arXiv:1709.05492v1 [quant-ph] 16 Sep 2017
Macroscopic Quantum Tunneling in Non-equilibrium Environment
Nasim Shahmansoori,
1
Farhad Taher Ghahramani,
2
and Afshin Shafiee
1, 2, ∗
1
Research Group On Foundations of Quantum Theory and Information, Department of Chemistry, Sharif University of Technology, P.O.Box 11365-9516, Tehran, Iran
2
Foundations of Physics Group, School of Physics, Institute for Research in Fundamental Sciences IPM, P.O. Box 19395-5531, Tehran, Iran
In this study, we examine the dynamics of a macroscopic quantum system in interaction with a non-equilibrium environment. The system is conveniently described as a particle confined in a
double-well potential. The environment is composed of two independent equilibrium environments at different temperatures. We use the time-dependent perturbation theory to describe the dynamics
without any explicit Born and Markov assumptions. We demonstrate that in two environments at same temperatures the short-time dynamics is affected by the interference between two environments
through the system. In the non-equilibrium environment, the quantum coherence of the system essentially has an oscillatory dependence on the temperature difference between two environments.
Nonetheless, for a wide range of temperature differences, the non-equilibrium environment enhances the quantum coherence. This effect is weakened by the force the macroscopic system exerts on
environmental particles.
Keywords
: Macroscopic Quantum Systems, Non-equilibrium Environment, Decoherence Theory
1. INTRODUCTION
Quantum coherence is the distinguishing feature of isolated microscopic systems. In macroscopic systems, however, it is destroyed due to the inevitable interaction between the system and the surrounding environment, a phenomenon
called decoherence [1, 2]. This interaction brings out some novel physics, such as lasing without inversion or extracting work from a single heat bath [3–6]. In the theory of open quantum systems, it is usually assumed that the environment
is in thermal equilibrium [7, 8]. Such an assumption not only faithfully projects most environments but also greatly simplifies theoretical analysis. Nonetheless, there are physical and especially biological situations where the environ-
ment is not in thermal equilibrium. In these cases, the environment has the opportunity to influence the quantum evolution in a manner that is more rich and complex than simply acting to randomize relative phases and dissipate
energy. Light-induced ultra-fast coherent electronic processes in chemical and biological systems, superconducting circuits and quantum dots are examples where non-equilibrium effects are important [9–14].
The dynamics of quantum systems in non-equilibrium environments has been studied in a number of contexts. Myatt and co-workers studied the decoherence of trapped ions coupled to engineered reservoirs, where the internal
state and the coupling strength can be controlled [15]. Schriefl and co-workers studied the dephasing of a two-level system, coupled to non-stationary noise modeling interacting defects [16] and to non-stationary classical intermittent
noise [17]. Kohler and Sols reported the emergence of recoherence in the dissipative dynamics of a harmonic oscillator, coupled linearly through its position and momentum to two independent heat baths at the same temperatures [18].
Gordon and co-workers discussed the control of quantum coherence and the inhibition of dephasing using stochastic control fields [19]. Clausen and co-workers demonstrated a bath-optimized minimal energy control scheme to use
arbitrary time-dependent perturbations to slow decoherence of quantum systems interacting with non-Markovian but stationary environments [20]. The well-known increase of the decoherence rate with the temperature, for a quantum
system coupled to a linear thermal bath, no longer holds for a different bath dynamics. This is shown by means of a simple classical nonlinear bath [21]. Emary considered two examples of nonlinear baths weakly coupled to a
quantum system and showed that the decoherence rate is a monotonic decreasing function of temperature [22]. Beer and Lutz discussed decoherence in a general non-equilibrium environment consisting of several equilibrium baths at
different temperatures, described as a single effective bath with a time-dependent temperature [23]. Martens studied the non-equilibrium response of the environment by a non-stationary random function which offers the possibility of
the control of quantum decoherence by the detailed properties of the environment [24]. Li and co-workers concluded that the amount of the steady quantum coherence increases with the temperature difference of the two heat baths
coupled to a three-state system [25]. If two heat baths have the same temperature, all quantum coherence vanishes and the dynamics returns to the equilibrium case. Moreno and co-workers showed that nested environments can improve
coherence of a central system as the coupling between near and far environment increases [26].
Non-equilibrium quantum dynamics is also attractive from fundamental point of view. Ludwig and co-workers showed that there is an optimal dissipation strength for which the entanglement between two coupled oscillators in-
teracting with a non-equilibrium environment is maximized [27]. Castillo and co-workers demonstrated that under non-equilibrium thermal conditions, in a certain range of temperature gradients, Leggett-Garg inequality violation can
be enhanced [28]. In all such studies, in principle, the possibility of controlling decoherence is of great importance.
Among all the researches mentioned, lack of a macroscopic quantum system as the case study is deeply felt. Such a system is of great importance not only in fundamental physics but also in modern quantum technology [29, 30]. To
be macroscopic, a quantum system should have macroscopically distinguishable, entangled states [31]. The effective
dynamics of the macroscopic system, especially the phenomenon of macroscopic quantum tunneling, can be studied in the typical double-well potential. At sufficiently low temperatures, the system’s Hamiltonian can be expanded by
two first states of energy. When the two-level system couples linearly to an oscillator environment, the result is the renowned Spin-Boson model [7, 32]. Due to decoherence, then, a mixture of localized states of the system appears.
Here, we examine the effective dynamics of a macroscopic quantum system, in interaction with a non-equilibrium environment. The system is conveniently modeled by the motion of a particle in a macroscopic double-well potential,
and the non-equilibrium environment is minimally described as two independent equilibrium environments at different temperatures. We analyze the dynamics of the system induced by such environment.
The paper is organized as follows. In the next section, we describe the physical model of the whole system, consisting of the macroscopic quantum system and surrounding environments. We examine the kinematics and dynamics of the
system in sections 3 and 4, respectively. The parameters of the model are estimated in section 5. The results are discussed in section 6. Our concluding remarks are presented in the last section.
2. MODEL
