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arXiv:2406.12481

Curvature effects on stimulated parametric down-conversion process: an analog model

Saeed Akbari-Kourbolagh, Ali Mahdifar, Hamidreza Mohammadi

Published Jun 18, 2024• 0 citations
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Abstract

In this paper, we utilize an analog model of the general relativity and investigate the influence of spatial curvature on quantum properties of stimulated parametric down-conversion process. For this purpose, we use two-mode sphere coherent state as the input beams of the aforementioned process. These states are realization of coherent states of two-dimensional harmonic oscillator, which lies on a two-dimension sphere. We calculate the entanglement of output states of stimulated parametric down conversion process, measured by linear entropy, and show that it depends on the spatial curvature. So, by preparing the suitable two-mode sphere coherent states, it is possible to control the entanglement between the output states in the laboratory. In addition, we consider mean number and Mandel parameter of the output states of the process and also, their cross-correlation function, as the convince measures of non-classical behaviors.

DOI
10.48550/arxiv.2406.12481

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In this paper, we utilize an analog model of the general relativity and investigate the influence of spatial curvature on quantum properties of stimulated parametric down-conversion process. For this purpose, we use two-mode sphere coherent state as the input beams of the aforementioned process. These states are realization of coherent states of two-dimensional harmonic oscillator, which lies on a two-dimension sphere. We calculate the entanglement of output states of stimulated parametric down conversion process, measured by linear entropy, and show that it depends on the spatial curvature. So, by preparing the suitable two-mode sphere coherent states, it is possible to control the entanglement between the output states in the laboratory. In addition, we consider mean number and Mandel parameter of the output states of the process and also, their cross-correlation function, as the convince measures of non-classical behaviors.
Abstract In this paper, we utilize an analog model of the general relativity and investigate the influence of spatial curvature on quantum properties of stimulated parametric down-conversion process. For this purpose, we use two-mode sphere coherent state as the input beams of the aforementioned process. These states are realization of coherent states of two-dimensional harmonic oscillator, which lies on a two-dimension sphere. We calculate the entanglement of output states of stimulated parametric down conversion process, measured by linear entropy, and show that it depends on the spatial curvature. So, by preparing the suitable two-mode sphere coherent states, it is possible to control the entanglement between the output states in the laboratory. In addition, we consider mean number and Mandel parameter of the output states of the process and also, their cross-correlation function, as the convince measures of non-classical behaviors.
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 In this paper, we investigate the influence of spatial curvature on the Jaynes–Cummings model (JCM). We employ an analog model of general relativity, where the cavity field is represented by oscillators on a circle instead of a straight line, so that increasing curvature corresponds to decreasing the circle’s radius. We investigate the nonclassical features of this quantum system arising from the interaction between a two-level atom and a deformed harmonic oscillator on a circle, which serves as curved-space counterpart to the flat oscillator. We also propose an experimental scheme to realize this curvature-dependent JCM, based on the intensity-dependent Jaynes–Cummings interaction that appears in a laser-driven trapped ion inside a Kerr medium. By analyzing the time evolution of the atom-field system, we examine how spatial curvature influences the Mandel parameter, entropy, and the behavior of the Wigner distribution function. Our results demonstrate that the spatial curvature plays a crucial role in controlling these nonclassical properties.
Stimulated parametric down-conversion (StimPDC) is the seeded version of the process that underlies much of photonic quantum information. Replacing the vacuum at one input port with a coherent seed leaves the interaction Hamiltonian, the phase-matching function and the two-photon amplitude unchanged, while raising the output to levels accessible with ordinary classical detectors. This review treats the transverse spatial physics of that process. We show that a single relation, in which the idler amplitude is the pointwise product of the pump field with the complex conjugate of the seed, organizes results usually presented separately: the image and coherence transfer experiments of the 1990s; phase conjugation and its use for wavefront correction; the conservation and conjugation of orbital angular momentum, together with the generation of radial modes and geometric intensity patterns; and the processing of vector vortex beams carrying spatially varying polarization. We then consider StimPDC as an instrument rather than as an object of study, covering stimulated emission tomography, the experimental realization of Klyshko's advanced-wave picture, and the transfer of partial coherence, including the conservation of the twist phase of twisted Gaussian Schell-model beams. We close with the quantum regime, reached when the seed approaches the single-photon level or the idler is used as a herald, and with an assessment of open problems and prospective applications.
In this paper, we consider the interaction of the nonlinear coherent states (CSs) on a sphere with a three-level atom. Since these generalized CSs depend on the curvature of the sphere, this model enables us to investigate the curvature effects of the physical space. By using the time-dependent state of the atom-field system, we first study the curvature effects on the occupation probabilities of the atomic levels. We especially study the relation between the revival time of the atomic occupation probabilities and the curvature. Then, to study the curvature effects on the dynamical properties of the cavity field, we consider photon distributions, correlation functions, and Mandel parameters of the field. The cavity field in this atom-field system exhibits nonclassical features which depend on the curvature of the physical space.
We study the harmonic entanglement and squeezing in a two-mode radiation produced in a degenerate parametric down conversion process coupled to a two-mode vacuum reservoir employing the linearization procedure. It is found that there is a quadrature entanglement between the harmonically related fundamental and second-harmonic modes and the superimposed radiation exhibits a significant two-mode squeezing. The entanglement exits even when there is no two-mode squeezing, since the correlation leading to these phenomena are essentially different. In addition, the more the external coherent light is down converted, the more stronger the entanglement and mean photon number of the two-mode radiation would be which is not generally true for squeezing.