Session Y4: Cold Quantum Gases in Reduced Dimensions

Tunneling-driven transitions in magnetization compressibility and density redistributions in a fermionic superfluid of cold atoms trapped in an array of one-dimensional tubes

We study two-species fermion gases with attractive interactions in optical lattices that are made as an array of one-dimensional tube confinements. With the decrease in lattice depth, we find that the increase in tunneling between tubes leads to an incompressible-compressible transition in magnetization. The role of pair tunneling is considered, as well as the experimental implications.   

Fermion Pairing in a One-Dimension Optical Lattice

Strongly correlated fermions in an array of two-dimensional planes coupled via tunneling serve as an important model system for high-temperature superconductors and layered organic conductors. We realize this model using ultracold fermionic $^6$Li atoms in a one-dimensional optical lattice near a Feshbach resonance. The depth of the lattice controls the interlayer coupling, and tunes the system between three and two dimensions. Pairing between fermions is studied using radio-frequency spectroscopy. The binding energy of fermion pairs is determined along the dimensional crossover and for different interaction strengths through the BEC-BCS crossover. Probes of superfluidity in the coupled layer system are also discussed.   

Entanglement-based perturbation theory for highly anisotropic Bose-Einstein condensates

We investigate the emergence of three-dimensional behavior in a reduced-dimension Bose-Einstein condensate trapped by a highly anisotropic potential. We handle the problem analytically by performing a perturbative Schmidt decomposition of the condensate wave function between the tightly confined direction(s) and the loosely confined direction(s). The perturbation theory is valid when the nonlinear scattering energy is small compared to the transverse energy scales. Our approach provides a straightforward way, first, to derive corrections to the transverse and longitudinal wave functions of the reduced-dimension approximation and, second, to calculate the amount of entanglement that arises between the transverse and longitudinal spatial directions. Numerical integration of the three-dimensional Gross-Pitaevskii equation for different cigar-shaped potentials and experimentally accessible parameters reveals good agreement with our analytical model even for relatively high nonlinearities. In particular, we show that even for such stronger nonlinearities the entanglement remains remarkably small, which allows the condensate to be well described by a product wave function that corresponds to a single Schmidt term.   

Phase Diagram of the Bose Hubbard Model with Weak Links

We study the ground state phase diagram of strongly interacting ultracold Bose gas in a one-dimensional optical lattice with a tunable weak link, by means of Quantum Monte Carlo simulation. This model contains an on-site repulsive interaction (U) and two different near-neighbor hopping terms, $J$ and $t$, for the weak link and the remainder of the chain, respectively. We show that by reducing the strength of $J$, a novel intermediate phase develops which is compressible and non-superfluid. This novel phase is identified as a Normal Bose Liquid (NBL) which does not appear in the phase diagram of the homogeneous bosonic Hubbard model. Further, we find a linear variation of the phase boundary of Normal Bose Liquid (NBL) to SuperFluid (SF) as a function of the strength of the weak link. These results may provide a new path to design advanced atomtronic devices in the future.   

The effective mass of ultracold atoms in one-dimensional optical lattices

According to the effective mass theorem, in the presence of an external force the wavepacket associated with a crystal electron in one band accelerates as a particle with an effective mass. However, when the force is turned on suddenly, the expectation value of the acceleration initially behaves according to the electron's bare mass, and afterwards oscillates around the value given by the usual effective mass.\footnote{D. Pfirsch and E. Spenke, Z. Physik \textbf{137}, 309 (1954).} These oscillations are difficult to measure in typical solid state systems because they decay after a time of the order of femtoseconds.\footnote{Y. M. Zhu, et al., phys. stat. sol. (c) \textbf{5}, 240 (2008).} We consider this oscillatory behaviour with ultracold atoms in a one-dimensional optical lattice where the time scale of the oscillations and the coherence times are much longer. Our theoretical analysis is based on a perturbation scheme that decouples the bands to any order in the external force.\footnote{G. H. Wannier, Phys. Rev. \textbf{117}, 432 (1960).} We check the validity of this perturbative approach, comparing its results with those obtained from a full numerical calculation. Experimental investigations are underway.\footnote{A. Steinberg, private communication.}   

Supercurrent decay via quantum nucleation of phase slips in one-dimensional lattice bosons

We study transport properties of one-dimensional (1D) Bose gases in a periodic potential. In 1D, superflow at zero temperature can decay via quantum nucleation of phase slips even when the flow velocity is much smaller than the critical velocity predicted by mean-field theories. We use instanton techniques to find that the decay rate $G$ is algebraically increases with the flow momentum $p$ as $G/L \propto p^{2K - 2}$, where $L$ is the system size, $K$ the Luttinger parameter. We also discuss the relation between the nucleation rate and the quantum superfluid-insulator transition in order to present a physical interpretation of the scaling formula.   

Compressibility and Entropy of One Dimensional Fermions in a combined Harmonic and Periodic Potential

We solve the homogeneous Hubbard model for repulsively interacting fermions using thermodynamic Bethe anzatz method. Treating the harmonic potential in local density approximation, we calculate particle density, various compressibilities, double occupancy, and entropy as a function of temperature and interaction. These quantities show characteristic features that can be used to detect temperature, metal-insulator transition, and coexistence of metallic and insulating phases.   

From GPE to KPZ: Finite temperature dynamical structure factor of the 1D Bose gas

Recent experiments on 1D Bose gases have raised interest in the investigation of dynamical properties at finite temperature such as the structure factor. For weak enough interaction and high enough temperature, we expect a classical description in terms of the Gross--Pitaevskii equation with thermally populated modes to be valid. Here, we present numerical results for the finite temperature dynamical structure factor and its universal anomalous scaling behavior, arising from resonant interactions between phonons. Our results are also relevant to sound damping in 1D classical fluids. Somewhat more surprisingly, there is a deep connection to systems in the Kardar--Parisi--Zhang universality class, describing growing fluctuating interfaces.   

Photoinduced phase transition in one dimensional extended Hubbard model

We illustrate one interesting example of the photoinduced phase transitions due to a nonequilibrium process. The impact of laser pump on one dimensional half-filled extended Hubbard model in the spin-density-wave (SDW) phase is investigated by using time-dependent density-matrix renormalization group. With proper laser frequencies and strengths, we find that charge-density wave (CDW) can be observed during the pulse. Further, in some situations, for instance, near the boundary between SDW and CDW in the ground state, the CDW signature can be sustained even after the pulse turned off. The underlying physics and possible experimental realization are discussed.   

Separation induced resonances in quasi-one-dimensional ultracold atomic gases

We study the effective one-dimensional (1D) scattering of two distinguishable atoms confined individually by {\it separated} transverse harmonic traps. With equal trapping frequency for two s-wave interacting atoms, we find that by tuning the trap separations, the system can undergo {\it double} 1D scattering resonance, named as the separation induced resonance(SIR), when the ratio between the confinement length and s-wave scattering length is within $(0.791,1.46]$. Near SIR, the scattering property shows unique dependence on the resonance position. Right at SIR, the universal property of a many-body system is manifested by studying the interaction effect of a localized impurity immersed in a Fermi sea of light atoms. The proposed SIR can be realized in cold atom experiment.   

Boson pairing and unusual criticality in a generalized XY model

Motivated by the physics of condensates of boson pairs, we study the generalized XY model in two dimension, which has a term proportional to cos(2 $\theta$) in addition to the normal XY Hamiltonian. This corresponds to having half vortices connected by solitons, as well as integer vortices. From both renormalization group analysis and Monte Carlo simulation using the worm algorithm, we find that the phase diagram includes Kosterlitz-Thouless transitions of half and integer vortices, together with an Ising transition. Remarkably, part of the Ising line is a direct transition from the quasi-long-ranged ordered state to the disordered state.   

Pairing and pseudogap for ultracold fermions in two dimensions

The T-matrix approach, straightforwardly applied to cold fermions in two dimensions, leads to a divergent fermion density for any finite temperature. We have shown that the Gaussian pair fluctuation theory, which is an improvement of the Nozi\`{e}res -- Schmitt-Rink approach, provides a convergent density in the paired fermion state. In our work, special attention is paid to the pseudogap state above the BKT transition temperature. In the pseudogap state, the modulus of the order parameter is finite, while phase coherence is absent. The pairing crossover temperature in 2D has been determined. Owing to the fluctuations, this pairing temperature is considerably lower than the mean-field critical temperature. With increasing coupling strength, the pairing temperature behaves non-monotonically reaching a maximum before decreasing to a finite value. For an imbalanced Fermi gas, the fluctuations lower the critical value of the imbalance at which the superfluid or non-coherent paired state is formed. This effect exists even at zero temperature, where only the quantum fluctuations survive. The obtained pairing temperatures and spectral functions are in fair agreement with recent experimental results on pairing of fermionic atoms in strongly anisotropic optical lattices.   

Excitation spectrum of two-dimensional cold fermionic gases in the dilute limit

Two-dimensional gases of fermionic atoms have been recently realized, and cooled down to temperatures a few tenths of the Fermi temperature. Such ultracold atom systems are ideal tools to investigate the fundamental properties of Fermi ensembles subject to short-range interactions. One of the key questions is whether the interaction changes the ground state and excitation spectrum in a non-perturbative way, or whether the weak-coupling perturbation theory and Fermi-liquid idea remain valid in two dimensions. In contrast to condensed-matter systems, in atomic gases the perturbation theory must be carried out at finite temperature and far from the Fermi surface for a meaningful comparison with experiment. We have calculated the electronic self-energy of dilute two-dimensional Fermi gases at arbitrary temperature and momentum, using the ladder approximation. This scheme is expected to become exact (in a perturbative sense) in the low-density limit. For short-range attractive interaction, we study the evolution of the excitation spectrum as a function of temperature and interaction strength, and we compare our results with recent experiments.