Condensation In Atomic Gases Research Articles

Non-linear mechanical analogue of quantum Rabi oscillations in coherent output coupler for atoms in Bose-Einstein condensate

The analogies between coherent matter waves in Bose–Einstein condensates of atomic gases and coherent photons have been discussed in connection with possible realization of an “atom laser”. Theoretical discussions of the atom laser have considered the case in which atoms are fed into and coupled out of the condensate continuously. Here, we discuss the analogy between the output coupler for the trapped coherent matter waves and collective non-linear energy transfer in a system of three-coupled mechanical oscillators (pendulums) with variable parameters. One pendulum in the system is weakly coupled through a spring with the pair of pendulums, which are tightly bound through a common string. We show that self-sustained oscillations of the energy distribution between the weakly coupled and tightly bound subsystems can occur. In our simulations, the coherent fraction of the total mechanical energy of the system, which is periodically transferred to the weakly linked subsystem, can be of the order of 1/1000 and even smaller. These periodic oscillations in vibrational energy distribution can be considered as mechanical analogue, with a similar time evolution, of the quantum Rabi oscillations in the populations of the trapped and untrapped (out-coupled) states in the coherent output coupler for atoms in the Bose–Einstein condensate. The described effects can be used for the coherent control of the transfer of mechanical energy on the micro- and nano-scales.

Coherence time of a Bose-Einstein condensate

Temporal coherence is a fundamental property of macroscopic quantum systems, such as lasers in optics and Bose-Einstein condensates in atomic gases and it is a crucial issue for interferometry applications with light or matter waves. Whereas the laser is an "open" quantum system, ultracold atomic gases are weakly coupled to the environment and may be considered as isolated. The coherence time of a condensate is then intrinsic to the system and its derivation is out of the frame of laser theory. Using quantum kinetic theory, we predict that the interaction with non-condensed modes gradually smears out the condensate phase, with a variance growing as A t^2+B t+C at long times t, and we give a quantitative prediction for A, B and C. Whereas the coefficient A vanishes for vanishing energy fluctuations in the initial state, the coefficients B and C are remarkably insensitive to these fluctuations. The coefficient B describes a diffusive motion of the condensate phase that sets the ultimate limit to the condensate coherence time. We briefly discuss the possibility to observe the predicted phase spreading, also including the effect of particle losses.

Bose–Einstein condensates and precision measurements

An ongoing challenge in physics is to make increasingly accurate measurements of physical quantities. Bose-Einstein condensates in atomic gases are ideal candidates for use in precision measurement schemes since they are extremely cold and have laser-like coherence properties. In this paper, we review these two attributes and discuss how they could be exploited to improve the resolution in a range of different measurements.

Creation of ultracold molecules from a Fermi gas of atoms.

Following the realization of Bose-Einstein condensates in atomic gases, an experimental challenge is the production of molecular gases in the quantum regime. A promising approach is to create the molecular gas directly from an ultracold atomic gas; for example, bosonic atoms in a Bose-Einstein condensate have been coupled to electronic ground-state molecules through photoassociation or a magnetic field Feshbach resonance. The availability of atomic Fermi gases offers the prospect of coupling fermionic atoms to bosonic molecules, thus altering the quantum statistics of the system. Such a coupling would be closely related to the pairing mechanism in a fermionic superfluid, predicted to occur near a Feshbach resonance. Here we report the creation and quantitative characterization of ultracold 40K2 molecules. Starting with a quantum degenerate Fermi gas of atoms at a temperature of less than 150 nK, we scan the system over a Feshbach resonance to create adiabatically more than 250,000 trapped molecules; these can be converted back to atoms by reversing the scan. The small binding energy of the molecules is controlled by detuning the magnetic field away from the Feshbach resonance, and can be varied over a wide range. We directly detect these weakly bound molecules through their radio-frequency photodissociation spectra; these probe the molecular wavefunction, and yield binding energies that are consistent with theory.

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.

ChemInform Abstract: Bose—Einstein Condensation of Atomic Gases

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TRAPPED BOSE GAS: MEAN-FIELD APPROXIMATION AND BEYOND

The recent realization of Bose-Einstein condensation in atomic gases opens new possibilities for observation of macroscopic quantum phenomena. There are two important features of the system - weak interaction and significant spatial inhomogeneity. Because of this inhomogeneity a non-trivial "zeroth-order" theory exists, compared to the "first-order" Bogolubov theory. This theory is based on the mean-field Gross-Pitaevskii equation for the condensate ψ-function. The equation is classical in its essence but contains the ℏ constant explicitly. Phenomena such as collective modes, interference, tunneling, Josephson-like current and quantized vortex lines can be described using this equation. The study of deviations from the zeroth-order theory arising from zero-point and thermal fluctuations is also of great interest. Thermal fluctuations are described by elementary excitations which define the thermodynamic behaviour of the system and result in Landau-type damping of collective modes. Fluctuations of the phase of the condensate wave function restrict the monochromaticity of the Josephson current. Fluctuations of the numbers of quanta result in the quantum collapse-revival of the collective oscillations. This phenomenon is considered in some details. Collapse time for the JILA experimental conditions turns out to be of the order of seconds.

Coherent versus incoherent dynamics during Bose-Einstein condensation in atomic gases

We review and extend the theory of the dynamics of Bose-Einstein condensation in weakly interacting atomic gases. We present in a unified way both the semiclassical theory as well as the full quantum theory. This is achieved by deriving a Fokker-Planck equation that incorporates both the coherent and incoherent effects of the interactions in a dilute Bose gas. In first instance we focus our attention on the nonequilibrium dynamics of a homogeneous Bose gas with a positive interatomic scattering length. After that we discuss how our results can be generalized to the inhomogeneous situation that exists in the present experiments with magnetically trapped alkali gases, and how we can deal with a negative interatomic scattering length in that case as well. We also show how to arrive at a discription of the collective modes of the gas that obeys the Kohn theorem at all temperatures. The theory is based on the many-body T-matrix approximation throughout, since this approximation has the correct physical behavior near the critical temperature and also treats the coherent and incoherent processes taking place in the gas on an equal footing.

Bose–Einstein condensation in magnetic traps. Introduction to the theory

The recent realization of Bose–Einstein condensation in atomic gases opens new possibilities for the observation of macroscopic quantum phenomena. There are two important features of these systems — weak interaction and significant spatial inhomogeneity. Because of this a non-trivial 'zeroth-order' theory exists, compared to the 'first-order' Bogolubov theory. The zeroth-order theory is based on the mean-field Gross–Pitaevskii equation for the condensate ψ-function. The equation is classical in its essence but contains the constant explicitly. Phenomena such as collective modes, interference, tunneling, Josephson-like current and quantized vortex lines can be described using this equation. Elementary excitations define the thermodynamic behavior of the system and result in a Landau-type damping of collective modes. Fluctuations of the phase of the condensate wave function restrict the monochromaticity of the Josephson current. Fluctuations of the numbers of quanta result in quantum collapse-revival of the collective oscillations.

Bose–Einstein condensates

The production of Bose–Einstein condensates in atomic gases of alkaline elements contained in magnetic traps has opened a new direction of research in the physics of superlow temperatures. This paper explains in plain words the theory of Bose–Einstein condensation in rarefied gases, and then offers a brief overview of the experimental results.

Local Spin-Gauge Symmetry of the Bose-Einstein Condensates in Atomic Gases.

The Bose-Einstein condensates of alkali atomic gases are spinor fields with local ``spin-gauge'' symmetry. This symmetry is manifested by a superfluid velocity ${\mathbf{u}}_{s}$ (or gauge field) generated by the Berry phase of the spin field. In ``static'' traps, ${\mathbf{u}}_{s}$ splits the degeneracy of the harmonic energy levels, breaks the inversion symmetry of the vortex nucleation frequency ${\mathbf{\ensuremath{\Omega}}}_{c1}$, and can lead to vortex ground states.