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arXiv:2404.12758

Nonclassicality in Two-Mode Stabilized Squeezed Coherent State: Quantum-to-Classical transition

Lee, C., Tai Hyun Yoon

Published Apr 19, 2024• 0 citations
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Abstract

We consider a two-mode stabilized squeezed coherent state (SSCS) of light and introduce the $Π_{\rm N}$ indicator, a novel measure for characterizing nonclassicality in the resulting EPR-entangled state. Unlike existing methods based on Cauchy-Schwarz or Murihead inequalities, $Π_{\rm N}$ leverages analytical solutions to the quantum Langevin equations to directly analyze nonclassicality arising from key processes like bichromatic injection, frequency conversion, and parametric down-conversion (both spontaneous and stimulated). This approach not only identifies the optimal phase for maximum nonclassicality but also reveals two new phenomena: first, both intra-cavity and extra-cavity fields exhibit the same degree of nonclassicality, and second, balanced seeding in phase-mismatched configurations induces nonclassicality across a broad range of squeezing and seeding parameters. Our work deepens the understanding of the intricate dependence of nonclassicality on system parameters in the context of SSCS, paving the way for investigations into the quantum-to-classical transition in entangled systems. The potential of $Π_{\rm N}$ holds significant promise for advancements in quantum optics and information science.

DOI
10.48550/arxiv.2404.12758

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We present a versatile method for producing two-mode stabilized squeezed coherent state (SSCS) of light with controllable nonclassicality. Our method involves seeding phase-coherent bichromatic fields into a nondegenerate optical parametric oscillator (OPO), where the global phase difference Φ\PhiΦ between the bichromatic seed and pump fields plays a central role. When Φ=2nπ\Phi=2n\piΦ=2nπ, where nnn is an integer, we show that the two-mode SSCS has its nonclassical measure at its minimum possible value with an effective displacement that compensates for single-photon losses with injected photons. As a result, the SSCS has a larger mean photon number and controllable nonclassicality compared to an OPO without seed fields. We also show that near-perfect squeezing level can be obtained at that effective displacement without being subject to injection rates. We believe that the proposed quantum source of two-mode SSCS with controllable nonclassicality would be useful for continuous-variable photonic quantum information processing.
We present a versatile method for producing two-mode stabilized squeezed coherent state (SSCS) of light with controllable nonclassicality. Our method involves seeding phase-coherent bichromatic fields into a nondegenerate optical parametric oscillator (OPO), where the global phase difference Φ\PhiΦ between the bichromatic seed and pump fields plays a central role. When Φ=2nπ\Phi=2n\piΦ=2nπ, where nnn is an integer, we show that the two-mode SSCS has its nonclassical measure at its minimum possible value with an effective displacement that compensates for single-photon losses with injected photons. As a result, the SSCS has a larger mean photon number and controllable nonclassicality compared to an OPO without seed fields. We also show that near-perfect squeezing level can be obtained at that effective displacement without being subject to injection rates. We believe that the proposed quantum source of two-mode SSCS with controllable nonclassicality would be useful for continuous-variable photonic quantum information processing.
The study of nonclassical properties of two-mode quantum states is particularly useful in quantum information theory because of the possibilities of obtaining entanglement and other two-mode quantum correlations in these states. Here we have investigated the possibilities of the existence of nonclassicality in a two-mode New generalized binomial state (TMNGBS). Specifically two-mode antibunching, Quadrature squeezing, sum \& difference squeezing, and various entanglement criteria e.g Shchukin-Vogel entanglement criterion, the uncertainty relation of SU(1,1) Algebra and EPR entanglement criterion are explored in two mode particular example of quantum state named as New generalized binomial state. Earlier we studied nonclassicality in single-mode NGBS, here we are extending our study toward the two-mode version of a quantum state. Here we provide the general expressions of moments for a two-mode quantum state (Fock basis) and explore the quantification in a particular example NGBS. It is found that antibunching, squeezing, and SV entanglement are possible with different limits of depending parameters but the entanglement criteria (EPR, SU (1,1) algebra and Cauchy - Schwarz inequality based)for NGBS are not possible. This study opens up the possibility of exploring the two-mode nonclassicality in other states too.
We re-examine the properties of the states produced by nondegenerate coherently stimulated parametric down-conversion wherein the signal and idler modes are seeded with coherent states of light and where the nonlinear crystal is driven by a strong classical field as described by the parametric approximation. The states produced are the two-mode squeezed coherent states defined with a specific ordering of operators, namely, the displacement operators of the two modes acting on the double vacuum state followed by the action of the two-mode squeeze operator representing the down-conversion process. Though mathematically equivalent to the reverse ordering of operators, but with different displacement parameters, the ordering we consider is closely related to what could most easily be implemented in the laboratory. The statistical properties of the state are studied with an emphasis on how they, and its average photon number, are affected by the various controllable phases, namely, those of the classical pump field of the two input coherent states. We then consider the multiphoton interference effects that arise if the two beams are overlapped on a 50:50 beam splitter, investigating the role of the phases in controlling the statistical properties of the output states. Finally, we study the prospects for the application of the states to quantum-optical interferometry to obtain sensitivities in phase-shift measurements beyond the standard quantum limit.
Abstract Recently, experimental demonstrations of the pair coherent state of microwave photons in superconducting cavities (PRX QUANTUM 4, 020319, 2023) and experimental results of photon addition and subtraction in multimode entangled optical fields (Physical Review Research 6, 013065, 2024) were reported. Motivated by these results, we study the nonclassical properties of non-Gaussian photon-added and subtracted pair coherent states. More specifically, we explore quantum polarization, quadrature squeezing, sum and difference squeezing, Shchukin-Vogel Entanglement, EPR entanglement correlation, two-mode higher-order antibunching, and quasiprobability distribution function (Q function). The effect of photon addition and subtraction is visible in this study with different parameters, as we compared our results with the original pair coherent state (PCS). This study provides a deeper understanding of the quantum behavior of modified pair coherent states, with potential implications for advancements in quantum optics and information processing.
In a recent paper [I. I. Arkhipov, Phys. Rev. A 98, 021803 (2018)], it was shown that one can completely identify the nonclassicality of single- and two-mode Gaussian states by means of certain nonclassicality witnesses which are based on intensity moments up to the third order of optical fields, provided that an appropriate coherent displacement is applied to a given Gaussian state. Here, we utilize a mathematical equivalence between the description of the coherent displaced Gaussian states generated in the spontaneous parametric processes and the Gaussian states generated in the corresponding stimulated parametric processes. Resorting to that equivalence, we study and compare the power of those nonclassicality witnesses in the detection of the nonclassicality of the two-mode Gaussian states generated in both the spontaneous and stimulated second subharmonic and down-conversion processes and which are subsequently subject to a beam splitter. We demonstrate that by means of an appropriate induced stimulated emission, one can completely identify the nonclassicality of the considered Gaussian states in comparison to the case of the spontaneous emission. This is important from the experimental point of view, as the stimulated emission can be easily implemented in running optical experiments, and such method can exploit just simple linear detectors.