A. Muñoz Mateo

Effective mean-field equations for cigar-shaped and disk-shaped Bose-Einstein condensates

By applying the standard adiabatic approximation and using the accurate analytical expression for the corresponding local chemical potential obtained in our previous work [Phys. Rev. A \textbf{75}, 063610 (2007)] we derive an effective 1D equation that governs the axial dynamics of mean-field cigar-shaped condensates with repulsive interatomic interactions, accounting accurately for the contribution from the transverse degrees of freedom. This equation, which is more simple than previous proposals, is also more accurate. Moreover, it allows treating condensates containing an axisymmetric vortex with no additional cost. Our effective equation also has the correct limit in both the quasi-1D mean-field regime and the Thomas-Fermi regime and permits one to derive fully analytical expressions for ground-state properties such as the chemical potential, axial length, axial density profile, and local sound velocity. These analytical expressions remain valid and accurate in between the above two extreme regimes. Following the same procedure we also derive an effective 2D equation that governs the transverse dynamics of mean-field disk-shaped condensates. This equation, which also has the correct limit in both the quasi-2D and the Thomas-Fermi regime, is again more simple and accurate than previous proposals. We have checked the validity of our equations by numerically solving the full 3D Gross-Pitaevskii equation.

Dynamical evolution of a doubly quantized vortex imprinted in a bose-einstein condensate

The recent experiment by Shin et al. [Phys. Rev. Lett. 93, 160406 (2004)] on the decay of a doubly quantized vortex is analyzed by numerically solving the Gross-Pitaevskii equation. Our results demonstrate that the vortex decay is mainly a consequence of dynamical instability. The monotonic increase observed in the vortex lifetimes is a consequence of the fact that the measured lifetimes incorporate the time it takes for the initial perturbation to reach the central slice. When considered locally, the splitting occurs approximately at the same time in every condensate.

Extension of the Thomas-Fermi approximation for trapped Bose-Einstein condensates with an arbitrary number of atoms

By incorporating the zero-point energy contribution we derive simple and accurate extensions of the usual Thomas-Fermi (TF) expressions for the ground-state properties of trapped Bose-Einstein condensates that remain valid for an arbitrary number of atoms in the mean-field regime. Specifically, we obtain approximate analytical expressions for the ground-state properties of spherical, cigar-shaped, and disk-shaped condensates that reduce to the correct analytical formulas in both the TF and the perturbative regimes, and remain valid and accurate in between these two limiting cases. Mean-field quasi-one-dimensional (quasi-1D) and -2D condensates appear as simple particular cases of our formulation. The validity of our results is corroborated by an independent numerical computation based on the 3D Gross-Pitaevskii equation.

Persistent currents supported by solitary waves in toroidal Bose-Einstein condensates

We analyze the generation of persistent currents in Bose-Einstein condensates of ultracold gases confined in a ring. This phenomenon has been recently investigated in an experiment [Nature 506, 200 (2014)], where hysteresis loops have been observed in the activation of quantized persistent currents by rotating weak links. In this work, we demonstrate the existence of 3D stationary currents with non-quantized angular momentum. They are generated by families of solitary waves that show a continuous variation in the angular momentum, and provide a bridge between different winding numbers. We show that the size of hysteresis loops is determined by the range of existence within the weak link region of solitary waves which configure the energy barrier preventing phase slips. The barrier vanishes when the critical rotation leads winding numbers and solitonic states to a matching configuration. At this point, Landau and Feynman criteria for phase slips meet: the fluid flow reaches the local speed of sound, and stationary vortex lines (which are the building blocks of solitons) can be excited inside the system.

Three-dimensional gap solitons in Bose-Einstein condensates supported by one-dimensional optical lattices

ER/¯ hω⊥ = 1 corresponds to the 87 Rb condensate, with s-wave scattering length as = 5.29 nm, confined by the combination of the transverse trapping frequency ω⊥/2π = 240 Hz and axial OL of period d = 1.55 µm (physical results given in this article correspond to this typical setting). In this regime, the axial GS structure may readily excite higher modes of the radial confinement; hence the 3D character of the dynamics is essential and the 1D reduction cannot be used. The situation is somewhat similar to that for quasi-1D GSs, which were predicted, in the framework of the density-functional description, in fermionic superfluids [12]. In that case, the underlying Fermi distribution implies the filling of many transverse energy levels. While there are models that generalize the 1D GPE by taking into account small deviations from the one-dimensionality [9,10], we consider the setting in which the axial and radial directions are equally important and inseparable; hence the use of the full 3D equation is necessary. We demonstrate that stable solitons, which are true gap modes in terms of the underlying 3D band-gap structure, exist in this regime, suggesting possibilities for the creation of robust 3D solitons. This objective is of principal significance because, thus far, no truly 2D or 3D matter-wave solitons, nor their counterparts in optical media with the Kerr nonlinearity, have been created, in spite of many theoretical predictions [13]. We also find solitons inside the bands, which may exist due to the difference in the azimuthal index between the soliton and the band.

Vortex lines attached to dark solitons in Bose-Einstein condensates and boson-vortex duality in 3+1 dimensions

We demonstrate the existence of stationary states composed of vortex lines attached to planar dark solitons in scalar Bose-Einstein condensates. Dynamically stable states of this type are found at low values of the chemical potential in channeled condensates, where the long-wavelength instability of dark solitons is prevented. In oblate, harmonic traps, U-shaped vortex lines attached by both ends to a single planar soliton are shown to be long-lived states. Our results are reported for parameters typical of current experiments, and open up a way to explore the interplay of different topological structures. These configurations provide Dirichlet boundary conditions for vortex lines and thereby mimic open strings attached to D-branes in string theory. We show that these similarities can be formally established by mapping the Gross-Pitaevskii theory into a dual effective string theory for open strings via a boson-vortex duality in 3+1 dimensions. Combining a one-form gauge field living on the soliton plane which couples to the endpoints of vortex lines and a two-form gauge field which couples to vortex lines, we obtain a gauge-invariant dual action of open vortex lines with their endpoints attached to dark solitons.

Accurate one-dimensional effective description of realistic matter-wave gap solitons

We consider stationary matter-wave gap solitons realized in Bose–Einstein condensates loaded in one-dimensional (1D) optical lattices and investigate whether the effective 1D equation proposed in Munoz Mateo and Delgado (2008 Phys. Rev. A 77 013617) can be a reliable alternative to the three-dimensional treatment of this kind of system in terms of the Gross–Pitaevskii equation (GPE). Our results demonstrate that, unlike the standard 1D GPE (which is not applicable in most realistic situations), the above effective model is able to correctly predict the distinctive trajectories characterizing the different gap soliton families as well as the corresponding axial wavefunctions along the entire band gaps. It can also predict the stability properties of the different gap soliton families as follows from both a linear stability analysis and a representative set of numerical computations. In particular, by numerically solving the corresponding Bogoliubov–de Gennes equations we show that the effective 1D model gives the correct spectrum of the complex eigenfrequencies responsible for the dynamical stability of the system, thus providing us with a useful tool for the physical description of stationary matter-wave gap solitons in 1D optical lattices.

Stable symmetry-protected 3D embedded solitons in Bose–Einstein condensates

Embedded solitons are rare self-localized nonlinear structures that, counterintuitively, survive inside a continuous background of resonant states. While this topic has been widely studied in nonlinear optics, it has received almost no attention in the field of Bose–Einstein condensation. In this work, we consider experimentally realizable Bose–Einstein condensates loaded in one-dimensional optical lattices and demonstrate that they support continuous families of stable three-dimensional (3D) embedded solitons. These solitons can exist inside the resonant continuous Bloch bands because they are protected by symmetry. The analysis of the Bogoliubov excitation spectrum as well as the long-term evolution after random perturbations proves the robustness of these nonlinear structures against any weak perturbation. This may open up a way for the experimental realization of stable 3D matter-wave embedded solitons as well as for monitoring the gap-soliton to embedded-soliton transition.

Multidimensional Josephson vortices in spin-orbit coupled Bose-Einstein condensates: snake instability and decay through vortex dipoles

We analyze the dynamics of Josephson vortex states in two-component Bose-Einstein condensates with Rashba-Dresselhaus spin-orbit coupling by using the Gross-Pitaevskii equation. In 1D, both in homogeneous and harmonically trapped systems, we report on stationary states containing doubly charged, static Josephson vortices. In multidimensional systems, we find stable Josephson vortices in a regime of parameters typical of current experiments with

Effective one-dimensional dynamics of elongated Bose–Einstein condensates

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