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Journal of Physics A Mathematical and General

Stochastic resonance in a fundamental quantum system

Thomas Wellens, Andreas Buchleitner

Published Jan 1, 1999• 8 citations
Publisher

Abstract

We provide a detailed description of the response of an experimentally accessible, open, driven quantum system in its stationary state to a weak periodic signal. The system, a single mode of the quantized radiation field in coherent interaction with a sequence of two-level atoms and coupled to an environment of temperature T , is shown to exhibit stochastic resonance on output, under changes of T . Furthermore, at vanishing temperature, the transition rates between the metastable states of the radiation field remain finite and are set by the quantum noise level at . Consequently, signal enhancement and synchronization can be achieved even in this very quantum limit, for a properly tuned signal frequency.

DOI
10.1088/0305-4470/32/15/015

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We provide a detailed description of the response of an experimentally accessible, open, driven quantum system in its stationary state to a weak periodic signal. The system, a single mode of the quantized radiation field in coherent interaction with a sequence of two-level atoms and coupled to an environment of temperature T , is shown to exhibit stochastic resonance on output, under changes of T . Furthermore, at vanishing temperature, the transition rates between the metastable states of the radiation field remain finite and are set by the quantum noise level at . Consequently, signal enhancement and synchronization can be achieved even in this very quantum limit, for a properly tuned signal frequency.
We demonstrate that quantum stochastic resonance allows for the noise-controlled synchronization of quantum jumps between the metastable states of the quantized radiation field in a micromaser. Under readily accessible experimental conditions optimal synchronization is achieved at a finite temperature T=500mKT\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}500\mathrm{mK}T=500mK of the environment.
We report the observation of quantum stochastic synchronization (QSS) in a dissipative quantum system---a moderately damped current-biased Josephson junction. We show that when the junction is biased subcritically by a combination of a constant current and a small sinusoidal modulation signal, forced phase synchronization between the otherwise random, incoherent quantum tunneling and the signal may arise as a consequence of the interplay between quantum fluctuation and the weak periodic drive. It is found that optimal synchronization occurs at a signal frequency fQSS{f}_{\text{QSS}}fQSS​ that is comparable to the quantum tunneling rate. We also find a phenomenon called ``modulation induced suppression of quantum noise'': for signal frequency well below fQSS,{f}_{\text{QSS}},fQSS​, the power spectral density of escape time distribution of the junction could be reduced substantially from the floor level of the unmodulated system. Furthermore, we demonstrate that the application of a small signal with proper phase can suppress the average tunneling rate and enhance the stability of the metastable system. Our experimental results agree well with the numerical calculations without the use of adjustable parameters.
In the first part of this thesis,we examine the preparation of a single- mode radiation field in arbitrary pure quantum states via resonant inter- action with a sequence of two-level atoms.The preparation is achieved by choosing an appropriate (in general entangled)initial state of the atomic sequence,and does neither require a final state measurement of the atoms,nor a control of the atom-field interaction.Furthermore,the method is applicable also when starting from mixed initial field states. We show how to determine the optimal initial atomic state which pre- pares the desired field state with the maximum fidelity,and prove the feasibility of our state preparation method by numerical calculations. In the second part,we demonstrate the noise-induced control of quantum jumps in a fundamental open quantum system.Here,in addition to the subsequent interaction with a flux of two-level atoms,the quantized field is also coupled to a thermal environment.Under certain experimental conditions,the photon field exhibits a bistable behavior,with quantum jumps between two metastable states.In the presence of a small peri- odic signal (i.e.,a modulation of the initial state of the two-level atoms crossing the single-mode resonator),the best synchronization of these quantum jumps with the signal is achieved at an optimal,nonvanishing temperature of the environment.This stochastic resonance e ffect can be observed in di fferent components of the atomic Bloch vector on exit from the cavity. The third part treats a speci fic problem concerning the characterization of entanglement between two quantum mechanical two-level systems. We consider the optimal decomposition of a two-qubit state into an en- tangled and a separable part,with maximal weight of the latter,and derive necessary and su fficient conditions for the optimality of the de- composition.
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 generalize the phenomenon of forced stochastic synchronization into the quantum domain within the framework of a paradigmatic spin‐boson model (tunneling charge, or flipping spin 1/2 coupled to an environment) which is driven by an external periodic rectangular field. The overdamped regime of dissipative quantum tunneling is studied. Thermal noise assisted synchronization of a very high quality is shown to occur in a broad range of temperatures, driving strengths and frequencies, if the external driving frequency exceeds the zero‐temperature limit of dissipative tunneling rate, the dissipation strength exceeds a critical value, and the driving is sufficiently strong. A simple criterion for such stochastic synchronization is established. Both the similarities and the profound differences with the akin phenomenon of quantum stochastic resonance are outlined.