Phase Separation in Bose-Fermi-Fermi Mixtures as a Probe of Fermi Superfluidity

We study the phase diagram of a mixture of Bose-Einstein condensate and a two-component Fermi gas. In particular, we identify the regime where the homogeneous system becomes unstable against phase separation. We show that, under proper conditions, the phase separation phenomenon can be exploited as a robust probe of Fermi superfluid

BCS-BEC crossover in a strongly correlated Fermi gas

We study the BCS-BEC crossover in the strongly correlated regime of an ultra-cold rotating two component Fermi gas. Strong correlations are shown to generate an additional long-range interaction which results in a modified crossover region compared to the non-rotating situation. The two-particle correlation function reveals a smooth crossover between the s-wave paired fermionic fractional quantum Hall state and the bosonic Laughlin state.Comment: 4 pages, 3 figure

Finite-Temperature Study of Bose-Fermi Superfluid Mixtures

Ultra-cold atom experiments offer the unique opportunity to study mixing of different types of superfluid states. Our interest is in superfluid mixtures comprising particles with different statistics- Bose and Fermi. Such scenarios occur naturally, for example, in dense QCD matter. Interestingly, cold atomic experiments are performed in traps with finite spatial extent, thus critically destabilizing the occurrence of various homogeneous phases. Critical to this analysis is the understanding that the trapped system can undergo phase separation, resulting in a unique situation where phase transition in either species (bosons or fermions) can overlap with the phase separation between possible phases. In the present work, we illustrate how this intriguing interplay manifests in an interacting 2-species atomic mixture - one bosonic and another fermionic with two spin components - within a realistic trap configuration. We further show that such interplay of transitions can render the nature of the ground state to be highly sensitive to the experimental parameters and the dimensionality of the system.Comment: 9 pages, 7 figures; Accepted for publication in Phys. Rev.

Unconventional Spin Density Waves in Dipolar Fermi Gases

The conventional spin density wave (SDW) phase (Overhauser, 1962), as found in antiferromagnetic metal for example (Fawcett 1988), can be described as a condensate of particle-hole pairs with zero angular momentum, $\ell=0$, analogous to a condensate of particle-particle pairs in conventional superconductors. While many unconventional superconductors with Cooper pairs of finite $\ell$ have been discovered, their counterparts, density waves with non-zero angular momenta, have only been hypothesized in two-dimensional electron systems (Nayak, 2000). Using an unbiased functional renormalization group analysis, we here show that spin-triplet particle-hole condensates with $\ell=1$ emerge generically in dipolar Fermi gases of atoms (Lu, Burdick, and Lev, 2012) or molecules (Ospelkaus et al., 2008; Wu et al.) on optical lattice. The order parameter of these exotic SDWs is a vector quantity in spin space, and, moreover, is defined on lattice bonds rather than on lattice sites. We determine the rich quantum phase diagram of dipolar fermions at half-filling as a function of the dipolar orientation, and discuss how these SDWs arise amidst competition with superfluid and charge density wave phases.Comment: 5 pages, 3 figure

Signatures of Strong Correlations in One-Dimensional Ultra-Cold Atomic Fermi Gases

Recent success in manipulating ultra-cold atomic systems allows to probe different strongly correlated regimes in one-dimension. Regimes such as the (spin-coherent) Luttinger liquid and the spin-incoherent Luttinger liquid can be realized by tuning the inter-atomic interaction strength and trap parameters. We identify the noise correlations of density fluctuations as a robust observable (uniquely suitable in the context of trapped atomic gases) to discriminate between these two regimes. Finally, we address the prospects to realize and probe these phenomena experimentally using optical lattices.Comment: 4 pages, 2 figure

A hemispherical, high-solid-angle optical micro-cavity for cavity-QED studies

We report a novel hemispherical micro-cavity that is comprised of a planar integrated semiconductor distributed Bragg reflector (DBR) mirror, and an external, concave micro-mirror having a radius of curvature $50\mathrm{\mu m}$. The integrated DBR mirror containing quantum dots (QD), is designed to locate the QDs at an antinode of the field in order to maximize the interaction between the QD and the cavity. The concave micro-mirror, with high-reflectivity over a large solid-angle, creates a diffraction-limited (sub-micron) mode-waist at the planar mirror, leading to a large coupling constant between cavity mode and QD. The half-monolithic design gives more spatial and spectral tuning abilities, relatively to fully monolithic structures. This unique micro-cavity design will potentially enable us to both reach the cavity quantum electrodynamics (QED) strong coupling regime and realize the deterministic generation of single photons on demand.Comment: 15 pages, 17 figures, final versio

Bond order solid of two-dimensional dipolar fermions

Recent experimental realization of dipolar Fermi gases near or below quantum degeneracy provides opportunity to engineer Hubbard-like models with long range interactions. Motivated by these experiments, we chart out the theoretical phase diagram of interacting dipolar fermions on the square lattice at zero temperature and half filling. We show that in addition to p-wave superfluid and charge density wave order, two new and exotic types of bond order emerge generically in dipolar fermion systems. These phases feature homogeneous density but periodic modulations of the kinetic hopping energy between nearest or next-nearest neighbors. Similar, but manifestly different, phases of two-dimensional correlated electrons have previously only been hypothesized and termed "density waves of nonzero angular momentum". Our results suggest that these phases can be constructed flexibly with dipolar fermions, using currently available experimental techniques.Comment: 5 pages, 3 figures, supplementary material also included; to appear in Phys. Rev. Lett. (in press

Analytic models of ultra-cold atomic collisions at negative energies for application to confinement-induced resonances

We construct simple analytic models of the $S$-matrix, accounting for both scattering resonances and smooth background contributions for collisions that occur below the s-wave threshold. Such models are important for studying confinement-induced resonances such as those occurring in cold collisions of $^{133}$Cs atoms in separated sites of a polarization-gradient optical lattice. Because these resonances occur at negative energy with respect to the s-wave threshold, they cannot be studied easily using direct numerical solutions of the Schr\"{o}dinger equation. Using our analytic model, we extend previous studies of negative-energy scattering to the multichannel case, accounting for the interplay of Feshbach resonances, large background scattering lengths, and inelastic processes.Comment: 9 page

Stationary quantum statistics of a non-Markovian atom laser

We present a steady state analysis of a quantum-mechanical model of an atom laser. A single-mode atomic trap coupled to a continuum of external modes is driven by a saturable pumping mechanism. In the dilute flux regime, where atom-atom interactions are negligible in the output, we have been able to solve this model without making the Born-Markov approximation. The more exact treatment has a different effective damping rate and occupation of the lasing mode, as well as a shifted frequency and linewidth of the output. We examine gravitational damping numerically, finding linewidths and frequency shifts for a range of pumping rates. We treat mean field damping analytically, finding a memory function for the Thomas-Fermi regime. The occupation and linewidth are found to have a nonlinear scaling behavior which has implications for the stability of atom lasers.Comment: 12 pages, 2 figures, submitted to PR