodyne detection with sidebands produced by rf phase modulation. Physical, optical, and electronic aspects of this discriminator/laser frequency stabilization system are considered in detail. We show that a high-speed domain exists in which the system responds to the phase (rather than frequency) change of the laser; thus with suitable design the servo loop bandwidth is not limited by the cavity response time. We report diagnostic experiments in which a dye laser and gas laser were independently locked to one stable cavity. Because of the precautions employed, the observed sub-100 Hz beat line width shows that the lasers were this stable. Applications of this system of laser stabilization include precision laser spectroscopy and interferometric gravity-wave detectors.
It is pointed out that single-frequency emission from a Nd:YAG laser at
1.06 microns at power levels in excess of 1 W would be useful for the
investigation of dynamic processes in nonlinear optics. The emission
could also be important for applications related to high-resolution
nonlinear spectroscopy. However, due to thermal loading of the laser
rod, it is very difficult to obtain submegahertz frequency stability for
Nd:YAG lasers at high levels of lamp pumping power. The present
investigation is concerned with a single-frequency Nd:YAG laser with an
output power exceeding 1.1 W and a frequency stability of 120-kHz rms.
This performance is obtained in a ring cavity. This approach makes it
possible to eliminate problems associated with spatial hole burning. The
ring cavity is designed to minimize laser fluctuations due to noise in
the pumping and cooling processes.
Quantum-mechanical calculations of the mean-square fluctuation spectra in optical homodyning and heterodyning are made for arbitrary input and local-oscillator quantum states. In addition to the unavoidable quantum fluctuations, it is shown that excess noise from the local oscillator always affects homodyning and, when it is broadband, also heterodyning. Both the quantum and the excess noise of the local oscillator can be eliminated by coherent subtraction of the two outputs of a 50-50 beam splitter. This result also demonstrates the fact that the basic quantum noise in homodyning and heterodyning is signal quantum fluctuation, not local-oscillator shot noise.
A general approach, within the framework of canonical quantization, is described for analyzing the quantum behavior of complicated electronic circuits. This approach is capable of dealing with electrical networks having nonlinear or dissipative elements. The techniques are applied to circuits capable of generating squeezed-state or two-photon coherent-state signals. Circuits capable of performing back-action-evading electrical measurements are also discussed.
The properties of a unique set of quantum states of the electromagnetic field are reviewed. These 'squeezed states' have less uncertainty in one quadrature than a coherent state. Proposed schemes for the generation and detection of squeezed states as well as potential applications are discussed.
The concept of a two-photon coherent state is introduced for applications in quantum optics. It is a simple generalization of the well-known minimum-uncertainty wave packets. The detailed properties of two-photon coherent states are developed and distinguished from ordinary coherent states. These two-photon coherent states are mathematically generated from coherent states through unitary operators associated with quadratic Hamiltonians. Physically they are the radiation states of ideal two-photon lasers operating far above threshold, according to the self-consistent-field approximation. The mean-square quantum noise behavior of these states, which is basically the same as those of minimum-uncertainty states, leads to applications not obtainable from coherent states or one-photon lasers. The essential behavior of two-photon coherent states is unchanged by small losses in the system. The counting rates or distributions these states generate in photocount experiments also reveal their difference from coherent states.