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Physical Review A

Effect of dissipation and measurement on a tunneling system

B. F. Wielinga, Gerard J Milburn

Published Oct 1, 1995• 2 citations
Publisher

Abstract

We consider a parametrically driven Kerr medium in which the pumping may be sinusoidally varied. It has been previously found that this system exhibits coherent tunneling between two fixed points which can be either enhanced or suppressed by altering the driving frequency and strength. We numerically investigate the dynamics when damping is included. This is done both by solving a master equation and using the quantum-trajectory method. In the latter case it is also possible to model the result of a continuous heterodyne measurement of the cavity output. The dissipation destroys the coherences which give rise to the tunneling, causing the sinusoidal oscillation of the mean to give way to a stochastic jumping between the fixed points, manifested as a random telegraph signal. In the quantum-trajectory picture we show that the coherences responsible for tunneling are an exponentially decreasing function of the signal-to-noise ratio for heterodyne measurements. However, evidence of both the bare tunneling rate and the driving modified tunneling rate are still apparent in the random telegraph signal.

DOI
10.1103/physreva.52.3323

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We consider a parametrically driven Kerr medium in which the pumping may be sinusoidally varied. It has been previously found that this system exhibits coherent tunneling between two fixed points which can be either enhanced or suppressed by altering the driving frequency and strength. We numerically investigate the dynamics when damping is included. This is done both by solving a master equation and using the quantum-trajectory method. In the latter case it is also possible to model the result of a continuous heterodyne measurement of the cavity output. The dissipation destroys the coherences which give rise to the tunneling, causing the sinusoidal oscillation of the mean to give way to a stochastic jumping between the fixed points, manifested as a random telegraph signal. In the quantum-trajectory picture we show that the coherences responsible for tunneling are an exponentially decreasing function of the signal-to-noise ratio for heterodyne measurements. However, evidence of both the bare tunneling rate and the driving modified tunneling rate are still apparent in the random telegraph signal.
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.
We consider a parametric amplifier driven by a periodically pulsed pump field inside a cavity containing a Kerr nonlinearity. The dynamics of the device is modeled as a kicked nonlinear system. The pulsed parametric amplifier constitutes the kick. In between kicks the dynamics is determined by the Kerr nonlinearity and damping. In the absence of damping, a classical description of the device exhibits a rich phase-space structure including fixed points of multiple period and chaos. We contrast the classical behavior of the mean intensity with that predicted by quantum dynamics. The mean photon number inside the cavity is shown to undergo regular collapse and revival in the regular region of the phase space and irregular revivals in the chaotic region. When damping is included, the quantum recurrences are rapidly suppressed, and the classical behavior is restored. In this case a stable steady state is possible. The damping represents the effect of photon-number measurements on the system. We also discuss the photon statistics in the steady state.
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.
The nonlinear dynamics of dissipative quantum systems in incoherent laser fields is studied in the framework of a master equation with the random telegraph model describing the laser noise and the Markovian approximation dealing with the system-bath couplings. Floquet theory and time-dependent perturbation methods are used to facilitate both analytical and numerical solutions. We develop a theoretical formalism that provides a powerful tool for the detailed analysis of the dissipative quantum dynamics of multilevel systems driven by intense stochastic laser fields. It is found that the system relaxes to a steady state from the effect of the laser phase and frequency noise and the kinetics of this relaxation increases with the addition of dissipative terms, introduced by the coupling to the reservoir. Amplitude fluctuations show a different behavior. Other results concerning the destruction of quantum coherence and the dynamical localization will be established and further relaxation mechanisms such as spontaneous emission and the ionization process will also be considered.
We study the quantal dynamics of a harmonically driven quartic double well in the presence of dissipation. A master equation for the reduced density operator is derived in the Floquet representation. In the classical limit, this system corresponds to a Duffing oscillator with Ohmic damping. We present numerical results for the transient time evolution and for the stationary sate. The influence of the weak dissipation on interference effects in the context of driven tunnelling is discussed on the basis of these results. We find that the coherent suppression of tunnelling can be stabilized by reservoir-induced noise for a suitably chosen temperature.