Phase-sensitive Kerr nonlinearity for closed-loop quantum systems

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 threeand 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.

Polarized dependence of nonlinear susceptibility in a single layer graphene system in infrared region

“…The self Kerr nonlinearity of the two, three and fourlevel atomic system has been studied theoretically and experimentally by Sheng et al [33]. Recently, Hamedi and Juzeliūnas proposed a phase sensitive model for achieving giant Kerr nonlinearity in a closed-loop configuration [34]. They realized that under the multiphoton resonance conditions, the Kerr nonlinearity can be manipulated by amplitudes and phases of the applied fields.…”

“…In nonlinear optics, due to significant role of Kerr nonlinearity in some important phenomena [26,27], it is favoraitable to have giant Kerr nonlinearity in low light intensities [28]. Recently it has been shown that the giant enhanced Kerr nonlinearity in multi-level atomic systems with zero linear absorption can be possible by different mechanisms [29][30][31][32][33][34][35][36][37][38]. Niu et al investigated giant Kerr nonlinearity via double dark resonances in a four-level atomic system [35].…”

Electromagnetically induced transparency and nonlinear pulse propagation in a combined tripod and Λ atom-light coupling scheme

“…where the detaied expressions for the coefficients κ 0 , κ 1 and κ 2 are given in Appendix C, while S 1 (ω) and Q(ω) can be found in Appendix D. In equation (30), κ i = d j κ(ω) dω j | ω=0 with j = 0, 1, 2 are the dispersion coefficients in different orders. In general, the real part of κ 0 = Υ + iχ/2 defines the phase shift Υ per unit length, while the imaginary part indicates the linear absorption χ of the probe pulse.…”

“…Closed-loop quantum configurations [30,45,[52][53][54][55] represent a class of atom-light coupling schemes in which the driving fields acting on atoms build closed paths for the transitions between atomic levels. The interference between different paths makes the system sensitive to relative phases of the applied fields.…”

“…The absorption is suppressed due to a quantum mechanical interference between different excitation pathways of atomic energy levels leading to the EIT. The EIT has various important applications in quantum and nonlinear optics, such as slow and stored light [7][8][9][10][11][12], stationary light [13,14], multiwave mixing [15][16][17], optical solitons [18][19][20][21][22][23], optical bistability [24,25] and Kerr nonlinearity [26][27][28][29][30]. Using the slow light greatly enhances the light-matter interaction and enables nonlinear optical processes to achieve significant efficiency even at a singlephoton level [26,[31][32][33][34][35][36][37][38].…”