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arXiv:2107.09995 · Annals of Physics

Dynamical indistinguishability and statistics in quantum fluids

Alessio Zaccone, Kostya Trachenko

Published Mar 9, 2023• 6 citations
arXivHTMLPDF

Abstract

For a system to qualify as a quantum fluid, quantum-statistical effects should operate in addition to quantum-mechanical ones. Here, we address the hitherto unexplored dynamical condition for the quantum-statistical effects to be manifested, and consider particle exchange events in the gaslike regime of fluid dynamics as a dynamical process with an intrinsic time scale. We subsequently propose a quantitative criterion of particle indistinguishability and associated quantum statistics to be inoperative at short time and emerge at long time. Experimentally verifiable, our predictions enable a systematic search for a transition between statistics-active and statistics-inactive regimes in quantum fluids.

DOI
10.1016/j.aop.2023.169272

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For a system to qualify as a quantum fluid, quantum-statistical effects should operate in addition to quantum-mechanical ones. Here, we address the hitherto unexplored dynamical condition for the quantum-statistical effects to be manifested, and consider particle exchange events in the gaslike regime of fluid dynamics as a dynamical process with an intrinsic time scale. We subsequently propose a quantitative criterion of particle indistinguishability and associated quantum statistics to be inoperative at short time and emerge at long time. Experimentally verifiable, our predictions enable a systematic search for a transition between statistics-active and statistics-inactive regimes in quantum fluids.
We develop an effective field theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics which systematically incorporates nonlinear interactions of noises. The dynamical variables are mappings between a "fluid spacetime" and the physical spacetime and an essential aspect of our formulation is to identify the appropriate symmetries in the fluid spacetime. The theory applies to nonlinear disturbances around a general density matrix. For a thermal density matrix, we require an additional Z2Z_2Z2​ symmetry, to which we refer as the local KMS condition. This leads to the standard constraints of hydrodynamics, as well as a nonlinear generalization of the Onsager relations. It also leads to an emergent supersymmetry in the classical statistical regime, and a higher derivative deformation of supersymmetry in the full quantum regime.
In recent years, new theoretical insights into decoherence and quantum measurements have emerged through the study of many-body dynamics in isolated quantum systems. It is now understood that the parameters and energy scales in system-environment interactions decisively affect how readily information spreads from a quantum system into its surroundings during a decoherence event. A popular choice for studying these effects is the framework of quantum Darwinism (QD), but so far few works have applied this to realistic many-body models. Inspired by experimentally-accessible setups, in this work we introduce a simple, flexible, numerically exact many-body model of a system broadcasting information into an environment: a 1D lattice of sites with hopping particles. We show that different choices of parameters lead to the recovery of known scenarios featuring different decoherence and QD effects, such as equilibration, revivals of coherence, and redundancy. In constructing this model we resolve the crucial issue of indistinguishability: we explain how to calculate the entropy of a fraction of the environment when said environment is composed of indistinguishable fermions or bosons (or lattice sites containing them). We then show that particle statistics can make a notable difference to the QD properties of the setup, with fermionic environments sometimes achieving redundancy much more readily than bosonic or site-based ones. Our work opens the door to much closer alignment between theoretical models and experimental tests of the dynamics of quantum measurements and the quantum-to-classical transition.
Quantum coherence, an essential feature of quantum mechanics allowing quantum superposition of states, is a resource for quantum information processing. Coherence emerges in a fundamentally different way for nonidentical and identical particles. For the latter, a unique contribution exists linked to indistinguishability that cannot occur for nonidentical particles. Here, we experimentally demonstrate this additional contribution to quantum coherence with an optical setup, showing that its amount directly depends on the degree of indistinguishability, and exploiting it in a quantum phase discrimination protocol. Furthermore, the designed setup allows for simulating fermionic particles with photons, thus assessing the role of exchange statistics in coherence generation and utilization. Our experiment proves that independent indistinguishable particles can offer a controllable resource of coherence and entanglement for quantum-enhanced metrology.
We discuss phenomenology associated with turbulent hydrodynamics in quantum fluids from a condensed-matter perspective. We begin with weakly-interacting superfluids, often modeled by a mean-field theory governed by the Gross-Pitaevskii equation. Considering the effect of quantum fluctuations beyond the mean-field approximation, we propose a study of many-body quantum effects in turbulent hydrodynamics, especially near zero temperature. We motivate examples of quantum many-body systems where such effects may be uncovered. These include bosons confined in a periodic potential in low spatial dimensions (one and two), and the associated quantum critical point of the superfluid-insulator transition, realized in present-day ultracold-atom and quantum computing platforms. We conclude by listing a set of (open) questions that may be answered using modern quantum many-body techniques. This article is part of the theme issue 'Frontiers of turbulence and statistical physics'.
We argue that measurement data in quantum physics can be rigorously interpreted only as a result of a statistical, macroscopic process, taking into account the indistinguishable character of identical particles. Quantum determinism is in principle possible on the condition that a fully-fledged quantum model is used to describe the measurement device in interaction with the studied object as one system. In contrast, any approach that relies on Born's rule discriminates the dynamics of a quantum system from that of the detector with which it interacts during measurement. In this work, we critically analyze the validity of this measurement postulate applied to single-event signals. In fact, the concept of ``individual'' particle becomes inadequate once both indistinguishability and a scattering approach allowing an unlimited interaction time for an effective detection, are considered as they should be, hence preventing the separability of two successive measurement events. In this context, measurement data should therefore be understood only as a result of statistics over many events. Accounting for the intrinsic noise of the sources and the detectors, we also show with the illustrative cases of the Schrödinger cat and the Bell experiment that once the Born rule is abandoned on the level of a single particle, realism, locality and causality are restored. We conclude that indiscernibility and long-time detection process make quantum physics not fundamentally probabilistic.
We report on experiments studying the Brownian motion of an optically trapped bead in air, and observe for the first time the short-time regime of ballistic motion. Einstein predicted this effect in 1907, but said the experiment would be impossible in practice. Our measurements were enabled by our development of a new detection system that is capable of real-time tracking of the motion of a trapped bead on unprecedented short time scales and correspondingly small length scales. We used the data to measure the average kinetic energy of a Brownian particle, and find good agreement with the energy equipartition theorem of statistical mechanics. Measurement of the instantaneous velocity also allows us to stably trap beads in vacuum, using active feedback to control and cool the center of mass motion to mK temperatures in three dimensions. The system of an optically trapped bead in vacuum can serve as a testing ground for macroscopic quantum superpositions and the role of decoherence. In the opposite extreme, a trapped bead in a fluid can be used to test basic questions in statistical mechanics, and fluid dynamics on the smallest scales.