We investigate the groundstates of weakly interacting bosons in a rotating trap as a function of the number of bosons, N , and the average number of vortices, NV . We identify the filling fraction ν ≡ N/NV as the parameter controlling the nature of these states. We present results indicating that, as a function of ν, there is a zero temperature phase transition between a triangular vortex lattice phase, and strongly-correlated vortex liquid phases. The vortex liquid phases appear to be the Read-Rezayi parafermion states.PACS Numbers: 03.75.Fi, 73.40.Hm, 67.57.Fg A fundamental characteristic of condensed Bose systems is their response to rotation [1]. A transition to a "normal" phase might be expected at sufficiently high angular velocities, ω, of the container (or trap) by loose analogy with a superconductor in a magnetic field. At zero temperature this phase would constitute a novel uncondensed ground state. Such a regime is entered when the vortex cores start to overlap. The corresponding value of ω is unattainable with bulk 4 He, but may be achievable in the very dilute degenerate atomic gases initially explored in Ref.[2], and studied extensively in Refs. [3][4][5][6][7][8][9], Apart from the identification [5] of the Laughlin state as the ground state at sufficiently high ω, work on the most interesting regime of large numbers of vortices has been restricted to either mean field theory [3] or exact diagonalisation [5][6][7][8]. These two approaches have exhibited apparently contradictory pictures. Within Gross-Pitaevskii (GP) mean-field theory, the groundstates are vortex lattices (distorted by the confinement), with broken rotational symmetry [3]. On the other hand, exact diagonalisations have identified groundstates which do not have crystalline correlations of vortex locations [5]; they are strongly correlated vortexliquids, closely related to incompressible liquid states responsible for the fractional quantum Hall effect [5][6][7].Here we present results of extensive exact diagonalisations (EDs) that elucidate the relationship between these two pictures. By using a periodic geometry, we have been able to study systems containing many vortices up to boson densities far in excess of previous EDs. Our results indicate that both crystalline and liquid phases of vortices exist. A clean distinction between these phases can only be made for a large number of vortices. In this limit, we argue that there is a zero-temperature phase transition as a function of the "filling fraction", ν ≡ N/N V , the ratio of the number of bosons, N , to the average number of vortices, N V . For large ν, the groundstate is a vortex lattice (characterised by broken translational/rotational symmetry). For small ν the groundstates are strongly-correlated vortex liquids. We find that the vortex-liquid groundstates are related to the ReadRezayi "parafermion" states [10] that were introduced in the context of fractional quantum Hall systems.In a frame of reference rotating with angular velocity ωẑ, the Hamiltonian for a particle of m...

Motivated by experiments on bose atoms in traps which have attractive interactions (e.g. 7 Li), we consider two models which may be solved exactly. We construct the ground states subject to the constraint that the system is rotating with angular momentum proportional to the number of atoms. In a conventional system this would lead to quantised vortices; here, for attractive interactions, we find that the angular momentum is absorbed by the centre of mass motion. Moreover, the state is uncondensed and is an example of a 'fragmented' condensate discussed by Nozières and Saint James. The same models with repulsive interactions are fully condensed in the thermodynamic limit.One of the most novel aspects of the creation of Bose condensates with neutral atoms in traps is the possibility of observing a bose gas with attractive interactions (negative scattering lengths). The case of 7 Li has been studied both experimentally [1,2] and theoretically. Condensation has been predicted to be stable for a sufficiently small number of particles or sufficiently weak interactions [3,4]. The instability to collapse when these conditions are not obeyed has also been discussed by several authors [5][6][7][8][9].In this Letter we show, using two exactly soluble models, that there may be other possibilities for noncondensed states with attractive interactions. The states are the 'fragmented' condensates discussed by Nozières and Saint James [10] in the context of excitonic bose condensates. The possibility of such states emerges from the realisation [11] that it is the exchange interaction which causes bosons with repulsive interactions to condense into a single one-particle state, if there are several one-particle ground states. Conversely for attractive interactions, the exchange term is negative and may prefer 'fragmented' [10] condensation into more than one state if there is a degeneracy (or perhaps if the interactions are sufficiently strong). Kagan et al. [4] argue that trapped gases with sufficiently large negative scattering lengths are unstable to the formation of clusters using a somewhat different argument, but with the same physical origin.The two models we examine are: particles in a harmonic trap with L quanta of angular momenta with attractive interactions treated as a degenerate perturbation [12]; rotating particles in a harmonic trap interacting with harmonic interactions [13][14][15][16]. (Both of these cases have been of interest for fermions [12,14], where rotation is replaced by a magnetic field and the phenomena are related to the fractional quantum Hall effect.) Rotation is considered in both cases, partly because the non-rotating ground state, in the thermodynamic limit, is trivial in both cases (for different reasons) and partly because the response to rotation is characteristic of superfluidity in the system [17,18].Consider the two-dimensional Hamiltonianin the limit where the dimensionless coupling is weak, |η| ≪ 1, so that the contact interaction can be treated perturbatively. We will now determine the gr...

We provide evidence for several novel phases in the dilute limit of rotating Bose-Einstein condensates. By exact calculation of wave functions and energies for small numbers of particles, we show that the states near integer angular momentum per particle are best considered condensates of composite entities, involving vortices and atoms. We are led to this result by explicit comparison with a description purely in terms of vortices. Several parallels with the fractional quantum Hall effect emerge, including the presence of the Pfaffian state.

We study the properties of rotating Bose-Einstein condensates in parabolic traps, with coherence length large compared to the system size. In this limit, it has been shown that unusual groundstates form which cannot be understood within a conventional many-vortex picture. Using comparisons with exact numerical results, we show that these groundstates can be well-described by a model of non-interacting "composite fermions". Our work emphasises the similarities between the novel states that appear in rotating Bose-Einstein condensates and incompressible fractional quantum Hall states.PACS Numbers: 03.75.Fi, 73.40.Hm, 67.57.Fg It has proved fruitful in fractional quantum Hall systems [1] to account for the many-body correlations induced by electron-electron interactions by introducing non-interacting "composite fermions" [2]. Recently a similar approach has been employed to show that the correlated states arising from interparticle interactions in dilute rotating confined bose atomic gases can be described in terms of the condensation of a type of composite boson [3]. Here, we demonstrate that a transformation of the system of rotating bosons to that of non-interacting composite fermions is also successful in accounting for these correlated states. Our results establish a close connection between the groundstates of rotating confined Bosesystems and the correlated states of fractional quantum Hall systems [1].While the trapped atom gases have been shown to Bose-condense [4,5], the response of these condensates to rotations has not, as yet, been measured experimentally. Theoretically, it is clear that there exist various different regimes. Within the Gross-Pitaevskii framework, which requires macroscopic occupation of the single particle states, the system forms vortex arrays at both long [6] and short [7] coherence lengths (compared to the size of the trap), which are reminiscent of Helium-4. Here, following Ref.[3], we choose to study the system in the limit of large coherence length without demanding macroscopic occupation numbers. This allows us to study both the regime considered in Ref. [6], as well as regimes of higher vortex density where the quantum mechanical nature of the vortices will be most prevalent. Indeed, in Ref. [3] it was shown that, in general, the groundstates of the rotating boson system cannot be described within a conventional many-vortex picture. Rather, the system was found to be better described in terms of the condensation of "composite bosons" -bound states of vortices and atoms -across the whole range of vortex density. In the present paper, we show that a description in terms of non-interacting composite particles with fermionic statistics also provides a highly accurate description of the rotating bose system: specifically, it enables us to predict many of the features in the energy spectrum and to form good overlaps with the exact groundstate wavefunctions. In addition, this description indicates a close relationship between the properties of rotating Bose systems and those of fr...

We consider a model of N two-dimensional bosons in a harmonic potential with weak repulsive delta-function interactions. We show analytically that, for angular momentum L ≤ N , the elementary symmetric polynomials of particle coordinates measured from the center of mass are exact eigenstates with energy N (N − L/2 − 1). Extensive numerical analysis confirms that these are actually the ground states, but we are currently unable to prove this analytically. The special case L = N can be thought of as the generalisation of the usual superfluid one-vortex state to Bose-Einstein condensates in a trap.

With the imminent advent of mesoscopic rotating BECs in the lowest Landau level (LLL) regime, we explore LLL vortex nucleation. An exact many-body analysis is presented in a weakly elliptical trap for up to 400 particles. Striking non-mean field features are exposed at filling factors ≫ 1. E. g. near the critical rotation frequency pairs of energy levels approach each other with exponential accuracy. A physical interpretation is provided by requantising a mean field (MF) theory, where 1/N plays the role of Planck's constant, revealing two vortices cooperatively tunneling between classically degenerate energy minima. The tunnel splitting variation is described in terms of frequency, particle number and ellipticity.PACS numbers: 03.75.Hh, 03.75.LmThe physics of vortices in slowly rotating degenerate gases [1] has reached the level of maturity where it is now used as a tool to study other phenomena, such as polarised fermi gases [2]. However achieving rapid rotation -to explore thoroughly the MF quantum Hall (QH) regime [3,4,5,6] in the lowest Landau level (LLL) [7] and to reach correlated QH states [7,8,9] -remains a challenge.A promising approach to accessing the QH regime is to have very dilute BECs, perhaps constructed by slicing up a condensate with an optical lattice [10]. In this Letter we show that even well away from the correlated regime there are pronounced quantum effects which become increasingly striking as the particle number decreases. We will show that the exact many-body ground states may be interpreted as exhibiting vortex tunneling leading to superpositions of mean-field states with vortices residing at different locations. This mesoscopic limit is consistent with the thrust of experimental effort in the near future. (In terms of ν = N/N v , where N is the number of particles, and N v the number of vortices, ν = 1/2 corresponds to the Laughlin state, and we will study 10 ν 400.) Vortex nucleation [11] has been studied in the ThomasFermi regime, both experimentally [12,13,14] and theoretically [15,16]. The conclusion is that under adiabatic ramping of the rotation frequency [13,14,15] the process is determined by an hydrodynamic instability. Under those conditions, the thermodynamic instability to vortex entry is apparently unobservable, occurring at lower rotation frequencies.It is known [17] that in a BEC in the LLL in an axisymmetric(AS) trap that there is a first-order thermodynamic instability to vortex entry (with no hydrodynamic instability needed). In this Letter, we will show that the situation is very different in a non-AS trap. The equilibrium of vortices in a non-AS trap has already been analysed at a MF level [18,19,20] within the LLL[21] and at the Bogoliubov level[22]).Our starting point is the standard model Hamiltonian, H, for a cold gas of N particles residing in a plane:Units of length, a ⊥ , and energy, ω ⊥ , are those provided by the harmonic trap; angular momenta, L z n are scaled by . There are two remaining dimensionless parameters. Firstly, Ω, is the angular velocity of ...

PACS. 74.60Ge -Flux pinning, flux creep, and flux-line lattice dynamics. PACS. 05.40+j -Fluctuation phenomena, random processes, and Brownian motion.Abstract. -We report on two-dimensional simulations of the avalanche response of vortices in the Bean critical state of type-II superconductors. Two different kinds of repulsive-particle models are considered in order to make the findings generic. We use repulsive two-body potentials to represent the vortex-vortex interaction and an attractive two-body potential to represent the interaction between the static pinning wells and the vortices. We find that a collection of very short-ranged dense pinning centres leads to a broad distribution of response avalanches, whereas broader and less dense pinning centres produce a narrow distribution of responses.c Les Editions de Physique

We investigate the effects of disorder on a layered superconductor. The clean system is known to have a first order phase transition which is clearly identified by a sharp peak in the specific heat. The peak is lost abruptly as the strength of the disorder is increased. Hence, for strong disorder there is no phase transition as a function of temperature but merely a crossover which is still detectable in the IV characteristic.Pacs Numbers:74.60.Ge, 64.60.Cn, 05. Disorder is known to play an important role in the phase diagram of even so-called clean superconductors at low temperatures and high magnetic fields. It has recently been show that these clean systems have a first order transition. It is believed that this transition is associated with melting or decoupling of the vortex system. The thermodynamic signal of the transition is lost at a 'critical point' below which pinning is thought to dominate the behaviour [1,2].Significant effort is currently being invested in attempting to understand theoretically the effect of disorder on the behaviour of the magnetic flux system in superconductors [3,4]. In this letter we discuss simulations of the phenomenological behaviour and response to disorder of a layered vortex system. Our model is deliberately made sufficiently simple that we are able to identify the mechanisms behind the effects we observe. We believe that our results demonstrate which degrees of freedom of the vortex system are necessary in order to interpret the real experimental data.We present the results of a 3D layered simulation in the presence of point disorder. We have included only the degrees of freedom associated with vortex lines, an approximation we believe to be valid away from the vicinity of the zero field transition, T c . The vortex lines consist of stacks of pancake vortices. These stacks are able to cross and to decouple when it becomes energetically favourable and this is an essential feature of the model. The clean system has a first order decoupling transition, with an entropy jump comparable to that seen experimentally away from T c : namely ≃ 0.4k B /pancake/layer. However, for strong disorder the first order transition is reduced to a gradual crossover. This can be seen in many aspects of the behaviour. The pronounced peak in the specific heat that is a feature of the clean system is no longer present and the diffusion becomes thermally activated with an energy scale set by the strength of the interlayer coupling. Thus the decoupling transition is replaced by a depinning crossover whose underlying mechanism is plastic cutting of the vortex lines. This is confirmed by direct measurement of the cutting frequency. Hence a vortex glass phase [5] cannot occur in this system since the divergence of the elastic creep barriers at vanishing driving force [6] will be cut-off by the finite activation energy barrier for plastic cutting of the flux lines. We analyze both thermodynamic and transport properties. The specific heat behaviour demonstrates that above a threshold disorder destroy...