Vortex rings and solitary waves in trapped Bose–Einstein condensates

We discuss nonlinear excitations in an atomic Bose–Einstein condensate which is trapped in a harmonic potential. We focus on axially symmetric solitary waves propagating along a cylindrical condensate. A quasi one-dimensional dark soliton is the only nonlinear mode for a condensate with weak interactions. For sufficiently strong interactions of experimental interest solitary waves are hybrids of one-dimensional dark solitons and three-dimensional vortex rings. The energy-momentum dispersion of these solitary waves exhibits characteristics similar to a mode proposed sometime ago by Lieb in a strictly 1D model, as well as some rotonlike features. We subsequently discuss interactions between solitary waves. Head-on collisions between dark solitons are elastic. Slow vortex rings collide elastically but faster ones form intermediate structures during collisions before they lose energy to the background fluid. Solitary waves and their interactions have been observed in experiments. However, some of their intriguing features still remain to be experimentally identified.     

Effects of spatially inhomogeneous atomic interactions on Bose–Einstein condensates in optical lattices

An interplay of optical lattices and nonlinear impurities in controlling the dynamics of Bose–Einstein condensate bright solitons is investigated using an effective potential approach. The ability of pushing the solitons into or away from the impurity region by changing both lattice and impurity parameters is suggested. A possibility for the existence of stable fundamental gap solitons, which appear to satisfy an inverted Vakhitov–Kolokolov criterion, is examined.     

Non-autonomous bright matter wave solitons in spinor Bose–Einstein condensates

We investigate the dynamics of bright matter wave solitons in spin-1 Bose–Einstein condensates with time modulated nonlinearities. We obtain soliton solutions of an integrable autonomous three-coupled Gross–Pitaevskii (3-GP) equations using Hirota?s method involving a non-standard bilinearization. The similarity transformations are developed to construct the soliton solutions of non-autonomous 3-GP system. The non-autonomous solitons admit different density profiles. An interesting phenomenon of soliton compression is identified for kink-like nonlinearity coefficient with Hermite–Gaussian-like potential strength. Our study shows that these non-autonomous solitons undergo non-trivial collisions involving condensate switching.     

Finite-temperature phase-locking transition in three-dimensional arrays of Josephson coupled Bose–Einstein condensates

We consider theoretically a phase-locking transition in Bose–Einstein condensate in an optical lattice in the regime where system can realized as a three-dimensional Josephson junction array. The coherence between adjacent Bose condensates (trapped in the valleys of the periodic potential) caused by the Josephson tunneling can lead to a phase transition with a global phase coherence at certain critical temperature. Using a model Hamiltonian of Josephson weakly coupled Bose condensates we calculate the critical temperature for the three-dimensional system placed in a simple cubic lattice and discuss the result in the context of system parameters and possible experiments.     

Macroscopic properties of triplon Bose–Einstein condensates

Magnetic insulators can be characterized by a gap separating the singlet ground state from the lowest-energy triplet, S=1 excitation. If the gap can be closed by the Zeeman interaction in applied magnetic field, the resulting quasiparticles, triplons, can have concentrations sufficient to undergo the Bose–Einstein condensates transition. We consider macroscopic properties of the triplon Bose–Einstein condensates in the Hartree–Fock–Bogoliubov approximation taking into account the anomalous averages. We prove that these averages play the qualitative role in the condensate properties. As a result, we show that with the increase in the external magnetic field at a given temperature, the condensate demonstrates an instability related to the appearance of nonzero phonon damping and a change in the characteristic dependence of the speed of sound on the magnetic field. The calculated magnetic susceptibility diverges when the external magnetic field approaches this instability threshold, providing a tool for the experimental verification of this approach.     

Vortices in a rotating two-component Bose–Einstein condensate with tunable interactions and harmonic potential

We consider a pair of coupled nonlinear Schrödinger equations modeling a rotating two-component Bose–Einstein condensate with tunable interactions and harmonic potential, with emphasis on the structure of vortex states by varying the strength of inter-component interaction, rotational frequency, and the aspect ratio of the harmonic potential. Our results show that the inter-component interaction greatly enhances the effect of rotation. For the case of isotropic harmonic potential and small inter-component interaction, the initial vortex structure remains unchanged. As the ratio of inter- to intra-component interactions increases, each component undergoes a transition from a vortex lattice (vortex line) in an isotropic (anisotropic) harmonic potential to an alternatively arranged stripe pattern, and eventually to the interwoven “serpentine” vortex sheets. Moreover, in the case of anisotropic harmonic potential the system can develop to a rotating droplet structure.     

Dipolar Bose–Einstein condensate soliton on a two-dimensional optical lattice

Using a three-dimensional mean-field model we study one-dimensional dipolar Bose–Einstein condensate (BEC) solitons on a weak two-dimensional (2D) square and triangular optical lattice (OL) potentials placed perpendicular to the polarization direction. The stabilization against collapse and expansion of these solitons for a fixed dipolar interaction and a fixed number of atoms is possible for short-range atomic interaction lying between two critical limits. The solitons collapse below the lower limit and escapes to infinity above the upper limit. One can also stabilize identical tiny BEC solitons arranged on the 2D square OL sites forming a stable 2D array of interacting droplets when the OL sites are filled with a filling factor of 1/2 or less. Such an array is unstable when the filling factor is made more than 1/2 by occupying two adjacent sites of OL. These stable 2D arrays of dipolar superfluid BEC solitons are quite similar to the recently studied dipolar Mott insulator states on 2D lattice in the Bose–Hubbard model by Capogrosso-Sansone et al. [B. Capogrosso-Sansone, C. Trefzger, M. Lewenstein, P. Zoller, G. Pupillo, Phys. Rev. Lett. 104 (2010) 125301].     

Quantum hydrodynamics

Quantum hydrodynamics in superfluid helium and atomic Bose–Einstein condensates (BECs) has been recently one of the most important topics in low temperature physics. In these systems, a macroscopic wave function (order parameter) appears because of Bose–Einstein condensation, which creates quantized vortices. Turbulence consisting of quantized vortices is called quantum turbulence (QT). The study of quantized vortices and QT has increased in intensity for two reasons. The first is that recent studies of QT are considerably advanced over older studies, which were chiefly limited to thermal counterflow in ⁴${}^4$He, which has no analog with classical traditional turbulence, whereas new studies on QT are focused on a comparison between QT and classical turbulence. The second reason is the realization of atomic BECs in 1995, for which modern optical techniques enable the direct control and visualization of the condensate and can even change the interaction; such direct control is impossible in other quantum condensates like superfluid helium and superconductors. Our group has made many important theoretical and numerical contributions to the field of quantum hydrodynamics of both superfluid helium and atomic BECs. In this article, we review some of the important topics in detail. The topics of quantum hydrodynamics are diverse, so we have not attempted to cover all these topics in this article. We also ensure that the scope of this article does not overlap with our recent review article (arXiv:1004.5458), “Quantized vortices in superfluid helium and atomic Bose–Einstein condensates”, and other review articles.     

Approximate solutions for half-dark solitons in spinor non-equilibrium Polariton condensates

In this work I generalize and apply an analytical approximation to analyze 1D states of non-equilibrium spinor polariton Bose–Einstein condensates (BEC). Solutions for the condensate wave functions carrying black solitons and half-dark solitons are presented. The derivation is based on the non-conservative Lagrangian formalism for complex Ginzburg–Landau type equations (cGLE), which provides ordinary differential equations for the parameters of the dark soliton solutions in their dynamic environment. Explicit expressions for the stationary dark soliton solution are stated. Subsequently the method is extended to spin sensitive polariton condensates, which yields ordinary differential equations for the parameters of half-dark solitons. Finally a stationary case with explicit expressions for half-dark solitons is presented.     

Dynamical instability induced by the zero mode under symmetry breaking external perturbation

A complex eigenvalue in the Bogoliubov–de Gennes equations for a stationary Bose–Einstein condensate in the ultracold atomic system indicates the dynamical instability of the system. We also have the modes with zero eigenvalues for the condensate, called the zero modes, which originate from the spontaneous breakdown of symmetries. Although the zero modes are suppressed in many theoretical analyses, we take account of them in this paper and argue that a zero mode can change into one with a pure imaginary eigenvalue by applying a symmetry breaking external perturbation potential. This emergence of a pure imaginary mode adds a new type of scenario of dynamical instability to that characterized by the complex eigenvalue of the usual excitation modes. For illustration, we deal with two one-dimensional homogeneous Bose–Einstein condensate systems with a single dark soliton under a respective perturbation potential, breaking the invariance under translation, to derive pure imaginary modes.     

Equilibrium vortex lattices of a binary rotating atomic Bose–Einstein condensate with unequal atomic masses

We perform a detailed numerical study of the equilibrium ground-state structures of a binary rotating Bose–Einstein condensate with unequal atomic masses. Our results show that the ground-state distribution and its related vortex configurations are complex events that differ markedly depending strongly on the strength of rotation frequency, as well as on the ratio of atomic masses. We also discuss the structures and radii of the clouds, the number and the size of the core region of the vortices, as a function of the rotation frequency, and of the ratio of atomic masses, and the analytical results agree well with our numerical simulations. This work may open an alternate way in the quantum control of the binary rotating quantum gases with unequal atomic masses.     

Quantum Tunneling of Spinor Bose–Einstein Condensates in an Optical Lattice

We have studied tunneling of spinor Bose–Einstein condensate in an optical lattice. It is found that, when the system being prepared in a squeezed coherent state, there exist the quantum tunneling between lattices l and l+1, l and l−1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, quantum tunneling disappear between lattices l and l+1, and that l and l−1, in this case the magnetic soliton appears.     

Dynamics of nonautonomous rogue waves in Bose–Einstein condensate

We study rogue waves of Bose–Einstein condensate (BEC) analytically in a time-dependent harmonic trap with a complex potential. Properties of the nonautonomous rogue waves are investigated analytically. It is reported that there are possibilities to ‘catch’ rogue waves through manipulating nonlinear interaction properly. The results provide many possibilities to manipulate rogue waves experimentally in a BEC system.     

Analogue model for an expanding universe

Over the last few years numerous papers concerning analogue models of (and for) gravity have been published. It has been shown that the dynamical equations for several condensed matter systems, (e.g., simple fluids, superfluids, Bose–Einstein condensates with a sink or a vortex) permit perturbations that are governed by the same type of wave equation as light in a curved spacetime—the curved-space d'Alembertian equation. More recently, several papers have been released which use analogue models to simulate the expanding universe. In this article the de Sitter universe will be simulated using a freely expanding three-dimensional Bose–Einstein condensate with spherical symmetry. Initially the condensate is in a harmonic trap, which is then suddenly switched off. At the same time a small perturbation is injected in the center of the condensate cloud. The motion of this perturbation in the expanding condensate will be discussed, and (after some transformations) the similarity of this system to an expanding universe will be exhibited. Finally, we briefly discuss questions of experimental observability of these effects. Presented at the 4th Australasian conference on General Relativity and Cosmology, Monash University, Melbourne, 7–9 January 2004     

Vacuum quark condensate,chiral Lagrangian,and Bose–Einstein statistics

In a series of articles it was recently claimed that the quantum chromodynamic (QCD) condensates are not the properties of the vacuum but of the hadrons and are confined inside them. We point out that this claim is incompatible with the chiral Lagrangian and Bose–Einstein statistics of the Goldstone bosons (pions) in chiral limit and conclude that the quark condensate must be the property of the QCD vacuum.     

Nonexponential decay of Bose–Einstein condensates: a numerical study based on the complex scaling method

We study the decay dynamics of an interacting Bose–Einstein condensate in the presence of a metastable trapping potential from which the condensate can escape via tunneling through finite barriers. The time-dependent decay process is reproduced by means of the instantaneous decay rates of the condensate at a given population of the quasi-bound state, which are calculated with the method of complex scaling. Both for the case of a double-barrier potential as well as for the case of a tilted periodic potential, we find pronounced deviations from a monoexponential decay behavior, which would generally be expected in the absence of the atom–atom interaction. PACS 03.75.Lm; 03.65.Xp; 03.75.Kk     

Manipulating nonclassical quantum statistical properties of light field by an f-deformed Bose–Einstein condensate

We consider the interaction between an f-deformed Bose–Einstein condensate and a single-mode quantized light field. By using the Gardiner’s phonon operators, we find that there exists a natural deformation in the model which modifies the Bogoliubov approximation under the condition of large but finite number of particles in condensate. This approach introduces an intrinsically deformed Bose–Einstein condensate, where the deformation parameter, well-defined by the particle number N in condensate, controls the strength of the associated nonlinearity. By introducing the deformed Gardiner’s phonon operators we modify the very dilute-gas approximation through including atomic collisions in condensate. The rate of atomic collisions κ, as a new deformation parameter in the deformed Bose–Einstein condensate, controls the nonlinearity related to the atomic collisions. We show that by controlling the nonlinearities in the f-deformed atomic condensate through the two atomic parameters N and κ, it is possible to generate and manipulate the nonclassical quantum statistical properties of radiation field, such as, the sub-Poissonian photon statistics and quadrature squeezing. Also, it is possible to control the collapses and revivals phenomena in the average number of photons by atomic parameters N and κ.     

Collective excitations of a 1D Bose–Einstein condensate in an anharmonic trap

We investigate the collective excitations of a one-dimension Bose–Einstein condensate trapped in an anharmonic potential by solving the time-dependent Tonks–Girardeau equation. The governing equations of motions for the low-energy excitations are obtained using variational approaches. The motion of a 1D BEC in a harmonic trap is just like the motion of one particle in a harmonic trap. And quartic distortion of the potential causes the blue-shift and red-shift on the excitation frequency while cube distortion only causes the red-shift.     

Bound diquarks and their Bose–Einstein condensation in strongly coupled quark matter

We explore the formation of diquark bound states and their Bose–Einstein condensation (BEC) in the phase diagram of three-flavor quark matter at nonzero temperature, T, and quark chemical potential, μ  . Using a quark model with a four-fermion interaction, we identify diquark excitations as poles of the microscopically computed diquark propagator. The quark masses are obtained by solving a dynamical equation for the chiral condensate and are found to determine the stability of the diquark excitations. The stability of diquark excitations is investigated in the T–μ$T\text{–}\mu$ plane for different values of the diquark coupling strength. We find that diquark bound states appear at small quark chemical potentials and at intermediate coupling strengths. Bose–Einstein condensation of non-strange diquark states occurs when the attractive interaction between quarks is sufficiently strong.