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Observation of Squeezed States Generated by Four-Wave Mixing in an Optical Cavity
Abstract
Squeezed states of the electromagnetic field have been generated by nondegenerate four-wave mixing due to Na atoms in an optical cavity. The optical noise in the cavity, comprised of primarily vacuum fluctuations and a small component of spontaneous emission from the pumped Na atoms, is amplified in one quadrature of the optical field and deamplified in the other quadrature. These quadrature components are measured with a balanced homodyne detector. The total noise level in the deamplified quadrature drops below the vacuum noise level.
... The earlier approach to the squeezed light generation primarily focuses on the use of the nonlinear optical technique [2,25,26]. With the advance in the understanding of quantum mechanics, Barberis-Blostein [27] utilized the quantum state transfer to create the squeezed state of light. ...
... This is in opposition to the mandatory requirement in Refs. [26,27,[87][88][89][90]. Lastly, there is no demand for either the artificial atomic or cavity reservoir. ...
It is generally accepted that the role of quantum decoherence is to spoil the quantum superpositions and to yield the emergence of the classical behaviors from quantum mechanics. Contrary to the common knowledge of decoherence, we propose a scheme to generate a steady-state bright source of strongly sub-Poissonian squeezed light using the environmentally induced decoherence. The disappearance of the process of decoherence disables the generation of the squeezed state of the combination modes, while the presence of the decoherence results in the strongly nonclassical light source at the sub-shot-noise level and even near-perfect sub-Poissonian squeezed state of light. This excludes the use of the paradigm that the good insulation of a quantum system from its surrounding environment is highly desirable to explore its quantum property and fuel the growth of quantum information science. The interactions with the atom make no contribution to the preparation of squeezed light. These counterintuitive results are originated from the intrinsic quantum reservoir in the dressed-atom combination mode picture, which may open the door to exploring high levels of squeezing induced by the decoherence in the stationary regime.
Published by the American Physical Society 2025
... Optical parametric amplification is at the heart of quantumstate production [1,2]. In an optical parametric amplifier (OPA), a signal optical field is amplified simultaneously with the creation of an idler field, through nonlinear coupling with one or more additional pumping fields. ...
Optical parametric amplifiers (OPAs) in traveling-wave configuration can generate localized spatial quantum correlations between a signal and an idler beam, a useful resource for quantum imaging. To characterize the spatial correspondence between the optical modes of the signal and those of the idler, we look at the classical transverse dynamics of these beams when they propagate in a generic thick OPA at a nominally small angle. In these conditions, the beams tend to copropagate while maintaining a fixed separation, a phenomenon that we term hitching. We develop a model for hitching, validated by a numerical simulation, and provide an experimental demonstration using four-wave mixing in a hot atomic vapor. They show that the OPA gain is the primary influence on the final hitching distance. These results have implications for the generation of multi-spatial-mode squeezed light for quantum imaging applications, where the exact spatial correlations between the quantum fluctuations of the signal and the idler are of prime importance.
Published by the American Physical Society 2025
... Furthermore, significant advancements in phase sensitivity and noise reduction have been achieved by modifying the standard MZI setup. By replacing the passive beam splitters with active nonlinear elements, such as four-wave mixers 32,33 or optical parametric amplifiers (OPAs), [34][35][36] as first proposed by Yurke et al., 18 the modified interferometers demonstrate a significant improvement in measurement precision. This modified interferometer is called an SU(1,1) interferometer. ...
We propose a novel method for enhancing phase estimation in the displacement-assisted SU(1,1) [DSU(1,1)] interferometer by incorporating the photon recycling technique, evaluated under both single-intensity detection (SID) and homodyne detection (HD) schemes. Our analysis shows that utilizing the photon recycling technique, the photon-recycled DSU(1,1) interferometer performs better than the conventional DSU(1,1) interferometer under certain conditions. We also demonstrate that this improvement is achievable in both SID and HD schemes. In addition, to discuss the maximum sensitivity achieved by our proposed model, we have calculated the quantum Cramér–Rao bound (QCRB) within the framework and found that our proposed model approaches the QCRB. Therefore, we believe that our findings offer a promising new approach to improving phase sensitivity through photon recycling.
... Since the seminal demonstration of 0.3 dB noise reduction in hot sodium vapor in 1985 [9], the field has made significant progress, culminating in the current record of 15 dB achieved using a periodically poled KTP crystal cavity [10]. In many systems, the squeezing process can be accompanied by competing nonlinear effects that can obstruct the observation of squeezing and hinder its practical utilization. ...
Squeezed states of light are essential for emerging quantum technology in metrology and information processing. Chip-integrated photonics offers a route to scalable and efficient squeezed light generation, however, parasitic nonlinear processes and optical losses remain significant challenges. Here, we demonstrate single-mode quadrature squeezing in a photonic crystal microresonator via degenerate dual-pump spontaneous four-wave mixing. Implemented in a scalable, low-loss silicon-nitride photonic-chip platform, the microresonator features a tailored nano-corrugation that modifies its resonances to suppress parasitic nonlinear processes. In this way, we achieve an estimated 7.8 dB of on-chip squeezing in the bus waveguide, with potential for further improvement. These results open a promising pathway toward integrated squeezed light sources for quantum-enhanced interferometry, Gaussian boson sampling, coherent Ising machines, and universal quantum computing.
... Squeezed states of light have oddity that one of the quadrature variance is less than that of vacuum state [1][2][3][4]. The definition of squeezed light is related to the squeezing of noise in one of the quadrature components. ...
We develop a method for generating a more squeezed than single-mode squeezed vacuum (SMSV) state by subtracting 2,4,6 photons from it. In general, the more photons are subtracted, the more gain of the squeezing (more of 3 dB) is observed in the measurement-induced continuous variable (CV) states of definite parity. However, the two-photon subtraction strategy is practically preferred. It can be implemented with higher success probability, wider squeezing gain width ~ 5 dB and least quadrature variance in the corresponding range of initial squeezing. We demonstrate the mitigating effect of a photon-number resolving (PNR) detector with non-unit quantum efficiency on the output characteristics of the measurement-induced CV states, resulting in their slight decrease compared to ideal photon subtraction. Use of a single photon in addition to the SMSV state at beam splitter (BS) input with subsequent registration of odd number of photons (say, 3 photons) allows the implementation of the measurement-induced even CV state which is several times brighter than the initial state and has lower quadrature noise.
The structure, bonding, and properties of diradicals, triradicals, and polyradicals have been investigated using broken symmetry (BS) molecular orbital (MO) and BS density functional theory (DFT) methods, which are regarded as the first steps in the mean-field approach toward strongly correlated electron systems (SCES). The natural orbital (NO) analyses of the BS MO and BS DFT solutions were performed to elucidate the natural orbitals of their occupation numbers, which are used for derivations of the diradical character (y) and several chemical indices for the open-shell molecules under investigation. These chemical indices are also obtained using SCES, the next theoretical step, which uses symmetry-recovered resonating BS (RBS) and multi-determinant methods such as multi-reference (MR) configuration interaction (CI) and MR-coupled cluster (CC) methods that employ the NOs generated in the first step. The nonlinear optical response properties of organic open-shell species were theoretically investigated with several procedures, such as MR CI (CC), the numerical Liouville, and Monte Carlo wavefunction methods, as the third step to SCES. The second-order hyperpolarizability (γ) of diradicals such as a phenalenyl radical dimer were mainly investigated in relation to the generation of quantum squeezed lights, which are used for the construction of the quantum entangled states for quantum optical devices such as quantum sensing and quantum computation. Basic quantum mechanical concepts, such as the Pegg–Barnett quantum phase operator, were also revisited in relation to the design and chemical synthesis of stable diradicals and polyradicals such as optical quantum molecular materials and future molecular qubits materials.
We report an all-fiber-based experimental setup to generate a correlated photon-pair comb using Four Wave Mixing (FWM) in Highly non-linear fiber (HNLF). Temporal correlations of the generated photons were confirmed through coincidence measurements. We observed a maximum of 32 kcps, with a coincidence to accidental ratio of . To further understand the underlying processes, we also simulated a generalized FWM event involving the interaction between an arbitrary frequency comb and a Continuous Wave (CW) pump. non-linear dynamics through the HNLF were modelled using Schrödinger propagation equations, with numerical predictions agreeing with our experimental results.
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 simple but rigorous analysis of the important sources of noise in homodyne detection is presented. Output noise and signal-to-noise ratios are compared for direct detection, conventional (one-port) homodyning, and two-port homodyning, in which one monitors both output ports of a 50–50 beam splitter. It is shown that two-port homodyning is insensitive to local-oscillator quadrature-phase noise and hence provides (1) a means of detecting reduced quadrature-phase fluctuations (squeezing) that is perhaps more practical than one-port homodyning and (2) an output signal-to-noise ratio that can be a modest to significant improvement over that of one-port homodyning and direct detection.
It is shown that degenerate four-wave mixing generates two-photon coherent states (TCS) of the radiation field for modes that are proper combinations of the output object and image waves. TCS light has novel quantum behavior, which can be probed by homodyne detection, intensity interferometry, or photocount statistics. Numerical estimates indicate that the generation and detection of TCS light via degenerate four-wave mixing and homodyne detection can be accomplished with current technology.
Cavity degenerate-parametric-amplifier and cavity four-wave-mixing configurations capable of producing a large amount of squeezing near the threshold of oscillation are discussed. Cavities allow one to reduce the pump power delivered to the gain medium, or to select a gain medium which has less gain per unit length, but may be better suited for squeezed-state production in other respects.
The performance of phase-sensing interferometers employing squeezed states and homodyne detection is analyzed and compared to the performance of systems employing direct detection. Standard differenced direct-detection Michelson and Mach-Zehnder interferometers are shown to be suboptimal in the sense that an observation/measurement-noise coupling occurs, which can degrade performance. Homodyne-detection interferometers in which the phase shift in one arm is the conjugate of that in the other arm do not suffer from the preceding drawback. Overall, however, the performance of differenced direct-detection and homodyne-detection interferometers is similar in single-frequency operation. In particular, both detection schemes reach the standard quantum limit on position-measurement sensitivity in single-frequency interferometric gravity-wave detectors at roughly the same average photon number. This limit arises from back action in the form of radiation pressure fluctuations entering through the energy-phase uncertainty principle. Multifrequency devices can circumvent this uncertainty principle, as illustrated by the conceptual design given for a two-frequency interferometer which can greatly surpass the standard quantum limit on position sensing. This configuration assumes that ideal photodetectors respond to photon flux rather than energy flux.
Degenerate four-wave mixing has been suggested as a possible generation scheme for squeezed-state light. A recent analysis of the quantum effects of probe-conjugate loss in backward degenerate four-wave mixing has shown that such loss puts an absolute limit on the squeezing that can be obtained via this generation scheme. In this Rapid Communication we show that it is the counter-propagating beam geometry of backward degenerate four-wave mixing that makes it ill suited for squeezed-state generation. On the other hand, the nominally copropagating beam geometry of forward degenerate four-wave mixing is shown to alleviate the absolute probe-conjugate loss limit on squeezing.
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 interferometers now being developed to detect gravitational waves work by measuring the relative positions of widely separated masses. Two fundamental sources of quantum-mechanical noise determine the sensitivity of such an interferometer: (i) fluctuations in number of output photons (photon-counting error) and (ii) fluctuations in radiation pressure on the masses (radiation-pressure error). Because of the low power of available continuous-wave lasers, the sensitivity of currently planned interferometers will be limited by photon-counting error. This paper presents an analysis of the two types of quantum-mechanical noise, and it proposes a new technique: the ''squeezed-state'' technique: that allows one to decrease the photon-counting error while increasing the radiation-pressure error, or vice versa. The key requirement of the squeezed-state technique is that the state of the light entering the interferometer's normally unused input port must be not the vacuum, as in a standard interferometer, but rather a ''squeezed state'': a state whose uncertainties in the two quadrature phases are unequal. Squeezed states can be generated by a variety of nonlinear optical processes, including degenerate parametric amplification.
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.