Session H3: Hubbard Model and Optical Lattices

Measuring the dynamic structure factor of a dissipative quantum many-body system

A Bose-Einstein condensate whose motional degrees of freedom are coupled to a high-finesse optical cavity via a transverse pump beam constitutes a dissipative quantum many-body system with long range interactions. These interactions can induce a structural phase transition from a flat to a density-modulated state. The transverse pump field simultaneously represents a probe of the atomic density via cavity-enhanced Bragg scattering. By spectrally analysing the light field leaking out of the cavity, we measure non-destructively the dynamic structure factor of the fluctuating atomic density while the system undergoes the phase transition. An observed asymmetry in the dynamic structure factor is attributed to the coupling to dissipative baths. Critical exponents for both sides of the phase transition can be extracted from the data. We further discuss our progress in adding strong short-range interactions to this system, in order to explore Bose-Hubbard physics with cavity-mediated long-range interactions and self-organization in lower dimensions.   

Quantum phases in an asymmetric double-well optical lattice

We study the superfluid (SF) and Mott insulator phases of ultracold atoms trapped in a double-well optical lattice. The lattice has an asymmetric double-well geometry along the $x$ axis and single wells along the other axes. We set up the Bose-Hubbard model and evaluate tunneling and atom-atom interaction energies from exact band-structure calculations. Only nearest-neighbor tunneling is considered. This leads to two tunneling energies, $t$ and $J$, to describe hopping along the $x$ axis, and $J_{\perp}$ along the other directions. We assume that the barrier between the double wells is low compared to that between double-well pairs and nearest-neighbor atom-atom interaction can not be ignored. A mean field calculation determines the SF and Mott phase boundaries as a function of lattice parameters and chemical potential $\mu$. The boundary is characterized by an effective tunneling $t_{\rm eff}=t+J$ along the $x$ axis. Moreover, we show that the Mott lobes within the $\mu-t_{\rm eff}$ plane are completely surrounded by SF regions. In future, we will use the results of these simulations to construct effective lattice models where the atom-atom interaction is zero and the interactions are governed by a three-body potential. Such systems might lead to unique many-body ground states.   

Particle-Hole Pair Coherence in Mott Insulator Quench Dynamics

We predict the existence of novel collapse and revival oscillations that are a distinctive signature of the short-range off-diagonal coherence associated with particle-hole pairs in Mott insulator states. Starting with an atomic Mott state in a one-dimensional optical lattice, suddenly raising the lattice depth freezes the particle-hole pairs in place and induces phase oscillations. The peak of the quasi-momentum distribution, revealed through time of flight interference, oscillates between a maximum occupation at zero quasi-momentum (the $\Gamma$ point) and the edge of the Brillouin zone. We find that the population enhancements at the edge of the Brillouin zone is due to coherent particle-hole pairs, and we show similar effects for fermions and Bose-Fermi mixtures in a lattice. Our results open a new avenue for probing strongly correlated many-body states with short-range phase coherence that goes beyond the familiar collapse and revivals previously observed in the long-range coherent superfluid regime.   

Spin Drag in the Disordered Hubbard Model

We report progress in measuring spin drag in a 3-dimensional disordered optical lattice to probe the role of disorder and localization effects in the Hubbard model. Relative motion between two spin states in an ultracold Fermi gas is prepared with a momentum selective Raman pulse. Disorder is introduced in a controlled fashion via optical speckle with correlation lengths comparable to the lattice spacing. Analogous transport measurements in a disordered harmonic trap are also discussed.   

Disordered Mott Insulator in heavy-light Fermi mixture in optical lattices

Ultracold mixtures of different atomic species have great promise of realizing novel many-body phenomena beyond Hubbard model. In a mixture of femionic atoms with large mass differences, a disordered Mott insulator can be formed as the result of the repulsive interaction between two species. The disorder Mott insulator leads to an incompressible total density of the mixture while the relative density is still compressible. Based on strong-coupling expansion and Monte Carlo calculations, we show that this phase can exist for a broad parameter region for ultracold mixtures confined by a harmonic trap and a three-dimensional optical lattice. The realization of such phase can lead to new ways of quantum control in ultracold mixtures.   

Mott-insulator to superfluid transition in the strong coupling regime and in the presence of a minority component

By means of perturbation theory, we study the Mott-insulator to superfluid transition in the strong coupling regime and in the presence of a minority second component. In the limit of zero hopping, ground-states are in general degenerate. This degeneracy is not always lifted by the first order perturbation theory. In such cases, the standard perturbation theory does not uniquely determine the ground-state correction. To resolve this issue, we proved that the ground state energy of the Hamiltonian is non-degenerate, and used this property along with symmetry properties of the lattice to determine the first order correction to the ground state.   

Mobility transition between ballistic and diffusive transport in PT-symmetric lattices

In this work, we show theoretically and experimentally that in non-hermitian time-independent systems ballistic and diffusive transport coexist, but on different time scales. Our study is based on a parity-time-symmetric (PT) optical waveguide array exhibiting an alternating loss profile with homogeneous coupling between neighboring guides. The key of this study is that the coupling is equal between all waveguides, leading to ``broken'' PT-symmetry and, hence, a complex band structure. Exciting a single waveguide of such a structure, initially all modes are excited and the evolution of the wavepacket is ballistic. The imaginary part of the band structure leads to a contraction of the wavepacket's spectrum around the mode whose eigenvalue possesses the smallest imaginary part. Due to this effect, for large propagation distances the variance of the wavepacket shows the diffusive spreading. We emphasize that these dynamics cannot be achieved within any Hermitian system. In order to probe the theoretical predictions experimentally, laser-written waveguide arrays inside fused silica were analysed. Losses were implemented by sinusoidally bending every second waveguide transverse to lattice plane. The experimental results show excellent agreement with the theoretical predictions.   

Self-Consistent Mathieu Equation Approach for Interacting Bosons in Optical Lattices

There has been much recent interest in the problem of interacting bosons confined to a periodic optical lattice. Instead of the commonly used tight-binding approach (applicable near the Mott insulating regime of the phase diagram), our theoretical study of this system starts from the exact single-particle states of bosons in an optical lattice, satisfying the Mathieu equation, an approach that can be particularly useful at large boson filling. We treat interaction effects using a self-consistent Hartree-Fock approximation, and make predictions for experimental observables such as the superfluid transition temperature, condensate fraction and boson momentum distribution.   

Ground states of hard-core dipolar bosons in coupled 1D optical lattices

We study the ground states of hard-core bosons interacting by dipolar forces and trapped in a stack of $N$ 1D optical lattices (tubes) parallel to each other with no inter-tube tunneling. Ab-initio quantum Monte Carlo simulations are performed by the novel $N$-Worm Algorithm and are compared with the results of the bosonization method. Several non-trivial ground states have been found: superfluids and countersuperfluids made of composites of particles from different tubes, 1D checkerboard insulators, and mixtures of these phases. As it turns out, such phases have zero threshold in the interaction and can invoke any number $M$ of tubes, $1 < M \leq N$, regardless of their geometrical positions. The inter-tube imbalance of filling factors is a ``tuning knob'' for inducing such phases and switching between them.   

Possibilities for experimental observation of dynamical quasicondensation in sudden expansion of hard-core bosons on optical lattices

Recent experiments with ultracold atomic gases give access to the studies of transport properties of interacting particles in optical lattices [1,2]. Sudden expansion of strongly interacting bosons and fermions exhibits rich phenomena [3]. For instance, it was shown experimentally that hard-core bosons expand ballistically in one dimension [2], in agreement with exact numerical studies. Nevertheless, dynamical quasicondensation of hard-core bosons [4] remains a challenge for experimentalist. We discuss the possibility how the quasicondensation of expanding bosons could be observed in realistic experimental conditions.\\[4pt] [1] Schneider et al. Nature Physics 8, 213 (2012).\\[0pt] [2] Ronzheimer et al., Phys. Rev. Lett. 110, 205301 (2013).\\[0pt] [3] Vidmar et al., Phys. Rev. B 88, 235117 (2013).\\[0pt] [4] Rigol and Muramatsu, Phys. Rev. Lett. 93, 230404 (2004).