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arXiv:2102.02660 · Physical Review Research

Exponential speedup of incoherent tunneling via dissipation

D. Maile, Sabine Andergassen, Wolfgang Belzig, Gianluca Rastelli

Published Jul 6, 2021• 4 citations
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Abstract

We study the escape rate of a particle in a metastable potential in the presence of a dissipative bath coupled to the momentum of the particle. Using the semiclassical bounce technique, we find that this rate is exponentially enhanced. In particular, the influence of momentum dissipation depends on the slope of the barrier that the particle is tunneling through. We investigate also the influence of dissipative baths coupled to the position, and to the momentum of the particle, respectively. In this case the rate exhibits a nonmonotonic behavior as a function of the dissipative coupling strengths. Remarkably, even in the presence of position dissipation, momentum dissipation can enhance exponentially the escape rate in a large range of the parameter space. The influence of the momentum dissipation is also witnessed by the substantial increase of the average energy loss during inelastic (environment-assisted) tunneling.

DOI
10.1103/physrevresearch.3.033019

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We study the escape rate of a particle in a metastable potential in the presence of a dissipative bath coupled to the momentum of the particle. Using the semiclassical bounce technique, we find that this rate is exponentially enhanced. In particular, the influence of momentum dissipation depends on the slope of the barrier that the particle is tunneling through. We investigate also the influence of dissipative baths coupled to the position, and to the momentum of the particle, respectively. In this case the rate exhibits a nonmonotonic behavior as a function of the dissipative coupling strengths. Remarkably, even in the presence of position dissipation, momentum dissipation can enhance exponentially the escape rate in a large range of the parameter space. The influence of the momentum dissipation is also witnessed by the substantial increase of the average energy loss during inelastic (environment-assisted) tunneling.
For the realistic theoretical descriptions of quantum devices, we have to take the unavoidable coupling to their surrounding environment into account. A lot of effort in theoretical physics has been made to describe decoherence effects and the corresponding quantum to classical transition in the past. In these studies, baths are coupled to certain observables making their behavior more classical. In the most general case, a quantum device is affected by environments coupled to different observables. In this thesis, we study the differences emerging from coupling the bath to different observables. In particular, we investigate the situation, where two baths are coupled simultaneously to two conjugate variables (e.g. xˆ and pˆ, denoted dissipative frustration). We study how the interplay of these two baths can lead to interesting effects. After an introduction of the topic, we discuss the results of this thesis in Part II and Part III. In Part II, we study the effect of quantum tunneling in presence of a dissipative interaction with two Ohmic environments to the position xˆ and/or to the momentum pˆ of a particle. In chapter 2, we consider a symmetric double well potential which is important in the context of coherent state preparation, as its ground state is a superposition of being in the left and in the right well. Using the semiclassical approximation to calculate instanton paths within the path integral method, we find that momentum dissipation enhances the coherent tunnel splitting. In presence of dissipative couplings to xˆ and pˆ, the momentum dissipation acts in favor of the delocalization of the particle shifting the critical coupling strength of the dissipative phase transition induced by the position dissipation. Chapter 3 contains a study of the escape rate out of a metastable well in presence of dissipation. Here we find that the incoherent tunneling rate is exponentially enhanced in presence of momentum dissipation. We further show that the influence of momentum dissipation depends on the slope of the part of barrier the particle escaping through. In presence of both dissipative couplings, we find a non-monotonic behavior of the escape rate as a function of the dissipative couplings strengths. In Part III, we show that it is possible to realize the situation of "dissipative frustration" in Josephson junction chains. In particular, we introduce charge dissipation as a physical realization of the afore introduced momentum coupling. After presenting the circuit elements needed for charge dissipation, we study a chain of Josephson junctions affected by Ohmic baths coupled to the charge and/or the phase. Using a self-consistent harmonic approximation, we determine the phase diagram at zero temperature which exhibits a quantum phase transition between an ordered phase, corresponding to the superconducting state, and a disordered phase, corresponding to the insulating state with localized superconducting charge. Interestingly, we find that the critical line separating the two phases has a non-monotonic behavior as a function of the dissipative coupling strength. Moreover, within the self-consistent harmonic approximation, we analyze the dissipation induced crossover between a first and second order phase transition, showing that dissipative frustration increases the range in which the phase transition is second order. The non-monotonic behavior is also reflected in the purity of the system that quantifies the degree of correlation between the system and the environment, and in the logarithmic negativity as an entanglement measure that encodes the internal quantum correlations in the chain.
Usually one finds that dissipation tends to make a quantum system more classical in nature. In this paper we study the effect of momentum dissipation on a quantum system. The momentum of the particle is coupled bilinearly to the momenta of a harmonic oscillator heat bath. For a harmonic oscillator system we find that the position and momentum variances for momentum coupling are respectively identical to momentum and position variances for spatial friction. This implies that momentum coupling leads to an increase in the fluctuations in position as the temperature is lowered, exactly the opposite of the classical like localization of the oscillator, found with spatial friction. For a parabolic barrier, momentum coupling causes an {\it increase} in the unstable normal mode barrier frequency, as compared to the lowering of the barrier frequency in the presence of purely spatial coupling. This increase in the frequency leads to an enhancement of the thermal tunneling flux, which below the crossover temperature becomes exponentially large. The crossover temperature between tunneling and thermal activation {\it increases} with momentum friction so that quantum effects in the escape are relevant at higher temperatures.
Usually one finds that dissipation tends to make a quantum system more classical in nature. We study the effect of momentum dissipation on a quantum system. The momentum of the particle is coupled bi-linearly to the momenta of a harmonic oscillator heat bath. For a harmonic oscillator system we find that the position and momentum variances for momentum coupling are, respectively, identical to momentum and position variances for spatial friction. This implies that momentum coupling leads to an increase in the fluctuations in position as the temperature is lowered, exactly the opposite of the classical-like localization of the oscillator, found with spatial friction. For a parabolic barrier, momentum coupling causes an increase in the unstable normal mode barrier frequency, as compared to the lowering of the barrier frequency in the presence of purely spatial coupling. This increase in the frequency leads to an enhancement of the thermal tunneling flux, which below the crossover temperature becomes exponentially large. The crossover temperature between tunneling and thermal activation increases with momentum friction so that quantum effects in the escape are relevant at higher temperatures.
The stabilizing effect of quantum fluctuations on the escape process and the relaxation dynamics from a quantum metastable state are investigated. Specifically, the quantum dynamics of a multilevel bistable system coupled to a bosonic Ohmic thermal bath in strong dissipation regime is analyzed. The study is performed by a non-perturbative method based on the real-time path integral approach of the Feynman-Vernon influence functional. We consider a strongly asymmetric double well potential with and without a monochromatic external driving, and with an out-of-equilibrium initial condition. In the absence of driving we observe a nonmonotonic behavior of the escape time from the metastable region, as a function both of the system-bath coupling coefficient and the temperature. This indicates a stabilizing effect of the quantum fluctuations. In the presence of driving our findings indicate that, as the coupling coefficient γ increases, the escape time, initially controlled by the external driving, shows resonant peaks and dips, becoming frequency-independent for higher γ values. Moreover, the escape time from the metastable state displays a nonmonotonic behavior as a function of the temperature, the frequency of the driving, and the thermal-bath coupling, which indicates the presence of a quantum noise enhanced stability phenomenon. Finally, we investigate the role of different spectral densities, both in sub-Ohmic and super-Ohmic dissipation regime and for different cutoff frequencies, on the relaxation dynamics from the quantum metastable state. The results obtained indicate that, in the crossover dynamical regime characterized by damped intrawell oscillations and incoherent tunneling, the spectral properties of the thermal bath influence non-trivially the short time behavior and the time scales of the relaxation dynamics from the metastable state.