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Results in Physics

Entanglement, nonclassical properties and geometric phase of Raman photon pairs in the presence of time-dependent coupling

Sadah Abdullah Alkhateeb, S. Abdel‐Khalek, K. Berrada, Eman M. A. Hilal

Published Jan 1, 2016• 2 citations
Publisher

Abstract

In this paper, we develop the model of the four-level double Raman pairs by exploiting the required optimal conditions for this system that are feasible with real experimental realization. We investigate qualitatively the entanglement, statistical properties, and geometric phase for the pair of Stokes and anti-Stokes photons in the presence of the time-dependent coupling effect. We show that these quantifiers are very sensitive to the change of the Rabi frequency and time, exhibiting substantial phenomena that are depending on the kind of coupling between the atom and photons. Finally, we explore the relationship between the quantum quantifiers in terms of the physical parameters with and without time-dependent coupling effect.

DOI
10.1016/j.rinp.2016.07.004

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In this paper, we develop the model of the four-level double Raman pairs by exploiting the required optimal conditions for this system that are feasible with real experimental realization. We investigate qualitatively the entanglement, statistical properties, and geometric phase for the pair of Stokes and anti-Stokes photons in the presence of the time-dependent coupling effect. We show that these quantifiers are very sensitive to the change of the Rabi frequency and time, exhibiting substantial phenomena that are depending on the kind of coupling between the atom and photons. Finally, we explore the relationship between the quantum quantifiers in terms of the physical parameters with and without time-dependent coupling effect.
Robustness of the geometric phase (GP) with respect to different noise effects is a basic condition for an effective quantum computation. Here, we propose a useful quantum system with real physical parameters by studying the GP of a pair of Stokes and anti-Stokes photons, involving Raman emission processes with and without photonic band gap (PBG) effect. We show that the properties of GP are very sensitive to the change of the Rabi frequency and time, exhibiting collapse phenomenon as the time becomes significantly large. The system allows us to obtain a state which remains with zero GP for longer times. This result plays a significant role to enhance the stabilization and control of the system dynamics. Finally, we investigate the nonlocal correlation (entanglement) between the pair photons by taking into account the effect of different parameters. An interesting correlation between the GP and entanglement is observed showing that the PBG stabilizes the fluctuations in the system and makes the entanglement more robust against the change of time and frequency.
Abstract In this paper, we propose a useful quantum system to perform different tasks of quantum information and computational technologies. We explore the required optimal conditions for this system that are feasible with real experimental realization. We present an active way to control the variation of some measures of nonclassicality considering the time-dependent coupling and photon transition effects under a model that closely describes a realistic experimental scenario. We investigate qualitatively the quantum measures for a two-level atom system interacting with a quantum field initially defined in a coherent state in the framework of power-law potentials (PLPCSs). We study the nonlocal correlation in the whole system state using the negativity as a measure of entanglement in terms of the exponent parameter, number of photon transition, and phase damping effect. The influences of the different physical parameters on the statistical properties and purity of the field are also demonstrated during the time evolution. The results indicate that the preservation and enhancement of entanglement greatly benefit from the combination of the choice of the physical parameters. Finally, we explore an interesting relationship between the different quantum measures of non-classicality during the time evolution in the absence and presence of time-dependent coupling effect.
Photon pairs possess nonclassical properties such as antibunching, squeezing and entanglement that are useful in quantum information science, and has so far been studied predominantly for fixed atom. Here, we quantized the center of mass motion and study the effect of atomic motion on the quantum correlation, entanglement and squeezing between a Stokes photon and an anti-Stokes photon generated in a coherently driven double Raman scheme. We study how the laser fields can be used to control these nonclassical properties. The underlying physics are explained via a simple model.
We present a comprehensive study of co- and counterpropagating Stokes and anti-Stokes quantum fields in double Raman four-wave mixing parametric oscillators using full quantum Heisenberg-Langevin framework with noise operators. General analytical solutions of the fields operators at any point in the Raman medium are obtained for four cases: two possible copropagating (forward) and two counterpropagating (backward) Stokes and anti-Stokes. We analyze the symmetrical properties of the complex linear and nonlinear susceptibilities spectra of the quantum fields, nonclassicality of two-photon correlation functions, spatial variations of the quantum fields, and the two-mode relative intensity squeezing. We compare the results of forward and backward cases for several limiting double Raman schemes. We find interesting resonant effects of medium length, laser detunings and laser field strengths (Rabi frequencies) for backward-propagating geometries. Analysis of the solutions provide insights on the resonant conditions while computation over multiple variables enables us to identify the values of laser detuning, field strength, and propagation length that give enhanced nonclassical intensity squeezing and persistent correlations. The present work sets the crucial foundations for optimization of the nonclassicality of photons in double Raman systems and would be useful for quantum information storage, quantum nonlinear optics, and quantum spectroscopy.
A quantum model of the Raman process with the independent Stokes and anti-Stokes nonlinear interactions is developed to study nonclassical correlations between the photons in the Stokes and anti-Stokes fields. The role of the laser pump amplitude, the ratio of the Stokes and anti-Stokes coupling constants, and the population and losses of the vibrational mode in forming the correlations is elucidated. The g(2){g}^{(2)}g(2) intensity cross-correlation function, noise-reduction factor, two-mode principal squeezing variance, logarithmic negativity, nonclassicality depth, steering parameter, and the Bell parameter are analyzed side by side to shed light to the correlations between the Stokes and anti-Stokes fields. Conditions for having the Stokes and anti-Stokes fields composed of only photon pairs, similarly as it occurs in twin beams in parametric down-conversion, are revealed. They allow for nonzero mean thermal phonon numbers.
We have theoretically analyzed nonclassical paired photons generated spontaneously from a four-level inverted-Y atomic system. We discuss the feasibility of biphoton generation due to different pumping arrangements. Two types of correlated photon pair emissions have been carefully examined: dressed cascade and dressed double-$\ensuremath{\Lambda}$ emissions. In the dressed cascade two-photon emission, the coincidence counting rate may exhibit a damped Rabi oscillation, in contrast with a simple exponential decay feature in the literatures. In the dressed double-$\ensuremath{\Lambda}$ configuration, we show that not only is the temporal correlation of entangled Stokes--anti-Stokes photons in agreement with discussions presented by Wen et al. [Phys. Rev. A 76, 013825 (2007)], but also the oscillation period may be manipulated by altering either the control Rabi frequency or the dressing Rabi frequency or both. All the observed damped Rabi oscillations in the two-photon coincidences result from the destructive interference among the possible four-wave mixing processes occurring in the atom-field interaction system. This feature of the two-photon amplitude is governed by the convolution between the phase matching and third-order nonlinear susceptibility. The methodology adopted here can be applied to other atomic-level configurations and provides a useful tool to study the spectroscopy of the system. The generated narrow-band photon pairs may have potential applications in long-distance quantum communication and quantum information processing.