Collisions of Doubly Spin-Polarized, Ultracold<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi /><mml:mrow><mml:msup><mml:mrow /><mml:mrow><mml:mn>85</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">Rb</mml:mi></mml:math>Atoms

Gardner, Jamie Ryan; Cline, R. A.; Miller, Joseph D.; Heinzen, D. J.; Boesten, H. M. J. M.; Verhaar, B.J.

doi:10.1103/physrevlett.74.3764

Cited by 130 publications

(99 citation statements)

References 25 publications

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“…For current traps the exponent η is of the order η ∼ 1000 demonstrating that the phase coherence of the bosons decays only very weakly and is experimentally undistinguishable from true BEC [21]. However for steeper magnetic traps, ω ⊥ ∼ 50 kHz, particle densities of ρ ∼ 10 4 particles/cm and assuming a scattering length of 110 a B for Rb [22], the exponent η is η ∼ 4 and it should be possible to observe LL behavior. Below T ∼ 0.4 nK only the linear mode is excited and the physics is described by LL physics.…”

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confidence: 99%

Trapped one-dimensional Bose gas as a Luttinger liquid

1998

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The low-energy fluctuations of a trapped, interacting quasi one-dimensional Bose gas are studied. Our considerations apply to experiments with highly anisotropic traps. We show that under suitable experimental conditions the system can be described as a Luttinger liquid. This implies that the correlation function of the bosons decays algebraically preventing Bose-Einstein condensation. At significantly lower temperatures a finite size gap destroys the Luttinger liquid picture and BoseEinstein condensation is again possible. PACS: 03.75.Fi, 05.30.jp, 32.80.Pj, 67.90.+z, 71.10.Pm The experimental realization of Bose-Einstein condensation (BEC) in atomic vapors of 87 Rb [1] and 23 Na [2,3] has attracted a lot of interest [4]. Recently, a highly anisotropic, quasi one-dimensional trap has been designed [5]. Up to now, the possibility of BEC in one dimension has mainly been discussed for the noninteracting Bose gas [6,7]. The role of dimensionality has been carefully examined for the ideal bose gas by van Druten and Ketterle [8]. In one dimension the interaction between bosons plays an essential role due to the strong constraint in phase space [9]. The question of BEC in a quasi one-dimensional system is therefore more complicated. The purpose of this paper is to demonstrate that under suitable experimental conditions the low energy excitations of this system are described by a Luttinger liquid (LL) [10] model. The superfluid correlations of a LL decay algebraically and the system is not Bose condensed. At much lower temperatures which are determined by the extension of the trap in the longitudinal direction the spectrum of the phase fluctuations is again cut off by finite size effects and the bosons could condense again.The realization of a Luttinger liquid in a onedimensional Bose gas would be a highly non-trivial example of an interacting quantum liquid. Fermionic systems which are believed to be described by a Luttinger liquid include quasi one-dimensional organic metals [11], magnetic chain compounds,quantum wires and edge states in the Quantum Hall Effect. While these systems are always embedded in a three-dimensional matrix and thus show a crossover to a three-dimensional behavior at low temperatures, the trapped one-dimensional Bose gas would provide a clean testing ground for the concept of a Luttinger liquid.The paper is organized as follows: First we discuss the circumstances under which a trapped Bose gas can be considered as a one-dimensional quantum system. Next we demonstrate in an explicit calculation that there is a gapless mode with a linear dispersion. We show that the Hamiltonian of the low-lying excitations can be identified as that of a Luttinger liquid and therefore the densitydensity correlation function decays algebraically. In the reminder of the paper we discuss the implication of the algebraic decay of the particle-particle correlation function for BEC and review the properties of a Luttinger liquid. We consider the Bose gas in a cylindrical symmetric trap confined to the z-axis by a ti...

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Trapped one-dimensional Bose gas as a Luttinger liquid

1998

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“…For ω ⊥ = 2π × 10 4 Hz and L = 3 cm the upper bound for the number of atoms is given by: N * Rb = 5 × 10 3 for rubidium 87 (F = 2, m F = +2, a = +110 a Bohr [15]); and N * Na = 6 × 10 2 for sodium (F = 1, m F = −1, a = +52 a Bohr [16]). Note that the above numbers can be improved in stronger traps since the bound N * increases approximately linearly with the confinement frequency.…”

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Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons

1998

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We calculate, within the pseudopotential approximation, a one-dimensional scattering amplitude and effective onedimensional interaction potential for atoms confined transversally by an atom waveguide or highly elongated "cigar"-shaped atomic trap. We show that in the low-energy scattering regime, the scattering process degenerates to a total reflection suggesting an experimental realization of a famous model in theoretical physics -a one-dimensional gas of impenetrable bosons ("Tonks" gas). We give an estimate for suitable experimental parameters for alkali atoms confined in waveguides.Rapid progress in producing Bose condensates of alkali atoms [1] opened up new areas of ultra-low energy collisional physics. Concurrently, work has progressed on confinement of atoms in the light-induced [2] and magnetic-field-induced [3] atom waveguides.We develop a theory for the binary atomic collisions in presence of a transverse external confinement. Using the pseudopotential approximation, we derive an expression for an effective one-dimensional scattering amplitude and show that the interparticle interaction can be approximated by an effective one-dimensional δ-potential of a known strength. In the case of a dilute atomic gas, when the three body collisions are negligible, our effective potential can also be used to describe quasi-one-dimensional many-body systems: a project on the experimental realization of the one-dimensional Bose condensate is already presented in the literature [4]. Results of our paper will allow one to properly take into account the trap-induced corrections to the strength of the atomic mean-field potential.Furthermore, we show that in the low-energy scattering limit (k z |a 1D | ≪ 1), the effective one-dimensional scattering degenerates to a total reflection (hk z is the longitudinal component of the atomic momentum and a 1D is the one-dimensional scattering length defined below). This conclusion allows us to suggest an experimental realization of another famous model in theoretical physics -a one-dimensional gas of impenetrable bosons [5] also referred to as a "Tonks" gas. Such a system provides us with an unusual example of a boson-fermion duality: the elementary excitations of such a bosonic system obey Fermi statistics [6] (which is possible only in one dimension [7]). The Tonks gas is, therefore, a system complementary to the one-dimensional Bose condensate: the latter requires the high-energy scattering regime (k z |a 1D | ≫ 1) [8] and its excitation spectrum is represented by the Bogoliubov bosons.To describe the binary collisions between cold atoms confined in a waveguide, we suggest the following model: where g = 2πh 2 a/µ is the potential strength, a is the s-wave scattering length for the "true" interaction potential, µ = m/2 is the reduced mass, m is the mass of the atoms. The regularization operator ∂ ∂r (r · ), that removes the 1/r divergence from the scattered wave (see [9]), plays an important role in the derivation below;(d) Atomic motion (both transverse and longitudinal component...

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“…Previous experimental studies of such spectra in alkali atoms have utilized the technique of laser-induced photoassociation (PA) in a magneto-optical trap (MOT) [2,3]. In addition to testing calculations of molecular structure, that work has produced precise measurements of excited-state lifetimes [4,5,6,7] and has led to accurate determinations of s-wave scattering lengths for alkali systems, which are of interest for studies of Bose Einstein condensates (BECs) [8,9]. This letter reports novel spectroscopic measurements and calculations for extraordinarily long-range molecules that are produced when two 4 He atoms in the metastable 2 3 S 1 state absorb laser light tuned close to the 2 3 S 1 − 2 3 P 0 (D 0 ) atomic line at λ = 1083 nm.…”

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Giant Helium Dimers Produced by Photoassociation of Ultracold Metastable Atoms

et al. 2003

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We produce giant helium dimers by photoassociation of metastable helium atoms in a magnetically trapped, ultracold cloud. The photoassociation laser is detuned red of the atomic 2 3 S1−2 3 P0 line and produces strong heating of the sample when resonant with molecular bound states. The temperature of the cloud serves as an indicator of the molecular spectrum. We report good agreement between our spectroscopic measurements and our calculations of the five bound states belonging to a 0 + u purely long-range potential well. These previously unobserved states have classical inner turning points of about 150 a0 and outer turning points as large as 1150 a0.PACS numbers: 34.20. Cf, 32.80.Pj, 34.50.Gb In the purely long-range molecules first proposed by Stwalley et al.[1], the binding potential depends only on the long-range part of the atom-atom interaction, and the internuclear distance is always large compared with ordinary chemical bond lengths. Theoretical description of these molecules involves only the leading C 3 /R 3 terms of the electric dipole-dipole interaction and the fine structure inside each atom. These well-known interactions allow precise calculation of potential wells and rovibrational energies. Previous experimental studies of such spectra in alkali atoms have utilized the technique of laser-induced photoassociation (PA) in a magneto-optical trap (MOT) [2,3]. In addition to testing calculations of molecular structure, that work has produced precise measurements of excited-state lifetimes [4,5,6,7] and has led to accurate determinations of s-wave scattering lengths for alkali systems, which are of interest for studies of Bose Einstein condensates (BECs) [8,9]. This letter reports novel spectroscopic measurements and calculations for extraordinarily long-range molecules that are produced when two 4 He atoms in the metastable 2 3 S 1 state absorb laser light tuned close to the 2 3 S 1 − 2 3 P 0 (D 0 ) atomic line at λ = 1083 nm. As compared with the alkali dimers considered previously, the potential wells are shallower, and molecules are much more tenuous, with an internuclear distance reaching values as large as 1150 a 0 (a 0 ≃ 0.53Å, the Bohr radius). At such large distances, retardation clearly influences the dipole-dipole interaction. Moreover, these purely longrange molecular states of metastable helium are distinctive in that each atom carries a high internal energy (the 2 3 S 1 state lies 20 eV above the ground state). While one normally expects Penning ionization to destabilize such * Electronic address: leonard@lkb.ens.fr † Permanent address: Calvin College, Grand Rapids, MI, USA. ‡ Permanent address: FOM instituut voor plasmafysica Rijnhuizen, and University of Twente, The Netherlands. § Present address: Institut für Quantenoptik, Universität Hannover, Germany.energetic molecules, we note that purely long-range interactions might rather suppress this process, since the atoms are effectively held apart by the same potential that binds them together. The absence of purely longrange resonances ...

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Collisions of Doubly Spin-Polarized, Ultracold85RbAtoms

Cited by 130 publications

References 25 publications

Trapped one-dimensional Bose gas as a Luttinger liquid

Trapped one-dimensional Bose gas as a Luttinger liquid

Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons

Giant Helium Dimers Produced by Photoassociation of Ultracold Metastable Atoms

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