Session D4: Long-range Interacting Rydberg and Dipolar Gases

Rydberg-Rydberg interactions in ultracold atomic gases

The giant size and large polarizibility of Rydberg-atoms make them ideal to study many-body collective effects. We present recent results from the ultra-cold Rydberg experiments in our group. Firstly, we discuss studies of F\"orster resonances, which appear when two-body-states are tuned into resonance. The resulting strong dipolar interatomic interactions vary in strength and angular dependency based on the magnetic substates involved. We study these interactions in a Ramsey atom interferometer, where the two interferometer arms are atoms in the ground and in the Rydberg state. Using this phase sensitive tool, F\"orster resonances are studied with unprecedented accuracy. The coherent technique enables to resolve several resonances and study their coherence properties. Secondly, we present our new setup for studying single Rydberg-excitations in optical traps smaller than the Rydberg-blockade sphere. Such ensembles, where all trapped atoms coherently share a single Rydberg-excitation, form a two-level ``superatom" whose Rabi-oscillation is collectively enhanced. Our new apparatus combines single ion-detection, sub-micron optical resolution, and highly flexible optical trapping potentials to study coherent dynamics of individual superatoms as well as interactions between superatoms.   

Towards single-photon optical nonlinearities using cold Rydberg atoms

Effects of the Rydberg blockade in cold atomic clouds have been intensively explored over the last few years. Optical fields can be coherently mapped onto atomic states with a Rydberg component using EIT techniques thanks to the long lifetime of the Rydberg states. As the dipole-dipole interaction between Rydberg atoms prevents several polaritons from propagating simultaneously within a Rydberg volume, it gives rise to strong non-linearities which are mapped back on the probe optical field. We aim at bringing the Rydberg-EIT into the single-photon regime in order to produce non-classical highly correlated states of light. Rubidium atoms are loaded in a far off-resonant (1064nm) optical dipole trap, where densities are typically large enough to reach high optical depths within a single blockade volume. In this regime, the outcoming photon-photon correlation function is expected to exhibit highly non-classical behavior, corresponding to trains of spatially separated single-photons. Moreover, EIT techniques together with a high-resolution imaging system allow the observation of Rydberg excitations in the quasi-1D configuration, and should pave the way to in-situ monitoring of strongly correlated many-body states such as the crystallisation of Rydberg atoms.   

Altering Photon Statistics using Strong Rydberg Interactions

The recent advance in coherently controlling and manipulating strong, long-range Rydberg interactions has triggered extensive research in studying interesting many-body effects as, e.g. the use of Rydberg blockade effects for quantum information processing and crystal formation. In this talk I show that Rydberg interactions can be used to alter the photon statistics of a weak probe field after propagating in a coherently prepared atomic Rydberg gas under conditions of Electromagnetically Induced Transparency (EIT). The Rydberg blockade mechanism leads to an effective two-level physics when two photons are separated less than the blockade radius resulting in a strong anti-correlation of two photons separated by an avoided volume. Implications of the formation of such hard-sphere photons for the recent experiment of Pritchard et al. [Phys. Rev. Lett. 105, 193603 (2010)] and the observation of such correlation in future experiments will be discussed.   

Collective quantum jumps of Rydberg atoms

A quantum system under constant observation may occasionally switch between two metastable states. These quantum jumps are usually observed in a single object, like an atom, electron, or superconducting qubit. We report on a collective type of quantum jump in a group of atoms with long-range Rydberg interaction, laser driving, and spontaneous emission. Over time, the system occasionally jumps between a state of low Rydberg population and a state of high Rydberg population. The jumps are inherently collective and in fact exist only for a large number of atoms. We explain how entanglement and quantum measurement enable the jumps, which are otherwise classically forbidden.   

Quantum crystals in a trapped Rydberg-dressed Bose-Einstein condensate

Spontaneously crystalline ground states, called quantum crystals, of a trapped Rydberg-dressed Bose-Einstein condensate are numerically investigated. As a result described by a mean-field order parameter, such states simultaneously possess crystalline and superfluid properties. A hexagonal droplet lattice is observed in a quasi-two-dimensional system when dressing interaction is sufficiently strong. Onset of these states is characterized by a drastic drop of the non-classical rotational inertia proposed by Leggett [Phys. Rev. Lett. \textbf{25}, 1543 (1970)]. In addition, an AB stacking bilayer lattice can also be attained. Due to an anisotropic interaction possibly induced by an external electric field, transition from a hexagonal to a nearly square droplet lattice is also observed.   

Quantum Magnetism with Polar Molecules: Tunable Generalized $t$-$J$ Model

We show that dipolar interactions between ultracold polar molecules in optical lattices can be used to realize a highly tunable generalization of the $t$-$J$ model, which we refer to as the $t$-$J$-$V$-$W$ model. The ``spin" is encoded in the rotational degree of freedom of the molecules, while the interactions are controlled by applied static electric and continuous-wave microwave fields. We show that the tunability and the long-range nature of the interactions in the $t$-$J$-$V$-$W$ model enable enhanced superfluidity in one dimension and controllable preparation of robust d-wave superfluids in two dimensions. The latter may provide fundamental insights into high-temperature superconductivity. [References: Phys. Rev. Lett. 107, 115301 (2011); Phys. Rev. A 84, 033619 (2011); arXiv:1110.5330]   

Tunable Superfluidity with Ultracold Polar Molecules on quasi-1D Optical Lattices

By selecting two dressed rotational states of ultracold polar molecules on an optical lattice, strong electric dipole-dipole interactions allow to directly emulate spin Hamiltonians and a highly tunable generalization of the $t-J$ model, the $t-J-V-W$ model. We present the phase diagram of the simplest experimentally realizable case, the $t-J_\perp$ model with long-range dipolar spin-exchange interactions, on (quasi) one-dimensional chain and ladder systems as obtained from extensive density matrix renormalization group (DMRG) calculations. For the chain, we discuss the possible realization of unconventional quasi-long-range-order caused by the dipolar interactions. While the phase diagram of the dipolar $t-J_\perp$ chain is similar at low filling to that of the standard t-J chain, the superconducting region is strongly enhanced. We approach the ladder systems by coupling square plaquettes and comparing the numerical results to a mean-field description. We discuss the possibility to enhance superconductivity in these ladder systems by the presence of the dipolar interactions.   

Dynamical generation and detection of entangled quantum magnetic states in ultracold polar molecules

We show that \textit{existing} ultracold polar molecule experiments in optical lattices may generate strongly correlated many-body states by mimicking far-from-equilibrium dynamics of models of quantum magnetism. Recent theory shows that molecules' rotational states can emulate quantum spins with strong ($100$-$10,000$Hz) ``spin-spin" interactions. Applying external fields generates a zoo of models: spin-1/2 and larger Heisenberg and XXZ models, and well beyond. We consider the dynamics of the easily prepared fully polarized initial state for the XXZ case predicted to be realized in current experiments. Our analytic and DMRG calculations show that the dynamics can: (i) verify and characterize the spin model (XXZ) description of the system, (ii) generate interesting, entangled states (e.g., cat states, GHZ), and (iii) explore behavior where no quantitative theory is presently possible.   

Interactions of polar molecules dressed by far-off-resonant light: Entangled dipoles up- or down-holding each other

We show that the electric dipole-dipole interaction between a pair of polar molecules undergoes an all-out transformation when superimposed by a far-off resonant optical field. The combined interaction potential becomes tunable by variation of wavelength, polarization and intensity of the optical field and its dependence on the intermolecular separation exhibits a crossover from an inverse-power to an oscillating behavior. The ability thereby offered to control molecular interactions opens up avenues toward the creation and manipulation of novel phases of ultracold polar gases among whose characteristics is a long-range entanglement of the dipoles' mutual orientation. We devised an accurate analytic model of such optical-field-dressed dipole-dipole interaction potentials, which enables a straightforward access to the optical-field parameters required for the design of intermolecular interactions in the laboratory.   

Clustering of cold polar molecules in arrays of one-dimensional tubes

Cold polar molecules allow to study exciting new phenomena which arise from the long-range and anisotropic nature of their mutual interactions. Here, we demonstrate that a Wigner crystal of polar molecules confined in planar arrays of one-dimensional tubes can be made unstable with respect to the formation of clusters of particles. By controlling the orientation of the external electric field which aligns the dipolar moments, increasingly complex structures with a varying number of particles per cluster and thus varying periodicity are formed. The spatial agglomeration of multiple polar molecules results from the interaction and can be described classically. However, we show that the effect survives when quantum fluctuations are present. For systems of a finite number of tubes, the result is a sequence of ''clustered`` Luttinger liquid states. Finally, we determine the ratio between the interaction and the kinetic energy which is necessary for the spatial agglomeration of polar molecules. We find that the requirements for clustering are reachable in current experiments with cold polar molecules.   

A dielectric superfluid of polar molecules

We consider a Bose-Einstein condensate of heteronuclear molecules in an applied electric field. In the strong field regime, the molecules are fully polarized and produce fields that tend to be weak compared to the applied field. However, in weaker applied fields the internal fields due to the polarization of the molecules can become comparable to the applied field, and the system develops a dielectric character. We derive a set of self-consistent mean-field equations that couple the condensate density to its polarization field, leading to the emergence of polarization modes that are coupled to the quasiparticle spectrum of the condensate. While the roton instability is suppressed in this system, the coupling gives rise to a phonon-like instability that is characteristic of a dielectric material with a negative static dielectric function.   

Dipolar gases in two coupled one-dimensional lattices

We consider dipolar bosons in two tubes of one-dimensional lattices, where the boson filling fraction is the same in each tube and the dipoles are aligned to be maximally repulsive. In the classical limit of zero inter-site hopping, the bosons arrange themselves into an ordered crystal for any rational filling fraction, forming a complete devil's staircase like in the single tube case [1]. When we turn on hopping within each tube, we obtain a competition between the crystalline Mott phases and a superfluid of defects or solitons. However, in contrast to the single tube case [2], we find that solitons in different tubes can bind into pairs for certain topologies of the filling fraction. This provides an intriguing example of pairing that is purely driven by correlations close to a Mott insulator.\\[4pt] [1] P. Bak and P. Bruinsma, Phys. Rev. Lett. 49, 249 (1982)\\[0pt] [2] F. J. Burnell, M. M. Parish, N. R. Cooper and S. L. Sondhi, Phys. Rev. B, 80, 174519 (2009)   

Paired Phases of Dipoles in a Bilayer System

By means of large scale quantum Monte Carlo simulations we study a system of dipolar lattice bosons in bilayers geometries and with no hopping between layers. We investigate under which conditions pairing (e.g. paired superfluidity, paired supersolidity) is stabilized and make estimates for current experimental setups. We also study temperature effects and possible experimental signatures of such phases.   

Bond Order Solid of Two-Dimensional Dipolar Fermions

Cold atoms provide a promising platform to solve problems that, although computationally infeasible, are of immense importance to condensed matter physics and material science. Ultra-cold bosonic atoms have been quite successful in emulating the Bose-Hubbard model. Experiments are now underway towards mapping out the unknown phase diagram of the Fermi-Hubbard model. Recent experimental advances in cooling dipolar gases to quantum degeneracy provide an unprecedented opportunity to engineer Hubbard- like models with long range interactions. Here, with the aid of functional renormalization group technique, we show that two new and exotic types of order emerge generically in dipolar fermion systems: bond order solids of p- and d-wave symmetry. Similar, but manifestly different, phases of two-dimensional correlated electronic systems have previously only been hypothesized. Our results suggest that these phases can be constructed flexibly with dipolar fermions, using currently available experimental techniques, providing detectable experimental signatures.   

Re-entrant first-order phase transitions and anomalous hysteresis of dipolar Bose gases in a triangular optical lattice

We study the hysteresis behavior of dipolar Bose gases loaded into a triangular optical lattice. A large-size cluster mean-field approximation is applied to the corresponding extended Bose-Hubbard model to take into account metastable states. We find that the phase transition between supersolid (or solid) and superfluid states is always first-order except for the particle-hole symmetric point. In the phase diagram, the supersolid and solid phases are sandwiched in between the superfluid phase, and the system exhibits a re-entrant behavior from superfluid to solid (to supersolid), and back to superfluid with varying the chemical potential. Our most remarkable finding is that in the hysteresis accompanying this ``re-entrant'' first-order phase transition, the quantum melting transition from supersolid or solid to superfluid can occur while the reverse process is impossible since the superfluid phase remains locally stable for any value of the chemical potential. Moreover, the hysteresis curve of density versus chemical potential does not form a ``hysteresis-loop'' structure unlike the case of the conventional first-order transition. We show that this anomalous behavior of the hysteresis is a common property of systems exhibiting a re-entrant first-order phase transition.