Dilute Atomic Gases Research Articles

Exploring quantum matter with ultracold atoms in optical lattices

Seventy years after Einstein's prediction, the seminal achievement of Bose–Einstein condensation in dilute atomic gases in 1995 has provided us with a new form of quantum matter. Such quantum matter can be described as a single giant matter wave. By loading it into an artificial periodic potential formed by laser light—a so-called optical lattice—it has become possible to probe matter far beyond the wave-like description. In a review of a series of experiments with ultracold quantum gases in optical lattices, we show that the granularity of the matter wave field, caused by the discreteness of atoms, gives rise to effects going beyond the simple single matter wave description. Bose–Einstein condensates in optical lattices have thereby opened novel possibilities for investigating strongly correlated many-particle phenomena of condensed matter physics and have opened new opportunities for quantum information processing with neutral atoms

Microscopic description of the twist mode in normal and superfluid trapped Fermi gases

We investigate the ``twist'' mode (rotation of the upper against the lower hemisphere) of a dilute atomic Fermi gas in a spherical trap. The normal and superfluid phases are considered. The linear response to this external perturbation is calculated within the microscopic Hartree-Fock-Bogoliubov approach. In the normal phase the excitation spectrum is concentrated in a rather narrow peak very close to the trapping frequency. In the superfluid phase the strength starts to be damped and fragmented and the collectivity of the mode is progressively lost when the temperature decreases. In the weak-pairing regime some reminiscence of the collective motion still exists, whereas in the strong-pairing regime the twist mode is completely washed out. The disappearance of the twist mode in the strong-pairing regime with decreasing temperature is interpreted in the framework of the two-fluid model.

Amplification of light in a dilute-gas Bose-Einstein condensate

A semiclassical theory is proposed to describe the light amplification in a Bose—Einstein condensate of a dilute atomic gas observed in [1]. Atomic states with well-defined momenta are taken as a basis of wave functions to derive the Maxwell—Bloch equations for the model of a dilute gas of atoms interacting with electromagnetic field. The evolution of light intensity and populations of coherent atomic states with different recoil momenta is described by solving these equations. The solutions obtained are used to demonstrate theoretically the effects observed in [1].

Effective photon-photon interaction in a two-dimensional “photon fluid”

We formulate an effective theory for the atom-mediated photon-photon interactions in a two-dimensional ``photon fluid'' confined in a Fabry-Perot resonator. With the atoms modelled by a collection of anharmonic Lorentz oscillators, the effective interaction is evaluated to second order in the coupling constant (the anharmonicity parameter). The interaction has the form of a renormalized two-dimensional delta-function potential, with the renormalization scale determined by the physical parameters of the system, such as density of atoms and the detuning of the photons relative to the resonance frequency of the atoms. For realistic values of the parameters, the perturbation series has to be resummed, and the effective interaction becomes independent of the ``bare'' strength of the anharmonic term. The resulting expression for the non-linear Kerr susceptibility, is parametrically equal to the one found earlier for a dilute gas of two-level atoms. Using our result for the effective interaction parameter, we derive conditions for the formation of a photon fluid, both for Rydberg atoms in a microwave cavity and for alkali atoms in an optical cavity.

Cold asymmetrical fermion superfluids

In this work we investigate the general properties and the ground state of an asymmetrical dilute gas of cold fermionic atoms, formed by two particle species having different densities. We have show in a recent paper, that a mixed phase composed of normal and superfluid components is the energetically favored ground state of such a cold fermionic system. Here we extend the analysis and verify that in fact, the mixed phase is the preferred ground state of an asymmetrical superfluid in various situatiations. We predict that the mixed phase can serve as a way of detecting superfluidity and estimating the magnitude of the gap parameter in asymmetrical fermionic systems.

Oscillations of Bose-Einstein condensates with vortex lattices: Finite temperatures

We derive the finite temperature oscillation modes of a harmonically confined Bose-Einstein condensed gas undergoing rigid body rotation supported by a vortex lattice in the condensate. The hydrodynamic modes separate into two classes corresponding to in-phase (center-of-mass) and counter-phase (relative) oscillations of the thermal cloud and the condensate. The in- and counter-phase oscillations are independent of each other in the case where the thermal cloud is inviscid for all modes studied, except the radial pulsations which couple them because the pressure perturbations of the condensate and the thermal cloud are governed by different adiabatic indices. If the thermal cloud is viscous, the two classes of oscillations are coupled, i.e. each type of motion involves simultaneously mass and entropy currents. The counter-phase oscillations are damped by the mutual friction between the condensate and the thermal cloud mediated by the vortex lattice. The damping is large for the values of the drag-to-lift ratio of the order of unity and becomes increasingly ineffective in either limit of small or large friction. An experimental measurement of a subset of these oscillation modes and their damping rates can provide information on the values of the phenomenological mutual friction coefficients, and hence the quasiparticle-vortex scattering processes in dilute atomic Bose gases.

Effective theory of Feshbach resonances and many-body properties of Fermi gases.

For calculating low-energy properties of a dilute gas of atoms interacting via a Feshbach resonance, we develop an effective theory in which the parameters that enter are an atom-molecule coupling strength and the magnetic moment of the molecular resonance. We demonstrate that, for resonances in the fermionic systems 6Li and 40K that are under experimental investigation, the coupling is so strong that many-body effects are appreciable even when the resonance lies at an energy large compared with the Fermi energy. We calculate a number of many-body effects, including the effective mass and the lifetime of atomic quasiparticles in the gas.

Topology-induced spatial Bose–Einstein condensation for bosons on star-shaped optical networks

New coherent states may be induced by pertinently engineering the topology of a network. As an example, we consider the properties of non-interacting bosons on a star network, which may be realized with a dilute atomic gas in a star-shaped deep optical lattice. The ground state is localized around the star centre and it is macroscopically occupied below the Bose–Einstein condensation temperature Tc. We show that Tc depends only on the number of the star arms and on the Josephson energy of the bosonic Josephson junctions and that the non-condensate fraction is simply given by the reduced temperature T/Tc.

From the superfluid to the Mott regime and back: triggering a non-trivial dynamics in an array of coupled condensates

We consider a system formed by an array of Bose–Einstein condensates trapped in a harmonic potential with a superimposed periodic optical potential. Starting from the boson field Hamiltonian, appropriate to describe a dilute gas of bosonic atoms, we reformulate the system dynamics within the Bose–Hubbard model scenario. Then we analyse the effective dynamics of the system when the optical-potential depth is suddenly varied according to a procedure applied in many of the recent experiments on superfluid–Mott transition in Bose–Einstein condensates. Initially the condensate array generated in a weak optical potential is assumed to be in the superfluid ground state which is well described in terms of coherent states. At a given time, the optical-potential depth is suddenly increased and, after a waiting time, it is quickly decreased so that the initial depth is restored. We compute the system-state evolution and show that the potential jump brings on an excitation of the system, incorporated in the final condensate wavefunctions, whose effects are analysed in terms of two-site correlation functions and of on-site population oscillations. Also we show how too long a waiting time can destroy completely the coherence of the final state, making it unobservable.

Vortices and novel superfluids in dilute atomic gases

In this paper, we present a review of some recent progress in the study of vortices in dilute Bose gases and in the search for superfluidity in dilute Fermi gases. In particular, we focus on Bose gases rotated at a stirring frequency close to the trap frequency. In this case, a hole appears in the center of the Bose condensed cloud. We propose a scheme to investigate the topological properties of this hole and show that using interferometry a distinction can be made between a density suppression without vorticity, a single giant vortex or a vortex conglomerate, and the merging of vortices can be studied.

On the theory of superradiant scattering of light from a Bose-Einstein condensate of dilute atomic gases

The theory of superradiant scattering of light from a Bose-Einstein condensate of a dilute atomic gas, which was earlier proposed by one of the authors, is used to study the spectral-kinetic characteristics of scattered radiation and the evolution of populations of coherent atomic states.

Gases bosônicos armadilhados

O espectro dos modos coerentes para gás atômico de Bose diluído, confinado em uma armadilha harmônica não isotrópica é determinado e utiliza-se da teoria de perturbação otimizada e a técnica das raízes aproximantes auto-similares. As expressões obtidas são válidas para níveis de energia arbitrários de todos os modos coerentes excitados. Este artigo deve ser utilizado como ponto de início para os alunos que querem se aprofundar no tema de condensação de Bose-Einstein atualmente presente em quase todos periódicos de Física.

Bose–Einstein condensation in a CO2-laser optical dipole trap

We report on the achieving of Bose-Einstein condensation of a dilute atomic gas based on trapping atoms in tightly confining CO_2-laser dipole potentials. Quantum degeneracy of rubidium atoms is reached by direct evaporative cooling in both crossed and single beam trapping geometries. At the heart of these all-optical condensation experiments is the ability to obtain high initial atomic densities in quasistatic dipole traps by laser cooling techniques. Finally, we demonstrate the formation of a condensate in a field insensitive m_F=0 spin projection only. This suppresses fluctuations of the chemical potential from stray magnetic fields.

Emergence of a molecular Bose-Einstein condensate from a Fermi gas.

The realization of superfluidity in a dilute gas of fermionic atoms, analogous to superconductivity in metals, represents a long-standing goal of ultracold gas research. In such a fermionic superfluid, it should be possible to adjust the interaction strength and tune the system continuously between two limits: a Bardeen-Cooper-Schrieffer (BCS)-type superfluid (involving correlated atom pairs in momentum space) and a Bose-Einstein condensate (BEC), in which spatially local pairs of atoms are bound together. This crossover between BCS-type superfluidity and the BEC limit has long been of theoretical interest, motivated in part by the discovery of high-temperature superconductors. In atomic Fermi gas experiments superfluidity has not yet been demonstrated; however, long-lived molecules consisting of locally paired fermions have been reversibly created. Here we report the direct observation of a molecular Bose-Einstein condensate created solely by adjusting the interaction strength in an ultracold Fermi gas of atoms. This state of matter represents one extreme of the predicted BCS-BEC continuum.

ENERGY SPECTRUM AND SUPERFLUID-MOTT INSULATOR PHASE TRANSITION OF ULTRACOLD BOSONS IN OPTICAL LATTICE

Green function metheod is introduced to investigate ultracold dilute gas of bosonic atoms in an optical lattice which can be described by a Bose–Hubbard model. The superfluid–Mott insulator phase transition condition is determined by the related energy-band structure with an obvious interpretation of the transition mechanism.

Optical detection of fractional particle number in an atomic Fermi-Dirac gas.

We study theoretically a Fermi-Dirac atomic gas in a one-dimensional optical lattice coupled to a coherent electromagnetic field with a topologically nontrivial soliton phase profile. We argue that the resulting fractional eigenvalues of the particle number operator can be detected via light scattering. This could be a truly quantum mechanical measurement of particle number fractionalization in a dilute atomic gas.

Quantum phase transition of condensed bosons in optical lattices

In this paper we study the superfluid--Mott-insulator phase transition of ultracold dilute gas of bosonic atoms in an optical lattice by means of Green function method and Bogliubov transformation as well. The superfluid--Mott-insulator phase transition condition is determined by the energy-band structure with an obvious interpretation of the transition mechanism. Moreover the superfluid phase is explained explicitly from the energy spectrum derived in terms of Bogliubov approach.

Quantum dynamics of a single vortex.

Vortices occur naturally in a wide range of gases and fluids, from macroscopic to microscopic scales. In Bose-Einstein condensates of dilute atomic gases, superfluid helium and superconductors, the existence of vortices is a consequence of the quantum nature of the system. Quantized vortices of supercurrent are generated by magnetic flux penetrating the material, and play a key role in determining the material properties and the performance of superconductor-based devices. At high temperatures the dynamics of such vortices are essentially classical, while at low temperatures previous experiments have suggested collective quantum dynamics. However, the question of whether vortex tunnelling occurs at low temperatures has been addressed only for large collections of vortices. Here we study the quantum dynamics of an individual vortex in a superconducting Josephson junction. By measuring the statistics of the vortex escape from a controllable pinning potential, we demonstrate the existence of quantized levels of the vortex energy within the trapping potential well and quantum tunnelling of the vortex through the pinning barrier.

Large amplitude spin waves in ultra-cold gases

We discuss the theory of spin waves in non-degenerate ultra-cold gases, and compare various methods which can be used to obtain appropriate kinetic equations. We then study non-hydrodynamic situations, where the amplitude of spin waves is sufficiently large to bring the system far from local equilibrium. The full position and momentum dependence of the distribution function must then be retained. In the first part of the article, we compare two general methods which can be used to derive a kinetic equation for a dilute gas of atoms (bosons or fermions) with two internal states (treated as a pseudo-spin 1/2). The collisional methods are in the spirit of Boltzmann's original derivation of his kinetic equation where, at each point of space, the effects of all sorts of possible binary collisions are added. We discuss two different versions of collisional methods, the Yvon-Snider approach and the S matrix approach. The second method uses the notion of mean field, which modifies the drift term of the kinetic equation, in the line of the Landau theory of transport in quantum liquids. For a dilute cold gas, it turns out that all these derivations lead to the same drift terms in the transport equation, but differ in the precise expression of the collision integral and in higher order gradient terms. In the second part of the article, the kinetic equation is applied to spin waves (or internal conversion) in trapped ultra-cold gases. Numerical simulations are used to illustrate the strongly non-hydrodynamic character of the spin waves recently observed with trapped 87Rb atoms. The decay of the phenomenon, which takes place when the system relaxes back towards equilibrium, is also discussed, with a short comment on decoherence. In two appendices we calculate the Wigner transform of the interaction term in the S matrix method, to first order in gradients; Appendix A.1 treats the case of spin-independent interactions, Appendix A.2 that of spin-dependent interactions.

Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose Einstein condensates and metallic nanograins

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose-Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunneling between two coupled Bose-Einstein condensates. It can be used not only for the study of tunneling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic-molecular Bose-Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics. Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions. In applying all of the above models to physical situations, the need for an exact analysis of small scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.