Session G9: Quantum Phases of Atoms in Optical Lattices

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 that the properties of lattice-trapped gases are insensitive to the specific lattice geometry once system energies are scaled by the coordination number $z$. We test this prediction by studying the superfluid to Mott insulator transition in an ultracold gas of rubidium atoms trapped in a two-dimensional optical superlattice which can be tuned from triangular ($z=6$) to kagome ($z=4$) geometries. We observe the coherent fraction to be less robust in the kagome lattice by tuning the ratio of the interaction energy $U$ to the tunneling energy $J$. Comparison of the coherent fraction in the triangular lattice to that in the kagome lattice in terms of the scaled ratio $U/Jz$ is consistent with the mean-field prediction.   

Inter-orbital interactions in state-dependent optical lattices

We report on the realization of a state-dependent optical lattice for the ground state $^1\mathrm{S}_0$ and metastable excited state $^3\mathrm{P}_0$ of fermionic $^{173}$Yb. While excited-state atoms are pinned by the lattice, ground-state atoms retain their mobility. Moreover, the optical lattice is nuclear-spin independent, conserving the SU(N) symmetry of the interactions, typical for earth-alkaline-like atoms. Together, these features make it a natural platform for the realization of Kondo-type physics. The effective inter-orbital interactions are influenced by the recently discovered magnetic Feshbach resonance as well as the lattice potential, inducing mixed dimensionality for the two atomic orbitals. We probe these interactions experimentally using high-resolution clock-line spectroscopy as well as collision dynamics.   

Compressibility phase diagram for the disordered Bose-Hubbard model

Developing a complete understanding of the effects of disorder in quantum many-particle systems is an outstanding problem with key implications for condensed matter physics and quantum information science. We report progress towards this goal in a 3D disordered Bose lattice gas consisting of strongly interacting $^{87}$Rb atoms, which realizes the disordered Bose-Hubbard model (DBHM). One of the distinguishing properties of the phases in the DBHM is compressibility. We experimentally map the compressibility of the DBHM phase diagram by measuring the change in double occupancies in the presence of disorder. Further complicating the problem is the introduction of finite temperature, and we explore how compressibility is affected by this additional ingredient.   

Progress towards localization in the attractive Hubbard model

The interplay between fermionic superfluidity and disorder is a topic of long-standing interest that has recently come within reach of ultracold gas experiments. Outstanding questions include the fate of Cooper pairs in a localized superfluid and the effect of disorder on the superfluid transition temperature. We report progress on tackling this problem using a realization of the Hubbard model with attractive interactions. Our system consists of two spin states of fermionic potassium-40 trapped in a cubic optical lattice. Disorder is introduced using an optical speckle potential, and interactions are controlled via a Feshbach resonance. We study the binding and unbinding of Cooper pairs in this system using rf spectroscopy, changes in $T_c$ by measuring the condensate fraction, and transport properties by observing the response to an applied impulse. We will discuss progress towards these measurements.   

Quantum Engineering of a Low-Entropy Gas of Heteronuclear Bosonic Molecules in an Optical Lattice

We present a novel method to prepare low-entropy samples of heteronuclear molecules confined to an optical lattice as an ideal starting point for dipolar quantum gas experiments based on ultracold molecules.\footnote{arXiv:1607.06536} Starting from two spatially separated BECs we efficiently form Rb-Cs atom pairs by overlapping a Cs Mott insulator with a superfluid Rb sample in an optical lattice. For sample mixing the Rb-Cs interaction is nulled at a Feshbach resonance's zero crossing. Subsequently the Rb atoms are localized by increasing the lattice depth. The paired atoms are then associated to Feshbach molecules. With this method we obtain low-entropy molecular samples with a filling fraction exceeding 30\%. Our method can now be combined with stimulated ground-state transfer (STIRAP) to produce dense and low-entropy samples of dipolar ground-state molecules as demonstrated on our previous work.\footnote{Phys. Rev. Lett. 113, 205301 (2014)} Our preparation procedure compares favorably with recent results from the JILA group on fermionic KRb molecules.\footnote{Science 350 , 659 (2015)}   

Analysis of spontaneous emission of a lattice trapped atom into free space

It has been predicted \footnote{I. de Vega \textit{et al.}, Phys. Rev. Lett. \textbf{101}, 260404 (2008) } that an atom confined in an optical lattice well that is coupled to free space through an internal state transition can exhibit behavior analogous to that of spontaneous emission in a photonic band gap material. We have recently performed a detailed theoretical analysis of such a system in a 1D geometry, including the lattice- confined population evolution, the momentum distribution of the emitted matter waves, and the structure of an evanescent matter-wave state below the continuum boundary \footnote{ M. Stewart \textit{et al.}, Phys. Rev. A \textbf{ 95 }, 013626 (2017) }. We compare our results for the transition from Markovian to non-Markovian behaviors to those previously obtained for three dimensions, and propose an experimental realization of the system.   

Observing Spontaneous Emission Phenomena Using Lattice-Trapped Atoms Coupled to Free Space

It has been predicted that quantum optical models for spontaneous emission in photonic band gap materials can be realized with ultracold atomic systems\footnote{I. de Vega et. al, Phys. Rev. Lett. \textbf{101}, 260404, 2008; M. Stewart et. al, Phys. Rev. A \textbf{95}, 013626, 2017}. We experimentally implement such a scenario using ultracold Rb-87 atoms initially trapped in a state selective optical lattice. Coupling to a freely propagating internal state releases matter-waves (wave-continuum), while a populated/unpopulated lattice site simulates the excited/ground states of an ``artificial atom''. We present recent experimental results on the time evolution of the system, for which we find both Markovian as well as strongly non-Markovian dynamics. We characterize the momentum distribution of the emitted matter waves, for which we find close agreement with theoretical predictions. A careful analysis allows for an identification of the equivalent of a Lamb shift, and provides indirect evidence for the analog of the atom-photon bound state in photonic band gap materials.   

Bipolarons in one-dimensional extended Peierls-Hubbard models

We study two particles in an infinite chain and coupled to phonons by interactions that modulate their hopping as described by the Peierls/Su-Schrieffer-Heeger (SSH) model. In the case of hard-core bare particles, we show that exchange of phonons generates effective nearest-neighbor repulsion between particles and also gives rise to interactions that move the pair as a whole. The two-polaron phase diagram exhibits two sharp transitions, leading to light dimers at strong coupling and the flattening of the dimer dispersion at some critical values of the parameters. This dimer (quasi)self-trapping occurs at coupling strengths where single polarons are mobile. On the other hand, in the case of soft-core particles/ spinfull fermions, we show that phonon-mediated interactions are attractive and result in strongly bound and mobile bipolarons in a wide region of parameter space. This illustrates that, depending on the strength of the phonon-mediated interactions and statistics of bare particles, the coupling to phonons may completely suppress or strongly enhance quantum transport of correlated particles.   

Equilibration dynamics of a many-body quantum system across the superfluid to Mott insulator phase transition

We report on the center-of-mass motion of ultracold $^{87}$Rb atoms on displacing an underlying potential. The atoms are adiabatically loaded into an optical lattice superimposed onto an optical dipole trap. The CO$_2$ laser beam forming the dipole trap is then shifted by $1\,\mathrm{\mu m}$ which forces the system out of equilibrium. The subsequent motion of the atoms center-of mass is imaged with a scanning electron microscope for various depths of the optical lattice spanning the superfluid to Mott-insulator phase transition. The observed dynamics range from fast oscillations in the superfluid regime to a steady exponential movement towards the new equilibrium position for higher lattice depths. By piecewise analysis of the system, we can also identify a thermal phase at the edges which moves with velocities in between those of the superfluid and the insulating phase. We will present the experiment and the results of theoretical modelling currently in progress.   

Real-space renormalization group methods and the prospect of observing conformal Calabrese-Cardy scaling

Numerical real-space renormalization group methods have contributed greatly to understanding the phase structure of lattice models in both condensed matter physics and lattice gauge theory over the past few decades. Using two of these methods, the tensor renormalization group and the density matrix renormalization group, we consider the possibility of experimentally observing the conformal Calabrese-Cardy scaling, and measuring the conformal charge in the superfluid phase of the Bose-Hubbard model in one spatial dimension. We propose using existing experimental methods to measure the quantum purity, however we take a unique approach in that the ground state of the proposed experimental set-up is adiabatically prepared at relatively small J/U and at \emph{half-filling}.