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Physical review. E

Quantum vibrational resonance in a dual-frequency-driven Tietz-Hua quantum well

Olasunkanmi Isaac Olusola, Oluwasijibomi Prince Shomotun, U. E. Vincent, P. V. E. McClintock

Published May 28, 2020• 32 citations
Publisher

Abstract

We investigate the response of a quantum particle in the Tietz-Hua quantum potential driven by biharmonic fields: a low-frequency force and a very high frequency force. The response is characterized by the occurrence of a maximum in the first-order transition probability amplitude |s|^{2} under the influence of the applied fields. It is shown that in the absence of the high-frequency component of the applied fields, |s|^{2} shows a distinct sequence of resonances, whereas an increase in the amplitude of the high-frequency field induces minima in |s|^{2}. However, the |s|^{2} maximum occurs in the low-frequency regime where it may be considered otherwise weak in the presence of a single harmonic force.

DOI
10.1103/physreve.101.052216

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We investigate the response of a quantum particle in the Tietz-Hua quantum potential driven by biharmonic fields: a low-frequency force and a very high frequency force. The response is characterized by the occurrence of a maximum in the first-order transition probability amplitude |s|^{2} under the influence of the applied fields. It is shown that in the absence of the high-frequency component of the applied fields, |s|^{2} shows a distinct sequence of resonances, whereas an increase in the amplitude of the high-frequency field induces minima in |s|^{2}. However, the |s|^{2} maximum occurs in the low-frequency regime where it may be considered otherwise weak in the presence of a single harmonic force.
We consider a two-level quantum system interacting with two classical time-periodic electromagnetic fields. The frequency of one of the fields far exceeds that of the other. The effect of the high-frequency field can be averaged out of the dynamics to realize an effective transition frequency of the field-dressed two-level system. We examine the linear response, second harmonic response and Stokes and anti-Stokes Raman response of the dressed two-level system, to the weak frequency field. The vibrational resonance enhancement in each case is demonstrated for optimal strength of the high-frequency field. Our theoretical scheme is corroborated by full numerical simulation of the two-level, two-field dynamics governed by loss-free Bloch equations. We suggest that quantum optics can offer an interesting arena for the study of the vibrational resonance. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.
We consider a quantum two-level system in bichromatic classical time-periodic fields, the frequency of one of which far exceeds that of the other. Based on systematic separation of timescales and averaging over the fast motion a reduced quantum dynamics in the form of a nonlinear forced Mathieu equation is derived to identify the stable oscillatory resonance zones intercepted by unstable zones in the frequency-amplitude plot. We show how this forcing of the dressed two-level system may generate the subharmonics and superharmonics of the weak field in the stable region, which can be amplified by optimization of the strength of the high frequency field. We have carried out detailed numerical simulations of the driven quantum dynamics to corroborate the theoretical analysis.
We investigate the nonlinear response of a vibrating suspended nanomechanical beam on external periodic driving. The amplitude of the fundamental transverse mode behaves like a weakly damped quantum particle in a driven anharmonic potential. Upon using a Born-Markovian master equation, we calculate the fundamental mode amplitude for varying driving frequencies. In the nonlinear regime, we observe resonances which are absent in the corresponding classical model. They are shown to be associated with resonant multiphonon excitations. Furthermore, we identify resonant tunneling in a dynamically induced bistable effective potential.
We investigate the linear and nonlinear response of a one-dimensional dissipative Bose-Josephson junction subjected simultaneously to a weak low-frequency probe and a rapidly oscillating high-frequency external drive. Starting from the dissipative two-mode Bose-Josephson equations, we derive an effective higher-order nonlinear equation for the population imbalance by retaining the leading nonlinear correction. Using time-scale separation and perturbative analysis, we obtain analytical expressions for both the linear response at the fundamental frequency and the nonlinear response at the second harmonic. We show that the high-frequency modulation modifies the effective potential landscape and dynamically breaks the symmetry around the stationary state, giving rise to a finite second-harmonic response that is absent without the rapidly oscillating field. Both the linear and nonlinear response amplitudes exhibit resonance-like enhancement for optimal values of the high-frequency driving strength. We further analyze the dependence of the resonance characteristics on interaction strength, dissipation, and driving parameters in both the zero-phase and πππ-phase modes and compare the analytical predictions with direct numerical simulations. Our results demonstrate a controllable mechanism toward realizing linear and nonlinear vibrational resonance in a one-dimensional dissipative Bose-Josephson junction and open new possibilities for controlling collective dynamics in driven ultracold bosonic systems.
We investigate quantum stochastic resonance (QSR) in the periodically driven spin-boson system with Ohmic dissipation. For the special case \ensuremath{\alpha}=1/2 of the Ohmic coupling strength we present exact QSR results. For arbitrary Ohmic coupling, the amplitude and the phase of the nonlinear response function vs temperature are studied in a vast regime of temperatures and frequencies. It encompasses a dissipative-dominated incoherent tunneling regime, occurring at ``high'' temperatures and adiabatic driving, as well as coherent tunneling regimes, reached either at ``low'' temperatures or/and nonadiabatic frequencies. As a general feature, a principal maximum appears only in parameter regimes where incoherent tunneling dominates over coherent transitions. Moreover, for adiabatic driving, the nonlinear QSR exhibits a noise-induced suppression of higher harmonics accompanied by a characteristic phase change. \textcopyright{} 1996 The American Physical Society.