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We define a quantum charger as an interacting quantum system that transfers energy between two drives. The key figure of merit characterizing a charger is its charging power. Remarkably, the presence of long-range interactions within the charger can induce a collective steady-state charging mode that depends superlinearly on the size of the charger, exceeding the performance of noninteracting, parallel units. Using the driven Lipkin-Meshkov-Glick model and power-law interacting spin chains, we show that this effect persists up to a critical system size set by the breakdown of the high-frequency regime. We discuss optimal work output as well as experimentally accessible initial states. The superlinear charging effect can be probed in trapped-ion experiments, and positions interacting Floquet systems as promising platforms for enhanced energy conversion. 

We study a stroboscopic quantum Ising model with Fibonacci dynamics. We use its boundary spin correlation functions in long but finite chains to identify regions in the phase diagram which exhibit Majorana zero modes (MZM) as well as Majorana golden-ratio modes (MGM). We find that these regions evolve in a self-similar manner with increasing simulation time and identify the self-similarity transform which governs this evolution of the phase diagram. Integrability-breaking perturbations lead to a temporal decay of the boundary spin correlations, ultimately limiting the self-similarity of the phase diagram. Our predictions are testable with current quantum information processors. 

We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by (i) the temporal trajectory of a quantum state under unitary evolution or (ii) the quantum states of small subsystems obtained by partial, local projective measurements performed on their complements. These cases, respectively, exemplify the phenomena of “Hilbert-space ergodicity” and “deep thermalization.” In both cases, the resultant ensembles are defined by a simple principle: The distributions of pure states have maximum entropy, subject to constraints such as energy conservation, and effective constraints imposed by thermalization. We present and numerically verify quantifiable signatures of this principle by deriving explicit formulas for all statistical moments of the ensembles, proving the necessary and sufficient conditions for such universality under widely accepted assumptions, and describing their measurable consequences in experiments. We further discuss information-theoretic implications of the universality: Our ensembles have maximal information content while being maximally difficult to interrogate, establishing that generic quantum state ensembles that occur in nature hide (scramble) information as strongly as possible. Our results generalize the notions of Hilbert-space ergodicity to time-independent Hamiltonian dynamics and deep thermalization from infinite to finite effective temperature. Our work presents new perspectives to characterize and understand universal behaviors of quantum dynamics using statistical and information-theoretic tools. 

We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by (i) the temporal trajectory of a quantum state under unitary evolution or (ii) the quantum states of small subsystems obtained by partial, local projective measurements performed on their complements. These cases, respectively, exemplify the phenomena of “Hilbert-space ergodicity” and “deep thermalization.” In both cases, the resultant ensembles are defined by a simple principle: The distributions of pure states have maximum entropy, subject to constraints such as energy conservation, and effective constraints imposed by thermalization. We present and numerically verify quantifiable signatures of this principle by deriving explicit formulas for all statistical moments of the ensembles, proving the necessary and sufficient conditions for such universality under widely accepted assumptions, and describing their measurable consequences in experiments. We further discuss information-theoretic implications of the universality: Our ensembles have maximal information content while being maximally difficult to interrogate, establishing that generic quantum state ensembles that occur in nature hide (scramble) information as strongly as possible. Our results generalize the notions of Hilbert-space ergodicity to time-independent Hamiltonian dynamics and deep thermalization from infinite to finite effective temperature. Our work presents new perspectives to characterize and understand universal behaviors of quantum dynamics using statistical and information-theoretic tools. Published by the American Physical Society2024