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arXiv:2306.12986 · Physical Review Letters

Measurement-Induced Quantum Synchronization and Multiplexing

Finn Schmolke, Eric Lutz

Published Jan 3, 2024• 17 citations
arXivHTMLPDF

Abstract

Measurements are able to fundamentally affect quantum dynamics. We here show that a continuously measured quantum many-body system can undergo a spontaneous transition from asynchronous stochastic dynamics to noise-free stable synchronization at the level of single trajectories. We formulate general criteria for this quantum phenomenon to occur and demonstrate that the number of synchronized realizations can be controlled from none to all. We additionally find that ergodicity is typically broken, since time and ensemble averages may exhibit radically different synchronization behavior. We further introduce a quantum type of multiplexing that involves individual trajectories with distinct synchronization frequencies. Measurement-induced synchronization appears as a genuine nonclassical form of synchrony that exploits quantum superpositions.

DOI
10.1103/physrevlett.132.010402

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Measurements are able to fundamentally affect quantum dynamics. We here show that a continuously measured quantum many-body system can undergo a spontaneous transition from asynchronous stochastic dynamics to noise-free stable synchronization at the level of single trajectories. We formulate general criteria for this quantum phenomenon to occur and demonstrate that the number of synchronized realizations can be controlled from none to all. We additionally find that ergodicity is typically broken, since time and ensemble averages may exhibit radically different synchronization behavior. We further introduce a quantum type of multiplexing that involves individual trajectories with distinct synchronization frequencies. Measurement-induced synchronization appears as a genuine nonclassical form of synchrony that exploits quantum superpositions.
Can synchronization -- the widespread spontaneous emergence of coordinated dynamics in classical nonlinear systems -- also occur in the quantum regime? This question has recently sparked intense research into collective behavior and temporal self-organization in quantum systems. Typical quantum features such as the linearity of time evolution and the presence of quantum noise seem to hinder the appearance of synchrony at the microscopic level. At the same time, quantum coherence and quantum correlations may provide novel mechanisms for enhancing synchronization beyond its classical counterpart. We here survey recent theoretical and experimental advances in quantum synchronization, ranging from the characterization of synchronous oscillations and genuinely nonclassical forms of synchrony to many-body synchronization on quantum networks.
We consider locally driven-dissipative quantum spins that undergo a continuous weak measurement of their collective spin. We show that such a system can exhibit full spin-synchronization in trajectories corresponding to the same measurement record. Mathematically, we demonstrate that this is a general consequence of the irreducibility of the quantum Markov semigroup generated by the Lindbladian, in combination with a transitive symmetry, in particular spin-permutation symmetry. When breaking the irreducibility, e.g. in the absence of local dissipation, the system can exhibit a weaker form of partial synchronization. Given the general origin, this measurement-induced phenomenon arises in a broad class of many-body systems.
In the quantum Zeno effect, quantum measurements can block the coherent oscillation of a two level system by freezing its state to one of the measurement eigenstates. The effect is conventionally controlled by the measurement frequency. Here we study the development of the Zeno regime as a function of the measurement strength for a continuous partial measurement. We show that the onset of the Zeno regime is marked by a cascade of transitions in the system dynamics as the measurement strength is increased. Some of these transitions are only apparent in the collective behavior of individual quantum trajectories and are invisible to the average dynamics. They include the appearance of a region of dynamically inaccessible states and of singularities in the steady-state probability distribution of states. These predicted dynamical features, which can be readily observed in current experiments, show the coexistence of fundamentally unpredictable quantum jumps with those continuously monitored and reverted in recent experiments.
Thanks to recent experimental advances in simulating and detecting quantum dynamics with high precision and controllability, our understanding of the physics of monitored quantum systems has considerably deepened over the past decades. In this article, we provide an introductory theoretical review on the basic formalisms governing open quantum dynamics under measurement, along with recent developments in their spectral and typical aspects. After reviewing quantum measurement theory, we introduce the concept of quantum trajectories, which are the conditional dynamics of monitored states shaped by a set of measurement outcomes. We then discuss the spectral properties of the dynamical map describing the evolution averaged over measurement outcomes. As has recently been recognized, these spectral features are intimately connected to whether quantum trajectories exhibit typical behaviors, such as ergodicity and purification. Moreover, we introduce Lyapunov exponents of typical quantum trajectories and discuss how these quantities serve as indicators of measurement-induced phase transitions in monitored quantum many-body systems.
The evolution of a quantum system subject to measurements can be described by stochastic quantum trajectories of pure states. Instead, the ensemble average over trajectories is a mixed state evolving via a master equation. Both descriptions lead to the same expectation values for linear observables. Recently, there is growing interest in the average entanglement appearing during quantum trajectories. The entanglement is a nonlinear observable that is sensitive to so-called measurement-induced phase transitions, namely, transitions from a system-size dependent phase to a quantum Zeno phase with area-law entanglement. Intriguingly, the mixed steady-state description of these systems is insensitive to this phase transition. Together with the difficulty of quantifying the mixed state entanglement, this favors quantum trajectories for the description of the quantum measurement process. Here, we study the entanglement of a single particle under continuous measurements (using the newly developed configuration coherence) in both the mixed state and the quantum trajectories descriptions. In both descriptions, we find that the entanglement at intermediate time scales shows the same qualitative behavior as a function of the measurement strength. The entanglement engenders a notion of coherence length, whose dependence on the measurement strength is explained by a cascade of underdamped-to-overdamped transitions. This demonstrates that measurement-induced entanglement dynamics can be captured by mixed states.
The concept of measure synchronization between two coupled quantum many-body systems is presented. In general terms we consider two quantum many-body systems whose dynamics gets coupled through the contact particle-particle interaction. This coupling is shown to produce measure synchronization, a generalization of synchrony to a large class of systems which takes place in absence of dissipation. We find that in quantum measure synchronization, the many-body quantum properties for the two subsystems, e.g., condensed fractions and particle fluctuations, behave in a coordinated way. To illustrate the concept we consider a simple case of two species of bosons occupying two distinct quantum states. Measure synchronization can be readily explored with state-of-the-art techniques in ultracold atomic gases and, if properly controlled, be employed to build targeted quantum correlations in a sympathetic way.