Decoherence of two-level systems can be very different from Brownian particles

Abstract

In quantum computation, it is of paramount importance to locate the parameter space where maximal coherence can be preserved in the qubit system. Considerable insight in environment-induced decoherence has been gained in the last decade from detailed studies using the quantum Brownian motion (QBM) models. A number of respectable authors have applied these insights derived from QBM models to two-level systems (2LS) interacting with a field. Their conclusions based on this particular type of qubit coupling to the environment had led to the general belief that 2LS are easily decohered. In a recent paper [1], we debunk such a myth and caution indiscriminate application of the QBM model of decoherence to arbitrary 2LS. We point out that at least for a two-level atom (2LA)–electromagnetic field (EMF) system alone, as used in the atom cavity prototypes of quantum computers, the decoherence time is rather long, comparable to the relaxation time. In the standard Hamiltonian of the 2LA, the dominant interaction is the σ ̂ ± type of coupling between the two levels (what constitutes the qubit) and the field, not the σ ̂ z type assumed in most previous discussions of qubit decoherence, which shows the QBM behavior. Depending on the coupling the field can act as a resonator (in an atom cavity) or as a bath (in QBM) and produce very different decoherent behavior. Our conclusion is based on a new exact master equation we derived at zero temperature which generalizes the text-book ones restricted by the Born–Markov approximation. Indeed many cavity experiments testify to the correctness of these results, and that the 2LA–EMF system maintaining its coherence in sufficiently long duration is the reason why experimentalists can manipulate them to show interesting quantum coherence effects.