Session S50: Strongly Interacting Bose and Fermi Gases

P-wave contacts for two dimensional quatum gas

The s-wave contact has played an important role in our understanding of the strongly interacting Fermi gases. Recently, theoretical and experimental work has shown that two similar contacts exist for a p-wave interacting Fermi gas in three-dimensions. In this work, we extend the considerations to two dimensional spineless Fermi gas and derive exact results regarding the energy, momentum distributions and in particular, shifts of monopole frequency in a harmonic trap. Asymptotic formula for the frequency shift is given at high temperature via virial expansion and this can be checked by future experiments.   

Multi-Branch Spin Chain Models for Strongly interacting Spinor Fermi and Bose gases in One-Dimension

By mapping a 1D spinor Fermi or Bose gases wavefunction to a direct product of a spinless fermion wavefunction and a spin chain wavefunction, we obtain a spin-charge coupling Hamiltonian which is a multi-branch spin chain model. The charge part of this model are p-wave $\overleftarrow{\partial}\delta(x)\overrightarrow{\partial_{-}}$ interactions. The spin part of this model are spin parity projection operators. Previously obtained spin chain models (Nature Commun. {\bf 5}, 5300. Phys. Rev. A {\bf 90}, 013611. Phys. Rev. A {\bf 91}, 043634.) are first order perturbation of this multi-branch spin chain model. With this model, for particles in a harmonic trap in strongly interacting regime, we study breathing mode frequencies and the system's response to a spin dependent magnetic gradient and quench dynamics. We also studied the properties of the system with large particle numbers under local density approximation. The resulted spin chain models are studied by exact numerical methods such as Matrix Product States. Other than harmonic trap we also considered traps with $\delta(x)$ impurity, which can not be approximated by local density approximation.   

Efimov correlations in strongly interacting Bose gases

A series of recent hallmark experiments have demonstrated that Bose gases can be created in the strongly interacting unitary limit in the non-degenerate high-temperature regime. These systems display the three-body Efimov effect, which poses a theoretical challenge to compute observables including these relevant three-body correlations. In this talk, I shall present our results for the virial coefficients, the contact parameters, and the momentum distribution of a strongly interacting three-dimensional Bose gas obtained by means of a virial expansion up to third order in the fugacity, which takes into account three-body correlations exactly. Our results characterize the non-degenerate regime of the interacting Bose gas, where the thermal wavelength is smaller than the interparticle spacing but the scattering length may be arbitrarily large. In addition, we provide a calculation of the momentum distribution at unitarity, which displays a universal high-momentum tail with a log-periodic momentum dependence - a direct signature of Efimov physics. In particular, we provide a quantitative description of the momentum distribution at high momentum as measured by the JILA group [Makotyn et al., Nat. Phys. 10, 116 (2014)]. Our results allow the spectroscopy of Efimov states at unitarity.   

Competing order parameters in Fermi systems with engineered band dispersion

We explore a variety of competing phases in 2D and 3D Fermi gases in the presence of novel dispersion relations resulting from a shaken optical lattice. We incorporate spin imbalance along with attractive interactions. In 3D, at the mean field level we present phase diagrams reflecting the stability of alternative order parameters in the pairing (including LOFF) and charge density wave channels. We perform analogous studies in 2D, where we focus on the competition between different paired phases. Important in this regard is that our 2D studies [1] are consistent with the Mermin Wagner theorem, so that, while there is competition, conventional superfluidity cannot occur. [1] C.-T. Wu, B. M. Anderson, R. Boyack, and K. Levin, arXiv:1509.00857 (to be published in Phys. Rev. Lett.)   

Spectral function and dark continuum of the resonant Fermi Polaron

The Fermi polaron is an impurity interacting with a sea of fermions. It is an exemplary system to study impurity problems, strongly imbalanced Fermi gases and quasiparticles. Experiments probe its spectral function, which is directly linked to many physical properties. We present the first numerical results for the polaron spectral function with controlled error bars, obtained from first principles with diagrammatic Monte Carlo and analytic continuation. The spectral function exhibits a narrow ground state peak and another broad peak at positive energy, which are separated by a region of extremely low spectral weight. This "dark continuum" surprisingly starts to emerge in the absence a small parameter, around $k_Fa\sim 1$, and quickly broadens into a gap-like structure deeper on the BEC side. We confirm that the dark continuum is indeed physical and not an artefact of approximate calculations and establish a controlled upper bound on its integrated weight.   

Finite Temperature Response of a 2D Dipolar Bose Gas at Different Dipolar Tilt Angles

We calculate finite temperature (T) response of a 2D Bose gas, subject to dipolar interaction, within the random phase approximation (RPA). We evaluate the appropriate 2D finite-T pair bubble diagram needed in RPA, and explore ranges of density and temperature for various dipolar tilt angles. We find the system to exhibit a collapse transition and a finite momentum instability, signaling a density wave or striped phase. We construct phase diagrams depicting these instabilities and resulting phases, including a normal Bose gas phase. We also consider the finite-T response of a quasi-2D dipolar Bose gas. We discuss how our results may apply to ultracold dense Bose gas of polar molecules, such as ${^{41}}$K${^{87}}$Rb, that has been realized experimentally.   

Strengthening Supersolids with Disorder in the Extended Bose-Hubbard Model

The extended Bose-Hubbard model captures the essential properties of a wide variety of physical systems including ultracold atoms and molecules in optical lattices, Josephson junction arrays, and narrow band superconductors. It exhibits a rich phase diagram including a supersolid phase where a lattice solid coexists with a superfluid. We use quantum Monte Carlo to map out the phase diagram of the extended Bose-Hubbard model on the simple cubic lattice where the supersolid is expected. We find that the supersolid is very delicate because unexpected phase separated states compete with the supersolid. We add disorder to the extended Bose-Hubbard model and find that the supersolid phase is enhanced by disorder as phase separation is suppressed. Our results establish optimal regimes for observing supersolids and therefore have important implications for their observation.   

$p$-wave superfluid shells for trapped fermions with population imbalance

We present the phase diagram for a p-wave fermionic superfluid with imbalanced populations in a potential trap. We find shells of various superfluid phases, whose realization is determined by the parameters of a trap. In order to compute the resulting phase diagram, we use weak-coupling BCS theory together with the local density approximation in which the effect of the trapping potential is accounted for by a spatially inhomogeneous chemical potential. We compare our phase diagram with the one found for the trapped population imbalanced $s$-wave fermionic superfluid [Lin, Yi \& Duan, Phys. Rev. A 74, 031604R (2006)], and also point out key differences with results for the population imbalanced $p$-wave case in the absence of a trap [Liao, Popescu \& Quader, Phys. Rev. B 88, 134507 (2013)].   

Quantum Criticality of the Two-dimensional Bose Gas with the Lifshitz dispersion

Bosonic systems with the synthetic spin-orbit coupling and Zeeman field can be tuned into a quantum Lifshitz point exhibiting the q$^4$-dispersion. They are fundamentally different from the conventional ones with the q$^2$-dispersion, and are also connected to quantum frustrated magnets. We set up a generic quantum $\phi^4$-theory at the Lifshitz point and investigate quantum critical behaviors at both zero and finite temperatures following the perturbative renormalization group method. Controlled by different fixed points, various physical quantities exhibit significantly different scalings from those of the conventional bosonic systems, exhibiting rich quantum critical physics in different interaction and temperature ranges.   

Equation of state of ultracold fermions in the 2D BEC-BCS crossover

We report the experimental measurement of the equation of state of a two-dimensional Fermi gas with attractive s-wave interactions throughout the crossover from a weakly coupled Fermi gas to a Bose gas of tightly bound dimers as the interaction strength is varied. We demonstrate that interactions lead to a renormalization of the density of the Fermi gas by several orders of magnitude. We compare our data near the ground state and at finite temperature to predictions for both fermions and bosons from Quantum Monte Carlo simulations and Luttinger-Ward theory. Our results serve as input for investigations of close-to-equilibrium dynamics and transport in the two-dimensional system.   

Fluctuation theory of Rashba Fermi gases: Gaussian and beyond

Fermi gases with generalized Rashba spin orbit coupling induced by a synthetic gauge field have the potential of realizing many interesting states such as rashbon condensates and topological phases. Here we address the key open problem of the fluctuation theory of such systems and demonstrate that beyond-Gaussian effects are {\it essential} to capture finite temperature physics of such systems. We obtain their phase diagram by constructing an approximate non-Gaussian theory. We conclusively establish that spin-orbit coupling can enhance the exponentially small transition temperature ($T_c$) of a weakly attracting superfluid to the order of Fermi temperature, paving a pathway towards high $T_c$ superfluids.   

Superfluidity and BCS-BEC crossover of ultracold atomic Fermi gases in mixed dimensions

Atomic Fermi gases have been under active investigation in the past decade. Here we study the superfluid and pairing phenomena of a two-component ultracold atomic Fermi gas in the presence of mixed dimensionality, in which one component is confined on a 1D optical lattice whereas the other is free in the 3D continuum. We assume a short-range pairing interaction and determine the superfluid transition temperature $T_c$ and the phase diagram for the entire BCS-BEC crossover, using a pairing fluctuation theory which includes self-consistently the contributions of finite momentum pairs. We find that, as the lattice depth increases and the lattice spacing decreases, the behavior of $T_c$ becomes very similar to that of a population imbalance Fermi gas in a simple 3D continuum. There is no superfluidity even at $T=0$ below certain threshold of pairing strength in the BCS regime. Nonmonotonic $T_c$ behavior and intermediate temperature superfluidity emerge, and for deep enough lattice, the $T_c$ curve will split into two parts. Implications for experiment will be discussed. References: 1. Q.J. Chen, Ioan Kosztin, B. Janko, and K. Levin, Phys. Rev. B 59, 7083 (1999). 2. Chih-Chun Chien, Qijin Chen, Yan He, and K. Levin, Phys. Rev. Lett. 97, 090402(2006).   

Bose polarons in the strongly interacting regime.

Impurities immersed in and interacting with a Bose-Einstein condensate (BEC) are predicted to form quasiparticle excitations called Bose polarons. I will present experimental evidence of Bose polarons in cold atoms obtained using radio-frequency spectroscopy to measure the excitation spectrum of fermionic $^{\mathrm{40}}$K impurities interacting with a BEC of $^{\mathrm{87}}$Rb atoms. We use an interspecies Feshbach resonance to tune the interactions between the impurities and the bosons, and we take data in the strongly interacting regime.   

Self consistent theories of superfluid density and collective modes in BCS-BEC

Establishing fully self consistent and sum rule compatible response functions in strongly correlated Fermi superfluids has been a historically challenging subject. In this talk, we present recent progress pertaining to response functions in many-body Fermi systems. We note that even in strict BCS theory, the textbook derivation of density and current response functions in the gradient expansion breaks certain conservation laws such as the compressibility sum rule. To include additional contributions that preserve all expected conservation laws, we show how to exploit Ward identities within two different t-matrix schemes. In this way we address the density-density response (including collective modes) and the superfluid density. Finally, we characterize approximations made in the literature where some consistency requirements have been dropped.