Reentrant behavior of breathing mode in one-dimensional Bose gas (original) (raw)
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Quench-induced breathing mode of one-dimensional Bose gases
2013
We measure the position-and momentum-space breathing dynamics of trapped one-dimensional Bose gases at finite temperature. The profile in real space reveals sinusoidal width oscillations whose frequency varies continuously through the quasicondensate to ideal Bose gas crossover. A comparison with theoretical models taking temperature into account is provided. In momentum space, we report the first observation of a frequency doubling in the quasicondensate regime, corresponding to a selfreflection mechanism due to the repulsive interactions. Its disappearance through the crossover is mapped out experimentally, giving insights to the dynamics of the breathing evolution.
Physical Review A, 2004
We present a theory for the linear dynamics of a weakly interacting Bose gas confined inside a harmonic trap at finite temperature. The theory treats the motions of the condensate and of the non-condensate on an equal footing within a generalized random-phase approximation, which (i) extends the second-order Beliaev-Popov approach by allowing for the dynamical coupling between fluctuations in the thermal cloud, and (ii) reduces to an earlier random-phase scheme when the anomalous density fluctuations are omitted. Numerical calculations of the low-lying spectra in the case of isotropic confinement show that the present theory obeys with high accuracy the generalized Kohn theorem for the dipolar excitations and demonstrate that combined normal and anomalous density fluctuations play an important role in the monopolar excitations of the condensate. Meanfield theory is instead found to yield accurate results for the quadrupolar modes of the condensate. Although the restriction to spherical confinement prevents quantitative comparisons with measured spectra, it appears that the non-mean field effects that we examine may be relevant to explain the features exhibited by the breathing mode as a function of temperature in the experiments carried out at JILA on a gas of 87 Rb atoms. PACS numbers: 03.75.Kk, 05.30.Jp, 67.40.Db
EQUATIONS OF COUPLED CONDENSATE AND NON-CONDENSATE DYNAMICS IN A TRAPPED BOSE GAS
We constructed equations of the condensed Bose gas dynamics at nonzero temperatures on the bases of the first principles of statistical mechanics. We derived the equation of motion for the con-densate wavefunction and the quantum kinetic equation for the distribution function of excited atoms. The obtained generalized Gross–Pitaevskii equation for a condensate includes the effect of collisions with thermal cloud atoms (non-condensate). The Boltz-mann quantum kinetic equation for a non-condensate was obtained by means of Zubarev's method of nonequilibrium statistical operator .
Condensate growth in trapped Bose gases
Physical Review A, 2000
We study the dynamics of condensate formation in an inhomogeneous trapped Bose gas with a positive interatomic scattering length. We take into account both the nonequilibrium kinetics of the thermal cloud and the Hartree-Fock mean-field effects in the condensed and the noncondensed parts of the gas. We solve our equations numerically by assuming that the thermal component behaves ergodically and that the condensate grows adiabatically. The condensate is also treated within the Thomas-Fermi approximation. We find excellent agreement between theory and experiment, for a broad range of equilibrium condensate numbers.
Collective and single-particle excitations of a trapped Bose gas
Physical Review A, 1997
The density of states of a Bose-condensed gas confined in a harmonic trap is investigated. The predictions of Bogoliubov theory are compared with those of Hartree-Fock theory and of the hydrodynamic model. We show that the Hartree-Fock scheme provides an excellent description of the excitation spectrum in a wide range of energy, revealing a major role played by single-particle excitations in these confined systems. The crossover from the hydrodynamic regime, holding at low energies, to the independent-particle regime is explicitly explored by studying the frequency of the surface mode as a function of their angular momentum. The applicability of the semiclassical approximation for the excited states is also discussed. We show that the semiclassical approach provides simple and accurate formulas for the density of states and the quantum depletion of the condensate.
Breathing oscillations of a trapped impurity in a Bose gas
EPL (Europhysics Letters), 2012
Motivated by a recent experiment [J. Catani et al., arXiv:1106.0828v1 preprint, 2011, we study breathing oscillations in the width of a harmonically trapped impurity interacting with a separately trapped Bose gas. We provide an intuitive physical picture of such dynamics at zero temperature, using a time-dependent variational approach. In the Gross-Pitaevskii regime we obtain breathing oscillations whose amplitudes are suppressed by self trapping, due to interactions with the Bose gas. Introducing phonons in the Bose gas leads to the damping of breathing oscillations and non-Markovian dynamics of the width of the impurity, the degree of which can be engineered through controllable parameters. Our results reproduce the main features of the impurity dynamics observed by Catani et al. despite experimental thermal effects, and are supported by simulations of the system in the Gross-Pitaevskii regime. Moreover, we predict novel effects at lower temperatures due to selftrapping and the inhomogeneity of the trapped Bose gas. PACS numbers: 67.85.-d,03.75.-b,67.85.De
Thermodynamics of a Trapped Bose-Condensed Gas
Journal of Low Temperature Physics, 1997
with repulsive forces and confined in a harmonic anisotropic trap. We develop the formalism of mean field theory for non uniform systems at finite temperature, based on the generalization of Bogoliubov theory for uniform gases. By employing the WKB semiclassical approximation for the excited states we derive systematic results for the temperature dependence of various thermodynamic quantities: condensate fraction, density profiles, thermal energy, specific heat and moment of inertia. Our analysis points out important differences with respect to the thermodynamic behaviour of uniform Bose gases. This is mainly the consequence of a major role played by single particle states at the boundary of the condensate. We find that the thermal depletion of the condensate is strongly enhanced by the presence of repulsive interactions and that the critical temperature is decreased with respect to the predictions of the non-interacting model. Our work points out an important scaling behaviour exhibited by the system in large N limit. Scaling permits to express all the relevant thermodynamic quantities in terms of only two parameters: the
Simulating quantum transport for a quasi-one-dimensional Bose gas
J. Phys. B: At. Mol. Opt. Phys. 46 (2013) 145307
We study the effect of quantum fluctuations on the dynamics of a quasi-one-dimensional Bose gas in an optical lattice at zero-temperature using the truncated Wigner approximation with a variety of basis sets for the initial fluctuation modes. The initial spatial distributions of the quantum fluctuations are very different when using a limited number of plane-wave (PW), simple-harmonic-oscillator (SHO) and self-consistently determined Bogoliubov (SCB) modes. The short-time transport properties of the Bose gas, characterized by the phase coherence in the PW basis are distinct from those gained using the SHO and SCB basis. The calculations using the SCB modes predict greater phase decoherence and stronger number fluctuations than the other choices. Furthermore, we observe that the use of PW modes overestimates the extent to which atoms are expelled from the core of the cloud, while the use of the other modes only breaks the cloud structure slightly which is in agreement with the experimental observations \cite{PRL.94.120403}.
Ground-state properties of interacting two-component Bose gases in a one-dimensional harmonic trap
The European Physical Journal D, 2009
We study ground-state properties of interacting two-component boson gases in a one-dimensional harmonic trap by using the exact numerical diagonalization method. Based on numerical solutions of many-body Hamiltonians, we calculate the ground-state density distributions in the whole interaction regime for different atomic number ratio, intra-and inter-atomic interactions. For the case with equal intra-and inter-atomic interactions, our results clearly display the evolution of density distributions from a Bose condensate distribution to a Fermi-like distribution with the increase of the repulsive interaction. Particularly, we compare our result in the strong interaction regime to the exact result in the infinitely repulsive limit which can be obtained by a generalized Bose-Fermi mapping. We also discuss the general case with different intra-and inter-atomic interactions and show the rich configurations of the density profiles.