Particle statistics plays a crucial role in a strongly interacting quantum many-body system. Here, we study the Hubbard model for distinguishable particles at unit filling. Starting from the superfluid-like state in the strong tunneling limit and gradually reducing the tunneling so that the on-site repulsive interaction dominates, the state ends up in a symmetric superposition of Mott insulator states. This result can be experimentally confirmed by the recovery of interference patterns in the density correlation functions. We also show that this state is a maximally entangled state, in contrast to the standard picture.
Particle statistics plays a crucial role in a strongly interacting quantum many-body system. Here, we study the Hubbard model for distinguishable particles at unit filling. Starting from the superfluid-like state in the strong tunneling limit and gradually reducing the tunneling so that the on-site repulsive interaction dominates, the state ends up in a symmetric superposition of Mott insulator states. This result can be experimentally confirmed by the recovery of interference patterns in the density correlation functions. We also show that this state is a maximally entangled state, in contrast to the standard picture.
Quantum phases of matter are routinely identified by coherence features, with interference patterns being one of the most directly observable quantities. In lattices, the superfluid-to-Mott-insulator (SF-MI) transition is commonly viewed as a change from wave-like coherence to particle-like localization: interference peaks are taken as a hallmark of superfluidity, whereas their disappearance is used to diagnose insulating behavior. Here, we challenge this picture for one-dimensional (1D) strongly interacting gases subject to a lattice potential. We realize a gapped Mott insulator through pinning in a shallow lattice and find that pronounced interference peaks persist deep in the insulating regime. Strikingly, the interference becomes stronger as the Mott fraction increases, demonstrating that a certain degree of coherence still exists in the insulator state. Measurements of the one-body correlation function reveal an oscillatory, exponentially decaying coherence pattern across several lattice sites, in quantitative agreement with quantum Monte Carlo (QMC) simulations. Our work shows that interference does not uniquely diagnose superfluidity and it exposes the unexpected wave nature of a 1D Mott insulator.
Quantum tunneling remains unexplored in many regimes of many-body quantum physics, including the effect of quantum phase transitions on tunneling dynamics. In general, the quantum phase is a statement about the ground state and has no relation to far-from-equilibrium dynamics. Although tunneling is a highly dynamical process involving many excited states, we find that the quantum phase of the Bose-Hubbard model determines phase-dependent tunneling outcomes for the quantum tunneling escape, or quasi-bound problem. Superfluid and Mott insulator correlations lead to a new quantum tunneling rate, the quantum fluctuation rate. This rate shows surprising and highly dynamical features, such as oscillatory interference between trapped and escaped atoms and a completely different macroscopic quantum tunneling behavior for superfluid and Mott insulator phases. In the superfluid phase we find that escape dynamics are wave-like and coherent, leading to interference patterns in the density with a rapid decay process which is non-exponential. Quantum entropy production peaks when about half the atoms have escaped. In the Mott phase, despite stronger repulsive interactions, tunneling is significantly slowed by the presence of a Mott gap, creating an effective extra barrier to overcome. Only one atom can tunnel at a time, yet the decay process is nearly linear, completely defying the single-particle exponential model. Moreover, quantum entropy peaks when only about one quarter of the atoms have escaped. These and many other such effects go beyond the usual notions of single-particle quantum tunneling, quantum statistical effects on tunneling, and well-known semi-classical approaches from WKB to instanton theory. These results thus open up a new regime of exploration of far-from-equilibrium dynamics for quantum simulators and quantum dynamics.
Mott tunneling dynamics are entirely distinct from the superfluid ones and ground state properties of quantum phases can predict highly non-equilibrium behavior. We consider quasi-bound state dynamics or tunneling escape in the Bose-Hubbard model from a behind a finite barrier, which can be realized in quantum simulators. In the superfluid regime we find that escape dynamics are wave-like and coherent, leading to interference patterns in the density with a non-exponential but still rapid decay process. Quantum entropy production peaks when about half the atoms have escaped. In contrast, in the Mott insulator regime we find the dynamics are atom-like and incoherent, with no interference fringes. Quantum entropy production peaks at double the value of the superfluid case and when only about one quarter of the atoms have escaped. Despite stronger repulsive interactions, tunneling is significantly slowed by the presence of a Mott gap, creating an effective extra barrier to overcome, and the decay process is nearly linear. Moreover, we introduce a new quantum tunneling rate, the fluctuation rate, which shows oscillatory interference between the trapped and the escaped atoms on short time scales beyond the constant waiting time known for single-particle tunneling before exponential decay ensues. The fluctuation rate is overall positive for the superfluid and initially negative for the Mott insulator, only turning positive in the latter case when about half the atoms have escaped. Finally, off-diagonal correlators show entirely different structure for the two quantum phases. In the superfluid case, the barrier height and interaction strength can be used to tune from pulsed to continuous-wave positive correlation emissions in the escape region. In the Mott insulator, negative correlations between the trap and the escape region emphasize emission one atom at a time.
The interference patterns of ultracold atoms, observed after ballistic expansion from optical lattices, encode essential information about strongly correlated lattice systems, including phase coherence and nonlocal correlations. While the interference of lattice bosons has been extensively investigated, quantitative studies of the lattice fermion interference remain challenging. Here, we report the observation and quantitative characterization of interference patterns in low-temperature, homogeneous fermionic Hubbard gases. We develop a general method to extract the quasimomentum distribution and the first-order correlation function from these patterns. In the noninteracting limit, the coherence length remains very close to the average spacing between identical fermions over a wide range of fillings, revealing the fundamental upper bound imposed by Pauli exclusion on first-order coherence. By tuning the interaction strength and filling, we identify their interplay in the suppression of first-order coherence across the metal-to-Mott-insulator crossover. Moreover, at half filling, the measured correlations agree well with quantum Monte Carlo calculations and remain finite in the strong repulsion regime, revealing virtual tunneling and the underlying superexchange physics.
We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose–Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling, the system features a phase transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background—instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of particle pairs localized on a single site (rather than being extended) on top of the Mott background appears. This happens at the same interaction strength where the Mott-insulator phase with two particles per site is destroyed completely by particle–hole fluctuations for arbitrarily small tunneling. In another regime, characterized by weak interaction but high occupation numbers, we observe a dynamical instability in the superfluid excitation spectrum. The new ground state is a superfluid, forming a two-dimensional (2D) slab, localized along one spatial direction that is chosen spontaneously.
We discuss how entanglement of strongly correlated fermions is influenced by a superlattice structure by considering a one-dimensional Hubbard superlattice, made up of a repeated pattern of LU repulsive sites followed by L0 free sites. Lanczos diagonalization of lattices up to 24 sites is used to calculate the von Neumann entropy and the negativity. The breakdown of particle-hole symmetry broadens the maxima of the entropy in the underdoped region, while the entanglement in the overdoped region is crucially influenced by the nature of the magnetic state, with dips at densities corresponding to repulsive-layer singlets and to $q=\ensuremath{\pi}$ (in units of inverse unit cell length, LU+L0) spin-density waves. At these special densities, the system is either a Mott insulator or a ``compressible insulator.'' We have also found that sites within the same repulsive layer (for ${L}_{U}\ensuremath{\ge}2$) are monogamically entangled with each other, which may provide a route to control entanglement simultaneously in different length scales.