Evidence for several dipolar quasi-invariants in liquid crystals

Abstract

The quasi-equilibrium states of an observed quantum system involve as many constants of motion as the dimension of the operator basis which spans the blocks of all the degenerate eigenvalues of the Hamiltonian that drives the system dynamics, however, the possibility of observing such quasiinvariants in solid-like spin systems in Nuclear Magnetic Resonance (NMR) is not a strictly exact prediction. The aim of this work is to provide experimental evidence of several quasi-invariants, in the proton NMR of small spin clusters, like nematic liquid crystal molecules, in which the use of thermodynamic arguments is not justified. We explore the spin states prepared with the Jeener-Broekaert pulse sequence by analyzing the time-domain signals yielded by this sequence as a function of the preparation times, in a variety of dipolar networks, solids, and liquid crystals. We observe that the signals can be explained with two dipolar quasi-invariants only within a range of short preparation times, however at longer times liquid crystal signals show an echo-like behaviour whose description requires assuming more quasi-invariants. We study the multiple quantum coherence content of such signals on a basis orthogonal to the z-basis and see that such states involve a significant number of correlated spins. Therefore, we show that the NMR signals within the whole preparation timescale can only be reconstructed by assuming the occurrence of multiple quasi-invariants which we experimentally isolate.

Evolution towards quasi-equilibrium in nematic liquid crystals studied through decoherence of multi-spin multiple-quantum coherences

“…The experiment starts by setting the time t p needed to prepare the initial state ρ S (t + p ) so that a subsequent free evolution drives the system to the so called "strong" (Sorder) or "weak" W-order [7]. We test the experiment by preparing the initial state in 5CB with t p = 27µs, since it has already been shown that after a transient t ∼ 1ms the system reaches the S quasi-equilibrium state [30], with only zero-quantum coherence (on the z-basis).…”

“…A last read pulse (π/4) y projects part of the QE state into observable single quantum coherence. The QE state which can be observed after the read pulse depends on the preparation time, in fact, it was shown that at least three different QE states can be observed in nematic liquid crystals [7].…”

“…Likewise, it has been shown that in spite of the small number of relevant spin degrees of freedom, the LC spin system can also develop quasi-equilibrium states within a time scale similar to solids [4,5]. Indeed, the experimental results clearly showed that it is possible to selectively prepare several QE states in LC by adequately setting the preparation pulse sequences [6,7].…”

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

“…Likewise, it is feasible to prepare and observe states of quasi-equilibrium, which the system attains over an early time scale, depending on the initial condition (ref jb, etc). In these states the dynamics of the NMR observables is described through a density matrix diagonal-inblocks in the eigenbasis of the system-environment interaction Hamiltonian [14][15][16]. On a longer timescale these states relax to thermal equilibrium.…”