Exotic vortex structures of the dipolar Bose–Einstein condensates trapped in harmonic-like and toroidal potential

Based on the tunable intensity and waist of Gaussian laser, harmonic-like and toroidal potentials can be achieved and the ground-state properties of the dipolar Bose–Einstein condensate (BEC) trapped in such potentials are investigated. It is found that, in the harmonic-like potential, the singly and doubly quantized vortices can exist in the scale condensate and translate respectively into vortex pairs and triangular vortex lattice with increasing dipole–dipole interaction (DDI). Especially, the sandwich-like structure can be observed in the ground-state density profiles by tuning the direction and strength of DDI for some rotating frequency. In the toroidal potential, the competition between the inter-component interaction and DDI can induce the transition between immiscible and miscible states, and results in the structures of a doubly quantized vortex surrounded by a vortex ring. It is worth emphasizing that, with the increasing of DDI, the doubly quantized vortex in the harmonic-like potential becomes two singly quantized vortices, while in the toroidal potential it is no happen due to the presence of Gaussian barrier.     

Bound states and Cooper pairs of molecules in 2D optical lattices bilayer

We investigate the formation of Cooper pairs, bound dimers and the dimer‐dimer elastic scattering of ultracold dipolar Fermi molecules confined in a 2D optical lattice bilayer configuration. While the energy and their associated bound states are determined in a variational way, the correlated two‐molecule pair is addressed as in the original Cooper formulation. We demonstrate that the 2D lattice confinement favors the formation of zero center mass momentum bound states. Regarding the Cooper pairs binding energy, this depends on the molecule populations in each layer. Maximum binding energies occur for non‐zero (zero) pair momentum when the Fermi system is polarized (unpolarized). We find an analytic expression for the dimer‐dimer effective interaction in the deep BEC regime. The present analysis represents a route for addressing the BCS‐BEC crossover in dipolar Fermi gases confined in 2D optical lattices within the current experimental panorama.     

线性与非线性光晶格中偶极孤立子的稳定性

利用变分法研究了线性和非线性交叉光晶格中偶极玻色-爱因斯坦凝聚(BEC)体系中物质波孤立子的稳定性.选用柱对称高斯型试探波函数,得出参数的Euler-Lagrange方程和体系的有效作用势能,根据有效势能是否具有局域最小值判断体系是否具有稳定孤立子解.结果表明,由于存在接触相互作用的空间调制,在排斥和吸引偶极相互作用下,均能形成稳定的孤立子解.给出了参数空间中存在稳定解的区域和物质波波包宽度随时间的变化曲线.     

Metastable states of a gas of dipolar bosons in a 2D optical lattice

We investigate the physics of dipolar bosons in a two-dimensional optical lattice. It is known that due to the long-range character of dipole-dipole interaction, the ground state phase diagram of a gas of dipolar bosons in an optical lattice presents novel quantum phases, like checkerboard and supersolid phases. In this Letter, we consider the properties of the system beyond its ground state, finding that it is characterized by a multitude of almost degenerate metastable states, often competing with the ground state. This makes dipolar bosons in a lattice similar to a disordered system and opens possibilities of using them as quantum memories.     

Effects of three-body interactions in the parametric and modulational instabilities of Bose-Einstein condensates

The parametric modulational instability for a discrete nonlinear Schrödinger equation with a cubic-quintic nonlinearity is analyzed. This model describes the dynamics of BECs, with both two- and three-body interatomic interactions trapped in an optical lattice. We identify and discuss the salient features of the three-body interaction in the parametric modulational instability. It is shown that the three-body interaction term can both, shift as well as narrow the window of parametric instability, and also change the behavior of a modulationally stable and parametrically unstable BEC with attractive two-body interaction. We explore this instability through the multiple-scale analysis and identify it numerically. The effect of the three body losses have also been investigated.     

Modulational instability of matter waves under strong nonlinearity management

We study modulational instability of matter-waves in Bose-Einstein condensates (BEC) under strong temporal nonlinearity-management. Both BEC in an optical lattice and homogeneous BEC are considered in the framework of the Gross-Pitaevskii equation, averaged over rapid time modulations. For a BEC in an optical lattice, it is shown that the loop formed on a dispersion curve undergoes transformation due to the nonlinearity-management. A critical strength for the nonlinearity-management strength is obtained that changes the character of instability of an attractive condensate. MI is shown to occur below (above) the threshold for the positive (negative) effective mass. The enhancement of number of atoms in the nonlinearity-managed gap soliton is revealed.     

Swallowtail band structure of the superfluid Fermi gas in an optical lattice

We investigate the energy band structure of the superfluid flow of ultracold dilute Fermi gases in a one-dimensional optical lattice along the BCS to Bose-Einstein condensate (BEC) crossover within a mean-field approach. In each side of the crossover region, a loop structure (swallowtail) appears in the Bloch energy band of the superfluid above a critical value of the interaction strength. The width of the swallowtail is largest near unitarity. Across the critical value of the interaction strength, the profiles of density and pairing field change more drastically in the BCS side than in the BEC side. It is found that along with the appearance of the swallowtail, there exists a narrow band in the quasiparticle energy spectrum close to the chemical potential, and the incompressibility of the Fermi gas consequently experiences a profound dip in the BCS side, unlike in the BEC side.     

Superfluid properties of a Bose-Einstein condensate in an optical lattice confined in a cavity

We study the effect of a one dimensional optical lattice in a cavity field with quantum properties on the superfluid dynamics of a Bose-Einstein condensate (BEC). In the cavity the influence of atomic backaction and the external driving pump become important and modify the optical potential. Due to the coupling between the condensate wavefunction and the cavity modes, the cavity light field develops a band structure. This study reveals that the pump and the cavity emerges as a new handle to control the superfluid properties of the BEC.     

Dynamical stability of dipolar condensate in a parametrically modulated one-dimensional optical lattice

We study the stabilization properties of dipolar Bose–Einstein condensate in a deep one-dimensional optical lattice with an additional external parametrically modulated harmonic trap potential. Through both analytical and numerical methods, we solve a dimensionless nonlocal nonlinear discrete Gross–Pitaevskii equation with both the short-range contact interaction and the long-range dipole–dipole interaction. It is shown that, the stability of dipolar condensate in modulated deep optical lattice can be controled by coupled effects of the contact interaction, the dipolar interaction and the external modulation. The system can be stabilized when the dipolar interaction, the contact interaction, the average strength of potential and the ratio of amplitude to frequency of the modulation satisfy a critical condition. In addition, the breather state, the diffused state and the attractive-interaction-induced-trapped state are predicted. The dipolar interaction and the external modulation of the lattice play important roles in stabilizing the condensate.     

Spatial structure of a collisionally inhomogeneous Bose-Einstein condensate

The spatial structure of a collisionally inhomogeneous Bose-Einstein condensate (BEC) in an optical lattice is studied. A spatially dependent current with an explicit analytic expression is found in the case with a spatially dependent BEC phase. The oscillating amplitude of the current can be adjusted by a Feshbach resonance, and the intensity of the current depends heavily on the initial and boundary conditions. Increasing the oscillating amplitude of the current can force the system to pass from a single-periodic spatial structure into a very complex state. But in the case with a constant phase, the spatially dependent current disappears and the Melnikov chaotic criterion is obtained via a perturbative analysis in the presence of a weak optical lattice potential. Numerical simulations show that a strong optical lattice potential can lead BEC atoms to a state with a chaotic spatial distribution via a quasiperiodic route.     

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].     

Matter wave interferometry for measuring a molecular transition dipole moment

We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting from the superposition of linear and nonlinear optical lattices and make use of Vakhitov-Kolokolov criterion to investigate the effect of nonlinear lattice on the stability of the soliton solutions in the linear optical lattice (LOL). For the single-component case we show that a weak nonlinear lattice has very little effect on the stability of such solitons while sufficiently strong nonlinear optical lattice (NOL) squeezes them to produce narrow bound states. For two-component condensates we find that when the strength of the NOL (γ ₁) is less than that of the LOL (V ₀) a relatively weak intra-atomic interaction (IAI) has little effect on the stability of the component solitons. This is true for both attractive and repulsive IAI. A strong attractive IAI, however, squeezes the BEC solitons while a similar repulsive IAI makes the component solitons wider. For γ ₁ > V ₀, only a strong attractive IAI squeezes the BEC solitons but the squeezing effect is less prominent than that found for γ ₁ < V ₀. We make useful checks on the results of our semianalytical stability analysis by solving the appropriate Gross-Pitaevskii equations numerically.     

转动冷原子研究的前沿介绍

环流的宏观量子化是超流体最引人瞩目的性质之一．1995年玻色一爱因斯坦凝聚的实现为超流提供了一个新的研究对象，使得人们可以对转动的超流体进行深入的研究．实验上在BEC中产生了涡旋激发，并进一步观测到了涡旋晶格．理论研究表明当冷原子的转速进一步增大，涡旋品格会融解成一种新的强关联系统——量子霍尔液体．文章主要介绍近年在转动冷原子方向上理论和实验的进展．     

Evolution of the vortex state in the BCS-BEC crossover of a quasi two-dimensional superfluid Fermi gas

We use the path-integral formalism to investigate the vortex properties of a quasi-two dimensional(2D) Fermi superfluid system trapped in an optical lattice potential.Within the framework of mean-field theory,the cooper pair density,the atom number density,and the vortex core size are calculated from weakly interacting BCS regime to strongly coupled while weakly interacting BEC regime.Numerical results show that the atoms gradually penetrate into the vortex core as the system evolves from BEC to BCS regime.Meanwhile,the presence of the optical lattice allows us to analyze the vortex properties in the crossover from three-dimensional(3D) to 2D case.Furthermore,using a simple re-normalization procedure,we find that the two-body bound state exists only when the interaction is stronger than a critical one denoted by G_c which is obtained as a function of the lattice potential's parameter.Finally,we investigate the vortex core size and find that it grows with increasing interaction strength.In particular,by analyzing the behavior of the vortex core size in both BCS and BEC regimes,we find that the vortex core size behaves quite differently for positive and negative chemical potentials.     

Unusual Destruction and Enhancement of Superfluidity of Atomic Fermi Gases by Population Imbalance in a One-Dimensional Optical Lattice

We study the superfluid behavior of a population imbalanced ultracold atomic Fermi gases with a short range attractive interaction in a one-dimensional(1 D) optical lattice,using a pairing fluctuation theory.We show that,besides widespread pseudogap phenomena and intermediate temperature superfluidity,the superfluid phase is readily destroyed except in a limited region of the parameter space.We find a new mechanism for pair hopping,assisted by the excessive majority fermions,in the presence of c...     

Topological defect formation in rotating binary dipolar Bose–Einstein condensate

We investigate the topological defects and spin structures of a rotating binary Bose–Einstein condensate, which consists of both dipolar and scalar bosonic atoms confined in spin-dependent optical lattices, for an arbitrary orientation of the dipoles with respect to their plane of motion. Our results show that the tunable dipolar interaction, especially the orientation of the dipoles, can be used to control the direction of stripe phase and its related half-vortex sheets. In addition, it can also be used to obtain a regular arrangement of various topological spin textures, such as meron, circular and cross disgyration spin structures. We point out that such topological defects and regular arrangement of spin structures arise primarily from the long-range and anisotropic nature of dipolar interaction and its competition with the spin-dependent optical lattices and rotation.     

Quantum phase transition between a Luttinger liquid and a gas of cold molecules

We consider cold polar molecules confined in a helical optical lattice similar to those used in holographic microfabrication. An external electric field polarizes molecules along the axis of the helix. The large-distance intermolecular dipolar interaction is attractive but the short-scale interaction is repulsive due to geometric constraints and thus prevents collapse. The interaction strength depends on the electric field. We show that a zero-temperature second-order liquid-gas transition occurs at a critical field. It can be observed under experimentally accessible conditions.     

Transport behaviour of a Bose Einstein condensate in a bichromatic optical lattice

We investigate the Bloch and dipole oscillations of a Bose Einstein condensate (BEC) in an optical superlattice. We show that, as the effective mass increases in an optical superlattice, the BEC is localized in accordance with recent experimental observations [J.E. Lye et. al. Phys. Rev. A 75, 061603 (2007)]. In addition, we find that the secondary optical lattice is a useful additional tool to manipulate the dynamics of the atoms.      

Controlled collapse of a Bose-Einstein condensate

The point of instability of a Bose-Einstein condensate (BEC) due to attractive interactions was studied. Stable 85Rb BECs were created and then caused to collapse by slowly changing the atom-atom interaction from repulsive to attractive using a Feshbach resonance. At a critical value, an abrupt transition was observed in which atoms were ejected from the condensate. By measuring the onset of this transition as a function of number and attractive interaction strength, we determined the stability condition to be N(absolute value of a) / a(ho) = 0.459+/-0.012+/-0.054, slightly lower than the predicted value of 0.574.     

Effective field theory for spinor dipolar Bose Einstein condensates

We show that the effective theory of long wavelength low energy behavior of a dipolar Bose-Einstein condensate(BEC) with large dipole moments (treated as a classical spin) can be modeled using an extended non-linear sigma model (NLSM) like energy functional with an additional non-local term that represents long ranged anisotropic dipole-dipole interaction. Minimizing this effective energy functional we calculate the density and spin-profile of the dipolar Bose-Einstein condensate in the mean-field regime for various trapping geometries. The resulting configurations show strong intertwining between the spin and mass density of the condensate, transfer between spin and orbital angular momentum in the form of Einstein-de Hass effect, and novel topological properties. We have also described the theoretical framework in which the collective excitations around these mean field solutions can be studied and discuss some examples qualitatively.