Quantum-Classical Transition Induced by Electrical Measurement

Abstract

A model of an electrical point contact coupled to a mechanical system (oscillator) is studied to simulate the dephasing effect of measurement on a quantum system. The problem is solved at zero temperature under conditions of strong non-equilibrium in the measurement apparatus. For linear coupling between the oscillator and tunneling electrons, it is found that the oscillator dynamics becomes damped, with the effective temperature determined by the voltage drop across the junction. It is demonstrated that both the quantum heating and the quantum damping of the oscillator manifest themselves in the current-voltage characteristic of the point contact.There is a dramatic difference in the observed behaviors of microscopic particles and of macroscopic objects. The everyday-scale objects obey the rules of classical Newtonian mechanics, while microscopic particles command the use of quantum physics for their description. The effects of quantum coherence are almost never observed at the macroscale. The only known exceptions are realized when the macroscopic quantum state is particularly robust against external perturbations, as is the case for superconductors and quantum Hall liquids. Hence, it appears natural to assume that it is the coupling to the external world, or environment, that leads to decoherence and consequently to a transition from quantum to classical behavior. This process was explored in detail in numerous works. It has been shown that within a phenomenological model of environment, at sufficiently high temperatures, a quantum mechanical system becomes effectively classical [1,2]. The environment provides both the decoherence and the dissipation needed for the quantum-classical transition.Another important distinction between the classical and quantum systems is in their response to measurement. Measurement of a classical system in principle can have no effect on the state of the system; on the other hand, in the quantum regime, the measurement itself is a source of decoherence that inevitably changes the state of the system [3]. The main difference between the measurement process and the environment induced dephasing is that measurement is an intrinsically non-equilibrium process. In this work we demonstrate that despite the apparent differences, the measurement can also induce a quantum-classical transition. Recently, Gurvitz et al. [4] and Korotkov et al. [5] have shown that electrical measurement leads to dephasing of a finite state system that is being measured. The systems that they have studied did not have however a classical analogue. Here, we extend their approach to the problem of the measurement of a mechanical system. Specifically, we consider a quantum oscillator coupled to an electrical point contact in the tunneling regime [6]. We solve this combined problem in the non-equilibrium limit of large voltage across the point contact. From the general solution, we separately extract the dynamics of the oscillator and of the current through the contact. For the oscillator, our main findings are...

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