Session H4: Focus Session: Phases of Strongly Interacting Cold Gases

Thermodynamics of Quantum Gases

Ultracold dilute atomic gases can be considered as model systems to address some pending problem in Many-Body physics that occur in condensed matter systems, nuclear physics, and astrophysics. We have developed a general method to probe with high precision the thermodynamics of locally homogeneous ultracold Bose and Fermi gases [1,2,3]. This method allows stringent tests of recent many-body theories. For attractive spin 1/2 fermions with tunable interaction, we will show that the gas thermodynamic properties can continuously change from those of weakly interacting Cooper pairs described by Bardeen-Cooper-Schrieffer theory to those of strongly bound molecules undergoing Bose-Einstein condensation. First, we focus on the finite-temperature Equation of State (EoS) of the unpolarized unitary gas. Surprisingly, the low-temperature properties of the strongly interacting normal phase are well described by Fermi liquid theory and we localize the superfluid phase transition. A detailed comparison with theories including Monte-Carlo calculations has revealed some surprises and the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids are directly measured for the first time. Despite orders of magnitude difference in density and temperature, our equation of state can be used to describe low density neutron matter such as the outer shell of neutron stars.\\[4pt] [1] S. Nascimb\`ene, N. Navon, K. Jiang, F. Chevy, and C. Salomon, Nature 463, 1057 (2010)\\[0pt] [2] N. Navon, S. Nascimb\`ene, F. Chevy, and C. Salomon, Science 328, 729 (2010)\\[0pt] [3] N. Navon, S. Piatecki, K. G\"unter, B. Rem, T. C Nguyen, F. Chevy, W. Krauth, and C. Salomon, arXiv:1103.4449   

Revealing the superfluid phase transition in strongly interacting Fermi gases in a precision measurement of the equation of state

We perform a high-precision measurement of the equation of state (EOS) of a Fermi gas at unitarity by in-situ imaging of ultracold $^6$Li at a Feshbach resonance. The reconstructed local density distribution directly probes the EOS under the local density approximation. We extract the chemical potential and the temperature from low density regions via the virial expansion, and validate our method using the non-interacting Fermi gas. The experimental results are compared to recent Monte-Carlo calculations. We observe the superfluid transition in the chemical potential, entropy, compressibility and heat capacity, which display characteristic lambda-like features. We provide a new value of the Bertsch parameter $\xi_S$ and directly obtain the critical temperature from the EOS, validated via a condensate fraction measurement.   

Pair-Supersolidity of Dipoles in a Bilayer System

We perform quantum Monte Carlo simulations of a bilayer dipolar system with induced dipole moments perpendicular to the layers and no inter-layer hopping. We show that a pair-supersolid phase can be stabilized for both, soft-core and hard-core bosons, upon doping the checkerboard solid. We study the robustness of the paired-supersolid upon increasing temperature and varying dipolar interaction.   

Quantum phase transition to a twisted superfluid phase in hexagonal optical lattices

We report on the observation of a novel superfluid phase with complex superfluid order parameters in binary spin mixtures. In this novel phase, the local phase angle of the complex order parameter is continuously twisted between the neighboring sites of the hexagonal optical lattice. Commonly, superfluids in the ground-state can be described on a mean-field level by a real s-band order parameter. In contrast, the observed twisted superfluid quantum phase occurs due to an interaction-induced admixture of the p-orbital. The strong coupling with the p-orbital is induced by the combination of the graphene-like band structure and the state-dependency of the optical potential. We observe a second-order quantum phase transition between the normal and the twisted superfluid being triggered by the competition of inter- and intraspecies interactions. The phase transition is accompanied by the breaking of the six-fold rotational symmetry in momentum space. This allows for a sensitive detection of the novel superfluid phase using time-of-flight imaging. We present experimental results and calculated phase diagrams for different binary mixtures. These results pave the way towards a deeper understanding of orbital aspects in superfluidity.   

Review of Universal Relations for Fermions with Large Scattering Length

The behavior of fermions with two spin states that interact with a large scattering length is constrained by universal relations that hold for any state of the system. These relations involve a central property of the system called the contact, which measures the number of pairs of fermions with different spins that have small separations. The contact controls the thermodynamics of the system as well as the large-momentum and high-frequency tails of correlation functions. This review summarizes the current theoretical and experimental status of these universal relations.   

Study of the Lee-Huang-Yang correction for atomic bosons

The famous Lee-Huang-Yang (LHY) term describes the first-order correction to the mean-field energy for strongly interacting bosons [1], yet it has only been detected with bosons composed of loosely bound fermion pairs [2,3]. Tan's universal relations, originally calculated for fermions [4], connect a property called the Contact to many macroscopic parameters of a quantum gas, such as its total energy. These relations have been verified experimentally for Fermi systems [5]. We apply these relations to a Bose gas to realize a unique tool to study the LHY correction. We perform RF spectroscopy on a BEC of $^{85}$Rb close to a Feshbach resonance, and measure the strength of the RF lineshape tail which decays as 1/w$^{3/2}$. From this we extract the Contact, which increases as a function of the interaction strength. This allows us to quantitatively study the LHY term for atomic bosons, as well as investigate time-dependent effects that arise from the rate of change of the interaction strength compared to various experimental time scales.   

Coherent dynamics and topological phases with ultracold atoms

Ultracold atoms and ions have the potential to answer several long-standing questions about many-particle physics. The first part of this talk discusses coherent quantum dynamics in many-particle systems, focusing on the role of integrability and using the quantum Ising model recently created in ion trap experiments as an example. We discuss universal scaling near quantum phase transitions, including the emergence of a remarkable spectrum of massive particles near the quantum Ising critical point as predicted by Zamolodchikov years ago, and the role of disorder and ``many-body localization.'' The second part of this talk discusses using the tunability of atoms in optical lattices to realize topological phases, including the recently discovered topological insulators in time-reversal invariant systems. Topological phases contain a type of order that is quite different from conventional symmetry breaking. The topological phases that have been experimentally confirmed to exist in condensed matter all have an energy gap in bulk but gapless edge or surface excitations. We review the origin of this behavior and discuss how ultracold atomic systems could bring new understanding to the study of topological phases.