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Ho, Tin-Lun; Ma, Michael

doi:10.1023/a:1021894713105

Cited by 78 publications

(80 citation statements)

References 11 publications

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“…It has been previously discussed that this is an accurate description for weak interactions between the bosons [51][52][53]. In this case we need to use a dressed single-particle wave functionf k…”

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confidence: 99%

Quantum impurity in a one-dimensional trapped Bose gas

2015

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We present a new theoretical framework for describing an impurity in a trapped Bose system in one spatial dimension. The theory handles any external confinement, arbitrary mass ratios, and a weak interaction may be included between the Bose particles. To demonstrate our technique, we calculate the ground state energy and properties of a sample system with eight bosons and find an excellent agreement with numerically exact results. Our theory can thus provide definite predictions for experiments in cold atomic gases.PACS numbers: 03.75. Mn,67.85.Pq An impurity interacting with a reservoir of quantum particles is an essential problem of fundamental physics. Famous examples include a single charge in a polarizable environment, the Landau-Pekar polaron [1, 2], a neutral particle in superfluid 4 He [3], a magnetic impurity in a metal resulting in the Kondo effect [4], and a single scattering potential inside an ideal Fermi gas [5,6]. The latter system is famous for the Anderson's orthogonality catastrophe [7]. In these settings the impurity behavior can provide key insights into the many-body physics and guide our understanding of more general setups.A complicating feature of many impurity problems is the presence of interactions at a level that often precludes the use of perturbative analysis and self-consistent mean-field approximations. This implies that analytical approaches are highly desirable and exact solutions are, when available, coveted tools for benchmarking other techniques. This is particularly true for one-dimensional (1D) homogeneous systems where solutions can often be found based on the Bethe ansatz [8][9][10][11][12][13]. These solutions are the essential ingredients for our analytical understanding of highly controllable experiments with cold atoms [14][15][16][17][18][19]. For instance, the exactly solvable problem of the single impurity in a 1D Fermi sea [10] -the Fermi polaron -can be used to study the atom-by-atom formation of a 1D Fermi sea [20].While Fermi polarons have been studied intensively in recent times using cold atomic setups both experimentally and theoretically [21][22][23][24][25], the physics of impurities in a bosonic environment is only now becoming a frontier in cold atom experiments [26][27][28][29]. This pursuit requires theoretical models for describing the Bose polaron [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], where, in contrast to the Fermi polaron, an exact solution is not known even for a homogeneous 1D system. Here we provide a new theoretical framework that captures the properties of an impurity in a bosonic bath confined in one spatial dimension. Our (semi)-analytical theory thus provides a state-of-the-art tool for exploring the properties of Bose polarons in 1D.The proposed framework works with a zero-range potential of any strength and handles any number of ma- FIG. 1: (color online) a)A sketch of the doubly-degenerate ground state for the system of one A and eight B particles trapped in a one-dimensional harmonic potential ...

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confidence: 99%

Quantum impurity in a one-dimensional trapped Bose gas

2015

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“…The spectrum and wavefunctions of low-energy excitations (ε ν ≪ µ) can be found analytically [36][37][38]. For the 1D and 2D weakly interacting trapped Bose gases this has been done in [40,41]. We analyze the character of BEC in a harmonically trapped symmetric 2D gas with repulsive interparticle interaction, relying on the calculation of the single-particle correlation function [20].…”

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confidence: 99%

Low-dimensional trapped gases

2004

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Recent developments in the physics of ultracold gases provide wide possibilities for reducing the dimensionality of space for magnetically or optically trapped atoms. The goal of these lectures is to show that regimes of quantum degeneracy in two-dimensional (2D) and one-dimensional (1D) trapped gases are drastically different from those in three dimensions and to stimulate an interest in low-dimensional systems. Attention is focused on the new physics appearing in currently studied low-dimensional trapped gases and related to finite-size and finite-temperature effects.

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“…Topological excitations such as solitons (in 1D) and vortices (in 2D) should be much more stable than in 3D, where solitons suffer from kink instabilities and vortices can bend. The character and spectrum of the collective excitations is expected to exhibit a qualtitative change in lower dimensions [18].…”

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Realization of Bose-Einstein Condensates in Lower Dimensions

et al. 2001

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Bose-Einstein condensates of sodium atoms have been prepared in optical and magnetic traps in which the energy-level spacing in one or two dimensions exceeds the interaction energy between atoms, realizing condensates of lower dimensionality. The cross-over into two-dimensional and onedimensional condensates was observed by a change in aspect ratio and saturation of the release energy when the number of trapped atoms was reduced.New physics can be explored when the hierarchy of physical parameters changes. This is evident in dilute gases, where the onset of Bose-Einstein condensation occurs when the thermal deBroglie wavelength becomes longer than the average distance between atoms. Dilutegas condensates of density n in axially-symmetric traps are characterized by four length scales: Their radius R ⊥ , their axial half-length R z , the scattering length a which parameterizes the strength of the two-body interaction, and the healing length ξ = (4πna) −1/2 . In almost all experiments on Bose-Einstein condensates, both the radius and length are determined by the interaction between the atoms and thus, R ⊥ , R z ≫ ξ ≫ a. In this regime, a BEC is three-dimensional and is well-described by the socalled Thomas-Fermi approximation [1]. A qualitatively different behavior of a BEC is expected when the healing length is larger than either R ⊥ or R z since then the condensate becomes restricted to one or two dimensions, respectively. New phenomena that may be observed in this regime are for example quasi-condensates [2-4] and a Tonk's gas of impenetrable bosons [4][5][6].In this Letter, we report the experimental realization of cigar-shaped one-dimensional condensates with R z > ξ > R ⊥ and disk-shaped two-dimensional condensates with R ⊥ > ξ > R z . The cross-over from 3D to 1D or 2D was explored by reducing the number of atoms in condensates which were trapped in highly elongated magnetic traps (1D) and disk-shaped optical traps (2D) and measuring the release energy. In harmonic traps, lower dimensionality is reached when µ 3D = 4π 2 a n/m < ω t . Here, ω t is the trapping frequency in the tightly confining dimension(s) and µ 3D is the interaction energy of a weakly interacting BEC, which in 3D corresponds to the chemical potential. Other experiments in which the interaction energy was comparable to the level spacing of the confining potential include condensates in onedimensional optical lattices [8] and the cross-over to an ideal-gas (zero-D) condensate [7], both at relatively low numbers of condensate atoms.Naturally, the number of interacting atoms in a lowerdimensional condensate is limited. The peak interaction energy of a 3D condensate of N atoms with mass m is given by1/2 are the oscillator lengths of the harmonic potential. The cross-over to 1D and 2D, defined by µ 3D = ω t or equivalently ξ = l t occurs if the number of condensate atoms becomeswhere we have used the scattering length (a = 2.75 nm) and mass of 23 Na atoms to derive the numerical factor. Our traps feature extreme aspect ratios resulting in N 1D > ...

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Cited by 78 publications

References 11 publications

Quantum impurity in a one-dimensional trapped Bose gas

Quantum impurity in a one-dimensional trapped Bose gas

Low-dimensional trapped gases

Realization of Bose-Einstein Condensates in Lower Dimensions

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