Condensate fraction in a 2D Bose gas measured across the Mott-insulator transition

Mott Transition for a Lieb-Liniger Gas in a Shallow Quasiperiodic Potential: Delocalization Induced by Disorder

Disorder or quasidisorder is known to favor localization in many-body Bose systems. Here, in contrast, we demonstrate an anomalous delocalization effect induced by incommensurability in quasiperiodic lattices. Loading ultracold atoms in two shallow periodic lattices with equal amplitude and either equal or incommensurate spatial periods, we show the onset of a Mott transition not only in the periodic case but also in the quasiperiodic case. Switching from periodic to quasiperiodic potential with the same amplitude, we find that the Mott insulator turns into a delocalized superfluid. Our experimental results agree with quantum Monte Carlo calculations, showing this anomalous delocalization induced by the interplay between the disorder and interaction.

Anomalous Behavior of Magnetic Susceptibility Obtained by Quench Experiments in Isolated Quantum Systems

We examine how the magnetic susceptibility obtained by the quench experiment on isolated quantum systems is related to the isothermal and adiabatic susceptibilities defined in thermodynamics. Under the conditions similar to the eigenstate thermalization hypothesis, together with some additional natural ones, we prove that for translationally invariant systems the quench susceptibility as a function of wave vector k is discontinuous at k=0. Moreover, its values at k=0 and the k→0 limit coincide with the adiabatic and the isothermal susceptibilities, respectively. We give numerical predictions on how these particular behaviors can be observed in experiments on the XYZ spin chain with tunable parameters, and how they deviate when the conditions are not fully satisfied.

Critical points of the three-dimensional Bose-Hubbard model from on-site atom number fluctuations

We discuss how positions of critical points of the three-dimensional Bose-Hubbard model can be accurately obtained from variance of the on-site atom number operator, which can be experimentally measured. The idea that we explore is that the derivative of the variance, with respect to the parameter driving the transition, has a pronounced maximum close to critical points. We show that Quantum Monte Carlo studies of this maximum lead to precise determination of critical points for the superfluid-Mott insulator transition in systems with mean number of atoms per lattice site equal to one, two, and three. We also extract from such data the correlation-length critical exponent through the finite-size scaling analysis and discuss how the derivative of the variance can be reliably computed from numerical data for the variance. The same conclusions apply to the derivative of the nearest-neighbor correlation function, which can be obtained from routinely measured time-of-flight images.

Mean-Field Scaling of the Superfluid to Mott Insulator Transition in a 2D Optical Superlattice

The mean-field treatment of the Bose-Hubbard model predicts properties of lattice-trapped gases to be insensitive to the specific lattice geometry once system energies are scaled by the lattice coordination number z. We test this scaling directly by comparing coherence properties of ^{87}Rb gases that are driven across the superfluid to Mott insulator transition within optical lattices of either the kagome (z=4) or the triangular (z=6) geometries. The coherent fraction measured for atoms in the kagome lattice is lower than for those in a triangular lattice with the same interaction and tunneling energies. A comparison of measurements from both lattices agrees quantitatively with the scaling prediction. We also study the response of the gas to a change in lattice geometry, and observe the dynamics as a strongly interacting kagome-lattice gas is suddenly "hole doped" by introducing the additional sites of the triangular lattice.

Locating the quantum critical point of the Bose-Hubbard model through singularities of simple observables

We show that the critical point of the two-dimensional Bose-Hubbard model can be easily found through studies of either on-site atom number fluctuations or the nearest-neighbor two-point correlation function (the expectation value of the tunnelling operator). Our strategy to locate the critical point is based on the observation that the derivatives of these observables with respect to the parameter that drives the superfluid-Mott insulator transition are singular at the critical point in the thermodynamic limit. Performing the quantum Monte Carlo simulations of the two-dimensional Bose-Hubbard model, we show that this technique leads to the accurate determination of the position of its critical point. Our results can be easily extended to the three-dimensional Bose-Hubbard model and different Hubbard-like models. They provide a simple experimentally-relevant way of locating critical points in various cold atomic lattice systems.

Quasiparticle dynamics in a bose insulator probed by interband bragg spectroscopy

We investigate experimentally and theoretically the dynamical properties of a Mott insulator in decoupled one-dimensional chains. Using a theoretical analysis of the Bragg excitation scheme, we show that the spectrum of interband transitions holds information on the single-particle Green's function of the insulator. In particular, the existence of particle-hole coherence due to quantum fluctuations in the Mott state is clearly seen in the Bragg spectra and quantified. Finally, we propose a scheme to directly measure the full, momentum-resolved spectral function as obtained in the angle-resolved photoemission spectroscopy of solids.

Time-reversal symmetry breaking of p-orbital bosons in a one-dimensional optical lattice

We study bosons loaded in a one-dimensional optical lattice of twofold p-orbital degeneracy at each site. Our numerical simulations find an anti-ferro-orbital p(x)+ip(y), a homogeneous p(x) Mott-insulator phase, and two kinds of superfluid phases distinguished by the orbital order (anti-ferro-orbital and paraorbital). The anti-ferro-orbital order breaks time-reversal symmetry. Experimentally observable evidence is predicted for the phase transition between the two different superfluid phases. We also discover that the quantum noise measurement is able to provide a concrete evidence of time-reversal symmetry breaking in the first Mott phase.

Universal thermometry for quantum simulation

Quantum simulation is a highly ambitious program in cold atom research currently being pursued in laboratories worldwide. The goal is to use cold atoms in optical lattices to simulate models for unsolved strongly correlated systems, so as to deduce their properties directly from experimental data. An important step in this effort is to determine the temperature of the system, which is essential for deducing all thermodynamic functions. This step, however, remains difficult for lattice systems at the moment. Here, we propose a method based on a generalized fluctuation-dissipation theorem. It does not rely on numerical simulations and gives a universal thermometry scheme for quantum gas systems including mixtures and spinor gases, provided that the local density approximation is valid.

Signature of quantum criticality in the density profiles of cold atom systems

In recent years, there has been considerable experimental effort using cold atoms to study strongly correlated many-body systems. One class of phenomena of particular interest is quantum critical (QC) phenomena. While prevalent in many materials, these phenomena pose notoriously difficult theoretical problems due to the vanishing of energy scales in the QC region. So far, there are no systematic ways to deduce the QC behavior of bulk systems from the data of trapped atomic gases. Here, we present a simple algorithm to use the experimental density profile to determine the T=0 phase boundary of bulk systems, as well as the scaling functions in the QC regime. We also present another scheme for removing finite-size effects of the trap. We demonstrate the validity of our schemes using exactly soluble models.

Phases of a two-dimensional bose gas in an optical lattice

Ultracold atoms in optical lattices realize simple condensed matter models. We create an ensemble of ≈60 harmonically trapped 2D Bose-Hubbard systems from a 87Rb Bose-Einstein condensate in an optical lattice and use a magnetic resonance imaging approach to select a few 2D systems for study, thereby eliminating ensemble averaging. Our identification of the transition from superfluid to Mott insulator, as a function of both atom density and lattice depth, is in excellent agreement with a universal state diagram [M. Rigol, Phys. Rev. A 79 053605 (2009)] suitable for our trapped system. In agreement with theory, our data suggest a failure of the local density approximation in the transition region.

Stroboscopic generation of topological protection

Trapped neutral atoms offer a powerful route to robust simulation of complex quantum systems. We present here a stroboscopic scheme for realization of a Hamiltonian with n-body interactions on a set of neutral atoms trapped in an addressable optical lattice, using only 1- and 2-body physical operations together with a dissipative mechanism that allows thermalization to finite temperature or cooling to the ground state. We demonstrate this scheme with application to the toric code Hamiltonian, ground states of which can be used to robustly store quantum information when coupled to a low temperature reservoir.

Slow mass transport and statistical evolution of an atomic gas across the superfluid-Mott-insulator transition

We study transport dynamics of ultracold cesium atoms in a two-dimensional optical lattice across the superfluid-Mott-insulator transition based on in situ imaging. Inducing the phase transition with a lattice ramping routine expected to be locally adiabatic, we observe a global mass redistribution which requires a very long time to equilibrate, more than 100 times longer than the microscopic time scales for on-site interaction and tunneling. When the sample enters the Mott-insulator regime, mass transport significantly slows down. By employing fast recombination loss pulses to analyze the occupancy distribution, we observe similarly slow-evolving dynamics, and a lower effective temperature at the center of the sample.

Dynamical properties of the one-dimensional spin-1/2 Bose-Hubbard model near a Mott-insulator to ferromagnetic-liquid transition

We investigate the dynamics of the one-dimensional strongly repulsive spin-1/2 Bose-Hubbard model for filling nu <or= 1. While at nu=1 the system is a Hubbard-Mott insulator exhibiting dynamical properties of the Heisenberg ferromagnet, at nu<1 it is a ferromagnetic liquid with complex spin dynamics. We find that close to the insulator-liquid transition the system admits for a complete separation of spin and density degrees of freedom valid at all energy and momentum scales within the t-J approximation. This allows us to derive the propagator of transverse spin waves and the shape of the magnon peak in the dynamic spin structure factor.

Role of interactions in 87Rb-40K Bose-Fermi mixtures in a 3D optical lattice

We investigate the effect of interspecies interaction on a degenerate mixture of bosonic 87Rb and fermionic 40K atoms in a three-dimensional optical lattice potential. Using a Feshbach resonance, the 87Rb-40K interaction is tuned over a wide range. Through an analysis of the 87Rb momentum distribution, we find a pronounced asymmetry between strong repulsion and strong attraction. In the latter case, we observe a marked shift in the superfluid to Mott insulator transition, which we attribute to a renormalization of the Bose-Hubbard parameters due to self-trapping.