In statistical mechanics, a small system exchanges conserved charges---heat, particles, electric charge, etc.---with a bath. The small system thermalizes to the canonical ensemble, or the grand canonical ensemble, etc., depending on the charges. The charges are usually represented by operators assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small system's long-time state was dubbed "the non-Abelian thermal state (NATS)." We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which form the system of interest. The conserved charges manifest as spin components. Heisenberg interactions push the charges between the system and the effective bath, the rest of the chain. We predict long-time expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting charges from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.

1 aHalpern, Nicole, Yunger1 aBeverland, Michael, E.1 aKalev, Amir uhttps://arxiv.org/abs/1906.0922702365nas a2200145 4500008004100000245006700041210006000108260001200168490000600180520192900186100002802115700001902143700002002162856003702182 2018 eng d00aThe quasiprobability behind the out-of-time-ordered correlator0 aquasiprobability behind the outoftimeordered correlator c04/20180 vA3 aTwo topics, evolving rapidly in separate fields, were combined recently: The out-of-time-ordered correlator (OTOC) signals quantum-information scrambling in many-body systems. The Kirkwood-Dirac (KD) quasiprobability represents operators in quantum optics. The OTOC has been shown to equal a moment of a summed quasiprobability. That quasiprobability, we argue, is an extension of the KD distribution. We explore the quasiprobability's structure from experimental, numerical, and theoretical perspectives. First, we simplify and analyze the weak-measurement and interference protocols for measuring the OTOC and its quasiprobability. We decrease, exponentially in system size, the number of trials required to infer the OTOC from weak measurements. We also construct a circuit for implementing the weak-measurement scheme. Next, we calculate the quasiprobability (after coarse-graining) numerically and analytically: We simulate a transverse-field Ising model first. Then, we calculate the quasiprobability averaged over random circuits, which model chaotic dynamics. The quasiprobability, we find, distinguishes chaotic from integrable regimes. We observe nonclassical behaviors: The quasiprobability typically has negative components. It becomes nonreal in some regimes. The onset of scrambling breaks a symmetry that bifurcates the quasiprobability, as in classical-chaos pitchforks. Finally, we present mathematical properties. The quasiprobability obeys a Bayes-type theorem, for example, that exponentially decreases the memory required to calculate weak values, in certain cases. A time-ordered correlator analogous to the OTOC, insensitive to quantum-information scrambling, depends on a quasiprobability closer to a classical probability. This work not only illuminates the OTOC's underpinnings, but also generalizes quasiprobability theory and motivates immediate-future weak-measurement challenges.

1 aHalpern, Nicole, Yunger1 aSwingle, Brian1 aDressel, Justin uhttps://arxiv.org/abs/1704.0197101416nas a2200133 4500008004100000245004200041210004200083260001500125490000600140520105200146100001901198700002801217856003701245 2018 eng d00aResilience of scrambling measurements0 aResilience of scrambling measurements c2018/06/180 vA3 aMost experimental protocols for measuring scrambling require time evolution with a Hamiltonian and with the Hamiltonian's negative counterpart (backwards time evolution). Engineering controllable quantum many-body systems for which such forward and backward evolution is possible is a significant experimental challenge. Furthermore, if the system of interest is quantum-chaotic, one might worry that any small errors in the time reversal will be rapidly amplified, obscuring the physics of scrambling. This paper undermines this expectation: We exhibit a renormalization protocol that extracts nearly ideal out-of-time-ordered-correlator measurements from imperfect experimental measurements. We analytically and numerically demonstrate the protocol's effectiveness, up to the scrambling time, in a variety of models and for sizable imperfections. The scheme extends to errors from decoherence by an environment.

1 aSwingle, Brian1 aHalpern, Nicole, Yunger uhttps://arxiv.org/abs/1802.01587