Superfluid Bose Gas Research Articles

Local atom-number fluctuations in quantum gases at finite temperature

We investigate the number fluctuations in small cells of quantum gases pointing out important deviations from the thermodynamic limit fixed by the isothermal compressibility. Both quantum and thermal fluctuations in weakly as well as highly compressible fluids are considered. For the two-dimensional (2D) superfluid Bose gas we find a significant quenching of fluctuations with respect to the thermodynamic limit, in agreement with recent experimental findings. An enhancement of the thermal fluctuations is instead predicted for the 2D dipolar superfluid Bose gas, which becomes dramatic when the size of the sample cell is of the order of the wavelength of the rotonic excitation induced by the interaction.

Second sound and the density response function in uniform superfluid atomic gases

Recently, there has been renewed interest in second sound in superfluid Bose and Fermi gases. By using two-fluid hydrodynamic theory, we review the density response χnn(q, ω) of these systems as a tool to identify second sound in experiments based on density probes. Our work generalizes the well-known studies of the dynamic structure factor S(q, ω) in superfluid 4He in the critical region. We show that, in the unitary limit of uniform superfluid Fermi gases, the relative weight of second versus first sound in the compressibility sum rule is given by the Landau–Placzek ratio for all temperatures below Tc. In contrast to superfluid 4He, ϵLP is much larger in strongly interacting Fermi gases, being already of order unity for T∼0.8Tc, thereby providing promising opportunities to excite second sound with density probes. The relative weights of first and second sound are quite different in S(q, ω) (measured in pulse propagation studies) as compared with Imχnn(q, ω) (measured in two-photon Bragg scattering). We show that first and second sound in S(q, ω) in a strongly interacting Bose-condensed gas are similar to those in a Fermi gas at unitarity. However, in a weakly interacting Bose gas, first and second sound are mainly uncoupled oscillations of the thermal cloud and condensate, respectively, and second sound has most of the spectral weight in S(q, ω). We also discuss the behaviour of the superfluid and normal fluid velocity fields involved in first and second sound.

Superfluid Bose gas in two dimensions

We investigate Bose-Einstein condensation for ultracold bosonic atoms in two-dimensional systems. The functional renormalization group for the average action allows us to follow the effective interactions from molecular scales (microphysics) to the characteristic extension of the probe $l$ (macrophysics). In two dimensions the scale dependence of the dimensionless interaction strength $\ensuremath{\lambda}$ is logarithmic. Furthermore, for large $l$ the frequency dependence of the inverse propagator becomes quadratic. We find an upper bound for $\ensuremath{\lambda}$, and for large $\ensuremath{\lambda}$ substantial deviations from the Bogoliubov results for the condensate depletion, the dispersion relation and the sound velocity. The melting of the condensate above the critical temperature ${T}_{c}$ is associated to a phase transition of the Kosterlitz-Thouless type. The critical temperature in units of the density ${T}_{c}∕n$ vanishes for $l\ensuremath{\rightarrow}\ensuremath{\infty}$ logarithmically.

Vortices and Persistent Currents: Rotating a Bose-Einstein Condensate Using Photons with Orbital Angular Momentum

We describe the coherent transfer of the orbital angular momentum of a photon to an atom in quantized units of ℏ, using a 2-photon stimulated Raman process with Laguerre-Gaussian beams to generate an atomic vortex state in a Bose-Einstein condensate (BEC) of sodium atoms. We show that the process is coherent by creating superpositions of different vortex states, where the relative phase between the states is determined by the relative phases of the optical fields. We use this technique to generate circular flow of a BEC confined in a toriodal shaped trap. We measure that the flow of atoms persists for up to 10 seconds, which we interpret as the first evidence of persistent currents in a superfluid Bose gas.

Nonlinear Schrödinger equation for a superfluid Bose gas from weak coupling to unitarity: Study of vortices

We introduce a nonlinear Schr\"odinger equation to describe the dynamics of a superfluid Bose gas in the crossover from the weak-coupling regime, where $a{n}^{1/3}\ensuremath{\ll}1$ with $a$ the interatomic $\mathit{s}$-wave scattering length and $n$ the bosonic density, to the unitarity limit, where $a\ensuremath{\rightarrow}+\ensuremath{\infty}$. We call this equation the unitarity Schr\"odinger equation (USE). The zero-temperature bulk equation of state of this USE is parametrized by the Lee-Yang-Huang low-density expansion and Jastrow calculations at unitarity. With the help of the USE we study the profiles of quantized vortices and vortex-core radius in a uniform Bose gas. We also consider quantized vortices in a Bose gas under cylindrically symmetric harmonic confinement and study their profile and chemical potential using the USE and compare the results with those obtained from the Gross-Pitaevskii-type equations valid in the weak-coupling limit. Finally, the USE is applied to calculate the breathing modes of the confined Bose gas as a function of the scattering length.

Critical Velocities in Two-Component Superfluid Bose Gases

On the ground of the Landau criterion we study the behavior of critical velocities in a superfluid two-component Bose gas. It is found that under motion of the components with different velocities the velocity of each component should not be lower than a minimum phase velocity of elementary excitations (s −). The Landau criterion yields a relation between the critical velocities of the components (v c1, v c2). The velocity of one or even both components may exceed s −. The maximum value of the critical velocity of a given component can be reached when the other component does not move. The approach is generalized for a two-component condensate confined in a cylindrical harmonic potential.

Thermodynamics of a Bose-Einstein condensate with weak disorder

We consider the thermodynamics of a homogeneous superfluid dilute Bose gas in the presence of weak quenched disorder. Following the zero-temperature approach of Huang and Meng, we diagonalize the Hamiltonian of a dilute Bose gas in an external random delta-correlated potential by means of a Bogoliubov transformation. We extend this approach to finite temperature by combining the Popov and the many-body T-matrix approximations. This approach permits us to include the quasi-particle interactions within this temperature range. We derive the disorder-induced shifts of the Bose-Einstein critical temperature and of the temperature for the onset of superfluidity by approaching the transition points from below, i.e., from the superfluid phase. Our results lead to a phase diagram consistent with that of the finite-temperature theory of Lopatin and Vinokur which was based on the replica method, and in which the transition points were approached from above.

Generating persistent currents states of atoms using orbital angular momentum of photons

We describe the coherent transfer of the orbital angular momentum of a photon to an atom in quantized units of \hbar, using a 2-photon stimulated Raman process with Laguerre-Gaussian beams to generate an atomic vortex state in a Bose-Einstein condensate (BEC) of sodium atoms. We show that the process is coherent by creating superpositions of different vortex states, where the relative phase between the states is determined by the relative phases of the optical fields. We use this technique to generate circular flow of a BEC confined in a toroidal shaped trap. We measure that the flow of atoms persists for up to 10 seconds, which we interpret as the first evidence of persistent currents in a superfluid Bose gas.

Instability of a superfluid Bose gas induced by a locked thermal gas in an optical lattice

We use a dissipative Gross–Pitaevskii equation derived from the Bose–Hubbard Hamiltonian to study the effect of the thermal component on the stability of a current-carrying superfluid state of a Bose gas in an optical lattice potential. We explicitly show that the superfluid state becomes unstable at certain quasi-momentum of the condensate due to a thermal component which is locked by an optical lattice potential. It is shown that this instability coincides with the Landau instability derived from the GP equation.

Itinerant-localized dual character of a strongly correlated superfluid Bose gas in an optical lattice

We investigate a strongly-correlated Bose gas in an optical lattice. Extending the standard-basis operator method developed by Haley and Erdos to a boson Hubbard model, we calculate excitation spectra in the superfluid phase, as well as in the Mott insulating phase, at T=0. In the Mott phase, the excitation spectrum has a finite energy gap, reflecting the localized character of atoms. In the superfluid phase, the excitation spectrum is shown to have an itinerant-localized dual structure, where the gapless Bogoliubov mode (which describes the itinerant character of superfluid atoms) and a band with a finite energy gap coexist. We also show that the rf-tunneling current measurement would give a useful information about the duality of a strongly-correlated superfluid Bose gas near the superfluid-insulator transition.

Nondissipative drag of superflow in a two-component Bose gas

A microscopic theory of a non-dissipative drag in a two-component superfluid Bose gas is developed. The expression for the drag current in the system with the components of different atomic masses, densities and scattering lengths is derived. It is shown that the drag current is proportional to the square root of the gas parameter. The temperature dependence of the drag current is studied and it is shown that at temperature of order or smaller than the interaction energy the temperature reduction of the drag current is rather small. A possible way of measuring the drag factor is proposed. A toroidal system with the drag component confined in two half-ring wells separated by two Josephson barriers is considered. Under certain condition such a system can be treated as a Bose-Einstein counterpart of the Josephson charge qubit in an external magnetic field. It is shown that the measurement of the difference of number of atoms in two wells under a controlled evolution of the state of the qubit allows to determine the drag factor.

“Cosmological” quasiparticle production in harmonically trapped superfluid gases

We show that a variety of cosmologically motivated effective quasiparticle space-times can be produced in harmonically trapped superfluid Bose and Fermi gases. We study the analogue of cosmological particle production in these effective space-times, induced by trapping potentials and coupling constants possessing an arbitrary time dependence. The WKB probabilities for phonon creation from the superfluid vacuum are calculated, and an experimental procedure to detect quasiparticle production by measuring density-density correlation functions is proposed.

On Vortices Induced in Superfluid Films by Crossed Electric and Magnetic Fields

The behaviour of a superfluid Bose-gas in crossed electric E and magnetic H fields is studied. It is shown that in the case when the two-dimensional divergence div2[E×H] differs from zero, the crossed fields induce the appearance of quantized vortex threads in the electroneutral superfluid system.

Crossover from BCS superconductivity to Bose-Einstein condensation: A self-consistent theory

A dilute three-dimensional Fermi liquid is considered with an instantaneous attractive short-range interaction. Two sets of self-consistent equations for the temperature dependent fermion Greens functiong and the four-point vertex function Γ are derived by field theoretic means. The interaction is taken into account using the results of low energys-wave scattering theory. The crossover region between BCS superconductivity and Bose-Einstein condensation of tightly bound pairs is located near the threshold where in the two-particle scattering problem a virtual or quasi-stationary state turns into a bound state. We show how from our self-consistent equations the BCS theory and the theory of a superfluid Bose gas can be recovered in the weak and strong coupling limit, respectively. In the strong coupling limit we find that there is a repulsive interaction between the composite bosons due to the Pauli exclusion principle. It is described by a positive scattering lengtha B which is twice the scattering length of the fermions,a B =2a F . Furthermore we find that this interaction reduces the Bose-Einstein transition temperature to leading order by ΔT c /T c, BE =−(k F a F )3/3π. We show that most of the previous theories of the crossover scenario can be obtained from our theory in mean-field approximation neglecting self consistency.