Connection between decoherence and fidelity decay in echo dynamics (5 pages)

T. Gorin, Tomaž Prosen, T. H. Seligman +1 more

Eli Kim

T. Gorin, Tomaž Prosen, T. H. Seligman +1 more

Entanglement between a quantum system and its environment leads to loss of coherence in the former. In general, the temporal fate of coherences is complicated. Here, we establish the connection between decoherence of a central system and fidelity decay in the environment for a variety of situations, including both energy conserving and dissipative couplings. We show how properties of unitary time evolution of the environment can be inferred from the nonunitary evolution of coherences in the central system. This opens up promising ways for measuring Loschmidt echoes in a variety of situations.

Michael B. Mensky

P. Korcyl, J. Wosiek, Leo Stodolsky

Tomaž Prosen, T. H. Seligman

We define a quantity, the so-called purity fidelity , which measures the rate of dynamical irreversibility due to decoherence, observed e.g. in echo experiments, in the presence of an arbitrary small perturbation of the total (system + environment) Hamiltonian. We derive a linear response formula for the purity fidelity in terms of integrated time correlation functions of the perturbation. Our relation predicts, similar to the case of fidelity decay, that the faster the decay of purity fidelity the slower is the decay of time correlations. In particular, we find exponential decay in quantum mixing regime and faster, initially quadratic and later typically Gaussian decay in the regime of non-ergodic, e.g. integrable quantum dynamics. We illustrate our approach by an analytical calculation and numerical experiments in the Ising spin 1/2 chain kicked with tilted homogeneous magnetic field where part of the chain is interpreted as a system under observation and part as an environment.