Experimental quantification of decoherence via the Loschmidt echo in a many spin system with scaled dipolar Hamiltonians

Abstract

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.

Loschmidt echo driven by hyperfine and electric-quadrupole interactions in nanoscale nuclear spin baths

“…The lower panel of Fig. 1 displays the dependency of size N ; as expected, larger NSB exhibits faster dephasing which is in agreement with the experimental observation that the decoherence rate increases with the number of dynamically coupled spins [23]. For a sufficiently large NSB (such as N ≥ 1000 here) these echos are periodic of the form cost αN I with a Gaussian revival envelope.…”

Loschmidt echo in many-spin systems: a quest for intrinsic decoherence and emergent irreversibility

“…In what follows, inspired by the LE experiments in NMR, we provide a framework for theoretical evaluations of LE of the polarization type. We do not consider here LE of the magic echo type, as in this case neither the numerical resolution of small systems [113] nor the actual experiments on scaled Hamiltonians [77] seem to evidence a PID regime. We start by summarizing the LE formulation in spin systems as a local autocorrelation function.…”

Quantum dynamics of excitations and decoherence in many-spin systems detected with Loschmidt echoes: its relation to their spreading through the Hilbert space

“…One of the main conclusions of the work of Buljubasich et al [40] was that non-secular terms, when acting at high order [43], produce the proliferation of effective secular terms. This reinforces the effect of the secular terms of equation (2.5) without its spin selectivity, and hence can contribute substantively to T 2 and also to the decoherence time T 3 , which has little dependence on k.…”

“…In this pulse sequence, the durations of forward and backward blocks are equal [40]. Again, this equality involves a truncation of non-secular terms which is only effective if the dipolar interactions are small compared with ω 2 1 + Ω 2 , the Zeeman energy in the effective rotating field.…”