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arXiv2014

Cavity-Assisted Dynamical Spin-Orbit Coupling in Cold Atoms

We consider ultracold atoms subjected to a cavity-assisted two-photon Raman transition. The Raman coupling gives rise to effective spin-orbit interaction which couples atom's center-of-mass motion to its pseudospin degrees of freedom. Meanwhile, the cavity photon is dynamically affected by the atom. This feedback between atom and photon leads to a dramatic modification of the atomic dispersion relation, and further leads to dynamical instability of the system. We propose to detect the change of cavity photon number as a direct way to demonstrate dynamical instability.

cond-mat.quant-gas↗

arXiv2014

Triangular Bose-Hubbard trimer as a minimal model for a superfluid circuit

The triangular Bose-Hubbard trimer is topologically the minimal model for a BEC superfluid circuit. As a dynamical system of two coupled freedoms it has mixed phase-space with chaotic dynamics. We employ a semiclassical perspective to study triangular trimer physics beyond the conventional picture of the superfluid-to-insulator transition. From the analysis of the Peierls-Nabarro energy landscape, we deduce the various regimes in the $(Ω,u)$ parameter-space, where $u$ is the interaction, and $Ω$ is the superfluid rotation-velocity. We thus characterize the superfluid-stability and chaoticity of the many-body eigenstates throughout the Hilbert space.

cond-mat.mes-hall↗

arXiv2013

Virial expansion of a harmonically trapped Fermi gas across a narrow Feshbach resonance

We theoretically investigate the high-temperature thermodynamics of a harmonically trapped Fermi gas across a narrow Feshbach resonance, by using the second-order quantum virial expansion, and point out some new features compared to the broad resonance. The interatomic interaction is modeled by the pseudopotential with an additional parameter, i.e., the effective range, to characterize the narrow resonance width. Deeply inside the width of a narrow Feshbach resonance, we find the second virial coefficient evolves with the effective range from the well-known universal value 1/4 in the broad-resonance limit to one another value 1/2 in the narrow-resonance limit. This means the Fermi gas is more strongly interacted at the narrow resonance. In addition, far beyond the resonance width, we find the harmonically trapped Fermi gas still manifests appreciable interaction effect across a narrow Feshbach resonance, which is contrary to our knowledge of the broad Feshbach resonance. All our results can be directly tested in current narrow Feshbach resonance experiments, which are generally carried out in a harmonic trap.

cond-mat.quant-gas↗

arXiv2014

Quantum phases of quadrupolar Fermi gases in coupled one-dimensional systems

Following the recent proposal to create quadrupolar gases [S.G. Bhongale et al., Phys. Rev. Lett. 110, 155301 (2013)], we investigate what quantum phases can be created in these systems in one dimension. We consider a geometry of two coupled one-dimensional systems, and derive the quantum phase diagram of ultra-cold fermionic atoms interacting via quadrupole-quadrupole interaction within a Tomonaga-Luttinger-liquid framework. We map out the phase diagram as a function of the distance between the two tubes and the angle between the direction of the tubes and the quadrupolar moments. The latter can be controlled by an external field. We show that there are two magic angles $θ^{c}_{B,1}$ and $θ^{c}_{B,2}$ between $0$ to $π/2$, where the intratube quadrupolar interactions vanish and change signs. Adopting a pseudo-spin language with regards to the two 1D systems, the system undergoes a spin-gap transition and displays a zig-zag density pattern, above $θ^{c}_{B,2}$ and below $θ^{c}_{B,1}$. Between the two magic angles, we show that polarized triplet superfluidity and a planar spin-density wave order compete with each other. The latter corresponds to a bond order solid in higher dimensions. We demonstrate that this order can be further stabilized by applying a commensurate periodic potential along the tubes.

cond-mat.quant-gas↗

arXiv2013

Phase-matching condition for enhanced entanglement of colliding indistinguishable quantum bright solitons in a harmonic trap

We investigate finite number effects in collisions between two states of an initially well defined number of identical bosons with attractive contact interactions, oscillating in the presence of harmonic confinement in one dimension. We investigate two $N/2$ atom bound states, which are initially displaced (symmetrically) from the trap center, and then left to freely evolve. For sufficiently attractive interactions, these bound states are like those found through use of the Bethe Ansatz (quantum solitons). However, unlike the free case, the integrability is lost due to confinement, and collisions can cause mixing into different bound state configurations. We study the system numerically for the simplest case of $N=4$, via an exact diagonalization of the Hamiltonian within a finite basis, investigating left/right number uncertainty as our primary measure of entanglement. We find that for certain interaction strengths, a phase matching condition leads to resonant transfer to different bound state configurations with highly non-Poissonian relative number statistics.

cond-mat.quant-gas↗

arXiv2014

Formulation for zero mode of Bose-Einstein condensate beyond Bogoliubov approximation

It is shown for the Bose-Einstein condensate of cold atomic system that the new unperturbed Hamiltonian, which includes not only the first and second powers of the zero mode operators but also the higher ones, determines a unique and stationary vacuum at zero temperature. From the standpoint of quantum field theory, it is done in a consistent manner that the canonical commutation relation of the field operator is kept. In this formulation, the condensate phase does not diffuse and is robust against the quantum fluctuation of the zero mode. The standard deviation for the phase operator depends on the condensed atom number with the exponent of $-1/3$, which is universal for both homogeneous and inhomogeneous systems.

cond-mat.quant-gas↗

arXiv2014

Goldstone modes and bifurcations in phase-separated binary condensates at finite temperature

We show that the third Goldstone mode, which emerges in binary condensates at phase-separation, persists to higher inter-species interaction for density profiles where one component is surrounded on both sides by the other component. This is not the case with symmetry-broken density profiles where one species is to entirely to the left and the other is entirely to the right. We, then, use Hartree-Fock-Bogoliubov theory with Popov approximation to examine the mode evolution at $T\neq0$ and demonstrate the existence of mode bifurcation near the critical temperature. The Kohn mode, however, exhibits deviation from the natural frequency at finite temperatures after the phase separation. This is due to the exclusion of the non-condensate atoms in the dynamics.

cond-mat.quant-gas↗

arXiv2014

Quantum Shock Waves and Population Inversion in Collisions of Ultracold Atomic Clouds

Using Time-Dependent Density Matrix Renormalization Group (TDMRG) we study the collision of one-dimensional atomic clouds confined in a harmonic trap and evolving with the Lieb-Liniger Hamiltonian. It is observed that the motion is essentially periodic with the clouds bouncing elastically, at least on the time scale of the first few oscillations that can be resolved with high accuracy. This is in agreement with the results of the "quantum Newton cradle" experiment of Kinoshita et al. [Nature 440, 900 (2006)]. We compare the results for the density profile against a hydrodynamic description, or generalized nonlinear Schrödinger equation, with the pressure term taken from the Bethe Ansatz solution of the Lieb-Liniger model. We find that hydrodynamics can describe the breathing mode of a harmonically trapped cloud for arbitrary long times while it breaks down almost immediately for the collision of two clouds due to the formation of shock waves (gradient catastrophe). In the case of the clouds' collision TDMRG alone allows to extract the oscillation period which is found to be measurably different from the breathing mode period. Concomitantly with the shock waves formation we observe a local energy distribution typical of population inversion, i.e., an effective negative temperature. Our results are an important step towards understanding the hydrodynamics of quantum many-body systems out of equilibrium and the role of integrability in their dynamics.

cond-mat.quant-gas↗

arXiv2013

Topological phases in small quantum Hall samples

Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to detect. One way to detect is via direct observation of anyonic properties of excitations which are usually discussed in the thermodynamic limit, but so far has not been realized in macroscopic quantum Hall samples. Here we consider a system of few interacting bosons subjected to the lowest Landau level by a gauge potential, and theoretically investigate vortex excitations in order to identify topological properties of different ground states. Our investigation demonstrates that even in surprisingly small systems anyonic properties are able to characterize the topological order. In addition, focusing on a system in the Laughlin state, we study the robustness of its anyonic behavior in the presence of tunable finite-range interactions acting as a perturbation. A clear signal of a transition to a different state is reflected by the system's anyonic properties.

cond-mat.quant-gas↗

arXiv2014

Route to observing topological edge modes in ultracold fermions

We show how to exploit the rich hyperfine structure of fermionic alkali atoms to produce a quasi-1D topological superfluid while avoiding excessive heating from off-resonant scattering. We model interacting fermions where four hyperfine states are coupled by a variety of optical and microwave fields. We calculate the local density of states in a trap, finding regimes with zero energy topological edge modes. Heating rates in this system are significantly suppressed compared to simple Raman-induced spin-orbit coupling approaches.

cond-mat.quant-gas↗

arXiv2014

Non-equilibrium topological phase transitions in two-dimensional optical lattices

Recently, concepts of topological phases of matter are extended to non-equilibrium systems, especially periodically driven systems. In this paper, we construct an example which shows non-equilibrium topological phase transitions using ultracold fermions in optical lattices. We show that the Rabi oscillation has the possibility to induce non-equilibrium topological phases which are classified into time-reversal-invariant topological insulators for a two-orbital model of alkaline-earth-metal atoms. Furthermore we study the non-equilibrium topological phases using time-dependent Schrieffer-Wolff-type perturbation theory, and we obtain an analytical expression to describe the topological phase transitions from a high-frequency limit of external driving fields.

cond-mat.quant-gas↗

arXiv2014

Two-species hard-core bosons on the triangular lattice: A quantum Monte Carlo study

Using worm-type quantum Monte Carlo simulations, we investigate bosonic mixtures on the triangular lattice of two species of bosons, which interact via nearest-neighbour intraspecies ($V$) and onsite interspecies ($U$) repulsions. For the case of symmetric hopping amplitude ($t_A/V=t_B/V$) and $U/V=1$, we determine a rich ground-state phase diagram that contains double solid, double superfluid (2SF), supersolid (SS), solid-superfluid (Solid-SF) and counterflow supersolid (CSS) states. The SS, Solid-SF and CSS states exhibit spontaneous symmetry breaking among the three sublattices of the triangular lattice and between the two species, which leads to nonzero crystalline density wave order in each species. We furthermore show that the CSS and the SS states are present for $t_A/V \neq t_B/V$, and the latter even survives up to $t_A/V \rightarrow \infty$ or $t_B/V \rightarrow \infty$ limit. The effects induced by the variation of $U/V$ and by the imbalance of particle numbers of the two species are also explored.

cond-mat.quant-gas↗

arXiv2014

Spin-Orbit Coupled One-Dimensional Fermi Gases with Infinite Repulsion

The current efforts of studying many-body effects with spin-orbit coupling (SOC) using alkali-metal atoms are impeded by the heating effects due to spontaneous emission. Here, we show that even for SOCs too weak to cause any heating, dramatic many-body effects can emerge in a one-dimensional(1D) spin 1/2 Fermi gas provided the interaction is sufficiently repulsive. For weak repulsion, the effect of a weak SOC (with strength $Ω$) is perturbative. inducing a weak spin spiral (with magnitude proportional to $Ω$). However, as the repulsion $g$ increases beyond a critical value ($g_c\sim 1/Ω$), the magnitude of the spin spiral rises rapidly to a value of order 1 (independent of $Ω$). Moreover, near $g=+\infty$, the spins of neighboring fermions can interfere destructively due to quantum fluctuations of particle motion, strongly distorting the spin spiral and pulling the spins substantially away from the direction of the local field at various locations. These effects are consequences of the spin-charge separation in the strongly repulsive limit. They will also occur in other 1D quantum gases with higher spins.

cond-mat.quant-gas↗

arXiv2013

Persistence of equilibrium states in an oscillating double-well potential

We investigate numerically parametrically driven coupled nonlinear Schrodinger equations modelling the dynamics of coupled wavefields in a periodically oscillating double-well potential. The equations describe among other things two coupled periodically-curved optical waveguides with Kerr nonlinearity or horizontally shaken Bose-Einstein condensates in a double-well magnetic trap. In particular, we study the persistence of equilibrium states of the undriven system due to the presence of the parametric drive. Using numerical continuations of periodic orbits and calculating the corresponding Floquet multipliers, we find that the drive can (de)stabilize a continuation of an equilibrium state indicated by the change of the (in)stability of the orbit. Hence, we show that parametric drives can provide a powerful control to nonlinear (optical or matter wave) field tunneling. Analytical approximations based on an averaging method are presented. Using perturbation theory the influence of the drive on the symmetry breaking bifurcation point is discussed.

cond-mat.quant-gas↗

arXiv2013

Inhomogeneities and impurities in a dense one-dimensional Rydberg lattice gas

We consider a dense one-dimensional laser-driven Rydberg lattice gas with perfect nearest-neighbor blockade. The ground state of this system can be found analytically in certain parameter regimes even when the applied fields are inhomogeneous in space. We will use this unique feature to investigate the effect of an impurity - introduced by the local variation of the laser parameters - on the correlations of the many-body ground state. Moreover, we explore the role of a staggered laser field which alternates from site to site thereby breaking the sublattice symmetry. We demonstrate that this technique, which can be applied experimentally, reveals insights into the role of long-range interactions on the critical properties of a Rydberg gas. Our work highlight novel possibilities for the exploration of many-body physics in Rydberg lattice gases based on locally tuneable laser fields.

cond-mat.quant-gas↗

arXiv2013

A nonlocal kinetic energy functional for an inhomogeneous two-dimensional Fermi gas

The average-density approximation is used to construct a nonlocal kinetic energy functional for an inhomogeneous two-dimensional Fermi gas. This functional is then used to formulate a Thomas-Fermi von Weizsäcker-like theory for the description of the ground state properties of the system. The quality of the kinetic energy functional is tested by performing a fully self-consistent calculation for an ideal, harmonically confined, two-dimensional system. Good agreement with exact results are found, with the number and kinetic energy densities exhibiting oscillatory structure associated with the nonlocality of the energy functional. Most importantly, this functional shows a marked improvement over the two-dimensional Thomas-Fermi von Weizsäcker theory, particularly in the vicinity of the classically forbidden region.

cond-mat.quant-gas↗

arXiv2014

Dynamical local and non-local Casimir atomic phases

We develop an open-system dynamical theory of the Casimir interaction between coherent atomic waves and a material surface. The system --- the external atomic waves --- disturbs the environment --- the electromagnetic field and the atomic dipole degrees of freedom --- in a non- local manner by leaving footprints on distinct paths of the atom interferometer. This induces a non-local dynamical phase depending simultaneously on two distinct paths, beyond usual atom-optics methods, and comparable to the local dynamical phase corrections. Non-local and local atomic phase coherences are thus equally important to capture the interplay between the external atomic motion and the Casimir interaction. Such dynamical phases are obtained for finite-width wavepackets by developing a diagrammatic expansion of the disturbed environment quantum state.

quant-ph↗

arXiv2014

Nonlinear quantum dynamics in a PT-symmetric double well

We investigate the mean-field dynamics of a Bose-Einstein condensate (BEC) described by the Gross-Pitaevskii equation (GPE) in a double-well potential with particle gain and loss, rendering the system PT-symmetric. The stationary solutions of the system show a change from elliptically stable behavior to hyperbolically unstable behavior caused by the appearance of PT-broken solutions of the GPE and influenced by the nonlinear interaction. The dynamical behavior is visualized using the Bloch sphere formalism. However, the dynamics is not restricted to the surface of the sphere due to the nonlinear and non-Hermitian nature of the system.

quant-ph↗