Rotating Bose-Einstein condensate with attractive interaction in one dimension: Single-<i>L</i>states and mesoscopics

Kartsev, P. F.

doi:10.1103/physreva.68.063613

Cited by 6 publications

(3 citation statements)

References 13 publications

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“…For n 2 and l 0 /r 0 → 0 this potential approaches the limit of a toroidal trap with zero width, which has been considered often in previous theoretical studies (see, e.g., Ref. [249]). In the following, we consider the case with n = 2, which is more realistic from the experimental point of view.…”

Section: Variational Description Of Rotating Boson Moleculesmentioning

confidence: 79%

Symmetry breaking and quantum correlations in finite systems: studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods

Yannouleas¹,

Landman²

2007

Rep. Prog. Phys.

240

358

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Investigations of emergent symmetry breaking phenomena occurring in small finite-size systems are reviewed, with a focus on the strongly correlated regime of electrons in two-dimensional semiconductor quantum dots and trapped ultracold bosonic atoms in harmonic traps. Throughout the review we emphasize universal aspects and similarities of symmetry breaking found in these systems, as well as in more traditional fields like nuclear physics and quantum chemistry, which are characterized by very different interparticle forces. A unified description of strongly correlated phenomena in finite systems of repelling particles (whether fermions or bosons) is presented through the development of a two-step method of symmetry breaking at the unrestricted Hartree–Fock level and of subsequent symmetry restoration via post Hartree–Fock projection techniques. Quantitative and qualitative aspects of the two-step method are treated and validated by exact diagonalization calculations. Strongly-correlated phenomena emerging from symmetry breaking include the following. Chemical bonding, dissociation and entanglement (at zero and finite magnetic fields) in quantum dot molecules and in pinned electron molecular dimers formed within a single anisotropic quantum dot, with potential technological applications to solid-state quantum-computing devices. Electron crystallization, with particle localization on the vertices of concentric polygonal rings, and formation of rotating electron molecules (REMs) in circular quantum dots. Such electron molecules exhibit ro-vibrational excitation spectra, in analogy with natural molecules. At high magnetic fields, the REMs are described by parameter-free analytic wave functions, which are an alternative to the Laughlin and composite-fermion approaches, offering a new point of view of the fractional quantum Hall regime in quantum dots (with possible implications for the thermodynamic limit). Crystalline phases of strongly repelling bosons. In rotating traps and in analogy with the REMs, such repelling bosons form rotating boson molecules (RBMs). For a small number of bosons, the RBMs are energetically favored compared with the Gross–Pitaevskii solutions describing vortex formation. We discuss the present status concerning experimental signatures of such strongly correlated states, in view of the promising outlook created by the latest experimental improvements that are achieving unprecedented control over the range and strength of interparticle interactions.

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Section: Variational Description Of Rotating Boson Moleculesmentioning

confidence: 79%

Symmetry breaking and quantum correlations in finite systems: studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods

Yannouleas¹,

Landman²

2007

Rep. Prog. Phys.

240

358

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“…For n ≫ 2 and l 0 /r 0 → 0 this potential approaches the limit of a toroidal trap with zero width, which has been considered often in previous theoretical studies (see, e.g., Ref. [11]). In the following, we consider the case with n = 2, which is more realistic from the experimental point of view.…”

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confidence: 87%

Bosonic Molecules in Rotating Traps

et al. 2006

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We present a variational many-body wave function for repelling bosons in rotating traps, focusing on rotational frequencies that do not lead to restriction to the lowest Landau level. This wave function incorporates correlations beyond the Gross-Pitaevskii (GP) mean field approximation, and it describes rotating boson molecules (RBMs) made of localized bosons that form polygonal-ring-like crystalline patterns in their intrinsic frame of reference. The RBMs exhibit characteristic periodic dependencies of the ground-state angular momenta on the number of bosons in the polygonal rings. For small numbers of neutral bosons, the RBM ground-state energies are found to be always lower than those of the corresponding GP solutions, in particular in the regime of GP vortex formation.PACS numbers: 05.30. Jp, 03.75.Hh Recent experimental advances in the field of trapped ultracold neutral bosonic gases have enabled control of the strength of interatomic interactions over wide ranges [1,2,3,4], from the very weak to the very strong. This control is essential for experimental realizations of novel states of matter beyond the well known Bose-Einstein condensate [2,3,4]. In this context, the linear 1D TonksGirardeau regime of impenetrable trapped bosons has generated intensive theoretical activity [5,6] and several experimental realizations of it have been reported most recently [3,4].Here we address the properties of strongly-repelling impenetrable bosons in rotating ring-shaped or 2D harmonic traps. To this end, we recall that impenetrable bosons are "localized" relative to each other [4,7] and exhibit nontrivial intrinsic crystalline correlations [7]. For a small number of bosons, N , these crystalline arrangements are reminiscent of the structures exibited by the well-studied rotating electron molecules (REMs) in quantum dots under high magnetic fields [8,9]. Consequently, we use in the following the term rotating boson molecules (RBMs). A central result of our study is that the point-group symmetries of the intrinsic crystalline structures give rise to characteristic regular patterns (see below) in the ground-state spectra and associated angular momenta of the RBMs as a function of the rotational frequency for neutral bosons (or the magnetic field for charged bosons).An unexpected result of our studies is that the rotation of repelling bosons (even those interacting weakly) does not necessarily lead to formation of vortices, as is familiar from the case of rotating Bose-Einstein condenstates (BECs). In particular, for small N , we will show that the Gross-Pitaevskii energies (including those corresponding to formation of vortices) remain always higher compared to the ground-state energies of the RBMs. Of course, we expect that the rotating BEC will become the preferred ground state for sufficiently large N in the case of weakly repelling neutral bosons. We anticipate, however, that it will be feasible to test our unexpected results for small N by using rotating optical lattices, where it is established that a small finite...

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“…This includes the study of the lack of superfluidity in attractive condensates [16] indicating the fact that, if the external rotation is stopped, the condensate relaxes to the non-rotating ground state, independently of the initial rotational state. Recently, these topics have been studied in one dimension where even exact results have been obtained [17,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

Collective modes and the broken symmetry of a rotating attractive Bose gas in an anharmonic trap

Collin¹

2006

Phys. Rev. A

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We study the rotational properties of an attractively interacting Bose gas in a quadratic + quartic potential. The low-lying modes of both rotational ground state configurations, namely the vortex and the center of mass rotating states, are solved. The vortex excitation spectrum is positive for weak interactions but the lowest modes decrease rapidly to negative values when the interactions become stronger. The broken rotational symmetry involved in the center of mass rotating state induces the appearance of an extra zero-energy mode in the Bogoliubov spectrum. The excitations of the center of mass rotational state also demonstrate the coupling between the center of mass and relative motions.

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Rotating Bose-Einstein condensate with attractive interaction in one dimension: Single-Lstates and mesoscopics

Cited by 6 publications

References 13 publications

Symmetry breaking and quantum correlations in finite systems: studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods

Symmetry breaking and quantum correlations in finite systems: studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods

Bosonic Molecules in Rotating Traps

Collective modes and the broken symmetry of a rotating attractive Bose gas in an anharmonic trap

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