Degenerate Bose Gas Research Articles

Bragg spectroscopy of discrete axial quasiparticle modes in a cigar-shaped degenerate Bose gas

We propose an experiment in which long wavelength discrete axial quasiparticle modes can be imprinted in a 3D cigar-shaped Bose-Einstein condensate by using two-photon Bragg scattering experiments, similar to the experiment at the Weizmann Institute [J. Steinhauer {\em et al.}, Phys. Rev. Lett. {\bf 90}, 060404 (2003)] where short wavelength axial phonons with different number of radial modes have been observed. We provide values of the momentum, energy and time duration of the two-photon Bragg pulse and also the two-body interaction strength which are needed in the Bragg scattering experiments in order to observe the long wavelength discrete axial modes. These discrete axial modes can be observed when the system is dilute and the time duration of the Bragg pulse is long enough.

Strongly Inhibited Transport of a Degenerate 1D Bose Gas in a Lattice

We report the observation of strongly damped dipole oscillations of a quantum degenerate 1D atomic Bose gas in a combined harmonic and optical lattice potential. Damping is significant for very shallow axial lattices (0.25 photon recoil energies), and increases dramatically with increasing lattice depth, such that the gas becomes nearly immobile for times an order of magnitude longer than the single-particle tunneling time. Surprisingly, we see no broadening of the atomic quasimomentum distribution after damped motion. Recent theoretical work suggests that quantum fluctuations can strongly damp dipole oscillations of a 1D atomic Bose gas, providing a possible explanation for our observations.

Vortices in spatially inhomogeneous superfluids

We study vortices in a radially inhomogeneous superfluid, as realized by a trapped degenerate Bose gas in a uniaxially symmetric potential. We show that, in contrast to a homogeneous superfluid, an off-axis vortex corresponds to an anisotropic superflow whose profile strongly depends on the distance to the trap axis. One consequence of this superflow anisotropy is vortex precession about the trap axis in the absence of an imposed rotation. In the complementary regime of a finite prescribed rotation, we compute the minimum-energy vortex density, showing that in the rapid-rotation limit it is extremely uniform, despite a strongly inhomogeneous (nearly) Thomas-Fermi condensate density $\rho_s(r)$. The weak radially-dependent contribution ($\propto \nabla^2\ln\rho_s(r)$) to the vortex distribution, that vanishes with the number of vortices $N_v$ as $\frac{1}{N_v}$, arises from the interplay between vortex quantum discretness (namely their inability to faithfully support the imposed rigid-body rotation) and the inhomogeneous superfluid density. This leads to an enhancement of the vortex density at the center of a typical concave trap, a prediction that is in quantitative agreement with recent experiments (cond-mat/0405240). One striking consequence of the inhomogeneous vortex distribution is an azimuthally-directed, radially-shearing superflow.

Coexistence of two Bose–Einstein condensates of two-dimensional magnetoexcitons. Exciton-plasmon collective elementary excitations

Possibility of the Bose–Einstein condensation of magnetic excitons in an ideal two-dimensional system in a strong perpendicular magnetic field is investigated theoretically taking into account the influence of virtual transitions to the excited Landau levels and Anderson-type coherent excited states. It was understood, that the Bose–Einstein condensed (BEC-ed) magnetoexcitons with considerable wave vector K and motional dipole moment Kl 2, where l is the magnetic length, can form the droplets of the metastable dielectric liquid phase, whereas the BEC-ed magnetoexcitons with K =0 can form a stable degenerate Bose-gas surrounding the droplet. We have shown that collective elementary excitations of the BEC of excitons are mixed with plasma oscillations of the electron–hole system in the presence of strong perpendicular magnetic field. Their mutual influence is determined by the coherence factor and essentially depends on the condensate wave vector K.

Vortex lattice inhomogeneity in spatially inhomogeneous superfluids

A trapped degenerate Bose gas exhibits superfluidity with spatially nonuniform superfluid density. We show that the vortex distribution in such a highly inhomogeneous rotating superfluid is nevertheless nearly uniform. The inhomogeneity in vortex density, which diminishes in the rapid-rotation limit, is driven by the discrete way vortices impart angular momentum to the superfluid. This effect favors highest vortex density in regions where the superfluid density is most uniform (e.g., the center of a harmonically trapped gas). A striking consequence of this is that the boson velocity deviates from a rigid-body form exhibiting a radial-shear flow past the vortex lattice.

Compression experiments with 2D atomic hydrogen gas on liquid He

We review experiments in which atomic hydrogen has been compressed magnetically or thermally to become a degenerate two-dimensional Bose gas on the surface of liquid helium.

Hyperbolicity in Extended Thermodynamics of Fermi and Bose gases

We consider the balance system of Extended Thermodynamics with 13 Moments in the case of Fermi and Bose gases, for processes not far from equilibrium. In this case, the hyperbolicity of the differential system holds only in a neighborhood of the equilibrium state. The main aim of the paper is to evaluate the hyperbolicity region of the differential system. The knowledge of this region in the state variables is mandatory to check the admissibility of the solutions and the corresponding boundary and Cauchy data in the limit of the approximation considered. The results are obtained through numerical evaluations of the Fermi and Bose integral functions \(I^{\pm}_{n}(\alpha)\) that appear in the characteristic polynomial. Particular attention is devoted to the completely degenerate case when Fermi gas reaches the 0 K and when the Bose gas is in proximity of the transition temperature Tc. In these limiting cases, the hyperbolicity requirement is lost according to previous results. In the last section we make use of the Maxwellian iteration in order to evaluate the heat conductivity and the viscosity for the degenerate Fermi and Bose gas.

Simple theoretical tools for low dimension Bose gases

We first consider an exactly solvable classical field model to understand the coherence properties and the density fluctuations of a one-dimensional (1D) weakly interacting degenerate Bose gas with repulsive interactions at temperatures larger than the chemical potential. In a second part, using a lattice model for the quantum field, we explain how to carefully generalize the usual Bogoliubov approach to study a degenerate and weakly interacting Bose gas in 1D, 2D or 3D in the regime of weak density fluctuations. In the last part, using the mapping to an ideal Fermi gas in second quantized formalism, we calculate and discuss physically the density fluctuations and the coherence properties of a gas of impenetrable bosons in 1D.

Nonlinear quantization of a degenerate charged Bose gas in an external Coulomb trap

We consider a degenerate charged Bose-Coulomb gas populating several discrete stationary boson bound states that are located in a spherical-symmetrical central Coulombian potential. Each such state is defined, through appropriate boundary conditions and normalization, by a so-called ``nonlinear eigenstate'' that is actually a solution of the coupled (linear) stationary Schr\"odinger-like Gross-Pitaevskii differential equation and the (nonlinear) Poisson equation. The corresponding eigenvalues allow us to define the energies of these degenerate boson states, much like the Koopmans orbital energy in atomic physics. This theory applies surprisingly well (compared with the corresponding Hartree-Fock results) to spherical-symmetrical $s$ orbital states in atomic physics (i.e., bosonlike restricted orbital states where the additional spin degree of freedom is already integrated out). Finally the superposition of two such stationary nonlinear eigenstates is investigated and given a semiclassical physical significance similar to a Thomas-Fermi approach. The resulting concepts apply particularly well (namely within an average 1% error bar with respect to spectroscopic data) to the $1{s}^{2}\text{\penalty1000-\hskip0pt}2{s}^{2}$ orbital states of the $3\ensuremath{\leqslant}Z\ensuremath{\leqslant}9$ atomic subsystems.

Observation of reduced three-body recombination in a correlated 1D degenerate Bose gas.

We investigate the correlation properties of a one-dimensional interacting Bose gas by loading a magnetically trapped 87Rb Bose-Einstein condensate (BEC) into a deep two-dimensional optical lattice. We measure the three-body recombination rate for both the BEC in the magnetic trap and the BEC loaded into the optical lattice. The recombination rate coefficient is a factor of 7 smaller in the lattice, which we interpret as a reduction in the local three-body correlation function in the 1D case. This is a signature of correlation intermediate between that of the uncorrelated, phase coherent, 1D, mean-field regime and the strongly correlated Tonks-Girardeau regime.

Degenerate exciton gases and macroscopic ordering in coupled quantum-well systems

Bound electron–hole pairs—excitons—are Bose particles with small mass. Quantum degeneracy of exciton gases and eventually exciton Bose–Einstein condensation is expected to occur at a few Kelvin—a temperature many orders of magnitude higher than for atoms. Experimentally, an exciton temperature well below 1 K is achieved in coupled quantum well semiconductor nanostructures. In this contribution, we briefly review experiments revealing bosonic stimulation of exciton scattering, which is a signature of a degenerate Bose-gas of excitons. Experiments with exciton rings in the photoluminescence patterns of excitons and macroscopically ordered exciton state are also presented.

Superfluidity of the 1D Bose gas

We have investigated the superfluid properties of a ring of weakly interacting and degenerate 1D Bose gas at thermal equilibrium with a rotating vessel. The conventional definition of superfluidity predicts that the gas has a significant superfluid fraction only in the Bose condensed regime. In the opposite regime, it is found that a superfluid behaviour can still be identified when the probability distribution of the total momentum of the gas has a multi-peaked structure, revealing unambiguously the existence of ‘superfluid’ supercurrent states that did not show up in the conventional definition of superfluidity. To cite this article: I. Carusotto, Y. Castin, C. R. Physique 5 (2004).

Exciting collective oscillations in a trapped 1D gas.

We report on the realization of a trapped one-dimensional Bose gas and its characterization by means of measuring its lowest lying collective excitations. The quantum degenerate Bose gas is prepared in a 2D optical lattice, and we find the ratio of the frequencies of the lowest compressional (breathing) mode and the dipole mode to be (omega(B)/omega(D))(2) approximately 3.1, in accordance with the Lieb-Liniger and mean-field theory. For a thermal gas we measure (omega(B)/omega(D))(2) approximately 4. By heating the quantum degenerate gas, we have studied the transition between the two regimes. For the lowest number of particles attainable in the experiment the kinetic energy of the system is similar to the interaction energy, and we enter the strongly interacting regime.

Two-component Bose gas in an optical lattice at single-particle filling

The Bose-Hubbard model of a two-fold degenerate Bose gas is studied in an optical lattice with one particle per site and virtual tunneling to empty and doubly-occupied sites. An effective Hamiltonian for this system is derived within a continued-fraction approach. The ground state of the effective model is studied in mean-field approximation for a modulated optical lattice. A dimerized mean-field state gives a Mott insulator whereas the lattice without modulations develops long-range correlated phase fluctuations due to a Goldstone mode. This result is discussed in comparison with the superfluid and the Mott-insulating state of a single-component hard-core Bose.

Condensation and pattern formation in cold exciton gases

AbstractExcitons are Bose particles with small mass. Exciton Bose–Einstein condensation is expected to occur at a few degrees Kelvin. Experimentally, an exciton temperature well below 1 Kelvin is achieved in coupled quantum wells (CQWs). In this contribution, we review briefly experiments that show a strong enhancement of the exciton scattering rate with increasing exciton concentration revealing bosonic stimulation of exciton scattering, which is a signature of a degenerate Bose‐gas of excitons. Novel experiments with exciton condensation in potential traps, pattern formation in exciton system and macroscopically ordered exciton state are also reviewed briefly.

Extension of Bogoliubov theory to quasicondensates

We present an extension of the well-known Bogoliubov theory to treat low dimensional degenerate Bose gases in the limit of weak interactions and low density fluctuations. We use a density-phase representation and show that a precise definition of the phase operator requires a space discretisation in cells of size $l$. We perform a systematic expansion of the Hamiltonian in terms of two small parameters, the relative density fluctuations inside a cell and the phase change over a cell. The resulting macroscopic observables can be computed in one, two and three dimensions with no ultraviolet or infrared divergence. Furthermore this approach exactly matches Bogoliubov's approach when there is a true condensate. We give the resulting expressions for the equation of state of the gas, the ground state energy, the first order and second order correlations functions of the field. Explicit calculations are done for homogeneous systems.

Schemes for loading a Bose Einstein condensate into a two-dimensional dipole trap

We propose two loading mechanisms of a degenerate Bose gas into a surface trap. This trap relies on the dipole potential produced by two evanescent optical waves far detuned from the atomic resonance, yielding a strongly anisotropic trap with typical frequencies 40 Hz × 65 Hz × 30 kHz. We present numerical simulations based on the time-dependent Gross–Pitaevskii equation of the transfer process from a conventional magnetic trap into the surface trap. We show that, despite a large discrepancy between the oscillation frequencies along one direction in the initial and final traps, a loading time of a few tens of milliseconds would lead to an adiabatic transfer. Preliminary experimental results are presented.

Peierls instability of the quasi-one-dimensional Bose–Fermi mixed gas

The mixtures of quantum degenerate Bose and Fermi gases in highly anisotropic traps at zero temperature are studied. It is found that under some conditions the system becomes unstable with respect to the spontaneous formation of the collective mode with wave vector 2 k F ( k F is a Fermi wave vector) by exploring the Bogoliubov phonon spectrum. This type of instability is the analogue of Peierls instability in quasi-one-dimensional conductors.

How should the dynamics of an interacting degenerate Bose gas be described?

We show how a semiclassical representation of the atomic field may describe the interacting base gas at finite temperatures.

Towards Bose-Einstein condensation of excitons in potential traps.

An exciton is an electron-hole bound pair in a semiconductor. In the low-density limit, it is a composite Bose quasi-particle, akin to the hydrogen atom. Just as in dilute atomic gases, reducing the temperature or increasing the exciton density increases the occupation numbers of the low-energy states leading to quantum degeneracy and eventually to Bose-Einstein condensation (BEC). Because the exciton mass is small--even smaller than the free electron mass--exciton BEC should occur at temperatures of about 1 K, many orders of magnitude higher than for atoms. However, it is in practice difficult to reach BEC conditions, as the temperature of excitons can considerably exceed that of the semiconductor lattice. The search for exciton BEC has concentrated on long-lived excitons: the exciton lifetime against electron-hole recombination therefore should exceed the characteristic timescale for the cooling of initially hot photo-generated excitons. Until now, all experiments on atom condensation were performed on atomic gases confined in the potential traps. Inspired by these experiments, and using specially designed semiconductor nanostructures, we have collected quasi-two-dimensional excitons in an in-plane potential trap. Our photoluminescence measurements show that the quasi-two-dimensional excitons indeed condense at the bottom of the traps, giving rise to a statistically degenerate Bose gas.