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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Tunneling through a fluctuating barrier: Two-level model

Jan Iwaniszewski

Published May 1, 2000• 15 citations
Publisher

Abstract

We investigate the problem of tunneling across a randomly fluctuating barrier in the presence of dissipation in the two-level approximation. The barrier fluctuations are induced by a random telegraph noise whose switching rate nu is taken as a control parameter. For infinitely fast fluctuations the dynamics of the system is similar to the static case, while, for very small nu, the barrier evolution is a superposition of static solutions for both configurations. This leads to a resonant beating or long-time periodic localization. For an intermediate value of nu we have found a resonancelike suppression of coherent tunneling. When the system levels are detuned, a resonant enhancement of decay in the incoherent regime also occurs.

DOI
10.1103/physreve.61.4890

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We investigate the problem of tunneling across a randomly fluctuating barrier in the presence of dissipation in the two-level approximation. The barrier fluctuations are induced by a random telegraph noise whose switching rate nu is taken as a control parameter. For infinitely fast fluctuations the dynamics of the system is similar to the static case, while, for very small nu, the barrier evolution is a superposition of static solutions for both configurations. This leads to a resonant beating or long-time periodic localization. For an intermediate value of nu we have found a resonancelike suppression of coherent tunneling. When the system levels are detuned, a resonant enhancement of decay in the incoherent regime also occurs.
Quantum tunnelling induces transitions not only through potential barriers, but also through energy barriers of dynamical origin. The coupling to a noisy environment introduces dissipation which affects tunnelling. This effect is studied by an analytic non-perturbative solution of a problem involving tunnelling through a dynamical barrier in the presence of a noisy environment. The accessibility to the classically forbidden energy region above the dynamical barrier is reduced (enhanced) by the friction(diffusion) effect. The occupation of each level above the dynamical barrier is characterized by the succession in time of two different regimes. The transition between both regimes is ruled by an energy criterion which is discussed.
We report a theoretical study of the macroscopic quantum tunneling (MQT) in small Josephson junctions containing randomly distributed two-level systems. We focus on the magnetic field dependent crossover temperature TcrT_{cr}Tcr​ between the thermal fluctuation and quantum regimes of switching from the superconducting (the zero-voltage) state to a resistive one. In the absence of two-levels systems the crossover temperature shows a smooth decrease with an applied magnetic field characterized by an external flux ΦΦΦ. Beyond that we predict a narrow peak in the dependence of Tcr(Φ)T_{cr}(Φ)Tcr​(Φ) occurring in the intermediate range of ΦΦΦ. The effect becomes more pronounced as the junction size increases. We explain this effect quantitatively by a strong resonant suppression of a potential barrier for the Josephson phase escape that is due to the coherent quantum Rabi oscillations in two-level systems present in the junction.
We report a theoretical study of the macroscopic quantum tunneling (MQT) in small Josephson junctions containing randomly distributed two-level systems. We focus on a Josephson phase escape for switching from the superconducting (the zero-voltage) state to a resistive one. Above the crossover temperature Tcr{T}_{cr}Tcr​ the thermal fluctuations of the Josephson phase induce such a switching, and as T<TcrT<{T}_{cr}T<Tcr​ the regime of the MQT occurs. In the absence of two-level systems (TLSs) a magnetic field applied parallel to the junction plane results in a smooth reduction of ${T}_{cr}(\mathrm{\ensuremath{\Phi}})$, where $\mathrm{\ensuremath{\Phi}}$ is an applied magnetic flux. As the TLSs are present in Josephson junctions we obtain a resonant enhancement of the MQT. This phenomenon manifests itself by a narrow peak in the dependence of ${T}_{cr}(\mathrm{\ensuremath{\Phi}})$ occurring in the intermediate range of $\mathrm{\ensuremath{\Phi}}$, i.e., $0<\mathrm{\ensuremath{\Phi}}<{\ensuremath{\phi}}_{0}$ (${\ensuremath{\phi}}_{0}$ is the magnetic flux quantum). We explain this effect quantitatively by a strong resonant suppression of the potential barrier for the Josephson phase escape that is due to the coherent quantum Rabi oscillations in two-level systems present in the junction.
Abstract The tunneling dynamics of a particle moving in a bistable potential with fluctuating barrier is studied. For barriers fluctuating randomly in time we show by exact numerical calculation the significant effect of barrier fluctuation on the tunneling behavior of the particle. At nonzero temperatures the computed tunneling rate constant passes through a maximum when plotted against fluctuation frequency. The resonant frequency (at which the maximum appears) slowly decreases with increase in temperature and attains a constant value at higher temperature and it increases linearly with increase in barrier height of the potential. Another important observation is that in presence of barrier fluctuation the dependence of tunneling rate constant on temperature is strongly guided by the barrier fluctuation frequency. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 280–285, 2003
We study the stabilization of coherent suppression of tunneling in a driven double-well system subject to random periodic delta-function "kicks." We model dissipation due to this stochastic process as a phase diffusion process for an effective two-level system, and derive a corresponding set of Bloch equations with phase damping terms that agree with the periodically kicked system at discrete times. We demonstrate that the ability of noise to localize the system on either side of the double-well potential arises from overdamping of the phase of oscillation, and not from any cooperative effect between the noise and the driving field. The model is investigated with a square wave drive, which has qualitatively similar features to the widely studied cosinusoidal drive, but has the additional advantage of allowing one to derive exact analytic expressions.
We investigate the role of interatomic interactions when a Bose gas, in a double-well potential with a finite tunneling probability (a ‘Bose–Josephson junction’), is exposed to external noise. We examine the rate of decoherence of a system initially in its ground state with equal probability amplitudes in both sites. The noise may induce two kinds of effects: firstly, random shifts in the relative phase or number difference between the two wells and secondly, loss of atoms from the trap. The effects of induced phase fluctuations are mitigated by atom–atom interactions and tunneling, such that the dephasing rate may be suppressed by half its single-atom value. Random fluctuations may also be induced in the population difference between the wells, in which case atom–atom interactions considerably enhance the decoherence rate. A similar scenario is predicted for the case of atom loss, even if the loss rates from the two sites are equal. We find that if the initial state is number-squeezed due to interactions, then the loss process induces population fluctuations that reduce the coherence across the junction. We examine the parameters relevant for these effects in a typical atom chip device, using a simple model of the trapping potential, experimental data, and the theory of magnetic field fluctuations near metallic conductors. These results provide a framework for mapping the dynamical range of barriers engineered for specific applications and set the stage for more complex atom circuits (‘atomtronics’).