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arXiv:1703.09363 · Physical Review A

Analytical results for a parity-time-symmetric two-level system under synchronous combined modulations

Xiaobing Luo, Baiyuan Yang, Xiao-Fei Zhang, Lei Li, Xiaoguang Yu

Published May 30, 2017• 18 citations
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Abstract

We propose a simple method of combined synchronous modulations to generate the analytically exact solutions for a parity-time symmetric two-level system. Such exact solutions are expressible in terms of simple elementary functions and helpful for illuminating some generalizations of appealing concepts originating in the Hermitian system. Some intriguing physical phenomena, such as stabilization of a non-Hermitian system by periodic driving, non-Hermitian analogs of coherent destruction of tunneling, and complete population inversion (CPI), are demonstrated analytically and confirmed numerically. In addition, by using these exact solutions we derive a pulse area theorem for such non-Hermitian CPI in the parity-time symmetric two-level system. Our results may provide an additional possibility for pulse manipulation and coherent control of the parity-time symmetric two-level system.

DOI
10.1103/physreva.95.052128

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We propose a simple method of combined synchronous modulations to generate the analytically exact solutions for a parity-time symmetric two-level system. Such exact solutions are expressible in terms of simple elementary functions and helpful for illuminating some generalizations of appealing concepts originating in the Hermitian system. Some intriguing physical phenomena, such as stabilization of a non-Hermitian system by periodic driving, non-Hermitian analogs of coherent destruction of tunneling, and complete population inversion (CPI), are demonstrated analytically and confirmed numerically. In addition, by using these exact solutions we derive a pulse area theorem for such non-Hermitian CPI in the parity-time symmetric two-level system. Our results may provide an additional possibility for pulse manipulation and coherent control of the parity-time symmetric two-level system.
Analytically exact solutions of a driven two-level system are extremely important in many areas of physics [E. Barnes and S. Das Sarma, Phys. Rev. Lett. 109, 060401 (2012)]. Here we present a simple method of synchronous and asynchronous combined modulations to generate such exact solutions, and apply several of the simplest solutions to perform the coherent control of quantum states. The interesting physical phenomena, such as the arbitrary population transfers between the different and/or asymptotic stationary states and the controlled coherent population oscillation, are achieved analytically and numerically. Simplification of the exact solutions and the modulated fields renders the control strategies more transparent and the qubit manipulation more convenient in experiments.
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In this work, we derive the exact solutions of the dynamical equation, which can describe all two-level Hermitian systems driven by periodic NNN-steps driving fields. The solutions are a set of quasi-periodic functions, and the expressions of the amplitudes and phases are obtained in the frequency-domain. Particularly, we develop a general formalism for the effective Hamiltonian without any approximations, and give the validity range according to the transition probability of the micromotion operator. With the guidance of the exact solutions and the effective Hamiltonian, we find that the coherent destruction of tunneling phenomenon, the resonance phenomenon, and the beat-frequency phenomenon can emerge in this system. Finally, some applications are demonstrated in quantum information processing by periodic NNN-steps driving fields.
Exact solutions for spin-orbit (SO) coupled cold atomic systems are very important and rare in physics. In this paper, we propose a simple method of combined modulations to generate the analytic exact solutions for an SO-coupled boson held in a driven double well. For the cases of synchronous combined modulations and the spin-conserving tunneling, we obtain the general analytical accurate solutions of the system respectively. For the case of spin-flipping tunneling under asynchronous combined modulations, we get the special exact solutions in simple form when the driving parameters satisfy certain conditions. Based on these obtained exact solutions, we reveal some intriguing quantum spin dynamical phenomena, for instance, the arbitrary population transfer (APT) with and/or without spin-flipping, the controlled coherent population conservation (CCPC), and the controlled coherent population inversion (CCPI). The results may have potential applications in the preparation of accurate quantum entangled states and quantum information processing.
We theoretically investigate the exact solutions for generalized parity–time( <?CDATA PT{\mathscr{P}}{\mathscr{T}}PT?> P T )-reversal-symmetric Rabi models driven by external fields with monochromatic periodic, linear, and parabolic forms, respectively. The corresponding exact solutions are presented in terms of the confluent Heun equations without any approximation. In principle, the analytic solutions derived here are valid in the whole parameter space. Such a kind of study may offer potential coherent control schemes of the <?CDATA PT{\mathscr{P}}{\mathscr{T}}PT?> P T -symmetric two-level systems.