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arXiv:2306.11150 · Physical review. B./Physical review. B

Measurement-induced chirality: Diffusion and disorder

Brian J. J. Khor, Matthew Wampler, Gil Refael, Israel Klich

Published Dec 8, 2023• 5 citations
arXivHTMLPDF

Abstract

Repeated quantum measurements can generate effective new nonequilibrium dynamics in matter. Here we combine such a measurement driven system with disorder. In particular, we investigate the diffusive behavior in the system and the effect of various types of disorder on the measurement induced chiral transport protocol. We begin by characterizing the diffusive behavior produced by the measurements themselves in a clean system. We then examine the edge flow of particles per measurement cycle for three different types of disorder: site dilution, lattice distortion, and disorder in on-site chemical potential. In the quantum Zeno limit, the effective descriptions for the disordered measurement system with lattice distortions and random on-site potential can be modeled as a classical stochastic model, and the overall effect of increasing these disorders induces a crossover from perfect flow to zero transport. On the other hand if vacancies are present in the lattice the flow of particles per measurement cycle undergoes a percolation phase transition from unity to zero with percolation threshold ${p}_{c}\ensuremath{\approx}0.26$, with critical exponent $\ensuremath{\nu}\ensuremath{\approx}1.35$. We also present numerical results away from Zeno limit and note that the overall effect of moving away from the Zeno effect is to reduce particle flow per cycle when the measurement frequency in our protocol is reduced.

DOI
10.1103/physrevb.108.214305

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Repeated quantum measurements can generate effective new nonequilibrium dynamics in matter. Here we combine such a measurement driven system with disorder. In particular, we investigate the diffusive behavior in the system and the effect of various types of disorder on the measurement induced chiral transport protocol. We begin by characterizing the diffusive behavior produced by the measurements themselves in a clean system. We then examine the edge flow of particles per measurement cycle for three different types of disorder: site dilution, lattice distortion, and disorder in on-site chemical potential. In the quantum Zeno limit, the effective descriptions for the disordered measurement system with lattice distortions and random on-site potential can be modeled as a classical stochastic model, and the overall effect of increasing these disorders induces a crossover from perfect flow to zero transport. On the other hand if vacancies are present in the lattice the flow of particles per measurement cycle undergoes a percolation phase transition from unity to zero with percolation threshold pc\ensuremath≈0.26{p}_{c}\ensuremath{\approx}0.26pc​\ensuremath≈0.26, with critical exponent \ensuremathν\ensuremath≈1.35\ensuremath{\nu}\ensuremath{\approx}1.35\ensuremathν\ensuremath≈1.35. We also present numerical results away from Zeno limit and note that the overall effect of moving away from the Zeno effect is to reduce particle flow per cycle when the measurement frequency in our protocol is reduced.
Measurement-induced phase transitions are nonequilibrium transitions between phases characterized by distinct entanglement scaling behaviors, driven by the competition between unitary dynamics and measurements. Despite recent numerical efforts, how quenched disorder affects these transitions remains unclear. In this work, we study a ddd-dimensional noninteracting fermionic system subject to both quenched disorder and continuous monitoring of the local particle density, and derive an effective field theory describing its long-time universal behaviors. We find that the system is governed by the same nonlinear sigma model as in the case of clean monitored fermions, with disorder entering only through a modification of model parameters. This result suggests that the presence or absence of a measurement-induced phase transition is unaffected by the introduction of disorder. In spatial dimension d=1d=1d=1, the system exhibits only an area law phase and no transition, whereas in d>1d>1d>1, a transition persists between an area×\times×log law phase and an area law phase, with the critical measurement rate suppressed by disorder. Numerical simulation confirms the absence of MIPT in d=1d=1d=1, and the linear shift of the critical measurement rate by disorder scattering rate in higher dimensions predicted by analytical theory.
Chirality in active and passive fluids gives rise to odd transport properties, most notably the emergence of robust edge currents that defy standard dissipative dynamics. While these phenomena are well-described by continuum hydrodynamics, a microscopic framework connecting them to their topological origins has remained elusive. Here, we present a lattice model for an isotropic chiral random walk that bridges the gap between classical stochastic diffusion and unitary quantum evolution. By equipping the walker with an internal degree of freedom and a tunable chirality parameter, ppp, we interpolate between a standard diffusive random walk and a deterministic, topologically non-trivial quantum walk. We show that the topological protection characteristic of the unitary limit (p=1p=1p=1) remarkably persists into the dissipative regime (p<1p<1p<1). This correspondence allows us to theoretically ground the robustness of edge flows in classical chiral systems using the bulk-boundary correspondence of Floquet topological insulators. Our results provide a discrete microscopic description for odd diffusion, offering a powerful toolkit to predict transport in confined geometries and disordered chiral media.
We demonstrate that repeated measurements in disordered systems can induce a quantum anti-Zeno effect under certain conditions to enhance quantum transport. The enhancement of energy transfer is really exhibited in multisite models under repeated measurements. The optimal measurement interval for the anti-Zeno effect and the maximal efficiency of energy transfer are specified in terms of the relevant physical parameters. Since the environment acts as frequent measurements on the system, the decoherence-induced energy transfer, which has been discussed recently for photosynthetic complexes, may be interpreted in terms of the anti-Zeno effect. We further find an interesting phenomenon in a specific three-site case, where local decoherence or repeated measurements may even promote entanglement generation between the nonlocal sites.
We address here the issue of quantum measurement in which the interaction between the system at hand and the measuring apparatus causes a collapse of the wave function or the density operator. The analysis is carried out for the prototypical tight-binding chain involving a quantum particle hopping between nearest-neighbour sites on a lattice, with the system subject to repeated projective measurements to a detector site. However, unlike previous work, the measurements are performed at random times. In the absence of measurement, the particle while starting from a site is known to spread out to farther sites as time progresses, leading to complete delocalization of the particle in time. In presence of measurements, we derive exact results for the probability at a given time for the particle to be found on different sites and averaged with respect to different realizations of the dynamics. We consider the representative case in which the time gap between successive measurements are sampled independently from an exponential distribution. The novel result of our findings is the revelation of the striking effect of Stochastic Localization, whereby the particle has at long times time-independent probabilities to be on different sites. This implies localization of the particle at long times, achieved through classical stochasticity involved with the random times for measurements. An extreme case of such localization is attained if the measurements are done very frequently, when the particle is completely localized at the detector site! We also point out the stochastic version of the Zeno effect, whereby dynamical evolution of a quantum system is arrested through repeated measurements at frequent-enough times. In the wake of recent experiments on projective measurements at random times achieved through randomly-pulsed sequences, our proposition is amenable to experimental realization.
We explore the Quantum Zeno Effect (QZE) as a dynamical mechanism for suppressing quantum information transport in open systems. Moving beyond the phenomenological decay of survival probabilities in zero-dimensional systems, we utilize a continuous measurement effective model governed by the Stochastic Schrödinger Equation (SSE). Our numerical investigations suggest that measurement-induced freezing can be mapped to the behavior of a Liouvillian Exceptional Point (EP). We demonstrate how this non-unitary backaction manifests in our simulations: from suppressing single-particle spatial transmission (showing a trend consistent with T ∝ γ^(-α)), to the qualitative reduction of information scrambling as indicated by the Tripartite Mutual Information (I₃ → 0). Finally, scaling this effective model to finite XXZ spin chains (N ≤ 10), our data indicates a transition-like behavior from volume-law to area-law entanglement scaling. While bounded by finite-size limitations, our results provide numerical evidence supporting the interpretation of Zeno dynamics as a suppressor of information geometry.
Ultracold atoms in optical lattices offer a unique platform for investigating disorder-driven phenomena. While static disordered site potentials have been explored in a number of experiments, a more general, dynamical control over site-energy and off-diagonal tunnelling disorder has been lacking. The use of atomic quantum states as synthetic dimensions has introduced the spectroscopic, site-resolved control necessary to engineer more tailored realisations of disorder. Here, we present explorations of dynamical and tunneling disorder in an atomic system by controlling laser-driven dynamics of atomic population in a momentum-space lattice. By applying static tunnelling phase disorder to a one-dimensional lattice, we observe ballistic quantum spreading. When the applied disorder fluctuates on time scales comparable to intersite tunnelling, we instead observe diffusive atomic transport, signalling a crossover from quantum to classical expansion dynamics. We compare these observations to the case of static site-energy disorder, where we directly observe quantum localisation.Cold atom quantum simulation has had challenges in realising the tailored, dynamic types of disorder relevant to real materials. Here, the authors use synthetic momentum-space lattices to engineer spatially and dynamically controlled disorder to observe ballistic, diffusive, and arrested atomic transport.