The decrease in the overall algorithmic complexity of the spin-echo effect

Seth Lloyd, Wojciech Hubert Zurek

Баруздин Сергей Анатольевич

The algorithm of excitation of a stimulated photon echo by two incoherent white noise Gaussian pulses and delta-like light pulses is studied. The average complex envelope of the echo is determined by solving Bloch equations. The results obtained can be used in spectroscopy and in the analysis of nonlinear characteristics of excitation in photon processors based on the saturation effect. The results can be also generalised to the analogous regime of excitation of a spin echo.

L. Buljubasich, Claudia M. Sánchez, Axel D. Dente +3 more

We performed Loschmidt echo nuclear magnetic resonance experiments to study decoherence under a scaled dipolar Hamiltonian by means of a symmetrical time-reversal pulse sequence denominated Proportionally Refocused Loschmidt (PRL) echo. The many-spin system represented by the protons in polycrystalline adamantane evolves through two steps of evolution characterized by the secular part of the dipolar Hamiltonian, scaled down with a factor |k| and opposite signs. The scaling factor can be varied continuously from 0 to 1/2, giving access to a range of complexity in the dynamics. The experimental results for the Loschmidt echoes showed a spreading of the decay rates that correlate directly to the scaling factors |k|, giving evidence that the decoherence is partially governed by the coherent dynamics. The average Hamiltonian theory was applied to give an insight into the spin dynamics during the pulse sequence. The calculations were performed for every single radio frequency block in contrast to the most widely used form. The first order of the average Hamiltonian numerically computed for an 8-spin system showed decay rates that progressively decrease as the secular dipolar Hamiltonian becomes weaker. Notably, the first order Hamiltonian term neglected by conventional calculations yielded an explanation for the ordering of the experimental decoherence rates. However, there is a strong overall decoherence observed in the experiments which is not reflected by the theoretical results. The fact that the non-inverted terms do not account for this effect is a challenging topic. A number of experiments to further explore the relation of the complete Hamiltonian with this dominant decoherence rate are proposed.

David A. Lavis

Charis Anastopoulos, Ntina Savvidou

Spin-echo experiments are often said to constitute an instant of antithermodynamic behavior in a concrete physical system that violates the second law of thermodynamics. We argue that a proper thermodynamic treatment of the effect should take into account the correlations between the spin and the translational degrees of freedom of the molecules. To this end, we construct an entropy functional using Boltzmann macrostates that incorporate both spin and translational degrees of freedom. With this definition there is nothing special in the thermodynamics of spin echoes: dephasing corresponds to Hamiltonian evolution and leaves the entropy unchanged; dissipation increases the entropy. In particular, there is no phase of entropy decrease in the echo. We also discuss the definition of macrostates from the underlying quantum theory and we show that the decay of net magnetization provides a faithful measure of entropy change.

Mei Bai, Alexander W. Chao, T. Roser +6 more