Partial decoherence in mesoscopic systems

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 that 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 that contains information on its initial quantum state, despite the coupling with the environment. This situation is called 'partial decoherence'. In this paper, we found the conditions for partial decoherence in a mesoscopic system (with N quantum states) that is coupled to its 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 a 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.