We investigate the low-temperature quantum stochastic resonance (QSR) phenomenon in a two-level system (TLS) which is coupled to an Ohmic heat bath. In contrast to common belief we find that QSR occurs also for symmetric (i.e., unbiased) TLS's if the viscous friction parameter alpha exceeds a critical value: We demonstrate that with respect to the spectral power amplification measure QSR always occurs for alpha>1; in contrast, the output signal-to-noise ratio exhibits an amplification only for alpha>3/2.
We investigate the low-temperature quantum stochastic resonance (QSR) phenomenon in a two-level system (TLS) which is coupled to an Ohmic heat bath. In contrast to common belief we find that QSR occurs also for symmetric (i.e., unbiased) TLS's if the viscous friction parameter alpha exceeds a critical value: We demonstrate that with respect to the spectral power amplification measure QSR always occurs for alpha>1; in contrast, the output signal-to-noise ratio exhibits an amplification only for alpha>3/2.
A study of (aperiodic) quantum stochastic resonance (QSR) in parallel is put forward. By doing so, a generally stochastic input signal is fed into an array of parallel dissipative quantum two-level systems (TLS) and its integral response is studied against increasing temperature. The response is quantified by means of an information-theoretic measure provided by the rate of mutual information per element and, in addition, by the cross-correlation between the information-carrying input signal and the output response. For ohmic-like quantum dissipation, both measures exhibit QSR for biased two-level systems. Our prime focus here, however, is on the case with zero asymmetry between the two localized stable states. We then find that the mutual information measure exhibits QSR only for sufficiently strong dissipation ( > 3/2), as measured by the dimensionless ohmic friction strength . Moreover, the mutual information measure relates QSR within quantum linear response theory to the signal-to-noise-ratio (SNR) , being independent of the input driving frequencies in this limit. In contrast, the cross correlation measure connects QSR to a genuine synchronization phenomenon . For a single symmetric TLS, aperiodic QSR is exhibited in the cross-correlation measure for a Gaussian exponentially correlated input signal for > 1 already. Upon feeding the aperiodic input signal into a parallel array of unbiased TLS's, QSR successively emerges above the critical ohmic dissipation strength > 1/2 with increasing number n of parallel units. Thus, QSR can occur in parallel despite the fact that it does not occur in each individual, unbiased, TLS for < 1. This paradoxical phenomenon - which can be tested with an array of bistable superconducting quantum interference devices - constitutes a true quantum effect: it is due to the power-law dependence on temperature of the tunnelling rate and the stochastic linearization of quantum fluctuations with increasing number of parallel units.
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.
In order to explore parity violating effects in chiral molecules, of interest in some models of evolution towards homochirality, quantum stochastic resonance (QSR) is studied for the population difference between the two enantiomers of a chiral molecule (hence for the optical activity of the sample), under low viscous friction and in the deep quantum regime. The molecule is described by a two-state model in an asymmetric double well potential where the asymmetry is given by the known predicted parity violating energy difference (PVED) between enantiomers. In the linear response to an external driving field that lowers and rises alternatively each one of the minima of the well, a signal of QSR is predicted only in the case that the PVED is different from zero, the resonance condition being independent on tunneling between the two enantiomers. It is shown that, at resonance, the fluctuations of the first order contribution to the internal energy are zero. Due to the small value of the PVED, the resonance would occur in the ultracold regime. Some proposals concerning the external driving field are suggested.
A Langevin canonical framework for a chiral two-level system coupled to a bath of harmonic oscillators is used within a coupling scheme different from the well-known spin-boson model to study the quantum stochastic resonance for chiral molecules. This process refers to the amplification of the response to an external periodic signal at a certain value of the noise strength, being a cooperative effect of friction, noise, and periodic driving occurring in a bistable system. Furthermore, from this stochastic dynamics within the Markovian regime and Ohmic friction, the competing process between tunneling and the parity violating energy difference present in this type of chiral systems plays a fundamental role. This mechanism is finally proposed to observe the so-far elusive parity-violating energy difference in chiral molecules.
We study analytically the quantum thermalization of two coupled two-level systems (TLSs), which are connected with either two independent heat baths (IHBs) or a common heat bath (CHB). We understand the quantum thermalization in eigenstate and bare-state representations when the coupling between the two TLSs is stronger and weaker than the TLS-bath couplings, respectively. In the IHB case, we find that, when the two IHBs have the same temperatures, the two coupled TLSs in eigenstate representation can be thermalized with the same temperature as those of the IHBs. However, in the case of two IHBs at different temperatures, just when the energy detuning between the two TLSs satisfies a special condition, the two coupled TLSs in eigenstate representation can be thermalized with an immediate temperature between those of the two IHBs. In bare-state representation, we find a counterintuitive phenomenon that, under some conditions, the temperature of the TLS connected with the high-temperature bath is lower than that of the other TLS, which is connected with the low-temperature bath. In the CHB case, the coupled TLSs in eigenstate representation can be thermalized with the same temperature as that of the CHB in nonresonant cases. In bare-state representation, the TLS with a larger energy separation can be thermalized to a thermal equilibrium with a lower temperature. In the resonant case, we find a phenomenon of antithermalization. We also study the steady-state entanglement between the two TLSs in both the IHB and CHB cases.
A master equation for a quantum system coupled to a heat bath with stochastically fluctuating energy levels is derived by making use of the ensemble averaging and the averaging with respect to a stochastic process in the bath. Relaxation terms are determined in the Born approximation with respect to the system-bath interaction and the damping parameters related to a relaxation kernel are specified. In parallel with the spectral strength of the bath, the damping parameters determine the transient times for the Markovian description creating the physical origin of the slippage [A. Suarez, R. Sibey, and I. Oppenheim, J. Chem. Phys. 97, 5101 (1992)]. The influence of energy fluctuations of the bath is analyzed for a two-level system including the solution of the corresponding non-Markovian equation for the level population difference. The conditions for the formation of Boltzmann's thermal ratio between steady-state populations are evaluated as well.