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Physical Review A

Phase-sensitive Kerr nonlinearity for closed-loop quantum systems

Hamid Reza Hamedi, Gediminas Juzeliūnas

Published May 14, 2015• 94 citations
Publisher

Abstract

The third-order susceptibility is investigated in a five-level atomic system in which the laser beams couple the ground state to a four-level closed-loop system. It is found that under the condition of the multiphoton resonance, one can enhance the Kerr nonlinearity of such a medium by properly adjusting the amplitudes and phases of the applied fields. In this case, the linear and nonlinear absorption reduce considerably in a region with a positive group velocity. It is demonstrated that the third-order susceptibility is very sensitive to the relative phase of the applied fields. An analytical model is presented to elucidate such phase control of the Kerr nonlinearity. A comparison is also made between the Kerr-nonlinear indices for the five-, four-, and three-level systems. It is realized that the magnitude of the Kerr nonlinearity for the five-level system is larger than that of the three- and four-level counterparts. Finally, it is shown that effect of Doppler broadening can lead to an enhanced Kerr nonlinearity while maintaining linear and nonlinear absorption.

DOI
10.1103/physreva.91.053823

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The third-order susceptibility is investigated in a five-level atomic system in which the laser beams couple the ground state to a four-level closed-loop system. It is found that under the condition of the multiphoton resonance, one can enhance the Kerr nonlinearity of such a medium by properly adjusting the amplitudes and phases of the applied fields. In this case, the linear and nonlinear absorption reduce considerably in a region with a positive group velocity. It is demonstrated that the third-order susceptibility is very sensitive to the relative phase of the applied fields. An analytical model is presented to elucidate such phase control of the Kerr nonlinearity. A comparison is also made between the Kerr-nonlinear indices for the five-, four-, and three-level systems. It is realized that the magnitude of the Kerr nonlinearity for the five-level system is larger than that of the three- and four-level counterparts. Finally, it is shown that effect of Doppler broadening can lead to an enhanced Kerr nonlinearity while maintaining linear and nonlinear absorption.
Abstract We propose to utilize a five-level Λ − Ξ system to achieve large self-Kerr nonlinearity under multiphoton resonance conditions. Using a density matrix formulation along with an iterative perturbation technique, analytic expressions of linear and nonlinear susceptibilities are derived for stationary as well as for moving atoms. Variation of first- and third-order susceptibilities with respect to frequency and intensity of switching field is then discussed. The dressed-state picture is employed to explain the amplitude and position of each peak in linear and nonlinear absorption profiles. It is found that under slow light conditions, large controllable Kerr nonlinearity with reduced linear and nonlinear absorption is achieved by properly adjusting the strength and detunings of strong electromagnetic (e.m.) fields. Our numerical results also reveal that the Kerr nonlinear index of our considered system is greater than that of existing three-level Λ and four-level N systems. Finally, it is substantiated that self-Kerr nonlinearity is proliferated by taking the Doppler effect into account.
In this work, we study the influence of Doppler broadening on cross-Kerr nonlinearity in a four-level inverted-Y atomic system under electromagnetically induced transparency (EIT) condition. The first- and third-susceptibilities in the presence of Doppler effect are derived as a function of probe, signal and coupling beams and temperature of medium. Under EIT condition, cross-Kerr nonlinearity is enhanced several orders of magnitude compared to that without EIT. The Doppler effect leads to a reduction in the transparent efficiency and thus reduces the amplitude of cross-Kerr nonlinear coefficient. For hot atomic gaseous medium, such consideration of the Doppler effect may be useful for experimental observations and apply to photonic devices operating at different temperature conditions.
A theoretical scheme for enhanced Kerr nonlinearity is proposed in a four-level ladder-type atomic system based on double dark resonances (DDRs). We solve the relevant density matrix equations in steady state and utilize the perturbation theory to obtain the analytical expressions for the third order susceptibility of the atomic system. The influence of system parameters on behavior of the first and third order susceptibilities is then discussed. In particular, it is found that an enhanced Kerr nonlinearity with reduced linear and nonlinear absorption is obtained around zero probe detuning under the slow light condition through proper adjusting the laser field intensity and frequency detuning of driving fields. The dressed state analysis is employed to explain the physical origin of the obtained result. The obtained results may be important for all-optical signal processing and quantum information technology.
Abstract A third-order nonlinear response is investigated theoretically using a closed lambda system. In this scheme, a pair of optical fields and a microwave field connect three hyperfine levels in a cyclic fashion, rendering the atomic response sensitive to the relative phase of all three fields. Changing the relative phase, we can suppress the linear response of the probe field and enhance its third order self-Kerr nonlinear response using the underlying electromagnetically induced transparency (EIT) effect. The resultant giant self-Kerr nonlinear response is comparable to or exceeding that found in atomic systems at room temperature. Most importantly, we show that the self-Kerr nonlinear response at an optical frequency can be controlled using the phase and amplitude of a frequency-separated microwave field.
We study enhancement of self-Kerr nonlinearity in three-level cascade EIT medium by the analytical method. The results apply to the 85Rb atoms and show that, in the presence of the EIT effect, the Kerr nonlinear coefficient is enhanced several order of magnitudes (about 10-5 cm2/W) around transparent region. That is, on the Kerr nonlinear graph the two positive and negative values are found on both sides of the resonant frequency. The amplitude and sign of the Kerr nonlinear coefficient can be controlled versus the intensity or frequency of the coupling laser field. Influence of Doppler broadening leads to a decrease in the amplitude of the Kerr nonlinear coefficient. Analytical results are useful for experimental observation and related applications.
In this paper, we propose an analytical model to study the effect of Doppler broadening on self-Kerr nonlinearity in a five-level ladder-type atomic system. First- and third-order susceptibilities and the self-Kerr nonlinear coefficient are found as the function of temperature and parameters of laser fields. The analytical model is applied to hot $^{85}{\rm Rb}$85Rb and $^{87}{\rm Rb}$87Rb atoms, and it is shown that under the electromagnetically induced transparency (EIT) effect, the self-Kerr nonlinear coefficient is enhanced around three transparent spectral regions. When the temperature of atomic vapor increases (i.e., Doppler width increases), the depth and width of the EIT windows decrease accordingly, and therefore the amplitude of the Kerr nonlinear coefficient decreases significantly. In addition, because the frequency gaps between hyperfine levels of upper excited state ${{5\rm D}_{5/2}}$5D5/2 of $^{85}{\rm Rb}$85Rb atoms are much smaller than those of $^{87}{\rm Rb}$87Rb atoms, the EIT windows as well as the nonlinear dispersion curves for $^{85}{\rm Rb}$85Rb atoms are closer than those for $^{87}{\rm Rb}$87Rb atoms as the Doppler effect presents. The analytical results agree well with the experimental observation when reducing to a three-level atomic system. The analytical model can be used to easily fit the experimental observations of self-Kerr nonlinearity in a five-level atomic system under different temperature conditions and apply to a variety of applications relating to all-optical-switching techniques.