Quantum irreversible decoherence behaviour in open quantum systems with few degrees of freedom: Application to 1H NMR reversion experiments in nematic liquid crystals

Abstract

An experimental study of NMR spin decoherence in nematic liquid crystals is presented. Decoherence dynamics can be put in evidence by means of refocusing experiments of the dipolar interactions. The experimental technique used in this work is based on the MREV8 pulse sequence. The aim of the work is to detect the main features of the irreversible quantum decoherence in liquid crystals, on the basis of the theory presented by the authors recently. The focus is laid on experimentally probing the eigen-selection process in the intermediate time scale, between quantum interference of a closed system and thermalization, as a signature of the quantum spin decoherence of the open quantum system, as well as on quantifying the effects of non-idealities as possible sources of signal decays which could mask the intrinsic decoherence. In order to contrast experiment and theory, the theory was adapted to obtain the decoherence function corresponding to the MREV8 reversion experiments. Non-idealities of the experimental setting, like external field inhomogeneity, pulse misadjustments and the presence of non-reverted spin interaction terms are analysed in detail within this framework, and their effects on the observed signal decay are numerically estimated. It is found that, though all these non-idealities could in principle affect the evolution of the spin dynamics, their influence can be mitigated and they do not present the characteristic behaviour of the irreversible spin decoherence. As unique characteristic of decoherence, the experimental results clearly show the occurrence of eigen-selectivity in the intermediate timescale, in complete agreement with the theoretical predictions. We conclude that the eigen-selection effect is the fingerprint of decoherence associated with a quantum open spin system in liquid crystals. Besides, these features of the results account for the quasi-equilibrium states of the spin system, which were observed previously in these mesophases, and lead to conclude that the quasi-equilibrium is a definite stage of the spin dynamics during its evolution towards equilibrium.

Evidence for several dipolar quasi-invariants in liquid crystals

“…Within this framework, the environment induced decoherence causes the irreversible decay of the spin density matrix to a diagonal-in-blocks form, over a timescale t qe intermediate between the quantum interference and relaxation. This hypothesis was theoretically formulated and experimentally confirmed recently on liquid crystal NMR, 1,3,42 and is also consistent with the results of similar approaches from other areas. 31,43 An arbitrary initial state ρ 0 of a closed system evolves, according to the Liouville equation, like…”

“…1,31,42,43 Irreversible decoherence originates in the interaction of a finite quantum system with the environment within the essentially adiabatic regime 1 (or "quasi-isolated" regime 31 ), characterized by the commutation relations 1. This decoherence process attenuates the off-diagonal elements of the spin state (in the basis of the spin-lattice interaction Hamiltonian) while preserves the diagonal in blocks, leaving a density operator ρ qe which commutes with the spin Hamiltonian and is therefore a constant of motion.…”

Irreversible adiabatic decoherence of dipole-interacting nuclear-spin pairs coupled with a phonon bath

“…Even when the variations of the inter-pair dipolar interactions were not included in the system-environment Hamiltonian, the mechanical correlation of the different pairs established by the phonon displacement field is reflected in the final result as a collective feature of the decoherence process. A similar discussion was given in the study of decoherence in nematic liquid crystals , where even when the molecules are magnetically isolated in average and the main contribution is calculated using the intramolecular spin-environment Hamiltonian, the calculated decoherence function reflects the influence on a given molecule exerted by the other molecules through their mechanical interaction as a quantum effect [30,31].…”

Adiabatic quantum decoherence in many non-interacting subsystems induced by the coupling with a common boson bath

“…On the contrary, as seen in ( 46) and (42a), the efficiency of the decoherence function goes as |λ m − λ n | k . This selective action that depends on the eigenvalues of the interaction Hamiltonian is a fingerprint of adiabatic decoherence in open quantum systems and has been referred to as eigenselection [17,24,25]. This effect allows calling the set of eigenvectors of the interaction Hamiltonian H I as the preferred basis [26] since it transforms an arbitrary initial state into one having a diagonal density matrix (when written on this basis).…”