Measurement-Induced Crossover of Quantum Jump Statistics in Postselection-Free Many-Body Dynamics (2503.02418v1)

Abstract: We reveal a nontrivial crossover of subsystem fluctuations of quantum jumps in continuously monitored many-body systems, which have a trivial maximally mixed state as a steady-state density matrix. While the fluctuations exhibit the standard volume law $\propto L$ following Poissonian statistics for sufficiently weak measurement strength, anomalous yet universal scaling law $\propto L^\alpha :(\alpha\sim 2.7)$ indicating super-Poissonian statistics appears for strong measurement strength. This drastically affects the precision of estimating the rate of quantum jumps: for strong (weak) measurement, the estimation uncertainty is enhanced (suppressed) as the system size increases. We demonstrate that the anomalous scaling of the subsystem fluctuation originates from an integrated many-body autocorrelation function and that the transient dynamics contributes to the scaling law rather than the Liouvillian gap. The measurement-induced crossover is accessed only from the postselection-free information obtained from the time and the position of quantum jumps and can be tested in ultracold atom experiments.

Measurement-Induced Crossover of Quantum Jump Statistics in Many-Body Dynamics

The paper "Measurement-Induced Crossover of Quantum Jump Statistics in Postselection-Free Many-Body Dynamics" explores the complex interplay between measurement and many-body dynamics in open quantum systems. The paper focuses on quantum jump statistics and reveals an intriguing measurement-induced crossover in the fluctuations of these jumps when continuously monitored.

Key Findings and Numerical Results

1. Subsystem Fluctuations of Quantum Jumps (SFQJ): The paper introduces the concept of SFQJ in the context of continuously monitored many-body quantum systems. It is shown that for weak measurement strength, the fluctuations in these subsystems obey a Poissonian scaling law (proportional to the system size, $L$). However, as measurement strength increases, a crossover to an anomalous super-Poissonian scaling occurs, characterized by a universal exponent of $\alpha\sim 2.7$.
2. Anomalous Scaling and Strong Measurement Impact: This crossover dramatically impacts the precision of quantum jump rate estimations, presenting an enhanced uncertainty for strong measurement strength as the system size grows. The paper highlights that traditional statistical approaches fall short in capturing these behaviors, as they do not exhibit the anomaly in whole-system fluctuations.
3. Methodological Approach: The authors employ a quantum trajectory method to simulate the dynamics of a Heisenberg chain, among other models, under continuous particle number measurement. They provide a detailed analysis of fluctuations, leveraging both numerical simulations and analytical evaluations to dissect the dynamical activities and autocorrelations involved in SFQJ.
4. Universality Across Many-Body Models: Anomalous scaling behavior was consistently observed across different many-body models (e.g., Heisenberg, XX, and XXZ spin chains), thereby suggesting a level of universality in these measurement-induced phenomena. This universality spans over different Hamiltonian parameters indicating a broad applicability of the results.
5. Experimental Relevance: The findings are not just of theoretical interest but are also amenable to experimental confirmation. The postselection-free nature of the measurement-induced dynamics discussed can be probed using current experimental setups with ultracold atoms, where the time and position of quantum jumps can be recorded with precision.

Theoretical and Practical Implications

Theoretical implications of the paper suggest a reevaluation of quantum statistical mechanics paradigms, especially regarding nonequilibrium systems and quantum measurements. The discovered crossover and associated statistics could inform future exploration of quantum measurement impacts on many-body systems, beyond the established frameworks of Poissonian statistics.

Practically, this work opens avenues for enhanced quantum simulations in experimental physics, particularly with ultracold atoms and quantum gas microscopy, to paper dynamic systems without the need for postselection. Such studies could deepen our understanding of quantum coherence and decoherence processes in realistic many-body environments.

Future Directions

The paper prompts several avenues for future exploration:

• A deeper understanding of the universal scaling exponent across other complex quantum systems and verification of its range of applicability.
• Exploration of how the discovered crossover behaviors influence other quantum phenomena, like thermalization and entanglement dynamics, under measurement.
• Establishing relations between the observable crossover phenomena and underlying theoretical constructs, such as boundary conformal field theory.

In conclusion, this paper contributes significant insights into measurement-induced dynamics in quantum many-body systems, elucidating nontrivial interactions between measurement strength and subsystem fluctuations of quantum jumps, proposing both theoretical advancements and experimental validations in the field.