Long-Time Coherence in Echo Spectroscopy with $\pi /2$--$\pi$--$\pi /2$ Pulse Sequence

Abstract

Motivated by atom optics experiments, we investigate a new class of fidelity functions describing the reconstruction of quantum states by time-reversal operations as $M_{\mathrm{Da}}(t)=|<\psi |e^{i{H}_{2}t/2}{e}^{i{H}_{1}t/2}{e}^{-i{H}_{2}t/2}{e}^{-i{H}_{1}t/2}|\psi >{|}^2$. We show that the decay of $M_{\mathrm{Da}}$ is quartic in time at short times, and that it freezes well above the ergodic value at long times, when $H_2-H_1$ is not too large. The long-time saturation value of $M_{\mathrm{Da}}$ contains easily extractable information on the strength of decoherence in these systems.

5 pages, 3 figures

References in corpus (3)

• Dynamics of Loschmidt echoes and fidelity decay
• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Dephasing representation of quantum fidelity for general pure and mixed states