Partial decoherence in mesoscopic systems

TL;DR

This paper investigates conditions under which mesoscopic quantum systems retain partial coherence despite environmental coupling, revealing new scenarios for non-adiabatic partial decoherence especially in systems with more than two states.

Contribution

It identifies the conditions for partial decoherence in mesoscopic systems, including non-adiabatic cases, expanding understanding beyond previously known adiabatic scenarios.

Findings

Partial decoherence occurs under specific Hamiltonian commutation conditions.

Circulating currents can be used to retrieve initial quantum information.

Non-adiabatic partial decoherence is possible when flux through the system is zero or an integer multiple of flux quanta.

Abstract

The coupling of a mesoscopic system with its environment usually causes total decoherence: at long times the reduced density matrix of the system evolves in time to a limit which is independent of its initial value, losing all the quantum information stored in its initial state. Under special circumstances, a subspace of the system's Hilbert space remains coherent, or "decoherence free", and the reduced density matrix approaches a non-trivial limit which contains information on its initial quantum state, despite the coupling to the environment. This situation is called "partial decoherence". Here we find the conditions for partial decoherence for a mesoscopic system (with $N$ quantum states) which is coupled to an environment. When the Hamiltonian of the system commutes with the total Hamiltonian, one has "adiabatic decoherence", which yields N-1 time-independent combinations of the reduced density matrix elements. In the presence of a magnetic flux, one can measure circulating currents around loops in the system even at long times, and use them to retrieve information on the initial state. For N=2, we demonstrate that partial decoherence can happen only under adiabatic decoherence conditions. However, for $N>2$ we find partial decoherence even when the Hamiltonian of the system does not commute with the total Hamiltonian, and we obtain the general conditions for such non-adiabatic partial decoherence. For an electron moving on a ring, with $N>2$ single-level quantum dots, non-adiabatic partial decoherence can arise only when the total flux through the ring vanishes (or equals an integer number of flux quanta), and therefore there is no asymptotic circulating current.