Condensate Mode Research Articles

Nonlinear coupling between scissors modes of a Bose-Einstein condensate

We explore the nonlinear coupling of the three scissors modes of an anisotropic Bose-Einstein condensate. We show that only when the frequency of one of the scissors modes is twice the frequency of another scissors mode, these two modes can be resonantly coupled and a down conversion can occur. We perform the calculation variationally using a gaussian trial wave function. This enables us to obtain simple analytical results that describe the oscillation and resonance behaviour of the two coupled modes.

Analysis of g2 for the cold collision frequency shift inthe hydrogen condensate experiments

We compute an approximate set of longitudinal quasiparticlemodes for a hydrogen condensate as produced in the MITexperiments. An expansion in quasiparticles using a simpleone-dimensional Bogoliubov picture shows however that at thehigh temperatures (≈44 µK) and in the very shallowtrap employed (ωz = 2π×10.2 Hz) thecontribution to the density from the quasiparticles is about20% of that from the condensate mode, leading to an effective g2(x,x) which varies between 1 and 3 depending onthe position in the condensate.

Transferring the atom statistics of a Bose-Einstein condensate to an optical field

We consider a single-mode Bose-Einstein condensate with an arbitrary initial density matrix. This mode is coupled to another condensate mode via a quantized optical-field. We describe a method for transferring the diagonal elements of the initial density matrix in a number state basis to the optical-field's density matrix.

Finite-temperature simulations of the scissors mode in Bose-Einstein condensed gases.

The dynamics of a trapped Bose-condensed gas at finite temperatures is described by a generalized Gross-Pitaevskii equation for the condensate order parameter and a semiclassical kinetic equation for the thermal cloud, solved using N-body simulations. The two components are coupled by mean fields as well as collisional processes that transfer atoms between the two. We use this scheme to investigate scissors modes in anisotropic traps as a function of temperature. Frequency shifts and damping rates of the condensate mode are extracted, and are found to be in good agreement with recent experiments.

Damped Bogoliubov excitations of a condensate interacting with a static thermal cloud

We calculate the contribution to the damping of condensate collective excitations at finite temperatures arising from the lack of equilibrium between the condensate and thermal atoms. Limiting our attention to collective modes that mainly involve the motion of the condensate, we treat the noncondensate as static as a first approximation. We derive a set of generalized Bogoliubov equations for finite temperatures that contain an explicit damping term due to the collisional exchange of atoms between the two components. We have numerically solved these Bogoliubov equations to obtain the temperature dependence of the damping of the condensate modes in a harmonic trap. These results agree quite well with our recent work based on the Thomas-Fermi approximation but predict a much larger damping near the transition temperature.

Multimode dynamics of a coupled ultracold atomic-molecular system.

We analyze the coherent multimode dynamics of a system of coupled atomic and molecular Bose gases. Starting from an atomic Bose-Einstein condensate with a small thermal component, we observe a complete depletion of the atomic and molecular condensate modes on a short time scale due to a significant population of excited states. Giant coherent oscillations between the two condensates for typical parameters are almost completely suppressed. Our results cast serious doubts on the common use of the 2-mode model for the description of coupled ultracold atomic-molecular systems and should be considered when planning future experiments with ultracold molecules.

Damping of condensate collective modes due to equilibration with the noncondensate

We consider the damping of condensate collective modes in the collisionless regime at finite temperatures arising from lack of equilibrium between the condensate and the noncondensate atoms, an effect that is ignored in the usual discussion of the collisionless region. As a first approximation, we ignore the dynamics of the thermal cloud. Our calculations should be applicable to collective modes of the condensate that are oscillating out-of-phase with the thermal cloud. We obtain a generalized Stringari equation of motion for the condensate at finite temperatures, which includes a damping term associated with the fact that the condensate is not in diffusive equilibrium with the static thermal cloud. This intercomponent collisional damping of the condensate modes is comparable in magnitude to the Landau damping considered in the recent literature.

Multiple pion production from an oriented chiral condensate

We consider an “oriented” chiral condensate produced in the squeezed states of the effective field theory with time- and space-dependent pion mass parameter. We discuss the general properties of the solution, identifying condensate modes and determining the resulting pion distributions. The implementation of the dynamics in the form of sudden perturbation allows us to look for exact solutions. In the region of condensation, the dramatic increase in pion production and charge fluctuations are demonstrated.

ATOM-OPTICAL BISTABILITY IN TRAPPED BOSE–EINSTEIN CONDENSATES

The close similarities between nonlinear optics and nonlinear atom optics motivate us to demonstrate the possibility of atom-optical bistability for a trapped Bose–Einstein condensate. Driven by an intense, coherent input matter wave, the trapped Bose–Einstein condensate might display the bistability when the Born–Markov master equation for the condensate mode is used. The atom-optical bistability provides a way to control atom lasers with atom lasers.

Quantum theory of an exciton condensate subject to radiative decay

Semiconductor excitons obey Bose-Einstein statistics in the low-density limit. In this paper, a two-level quantum model for an exciton condensate subject to radiative decay is presented. The condensate state has a well-defined exciton number and a slow phase diffusion rate analogous to a coherent state created by a (photon) laser. Since excitons recombine radiatively, the statistics of the device can be observed by photodetection. Our analytical and numerical results at steady state reveal that the change in population statistics of the ground state is gradual across the threshold region, above which a condensate forms. When radiative losses are present, the condensate mode is ``quasicoherent;'' in the limit of no losses a coherent state is approached. Far below threshold the ground state is well described by a thermal distribution. The higher level, that is the ``pump,'' remains thermally distributed at all times.

Markov approximation for the atomic output coupler

The regions of validity of the Markov approximation for the coupling of atoms out of an atomic trap are determined. We consider radio-frequency output coupling in the presence of gravity and collisional repulsion, and Raman output coupling. The Markov approximation is crucial in most theoretical descriptions of an atom laser that assume a continuous process of output coupling from a trapped Bose-Einstein condensate. In this regime many techniques proved to be useful for modeling the optical laser, such as master equations, can be used to describe the dynamics of the damping of the condensate mode undergoing output coupling.

Normal modes of a vortex in a trapped Bose-Einstein condensate

A hydrodynamic description is used to study the normal modes of a vortex in a zero-temperature Bose-Einstein condensate. In the Thomas-Fermi limit, the circulating superfluid velocity far from the vortex core provides a small perturbation that splits the originally degenerate normal modes of a vortex-free condensate. The relative frequency shifts are small in all cases considered (they vanish for the lowest dipole mode with $|m|=1$), suggesting that the vortex is stable. The Bogoliubov equations serve to verify the existence of helical waves, similar to those of a vortex line in an unbounded weakly interacting Bose gas. In the large-condensate (small-core) limit, the condensate wave function reduces to that of a straight vortex in an unbounded condensate; the corresponding Bogoliubov equations have no bound-state solutions that are uniform along the symmetry axis and that decay exponentially far from the vortex core.

First and Second Sound Modes of a Bose-Einstein Condensate in a Harmonic Trap

We have calculated the first and second sound modes of a dilute interacting Bose gas in a spherical trap for temperatures $(0.6<{T/T}_{c}<1.2)$ and for systems with ${10}^{4}$ to ${10}^{8}$ particles. The second sound modes (which exist only below ${T}_{c}$) generally have a stronger temperature dependence than the first sound modes. The puzzling temperature variations of the sound modes near ${T}_{c}$ recently observed at JILA in systems with ${10}^{3}$ particles match surprisingly well with those of the first and second sound modes of much larger systems.

Sound propagation in a cylindrical Bose-condensed gas

We study the normal modes of a cylindrical Bose condensate at $T=0$ using the linearized time-dependent Gross-Pitaevskii equation in the Thomas-Fermi limit. These modes are relevant to the recent observation of pulse propagation in long, cigar-shaped traps. We find that pulses generated in a cylindrical condensate propagate with little spread at a speed $c=\sqrt{g\mathrm{n\ifmmode \bar{}\else \={}\fi{}}/m},$ where $\mathrm{n\ifmmode \bar{}\else \={}\fi{}}$ is the average density of the condensate over its cross-sectional area.

Kinetics of Bose-Einstein Condensation in a Trap

The formation process of a Bose-Einstein condensate in a trap is described using a master equation based on quantum kinetic theory, which can be well approximated by a description using only the condensate mode in interaction with a thermalized bath of noncondensate atoms. A rate equation of the form n = 2W(n)[(1-exp((mu_n - mu)/kT))n + 1] is derived, in which the difference between the condensate chemical potential mu_n and the bath chemical potential mu gives the essential behavior. Solutions of this equation, in conjunction with the theoretical description of the process of evaporative cooling, give a characteristic latency period for condensate formation and appear to be consistent with the observed behavior of both rubidium and sodium condensate formation.

Quantum dephasing of normal modes of a Bose-Einstein condensate in a magnetic trap

Quantum evolution of a collective mode of a Bose-Einstein condensate containing a finite number N of particles can demonstrate the phenomena of collapses and revivals. The characteristic collapse time depends on the scattering length, the initial amplitude of the mode, and N. The corresponding time values have been derived analytically under certain approximations and numerically for the parabolic atomic trap. The revival of the mode amplitude at a time of several seconds, as direct evidence of the effect, can occur if the normal component is significantly suppressed.

Collective excitations of weakly coupled Bose condensates confined in harmonic traps

We use ordinary first-order perturbation theory in the mean-field interaction to derive analytic expressions for the frequencies of the excitation modes of a dilute Bose-Einstein condensate under confinement. The confining trap is modelled by a harmonic potential having either spherical or cylindrical symmetry. The expressions obtained are valied for all quantum numbers of the appropriate symmetry and for attractive as well as repulsive effective interactions. Comparison with available numerical calculations is made.

Temperature-Dependent Damping and Frequency Shifts in Collective Excitations of a Dilute Bose-Einstein Condensate

We extend to finite temperature the study of collective excitations of a Bose-Einstein condensate in a dilute gas of ${}^{87}\mathrm{Rb}$. Measurements of two modes with different angular momenta show unexpected temperature-dependent frequency shifts, with very different behavior for the two symmetries; in addition there is a sharp feature in the temperature dependence of one mode. The damping of these excitations exhibits dramatic temperature dependence, with condensate modes at temperatures near the transition damping even faster than analogous noncondensate oscillations.

Centrifugal effects in a Bose-Einstein condensate in the time-orbiting-potential magnetic trap

Single-particle states in the atomic trap employing the rotating magnetic field are found using the full time-dependent instantaneous trapping potential. These states are compared with those of the effective time-averaged potential. We show that the trapping is possible when the frequency of the rotations exceeds some threshold. Slightly above this threshold the weakly interacting gas of the trapped atoms acquires the properties of a quasi-one-dimensional system in the frame rotating together with the field. The role of the atom-atom interaction in changing the ideal gas solution is discussed. We show that in the limit of large numbers of particles the rotating field whose frequency is appropriately modulated can be utilized as a driving force principally for the center-of-mass motion as well as for the angular momentum L=2 normal modes of the Bose condensate. A mechanism of quantum evaporation forced by the rotating field is analyzed.

Study on Condensation Heat Transfer for Steam-Ethanol Vapor Mixture. Relation between Condensation Characteristic Curves and Modes of Condensate.

The relation between the condensation characteristic curves, which show the variations of heat flux or heat transfer coefficient with the changes in surface subcooling, and the aspects of condensate on the heat transfer surface was investigated. The aspects of condensate were divided into six different characteristic modes, that is, ordinary smooth film, rivulets on smooth film, relatively large drops on smooth film, dropwise with drops of various sizes, rivulets on dropwise and wavy film, which appeared in order of increasing surface subcooling for all ethanol concentrations (mass fraction between 0.17 and 0.74). Furthermore, on the basis of photographs taken simultaneously with the measurement, the coverages of the surface by the condensate, which were the main heat transfer resistances for each mode of condensate, were measured. The correspondence among the heat transfer characteristic curves, the modes of condensate and the surface coverage of condensate of main resistance are shown quantitatively.