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arXiv:2106.06277

Self-induced entanglement resonance in a disordered Bose-Fermi mixture

Juan José Mendoza-Arenas, Berislav Buča

Published Jun 11, 2021• 2 citations
arXivHTMLPDF

Abstract

Different regimes of entanglement growth under measurement have been demonstrated for quantum many-body systems, with an entangling phase for low measurement rates and a disentangling phase for high rates (quantum Zeno effect). Here we study entanglement growth on a disordered Bose-Fermi mixture with the bosons playing the role of the effective self-induced measurement for the fermions. Due to the interplay between the disorder and a non-Abelian symmetry, the model features an entanglement growth resonance when the boson-fermion interaction strength is varied. With the addition of a magnetic field, the model acquires a dynamical symmetry leading to experimentally measurable long-time local oscillations. At the entanglement growth resonance, we demonstrate the emergence of the cleanest oscillations. Furthermore, we show that this resonance is distinct from both noise enhanced transport and a standard stochastic resonance. Our work paves the way for experimental realizations of self-induced correlated phases in multi-species systems.

DOI
10.48550/arxiv.2106.06277

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Different regimes of entanglement growth under measurement have been demonstrated for quantum many-body systems, with an entangling phase for low measurement rates and a disentangling phase for high rates (quantum Zeno effect). Here we study entanglement growth on a disordered Bose-Fermi mixture with the bosons playing the role of the effective self-induced measurement for the fermions. Due to the interplay between the disorder and a non-Abelian symmetry, the model features an entanglement growth resonance when the boson-fermion interaction strength is varied. With the addition of a magnetic field, the model acquires a dynamical symmetry leading to experimentally measurable long-time local oscillations. At the entanglement growth resonance, we demonstrate the emergence of the cleanest oscillations. Furthermore, we show that this resonance is distinct from both noise enhanced transport and a standard stochastic resonance. Our work paves the way for experimental realizations of self-induced correlated phases in multi-species systems.
We establish a conceptual framework for the identification and the characterization of induced interactions in binary mixtures and reveal their intricate relation to entanglement between the components or species of the mixture. Exploiting an expansion in terms of the strength of the entanglement among the two species enables us to deduce an effective single-species description. In this way, we naturally incorporate the mutual feedback of the species and obtain induced interactions for both species which are effectively present among the particles of same type. Importantly, our approach incorporates few-body and inhomogeneous systems extending the scope of induced interactions where two particles interact via a bosonic bath-type environment. Employing the example of a one-dimensional ultracold Bose-Fermi mixture, we obtain induced Bose-Bose and Fermi-Fermi interactions with short-range attraction and long-range repulsion. With this, we show how beyond species mean-field physics visible in the two-body correlation functions can be understood via the induced interactions.
The exploration of novel quantum states of matter remains a central theme in condensed matter physics. Among these, topological order stands out for its robust properties against local perturbations and its potential applications in quantum information processing. While considerable progress has been made in understanding topological order in purely bosonic or fermionic systems, the interplay between different quantum statistics in interacting Bose-Fermi mixtures offers a rich platform for discovering new forms of topological order. This paper investigates the theoretical conditions and characteristic signatures for the emergence of topological order in these hybrid quantum systems. We propose that tunable interspecies interactions, combined with appropriate lattice geometries or synthetic gauge fields, can drive Bose-Fermi mixtures into exotic phases exhibiting non-trivial topological properties. Specifically, we explore scenarios where bosonic particles mediate effective interactions between fermions, or where bosonic condensation leads to a modification of the fermionic band structure, thereby inducing topological phases. Our analysis focuses on identifying key experimental observables, such as fractionalized excitations, robust edge modes, and entanglement properties, which can serve as hallmarks of emergent topological order. The theoretical framework incorporates mean-field approaches, variational methods, and numerical simulations to characterize the phase diagram of interacting Bose-Fermi mixtures, providing a pathway for experimental realization and verification of these fascinating quantum states.
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Generically a quantum system initialized in an unentangled state will, under unitary dynamics, rapidly become entangled, a process closely related to information transport and to thermalization. Disorder can suppress the growth of entanglement and result in memory of initial conditions. In non-interacting systems this arises from localization of single-particle states, the occupancy of which is fixed by the initial condition. In interacting systems similar localized conserved quantities persist, but with the added feature that they are coupled, resulting in entanglement growth which is distinct from both non-interacting localized systems and from generic ergodic systems. The Fermi-Hubbard model has two degrees of freedom per site -- charge and spin -- and disorder may be present in both of these. We study the growth of entanglement in two scenarios -- disorder in charge equal and unequal to that in spin, and determine the distinct contributions of charge and spin degrees of freedom by expanding the Hamiltonian in terms of a set of optimally localized conserved quantities with separate charge and spin character. We find that coupling between charge and spin is significantly weaker than charge-charge and spin-spin coupling. While this decoupling is present in all our results, it is only apparent when the strength of the disorder in the two sectors is different such that there is a separation between the characteristic timescales of the contributions to entanglement made by charge and by spin.
An interacting quantum system that is subject to disorder may cease to thermalize owing to localization of its constituents, thereby marking the breakdown of thermodynamics. The key to understanding this phenomenon lies in the system's entanglement, which is experimentally challenging to measure. We realize such a many-body-localized system in a disordered Bose-Hubbard chain and characterize its entanglement properties through particle fluctuations and correlations. We observe that the particles become localized, suppressing transport and preventing the thermalization of subsystems. Notably, we measure the development of nonlocal correlations, whose evolution is consistent with a logarithmic growth of entanglement entropy, the hallmark of many-body localization. Our work experimentally establishes many-body localization as a qualitatively distinct phenomenon from localization in noninteracting, disordered systems.
We study the effect of decoherence on dynamical phase diffusion in the two-site Bose-Hubbard model. Starting with an odd parity excited coherent state, the initial loss of single-particle coherence varies from small bound oscillations in the Rabi regime, through hyperbolic depletion in the Josephson regime, to a Gaussian decay in the Fock regime. The inclusion of local-site noise, measuring the relative number difference between the modes, is shown to enhance phase diffusion. In comparison, site-indiscriminate noise measuring the population imbalance between the two quasimomentum modes slows down the loss of single-particle coherence. Decoherence thus either enhances or suppresses phase diffusion, depending on the details of system-bath coupling and the overlap of decoherence pointer states with collisional-entanglement pointer states. The deceleration of phase diffusion due to the coupling with the environment may be viewed as a many-body quantum Zeno effect. The extended effective decay times in the presence of projective measurement are further enhanced with increasing number of particles NNN by a bosonic factor of N\sqrt{N}N​ in the Fock regime and N/log NN/\text{log}\text{ }NN/log N in the Josephson regime.