We investigate the origin of a disagreement between the two-mode model and the exact Gross-Pitaevskii dynamics applied to double-well systems. In general this model, even in its improved version, predicts a faster dynamics and underestimates the critical population imbalance separating Josephson and self-trapping regimes. We show that the source of this mismatch in the dynamics lies in the value of the on-site interaction energy parameter. Using simplified Thomas-Fermi densities, we find that the on-site energy parameter exhibits a linear dependence on the population imbalance, which is also confirmed by Gross-Pitaevskii simulations. When introducing this dependence in the two-mode equations of motion, we obtain a reduced interaction energy parameter which depends on the dimensionality of the system. The use of this new parameter significantly heals the disagreement in the dynamics and also produces better estimates of the critical imbalance.Comment: 5 pages, 4 figures, accepted in PR

We present full three-dimensional numerical calculations of single vortex states in rotating dipolar condensates. We consider a Bose-Einstein condensate of 52 Cr atoms with dipole-dipole and swave contact interactions confined in an axially symmetric harmonic trap. We obtain the vortex states by numerically solving the Gross-Pitaevskii equation in the rotating frame with no further approximations. We investigate the properties of a single vortex and calculate the critical angular velocity for different values of the s-wave scattering length. We show that, whereas the standard variational approach breaks down in the limit of pure dipolar interactions, exact solutions of the Gross-Pitaevskii equation can be obtained for values of the s-wave scattering length down to zero. The energy barrier for the nucleation of a vortex is calculated as a function of the vortex displacement from the rotation axis for different values of the angular velocity of the rotating trap.

We study a Bose-Einstein condensate of 52 Cr atoms confined in a toroidal trap with a variable strength of s-wave contact interactions. We analyze the effects of the anisotropic nature of the dipolar interaction by considering the magnetization axis to be perpendicular to the trap symmetry axis. In the absence of a central repulsive barrier, when the trap is purely harmonic, the effect of reducing the scattering length is a tuning of the geometry of the system: from a pancakeshaped condensate when it is large, to a cigar-shaped condensate for small scattering lengths. For a condensate in a toroidal trap, the interaction in combination with the central repulsive Gaussian barrier produces an azimuthal dependence of the particle density for a fixed radial distance. We find that along the magnetization direction the density decreases as the scattering length is reduced but presents two symmetric density peaks in the perpendicular axis. For even lower values of the scattering length we observe that the system undergoes a dipolar-induced symmetry breaking phenomenon. The whole density becomes concentrated in one of the peaks, resembling an origindisplaced cigar-shaped condensate. In this context we also analyze stationary vortex states and their associated velocity field, finding that this latter also shows a strong azimuthal dependence for small scattering lengths. The expectation value of the angular momentum along the z direction provides a qualitative measure of the difference between the velocity in the different density peaks.

We study the population dynamics of a ring-shaped optical lattice with a high number of particles per site and a low (less than ten) number of wells. Using a localized on-site basis defined in terms of stationary states, we were able to construct a multiple-mode model depending on relevant hopping and on-site energy parameters. We show that in the case of two wells, our model corresponds exactly to a recent improvement of the two-mode model. We derive a formula for the self-trapping period, which turns out to be chiefly ruled by the on-site interaction energy parameter. By comparing to time-dependent Gross-Pitaevskii simulations, we show that the multimode model results can be enhanced in a remarkable way over all the regimes by only renormalizing such a parameter. Finally, using a different approach which involves only the ground-state density, we derive an effective interaction energy parameter that turns out to be in accordance with the renormalized one.

Using a functional-integral approach, we have determined the temperature below which cavitation in liquid helium is driven by thermally assisted quantum tunneling. For both helium isotopes, we have obtained the crossover temperature in the whole range of allowed negative pressures. Our results are compatible with recent experimental results on 4 He. ͓S0163-1829͑96͒01946-7͔The possibility of having observed quantum cavitation in superfluid 4 He has been put forward by Balibar et al. 1 These authors have used a hemispherical transducer that focuses a sound wave in a small region of a cell where cavitation is induced in liquid 4 He at low temperature. The analysis of their experimental data is complicated by the fact that neither the pressure ( P) nor the temperature (T) at the focus can be directly measured. This makes the determination of the thermal-to-quantum cavitation crossover temperature T* depend on the theoretical equation of state ͑EOS͒ near the spinodal point. Using the results of Ref. 2, they conclude that T*ϳ 200 mK, in agreement with the prediction of Ref. 2. However, using for instance the EOS of Ref. 3, which reproduces the spinodal point microscopically calculated by Boronat et al.,4,5 the ''experimental'' result becomes 120 mK. The first detailed description of the cavitation process in liquid helium was provided by Lifshitz and Kagan, 6 who used the classical capillarity model near the saturation line, and a density functional-like description near the spinodal line. More recently, the method has been further elaborated by Xiong and Maris.7 These authors conclude that there is no clear way to interpolate between these two regimes, which makes quite uncertain the range of pressures in which each of them is valid.In this work, we determine T* for 3 He and 4 He using a functional-integral approach ͑FIA͒ in conjunction with a density functional description of liquid helium. The method overcomes the conceptual limitations of previous works based on the application of zero-temperature multidimensional WKB methods, 2 and the technical ones inherent to the use of parametrized bubble density profiles, 8 thus putting on firmer grounds the theoretical results. Moreover, it gives T* in the whole pressure range.Thermally assisted quantum tunneling is nowadays well understood ͑see for example Ref. 9 and references therein͒. Let us simply recall that at high temperatures, the cavitation rate, i.e., the number of bubbles formed per unit time and volume, is given bywhere ⌬⍀ max is the barrier height for thermal activation and J 0T is a prefactor which depends on the dynamics of the cavitation process. At low T, it becomeswhere S min is the minimum of the imaginary-time action ͑3͒L being the imaginary-time classical Lagrangian density of the system and the time integration is extended over a period in the potential well obtained by inverting the potential barrier. These equations hold provided the rate can be calculated in the semiclassical limit, i.e., S min ӷ1, which is the present case. For a given value of T,...

We propose a new scheme for observing Josephson oscillations and macroscopic quantum self-trapping in a toroidally confined Bose-Einstein condensate: a dipolar self-induced Josephson junction. Polarizing the atoms perpendicularly to the trap symmetry axis, an effective ring-shaped, double-well potential is achieved which is induced by the dipolar interaction. By numerically solving the three-dimensional time-dependent Gross-Pitaevskii equation we show that coherent tunneling phenomena such as Josephson oscillations and quantum self-trapping can take place. The dynamics in the self-induced junction can be qualitatively described by a two-mode model taking into account both s-wave and dipolar interactions.

We study a confined mixture of bosons and fermions in the quantal degeneracy regime with attractive boson-fermion interaction. We discuss the effect that the presence of vortical states and the displacement of the trapping potentials may have on mixtures near collapse, and investigate the phase stability diagram of the K-Rb mixture in the mean-field approximation supposing in one case that the trapping potentials felt by bosons and fermions are shifted from each other, as it happens in the presence of a gravitational sag, and in another case, assuming that the Bose condensate sustains a vortex state. In both cases, we have obtained an analytical expression for the fermion effective potential when the Bose condensate is in the Thomas-Fermi regime, that can be used to determine the maxima of the Fermionic density. We have numerically checked that the values one obtains for the location of these maxima using the analytical formulas remain valid up to the critical boson and fermion numbers, above which the mixture collapses.

The high-barrier quantum tunneling regime of a Bose-Einstein condensate confined in a ring-shaped optical lattice is investigated. By means of a change of basis transformation, connecting the set of "vortex" Bloch states and a Wannier-like set of localized wave functions, we derive a generalized Bose-Hubbard Hamiltonian. In addition to the usual hopping rate terms, such a Hamiltonian takes into account interaction-driven tunneling processes, which are shown to play a principal role at high filling factors, when the standard hopping rate parameter turns out to be negative. By calculating the energy and atomic current of a Bloch state, we show that such a hopping rate must be replaced by an effective hopping rate parameter containing the additional contribution an interaction-driven hopping rate. Such a contribution turns out to be crucial at high filling factors, since it preserves the positivity of the effective hopping rate parameter. Level crossings between the energies per particle of a Wannier-like state and the superfluid ground state are interpreted as a signature of the transition to configurations with macroscopically occupied states at each lattice site.