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

TL;DR

This work investigates how quasi-equilibrium (QE) states arise in nematic liquid crystals by testing the hypothesis that irreversible adiabatic decoherence (AQD) drives the transition from initial multi-spin coherence to QE. Using a Jeener-Broekaert sequence combined with dipolar reversion and multiple-quantum coherence encoding, the authors visualize the time evolution of coherence spectra and demonstrate frequency-selective attenuation consistent with eigen-selection, a hallmark of AQD in open quantum systems. The results show that higher dipolar-frequency components decay faster while the zero-frequency component remains robust, aligning with AQD predictions and distinguishing decoherence from simple relaxation. The findings support QE as genuine open-system states with diagonal-in-block density matrices, offering insights into quantum coherence in condensed-matter spin systems and potential applications as robust memory-like quasi-invariants in quantum information contexts.

Abstract

New evidence is presented in favor of irreversible decoherence as the mechanism which leads an initial out-of-equilibrium state to quasi-equilibrium in nematic liquid crystals. The NMR experiment combines the Jeener-Broekaert sequence with reversal of the dipolar evolution and decoding of multiple-quantum coherences to allow visualizing the evolution of the multi-spin coherence spectra during the formation of the quasi-equilibrium states. We vary the reversion strategies and the preparation of initial states and observe that the spectra amplitude attenuate with the reversion time, and notably, that the decay is frequency selective. We interpret this effect as evidence of "eigen-selection", a signature of the occurrence of irreversible adiabatic decoherence, which indicates that the spin system in liquid crystal NMR experiments conforms an actual open quantum system.

Figures (10)

• Figure 1: (a) The pulse sequence used to trace the formation of quasi-equililibrim starts with the phase-shifted pulse pair of the JB sequence, where $t_p$ allows selecting the QE state that develops at the end of the sequence. The waiting time $t$ and the phase $\varphi$ of the read pulse are increased in steps. Fourier Transform on $t$ and $\varphi$ gives the spectra of each coherence order separately. The reversion block $D$ of length $\tau$, suspends evolution under the secular dipolar Hamiltonian, highlighting the effect of decoherence while evolving towards QE. The reversion sequences within $D$ blocks are (b): the MREV8, where $\tau = 12\,\tau_1$; or (c): 'magic-sandwich' , where $\tau= 1.5\,\tau_M$
• Figure 2: Comparison of the amplitude of single-quantum multi-spin spectrum produced by ${\bf I}_{{\bf y}} + {\bf T}_{2,+1} + {\bf T}_{2,-1}$ under relaxation (a.1) and decoherence (b.1) for a 4 1/2-spins system in the $\mathcal{W}$-order initial condition, $t_p = 81.4{\rm\,\mu s}$ and evolution in the time $\tau$. Evolution of the normalized amplitude of spectral lines; (a.2) relaxation and (b.2) decoherence.
• Figure 3: Comparison of the amplitude of double-quantum multi-spin spectrum produced by ${\bf T}_{2,+2} + {\bf T}_{2,-2}$ under relaxation (a.1) and decoherence (b.1) for a 4 1/2-spins system in the $\mathcal{W}$-order initial condition, $t_p = 81.4{\rm\,\mu s}$ and evolution in the time $\tau$. Evolution of the normalized amplitude of spectral lines; (a.2) relaxation and (b.2) decoherence.
• Figure 4: Comparison of the matrix density amplitude dynamics of the deviation matrix $\widetilde{\Delta}\sigma(\tau)$ under relaxation and decoherence for a 4 1/2-spins system in the $\mathcal{W}$-order initial condition, $t_p = 81.4{\rm\,\mu s}$ and evolution in the time $\tau$.
• Figure 5: Experimental spectra of the coherences measured in nematic 5CB. The time $t_p$ is set to prepare the strong or $\mathcal{S}$-order ($t_p = 27{\rm\,\mu s}$). The $\mu$-axis shows the series of MQC spectra (symmetric with respect to zero-order). Each spectrum is limited to $\nu_M = 25{\rm\,kHz}$ and to a maximum coherence time $t_M = 400{\rm\,\mu s}$. The reversion block in (a) is a single MREV8 sequence with total reversion time $\tau$ varied in steps of $120{\rm\,\mu s}$; (b) increasing number of short blocks with a characteristic step-time of $\tau_c = 90.36{\rm\,\mu s}$.