Bosonic Molecules in Rotating Traps

Abstract

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...

Rapidly rotating boson molecules with long- or short-range repulsion: An exact diagonalization study

“…Motivated by the discovery in the case of electrons of REMs at high B (and from the fact that Wigner molecules form also at zero magnetic field [28,29,30,31,32,33]) some theoretical studies have most recently shown that analogous molecular patterns of localized bosons do form in the case of a small number of particles inside a static or rotating harmonic trap [34,35,36,37,38]. In analogy with the electron case, the bosonic molecular structures can be referred to [36] as rotating boson molecules (RBMs); a description of RBMs via a variational wave function [39] built from symmetry-breaking displaced Gaussian orbitals with subsequent restoration of the rotational symmetry was presented in Refs.…”

“…The quantity P (r, r 0 ) is proportional to the probability of finding a boson at r given that there is another boson at the observation point r 0 , and it is often referred to as the conditional probability distribution [22,23,30,33,34,36] (CPD). A main finding of our study is that consideration solely of the CPDs is not sufficient for the boson case at high fractional fillings ν ≥ 1/2; in this case, one needs to calculate even higher-order correlation functions, e.g., the full N -point correlation function P (r; r 1 , r 2 , ..., r N −1 ) [see Eq.…”

“…In analogy with the electron case, the bosonic molecular structures can be referred to [36] as rotating boson molecules (RBMs); a description of RBMs via a variational wave function [39] built from symmetry-breaking displaced Gaussian orbitals with subsequent restoration of the rotational symmetry was presented in Refs. [34,35,36].…”

Vortex patterns in moderately rotating Bose-condensed gas

“…The rotational properties of BEC and creation of vortices in a harmonic trap have been analyzed mostly by the mean-field approach like Gross-Pitaevskii scheme as in Refs. [22][23][24][25][26][27] or beyond the mean-field approximation [23,[28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”

Particle entanglement in rotating gases

“…Many excellent experimental and theoretical papers focus on the formation and melt of vortex lattice [5], many-body energy spectrum [6,7], its analogy to quantum Hall effect of electrons in a magnetic field [8][9][10][11][12][13], particle localization and vortex localization [14][15][16][17], the comparison between the results of exact quantum numerical solution and mean-field theory [18] and so on. However, the entanglement in this system has not been investigated as extensively as in other condensed matter systems, for example in spin chain systems.…”