Emergent Prethermalization Signatures in Out-of-Time Ordered Correlations

Prethermalization and the Local Robustness of Gapped Systems

We prove that prethermalization is a generic property of gapped local many-body quantum systems, subjected to small perturbations, in any spatial dimension. More precisely, let H_{0} be a Hamiltonian, spatially local in d spatial dimensions, with a gap Δ in the many-body spectrum; let V be a spatially local Hamiltonian consisting of a sum of local terms, each of which is bounded by ε≪Δ. Then, the approximation that quantum dynamics is restricted to the low-energy subspace of H_{0} is accurate, in the correlation functions of local operators, for stretched exponential timescale τ∼exp[(Δ/ε)^{a}] for any a<1/(2d-1). This result does not depend on whether the perturbation closes the gap. It significantly extends previous rigorous results on prethermalization in models where H_{0} was frustration-free. We infer the robustness of quantum simulation in low-energy subspaces, the existence of athermal "scarred" correlation functions in gapped systems subject to generic perturbations, the long lifetime of false vacua in symmetry broken systems, and the robustness of quantum information in non-frustration-free gapped phases with topological order.

Improving metrology with quantum scrambling

Quantum scrambling describes the spreading of information into many degrees of freedom in quantum systems, such that the information is no longer accessible locally but becomes distributed throughout the system. This idea can explain how quantum systems become classical and acquire a finite temperature, or how in black holes the information about the matter falling in is seemingly erased. We probe the exponential scrambling of a multiparticle system near a bistable point in phase space and utilize it for entanglement-enhanced metrology. A time-reversal protocol is used to observe a simultaneous exponential growth of both the metrological gain and the out-of-time-order correlator, thereby experimentally verifying the relation between quantum metrology and quantum information scrambling. Our results show that rapid scrambling dynamics capable of exponentially fast entanglement generation are useful for practical metrology, resulting in a 6.8(4)-decibel gain beyond the standard quantum limit.

1H multiple quantum NMR in alternating quasi-one-dimensional spin chains of hambergite

Multiple quantum (MQ) dynamics was investigated in quasi-one-dimensional ¹H zigzag spin chains in hambergite (Be₂BO₃OH) single crystals. Due to the non-linear arrangement of the spins, dipolar coupling strengths alternate along the chain. To solve the problem of MQ NMR experiments taking too much time due to extremely long ¹H spin-lattice relaxation times, the samples were exposed to gamma irradiation to produce the defects accelerating the relaxation. The influence of the radiation dose was investigated. The experimental dependencies of MQ coherence intensities on the MQ excitation time in alternating spin chains were obtained and compared with the theory for inhomogeneous spin chains with nearest neighbor interactions developed earlier. The correspondence of the observed MQ dynamics to the alternating spin chain was demonstrated.

Anomalous transport from hot quasiparticles in interacting spin chains

Many experimentally relevant quantum spin chains are approximately integrable, and support long-lived quasiparticle excitations. A canonical example of integrable model of quantum magnetism is the XXZ spin chain, for which energy spreads ballistically, but, surprisingly, spin transport can be diffusive or superdiffusive. We review the transport properties of this model using an intuitive quasiparticle picture that relies on the recently introduced framework of generalized hydrodynamics. We discuss how anomalous linear response properties emerge from hierarchies of quasiparticles both in integrable and near-integrable limits, with an emphasis on the role of hydrodynamic fluctuations. We also comment on recent developments including non-linear response, full-counting statistics and far-from-equilibrium transport. We provide an overview of recent numerical and experimental results on transport in XXZ spin chains.

Quantum computation of molecular structure using data from challenging-to-classically-simulate nuclear magnetic resonance experiments

We propose a quantum algorithm for inferring the molecular nuclear spin Hamiltonian from time-resolved measurements of spin-spin correlators, which can be obtained via nuclear magnetic resonance (NMR). We focus on learning the anisotropic dipolar term of the Hamiltonian, which generates dynamics that are challenging to classically simulate in some contexts. We demonstrate the ability to directly estimate the Jacobian and Hessian of the corresponding learning problem on a quantum computer, allowing us to learn the Hamiltonian parameters. We develop algorithms for performing this computation on both noisy near-term and future fault-tolerant quantum computers. We argue that the former is promising as an early beyond-classical quantum application since it only requires evolution of a local spin Hamiltonian. We investigate the example of a protein (ubiquitin) confined on a membrane as a benchmark of our method. We isolate small spin clusters, demonstrate the convergence of our learning algorithm on one such example, and then investigate the learnability of these clusters as we cross the ergodic to non-ergodic phase transition by suppressing the dipolar interaction. We see a clear correspondence between a drop in the multifractal dimension measured across many-body eigenstates of these clusters, and a transition in the structure of the Hessian of the learning cost function (from degenerate to learnable). Our hope is that such quantum computations might enable the interpretation and development of new NMR techniques for analyzing molecular structure.

Experimental Detection of the Correlation Rényi Entropy in the Central Spin Model

We propose and experimentally measure an entropy that quantifies the volume of correlations among qubits. The experiment is carried out on a nearly isolated quantum system composed of a central spin coupled and initially uncorrelated with 15 other spins. Because of the spin-spin interactions, information flows from the central spin to the surrounding ones forming clusters of multispin correlations that grow in time. We design a nuclear magnetic resonance experiment that directly measures the amplitudes of the multispin correlations and use them to compute the evolution of what we call correlation Rényi entropy. This entropy keeps growing even after the equilibration of the entanglement entropy. We also analyze how the saturation point and the timescale for the equilibration of the correlation Rényi entropy depend on the system size.

Quantum chaos and the correspondence principle

The correspondence principle is a cornerstone in the entire construction of quantum mechanics. This principle has been recently challenged by the observation of an early-time exponential increase of the out-of-time-ordered correlator (OTOC) in classically nonchaotic systems [E. B. Rozenbaum et al., Phys. Rev. Lett. 125, 014101 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.014101]. Here, we show that the correspondence principle is restored after a proper treatment of the singular points. Furthermore, our results show that the OTOC maintains its role as a diagnostic of chaotic dynamics.

Noncommuting conserved charges in quantum many-body thermalization

In statistical mechanics, a small system exchanges conserved quantities-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 quantities. The conserved quantities are represented by operators usually 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 forms the system of interest. The conserved quantities manifest as spin components. Heisenberg interactions push the conserved quantities 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 near 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 conserved quantities from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.

Perturbation Independent Decay of the Loschmidt Echo in a Many-Body System

When a qubit or spin interacts with others under a many-body Hamiltonian, the information it contains progressively scrambles. Here, nuclear spins of an adamantane crystal are used as a quantum simulator to monitor such dynamics through out-of-time-order correlators, while a Loschmidt echo (LE) asses how weak perturbations degrade the information encoded in these increasingly complex states. Both observables involve the implementation of a time-reversal procedure which, in practice, involves inverting the sign of the effective Hamiltonian. Our protocols use periodic radio frequency pulses to modulate the natural dipolar interaction implementing a Hamiltonian that can be scaled down at will. Meanwhile, experimental errors and strength of perturbative terms remain constant and can be quantified through the LE. For each scaling factor, information spreading occurs with a timescale, T_{2}, inversely proportional to the local second moment of the Hamiltonian. We find that, when the reversible interactions dominate over the perturbations, the information scrambled among up to 10^{2} spins can still be recovered. However, we find that the LE decay rate cannot become smaller than a critical value 1/T_{3}≈(0.15±0.02)/T_{2}, which only depends on the interactions themselves, and not on the perturbations. This result shows the emergence of a regime of intrinsic irreversibility in accordance to a central hypothesis of irreversibility, hinted from previous experiments.

Integrable Many-Body Quantum Floquet-Thouless Pumps

We construct an interacting integrable Floquet model featuring quasiparticle excitations with topologically nontrivial chiral dispersion. This model is a fully quantum generalization of an integrable classical cellular automaton. We write down and solve the Bethe equations for the generalized quantum model and show that these take on a particularly simple form that allows for an exact solution: essentially, the quasiparticles behave like interacting hard rods. The generalized thermodynamics and hydrodynamics of this model follow directly, providing an exact description of interacting chiral particles in the thermodynamic limit. Although the model is interacting, its unusually simple structure allows us to construct operators that spread with no butterfly effect; this construction does not seem possible in other interacting integrable systems. This model exemplifies a new class of exactly solvable, interacting quantum systems specific to the Floquet setting.

Gauging classical and quantum integrability through out-of-time-ordered correlators

Out-of-time-ordered correlators (OTOCs) have been proposed as a probe of chaos in quantum mechanics, on the basis of their short-time exponential growth found in some particular setups. However, it has been seen that this behavior is not universal. Therefore, we query other quantum chaos manifestations arising from the OTOCs, and we thus study their long-time behavior in systems of completely different nature: quantum maps, which are the simplest chaotic one-body system, and spin chains, which are many-body systems without a classical limit. It is shown that studying the long-time regime of the OTOCs it is possible to detect and gauge the transition between integrability and chaos, and we benchmark the transition with other indicators of quantum chaos based on the spectra and the eigenstates of the systems considered. For systems with a classical analog, we show that the proposed OTOC indicators have a very high accuracy that allow us to detect subtle features along the integrability-to-chaos transition.