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 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.
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 present a study of the superfluid properties of atomic Bose gases in optical lattice potentials using the Bose-Hubbard model. To do this, we use a microscopic definition of the superfluid fraction based on the response of the system to a phase variation imposed by means of twisted boundary conditions. We compare the superfluid fraction to other physical quantities, i.e., the interference pattern after ballistic expansion, the quasimomentum distribution, and number fluctuations. We have performed exact numerical calculations of all these quantities for small one-dimensional systems. We show that the superfluid fraction alone exhibits a clear signature of the Mott-insulator transition. Observables like the fringe visibility, which probe only ground-state properties, do not provide direct information on superfluidity and the Mott-insulator transition.
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.
We study 1D trapped Bose gases in the strongly interacting regime. The systems are created in an optical lattice and are subject to a longitudinal periodic potential. Bragg spectroscopy enables us to investigate the excitation spectrum in different regimes. In the superfluid phase a broad continuum of excitations is observed which calls for an interpretation beyond the Bogoliubov spectrum taking into account the effect of strong interactions. In the Mott insulating phase a discrete spectrum is measured. Both phases are compared to the 3D situation and to the crossover regime from 1D to 3D. The coherence length and coherent fraction of the gas are measured in all configurations. We observe signatures for increased fluctuations characteristic for 1D systems. Moreover, the collective oscillations cease near the transition to the Mott insulator phase.
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.