We consider a Bose-Josephson junction (BJJ) formed by a binary mixture of ultracold atoms to investigate the manifestation of coherent collective dynamics on ergodicity and quantum scars, unfolding the connection between them. By tuning the inter- and intraspecies interaction, we demonstrate a rich variety of Josephson dynamics and transitions between them, which plays a crucial role in controlling the overall ergodic behavior. The signature of underlying classicality is revealed from the entanglement spectrum, which also elucidates the formation of quantum scars of unstable steady states and of periodic orbits leading to athermal behavior. The degree of ergodicity across the energy band and scarring phenomena can be probed from the autocorrelation function as well from the phase fluctuation of the condensates, which has relevance in cold atom experiments.
We consider a Bose-Josephson junction (BJJ) formed by a binary mixture of ultracold atoms to investigate the manifestation of coherent collective dynamics on ergodicity and quantum scars, unfolding the connection between them. By tuning the inter- and intraspecies interaction, we demonstrate a rich variety of Josephson dynamics and transitions between them, which plays a crucial role in controlling the overall ergodic behavior. The signature of underlying classicality is revealed from the entanglement spectrum, which also elucidates the formation of quantum scars of unstable steady states and of periodic orbits leading to athermal behavior. The degree of ergodicity across the energy band and scarring phenomena can be probed from the autocorrelation function as well from the phase fluctuation of the condensates, which has relevance in cold atom experiments.
We consider a model describing Bose-Josephson junction (BJJ) coupled to a single bosonic mode exhibiting quantum phase transition (QPT). Onset of chaos above QPT is observed from semiclassical dynamics as well from spectral statistics. Based on entanglement entropy, we analyze the ergodic behavior of eigenstates with increasing energy density which also reveals the influence of dynamical steady state known as π-mode on it. We identify the imprint of unstable π-oscillation as many body quantum scar (MBQS), which leads to the deviation from ergodicity and quantify the degree of scarring. Persistence of phase coherence in nonequilibrium dynamics of such initial state corresponding to the π-mode is an observable signature of MBQS which has relevance in experiments on BJJ.
We consider a model describing Bose-Josephson junction (BJJ) coupled to a single bosonic mode exhibiting a quantum phase transition (QPT). Onset of chaos close to QPT is observed from semiclassical dynamics of collective modes and from spectral statistics. A detailed analysis of entanglement entropy and multifractal nature of states reveals a non-ergodic to weakly ergodic crossover at a critical energy. We identify the imprint of collective π-oscillation as many body quantum scar (MBQS), which leads to the deviation from ergodicity. Persistence of phase coherence in non-equilibrium dynamics of such initial state corresponding to the π-mode is an observable signature of MBQS which can be relevant for experiments on BJJ.
The modern framework for quantum thermalization is grounded in the Eigenstate Thermalization Hypothesis (ETH), in which non-integrability and chaos are historically assumed as prerequisites. This work investigates this relationship in a three-species Bose-Josephson Junction (BJJ) with mutual interactions, experimentally achievable in current ultracold-atom platforms. After a thorough characterization of quantum chaos in this system, we examine the occurrence of thermal behavior expected when ETH holds. We identify three distinct regimes: chaotic, integrable, and separable. Remarkably, quantum thermalization occurs in both the chaotic and integrable regimes, while it breaks down in and near the separable limit — supporting that non-integrability is not a necessary condition for thermalization. Furthermore, since the system exhibits collective phenomena in the semiclassical limit, we identify ergodicity breaking phenomena such as athermal states in the chaotic regime classifiable as quantum scars, which show no signs of thermalization, consistently with a weak form of ETH.
Quantum many-body scars consist of a few low-entropy eigenstates in an otherwise chaotic many-body spectrum, and can weakly break ergodicity resulting in robust oscillatory dynamics. The notion of quantum many-body scars follows the original single-particle scars introduced within the context of quantum billiards, where scarring manifests in the form of a quantum eigenstate concentrating around an underlying classical unstable periodic orbit. A direct connection between these notions remains an outstanding problem. Here, we study a many-body spinor condensate that, owing to its collective interactions, is amenable to the diagnostics of scars. We characterize the system's rich dynamics, spectrum, and phase space, consisting of both regular and chaotic states. The former are low in entropy, violate the eigenstate thermalization hypothesis, and can be traced back to integrable effective Hamiltonians, whereas most of the latter are scarred by the underlying semiclassical unstable periodic orbits, while satisfying the eigenstate thermalization hypothesis. We outline an experimental proposal to probe our theory in trapped spin-1 Bose-Einstein condensates.
We introduce the concept of ergodicity and explore its deviation caused by quantum scars in an isolated quantum system, employing a pedagogical approach based on a toy model. Quantum scars, originally identified as traces of classically unstable orbits in certain wavefunctions of chaotic systems, have recently regained interest for their role in non-ergodic dynamics, as they retain memory of their initial states. We elucidate these features of quantum scars within the same framework of this toy model. The integrable part of the model consists of two large spins, with a classical counterpart, which we combine with a random matrix to induce ergodic behavior. Scarred states can be selectively generated from the integrable spin Hamiltonian by protecting them from the ergodic states using a projector method. Deformed projectors mimic the ‘quantum leakage’ of scarred states, enabling tunable mixing with ergodic states and thereby controlling the degree of scarring. In this simple model, we investigate various properties of quantum scarring and shed light on different aspects of many-body quantum scars observed in more complex quantum systems. Notably, the underlying classicality can be revealed through the entanglement spectrum and the dynamics of ‘out-of-time-ordered correlators’.
We consider an interacting collective spin model known as coupled top (CT), exhibiting a rich variety of phenomena related to quantum transitions, ergodicity, and formation of quantum scars, discussed in our previous work [Mondal, Sinha, and Sinha, Phys. Rev. E 102, 020101(R) (2020)2470-004510.1103/PhysRevE.102.020101]. In this work, we present a detailed analysis of the different type of transitions in the CT model, and find their connection with the underlying collective spin dynamics. Apart from the quantum scarring phenomena, we also identify another source of deviation from ergodicity due to the presence of nonergodic multifractal states. The degree of ergodicity of the eigenstates across the energy band is quantified from the relative entanglement entropy as well as multifractal dimensions, which can be probed from nonequilibrium dynamics. Finally, we discuss the detection of nonergodic behavior and different types of quantum scars using "out-of-time-order correlators," which has relevance in the recent experiments.