Continuous quantum systems in a fluctuating environment

Victor V. Albert

Alexander I. Nesterov, G. P. Berman

We study the dynamics of dephasing in a quantum two-level system by modeling both $1/f$ and high-frequency noise by random telegraph processes. Our approach is based on a so-called spin-fluctuator model in which a noisy environment is modeled by a large number of fluctuators. In the continuous limit we obtain an effective random process (ERP) that is described by a distribution function of the fluctuators. In a simplified model, we reduce the ERP to the two (slow and fast) ensembles of fluctuators. Using this model, we study decoherence in a superconducting flux qubit and we compare our theoretical results with the available experimental data. We demonstrate good agreement of our theoretical predictions with the experiments. Our approach can be applied to many quantum systems, such as biological complexes, semiconductors, superconducting, and spin qubits, where the effects of interaction with the environment are essential.

Vladimir R. Chechetkin, V. S. Lutovinov

The Schrodinger equation with Gaussian dynamic fluctuating potentials is considered. This model gives a convenient example of an open quantum system coupled to a given external environment. The evolution equations for averaged correlators are derived and it is shown that a system coupled to a thermoequilibrium environment tends asymptotically with time to a thermodynamic density matrix. At high temperatures the quantum evolution equation for the density matrix can be approximated by the quasiclassical Fokker-Planck equation. The generalisation for multiparticle systems is also given. The results are illustrated by the particular examples of coupling with phonons and of two-level systems. Finally, it is shown how the problem can be reformulated in terms of continuous stochastic evolution in the space of psi functions and a corresponding functional formalism based on the continuous Fokker-Planck equation in the space of psi functions.

Ola Bratteli, Derek W. Robinson

Jacopo Trapani, Matteo G. A. Paris

We address the dynamics of quantum correlations for a bipartite continuous-variable quantum system interacting with its fluctuating environment. In particular, we consider two independent quantum oscillators initially prepared in a Gaussian state, e.g., a squeezed thermal state, and compare the dynamics resulting from local noise, i.e., oscillators coupled to two independent external fields, to that originating from common noise, i.e., oscillators interacting with a single common field. We prove non-Markovianity (nondivisibility) of the dynamics in both regimes and analyze the connections between nondivisibility, backflow of information, and revivals of quantum correlations. Our main results may be summarized as follows: (i) revivals of quantumness are present in both scenarios, however, the interaction with a common environment better preserves the quantum features of the system; (ii) the dynamics is always nondivisible but revivals of quantum correlations are present only when backflow of information is present as well. We conclude that nondivisibility in its own is not a resource to preserve quantum correlations in our system, i.e., it is not sufficient to observe recoherence phenomena. Rather, it represents a necessary prerequisite to obtain backflow of information, which is the true ingredient to obtain revivals of quantumness.

Takaya Matsuura