Session R43: One Dimensional Bose Gases

Interference between fluctuating condensates

Two independent Bose condensates that are released from their traps and let to overlap produce a sharp interference pattern. How does this picture change if each condensate lacks true long range order? As an example we consider the interference between a pair of one dimensional interacting Bose liquids at low temperature. We show that the average fringe contrast scales as a universal function of the system size that depends only on the Luttinger parameter. Moreover the full distribution of the fringe contrast changes with interaction strength and lends information on high order correlation functions. We also demonstrate that the interference between two-dimensional condensates at finite temperature can be used as a direct probe of the Kosterlitz-Thouless transition.   

Bose-Einstein Condensation in low dimensionality

Using path integral Monte Carlo simulation methods[1], we have studied properties of Bose-Einstein Condensates harmonically trapped in low dimemsion. Each boson has a hard-sphere potential whose core radius equals its corresponding scattering length. We have tightly confined the motion of trapped particles in one or more direction by increasing the trap anisotropy in order to simulate lower dimensional atomic gases. We have investigated the effect of both the temperature and the dimemsionality on the energetics and structural properties such as the total energy, the density profile, and the superfluid fraction. Our results show that the physics of low dimensional bosonic systems is very different from that of their three dimensional counterparts[2]. The superfluid fraction for a quasi-2D boson gas decreases faster than that for both a quasi-1D system[3] and a true 3D system with increasing temperature. The superfluid fraction decreases gradually as the two-body interaction strength increases although it shows no noticable dependence for both a quasi-1D system and a true 3D system. \newline \noindent [1] K.~Nho and D.~P.~Landau, Phys. Rev. A. {\bf 70}, 53614 (2004).\\ \noindent [2] N.~D.~Mermin and H.~Wagner, Phys. Rev. Lett. {\bf 22}, 1133 (1966);\\ \noindent \hspace{1.5in}P.~C.~Hohenberg, Phys. Rev. {\bf 158}, 383 (1967).\\ \noindent [3] K.~Nho and D.~Blume, Phys. Rev. Lett. {\bf 95}, 193601 (2005).\\   

Path-Integral quantum Monte Carlo study of Bose-Einstein condensates under attractive interactions

A hard-core one-dimensional boson ring under attractive interactions is studied by using the path-integral quantum Monte Carlo method at low temperature. Condesate fraction, total energy, and angular pair correlation functions are obtained as a function of the interaction strength. Our simulation predicts a possible quantum phase transition from a uniform condensation state to a symmetry-broken cluster as the attractive interaction increases. The dependence of such a phase transition on temperature, hard-core size, and total number of particles in the system will be discussed.   

One Dimensional Gas of Bosons with Feshbach Resonant Interactions

We present a study of a gas of bosons confined in one dimension with Feshbach resonant interactions, at zero temperature. Unlike the gas of one dimensional bosons with non-resonant interactions, which is known to be equivalent to a system of interacting spinless fermions and can be described using the Luttinger liquid formalism, the resonant gas possesses novel features. Depending on its parameters, the gas can be in one of several regimes. In the most interesting of them, it is equivalent to a Luttinger liquid at low density only. At higher density its excitation spectrum develops a minimum, similar to the roton minimum in helium, at momenta where the excitations are in resonance with the Fermi sea. As the density of the gas is increased further, the minimum dips below the Fermi energy, thus making the ground state unstable. At this point the standard ground state gets replaced by a more complicated one, where not only the states with momentum below the Fermi points, but also the ones with momentum close to that minimum, get filled, and the excitation spectrum develops several branches.   

QMC study of the 1D boson Hubbard model with a superlattice potential

We use QMC simulations to explore the phase diagram of the Bose-Hubbard model with an additional superlattice potential. We first analyse the hard-core limit where an exact analytic treatment is possible, and then use QMC to solve the soft-core case and find the insulator/superfluid phase diagram as a function of potential strength and filling. These results are relevant to the behavior of cold atoms in optical superlattices which are beginning to be achieved experimentally.   

Quantum coherence of Hard Core Bosons and Fermions in one dimensional quasi-periodic potentials: superfluid, Mott and glassy phases

We use Hanbury- Brown-Twiss interferometry (HBTI) to characterize and contrast the different quantum phases exhibited by hard core bosons (HCBs) and ideal fermions confined in a one-dimensional quasi-periodic potential. In addition to the Bose-glass, superfluid and Mott insulator phases characteristic of interacting disordered bosons, we show the quasi-periodic potential induces a cascade of Mott-like band insulator transitions triggered by the fermion-type statistics of HCBs~. A comparative study of the fermion model shows that except for a sign difference, HCB and fermion interferometric patterns~coincide~in the localized phases. In the extended phase,~~however, fermions~behave quite differently~; ~their correlation functions reflect some of the multi-fractal properties characteristic of the metal-insulator transition. When plotted as a function of the filling factor, their quasi-momentum distribution displays an Arnold tongue-like structure and the HBTI peak intensity follows a step-like pattern which resembles a devil's staircase at the onset of the localization transition.   

Bose/Anderson glass and re-entrant superfluidity in strongly correlated bosons in a disordered optical lattice

We investigate the one-dimensional Bose-Hubbard model in presence of a random bimodal on-site chemical potential, modeling strongly correlated bosons in an optical lattice in presence of a second species of bosons randomly frozen in the minima of the optical potential [U. Gavish and Y. Castin, Phys. Rev. Lett. 95, 020401 (2005)]. Making use of quantum Monte Carlo simulations, we investigate both the strongly and the weakly interacting regime. In the strongly interacting case, superfluidity is found to be robust against disorder, due to effective screening of the disorder potential. Close to commensurate filling disorder is seen to promote superfluidity vs. Mott insulating behavior, leading to re-entrant superfluid order. Moreover the presence of disorder introduces a disordered Anderson-glass phase for small interparticle repulsion and a Bose-glass phase for large repulsion, separated by the superfluid phase. Clear signature of these phases are observed on realistic sizes ($\sim 60$ lattice sites) making the above scenario amenable to experimental realization.   

Bogoliubov Excitations and Superfluidity in a Kronig-Penney Potential

We study the elementary excitations of Bose-Einstein condensates in a Kronig-Penney potential. We solve the Bogoliubov equations analytically and obtain the band structure of the excitation spectrum. We show that the excitation spectrum is phononlike at low energies. It is found that the anomalous tunneling of low-energy excitations is crucial to the phonon dispersion, which is directly connected to the superfluidity of the condensate.   

Atomic Josephson Vortex

We show that atomic Josephson vortices [1] in a quasi-1D atomic junction can be controllably manipulated by imposing a tunneling bias current created by a difference of chemical potentials on the atomic BEC waveguides forming the junction. This effect, which has its origin in the Berry phase structure of a vortex, turns out to be very robust in the whole range of the parameters where such vortices can exist [2]. Acceleration of the vortex up to a certain threshold speed, determined by the strength of the Josephson coupling, results in the phase slip causing switching of the vorticity. This effect is directly related to the interconversion [1], when slow variation of the coupling can cause transformation of the vortex into the dark soliton and vice verse. We also propose that a Josephson vortex can be created by the phase imprinting technique and can be identified by a specific \textit{tangential} feature in the interference picture produced by expanding clouds released from the waveguides [2]. \newline \newline [1] V. M. Kaurov , A. B. Kuklov, Phys. Rev. A 71, 11601(R) (2005). \newline [2] V. M. Kaurov , A. B. Kuklov cond-mat/0508342