Quantum Reversibility: Is there an Echo?

Abstract

We study the possibility to undo the quantum mechanical evolution in a time reversal experiment. The naive expectation, as reflected in the common terminology ("Loschmidt echo"), is that maximum compensation results if the reversed dynamics extends to the same time as the forward evolution. We challenge this belief, and demonstrate that the time $t_r$ for maximum return probability is in general shorter. We find that $t_r$ depends on $lambda=ep{s}_{e}vol/ep{s}_{p}rep$, being the ratio of the error in setting the parameters (fields) for the time reversed evolution to the perturbation which is involved in the preparation process. Our results should be observable in spin-echo experiments where the dynamical irreversibility of quantum phases is measured.

4 pages, 4 figures, to be published in Phys. Rev. Lett

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Cited by in corpus (12)

• Dynamics of Loschmidt echoes and fidelity decay
• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Quantum Fidelity Decay of Quasi-Integrable Systems
• Probing Localization in Absorbing Systems via Loschmidt Echos
• Complexity of Quantum States and Reversibility of Quantum Motion
• Wavepacket Dynamics, Quantum Reversibility and Random Matrix Theory
• Hyperfine Spectroscopy of Optically Trapped Atoms
• Engineering fidelity echoes in Bose-Hubbard Hamiltonians
• Path integral approach to the quantum fidelity amplitude
• Classical versus quantum errors in quantum computation of dynamical systems
• Time-reversal Characteristics of Quantum Normal Diffusion
• Time Reversibility of Quantum Diffusion in Small-world Networks