Collective excitation of Bose-Einstein condensates in the transition region between three and one dimensions

Abstract

We measure the frequency of the low m=0 quadrupolar excitation mode of weakly interacting Bose-Einstein condensates in the transition region from the 3D to the 1D mean-field regime. Various effects shifting the frequency of the mode are discussed. In particular we take the dynamic coupling of the condensate with the thermal component at finite temperature into account using a timedependent Hartree-Fock-Bogoliubov treatment developed in [1]. We show that the frequency rises in the transition from 3D to 1D, in good agreement with the theoretical prediction [2].PACS numbers: 03.75. Kk, 03.75.Nt, 39.25.+k One-dimensional (1D) quantum degenerate Bose gases have recently attracted considerable theoretical and experimental interest [3]. On the one hand this interest is due to their remarkable physical properties which are absent in three-dimensional systems. On the other hand a rapid advance in trapping techniques for ultracold gases has put these systems within experimental reach. In particular optical lattices [4], optical dipole traps [5], and atom chips [6] have recently been used to realize such low-dimensional systems. For further experiments under these conditions a good understanding of the transition between the 3D and the 1D regime is therefore of crucial importance. In this paper this transition region is characterized experimentally by monitoring the oscillation of a quantum degenerate Bose gas.From a fundamental point of view, one of the most striking features of 1D quantum degenerate Bose gases is the predominant role played by quantum fluctuations. For spatially homogeneous 1D systems, fluctuations of the phase rule out the existence of any off-diagonal longrange order (ODLRO) [7] even at temperature T = 0 [8]. The finite size of trapped 1D gases however allows for a rich variety of possible scenarios, including true phase-coherent Bose-Einstein condensates (BECs) as well as phase-fluctuating BECs, the so-called quasicondensates [9].The behavior of these 1D Bose gases is governed by the ratio of interaction and kinetic energywhere n 1D is the 1D atomic density, m the atomic mass and g 1D the 1D coupling constant. Since this ratio scales as 1/n these gases counter-intuitively become more nonideal when the density is decreased. The fascinating features of these systems have led to continued theoretical interest over the past decades. For homogeneous 1D Bose gases with short-range interactions, the ground state [10], excitation spectrum [11] and thermodynamic properties [12] of the system can be determined with a Bethe Ansatz for arbitrary values of γ. In the case of trapped systems the equation of state can be found by combining this approach with the local density approximation [13]. For high densities the system is in the weakly interacting regime, where it can be well described in the frame of mean-field theories and ODLRO is present. On the contrary, for low densities the system enters the strongly interacting or strongly correlated regime, where a description by mean-field theories fails and ODLRO ...

Collective excitation of a Bose-Einstein condensate by modulation of the atomic scattering length

“…5. There is an additional frequency shift due to nonzero temperature [4][5][6][7] which is estimated to be negligible given our low temperatures and interaction strength [43]. Even though we can neglect temperature effects in the measurements presented here, our method of excitation of the quadrupole mode may be used to study these effects in further detail in regimes of stronger interactions.…”

“…In this work, we demonstrate the excitation of the lowestlying quadrupole mode in a BEC of 7 Li by modulating the atomic scattering length via a magnetic Feshbach resonance. In contrast to abruptly changing the scattering length [26], sinusoidal modulation enables the controlled excitation of a single mode at a specific frequency.…”

“…Collective excitation of a Bose-Einstein condensate (BEC) is an essential diagnostic tool for investigating properties of the ultracold quantum state. Fundamental information about condensate dynamics can be determined from observations of collective modes [1][2][3], including the effects of temperature [4][5][6], and the dimensionality of the system [7]. In addition, the interplay between these modes and external agents, such as random potentials [8,9], lattices [10,11], as well as other atoms [12][13][14][15][16], can be investigated.…”

“…Our methods for creating an ultracold gas of 7 Li have been described previously [36,37]. We confine atoms in the |1,1 hyperfine state of 7 Li in an optical trap and use a set of Helmholtz coils to provide an axially oriented bias field. We determine the radial trapping frequency by parametric heating to be ω r = (2π )235(10) Hz, and the axial trapping frequency by dipole oscillation to be ω z = (2π )4.85(1) Hz.…”

Quantum information and many body physics with cold atoms

“…In real experiments, both amplitude and sign of the scattering length can be modified by utilizing the Feshbach resonance. This technique provides a very promising method for the manipulation of atomic matter waves and the nonlinear excitations in BEC by tuning the interatomic interaction.With the development of the experiments, a new developing technology called optical lattices presents a highly controllable and clean system for studying strongly correlated system, in which the relevant parameter can be adjusted independently [6][7][8][9][10][11]. Optical lattices with different geometrical property can be set up by adjusting the propagation direc-*Corresponding author (email: wmliu@iphy.ac.cn) tions of laser beams, such as triangular [12], honeycomb [13] and optical lattice.…”