Matter-wave Vortices Research Articles

Synthetic superfluid chemistry with vortex-trapped quantum impurities

We explore the effect of using two-dimensional matter-wave vortices to confine an ensemble of bosonic quantum impurities. This is modelled theoretically using a mass-imbalanced homogeneous two component Gross-Pitaevskii equation where each component has independent atom numbers and equal atomic masses. By changing the mass imbalance of our system we find the shape of the vortices are deformed even at modest imbalances, leading to barrel shaped vortices; which we quantify using a multi-component variational approach. The energy of impurity carrying vortex pairs are computed, revealing a mass-dependent energy splitting. We then compute the excited states of the impurity, which we in turn use to construct `covalent bonds' for vortex pairs. Our work opens a new route to simulating synthetic chemical reactions with superfluid systems.

Electron Matter-Wave Vortices in Double Photoionization of Helium by Attosecond Pulses

Electron Matter-Wave Vortices in Double Photoionization of Helium by Attosecond Pulses

Origins and demonstrations of electrons with orbital angular momentum.

The surprising message of Allen et al. (Allen et al. 1992 Phys. Rev. A 45, 8185 (doi:10.1103/PhysRevA.45.8185)) was that photons could possess orbital angular momentum in free space, which subsequently launched advancements in optical manipulation, microscopy, quantum optics, communications, many more fields. It has recently been shown that this result also applies to quantum mechanical wave functions describing massive particles (matter waves). This article discusses how electron wave functions can be imprinted with quantized phase vortices in analogous ways to twisted light, demonstrating that charged particles with non-zero rest mass can possess orbital angular momentum in free space. With Allen et al. as a bridge, connections are made between this recent work in electron vortex wave functions and much earlier works, extending a 175 year old tradition in matter wave vortices.This article is part of the themed issue 'Optical orbital angular momentum'.

Interaction of atom with nonparaxial Laguerre-Gaussian beam: Forming superposition of vortex states in Bose-Einstein condensates

The exchange of orbital angular momentum (OAM) between paraxial optical vortex and a Bose-Einstein condensate (BEC) of atomic gases is well known. In this paper, we develop a theory for the microscopic interaction between matter and an optical vortex beyond paraxial approximation. We show how superposition of vortex states of BEC can be created with a focused optical vortex. Since, the polarization or spin angular momentum (SAM) of the optical field is coupled with OAM of the field, in this case, these angular momenta can be transferred to the internal electronic and external center-of-mass (c.m.) motion of atoms provided both the motions are coupled. We propose a scheme for producing the superposition of matter-wave vortices using Gaussian and a focused Laguerre-Gaussian (LG) beam. We study how two-photon Rabi frequencies of stimulated Raman transitions vary with focusing angles for different combinations of OAM and SAM of optical states. We demonstrate the formation of vortex-antivortex structure and discuss interference of three vortex states in a BEC.

Optical manipulation of matter-wave vortices: An analog of circular dichroism

The transfer of orbital angular momentum from an optical vortex to an atomic Bose-Einstein condensate changes the vorticity of the condensate. The spatial mismatch between initial and final center-of-mass wavefunctions of the condensate influences significantly the two-photon optical dipole transition between corresponding states. We show that the transition rate depends on the handedness of the optical orbital angular momentum leading to optical manipulation of matter-wave vortices and circular dichroism-like effect. Based on this effect, we propose a method to detect the presence and sign of matter-wave vortex of atomic superfluids. Only a portion of the condensate is used in the proposed detection method leaving the rest in its initial state.

Exact matter-wave vortices in a driven optical lattice

We investigate vortex dynamics of a periodically driven Bose-Einstein condensate confined in a spatially two-dimensional optical lattice. An exact Floquet solution of the Gross-Pitaevskii equation is obtained for a certain parameter region which can be divided into the phase-jumping and phase-continuing regions. In the former region, the exact solution can describe spatiotemporal evolution of multiple vortices. For a small ratio of driving strength to optical lattice depth the vortices keep nearly unmoved. With the increase of the ratio, the vortices undergo an effective interaction and periodically evolve along some fixed circular orbits that leads the vortex dipoles and quadrupoles to produce and break alternatively. There is a critical ratio in the phase-jumping region beyond which the vortices generate and melt periodically. In the phase-continuing region, the condensate in the exact Floquet state evolves periodically without zero-density nodes. It is numerically demonstrated that the exact solution is stable under an initial perturbation for both parameter regions, except for a subregion of the phase-jumping region in which stability of the condensate is lost. However, the solution is structurally stable under a small parameter perturbation only for the phase-continuing region, while for the whole phase-jumping region the structural stability is destroyed. The results suggest a scheme for creating and controlling matter-wave vortices.

Coherent cross talk and parametric driving of matter-wave vortices

We show that the interaction between vortices and sound waves in atomic Bose-Einstein condensates can be elucidated in a double-well trap: with one vortex in each well, the sound emitted by each precessing vortex can be driven into the opposing vortex (if of the same polarity). This cross-talk leads to a periodic exchange of energy between the vortices which is long-range and highly efficient. The increase in vortex energy (obtained by numerical simulations of the Gross-Pitaevskii equation) is significant and experimentally observable as a migration of the vortex to higher density over just a few precession periods. Similar effects can be controllably engineered by introducing a precessing localised obstacle into one well as an artificial generator of sound, thereby demonstrating the parametric driving of energy into a vortex.

Stability and dynamics of matter-wave vortices in the presence of collisional inhomogeneities and dissipative perturbations

In this work, the spectral properties of a singly charged vortex in a Bose–Einstein condensate confined in a highly anisotropic (disc-shaped) harmonic trap are investigated. Special emphasis is placed on the analysis of the so-called anomalous (negative energy) mode of the Bogoliubov spectrum. We use analytical and numerical techniques to illustrate the connection of the anomalous mode to the precession dynamics of the vortex in the trap. Effects due to inhomogeneous interatomic interactions and dissipative perturbations motivated by finite-temperature considerations are explored. We find that both of these effects may give rise to oscillatory instabilities of the vortex, which are suitably diagnosed through the perturbation-induced evolution of the anomalous mode, and monitored by direct numerical simulations.

Vortex replication in Bose-Einstein condensates trapped in double-well potentials

In this work we demonstrate, by means of numerical simulations, the possibility of replicating matter-wave vortices in a Bose-Einstein condensate trapped in a double-well potential. The most remarkable result is the generation of replicas of an initial vortex state located in one side of the double potential, which evolves into two copies, each one located in one of the potential minima. A simple linear theory gives the basic explanation of the phenomenon and predicts experimental realistic conditions for observation. A complementary strategy of easy experimental implementation to dramatically decrease the replication time is presented and numerically tested for the general case of nonlinear atomic interactions.

Matter-wave vortices in cigar-shaped and toroidal waveguides

We study vortical states in a Bose-Einstein condensate (BEC) filling a cigar-shaped trap. An effective one-dimensional (1D) nonpolynomial Schroedinger equation (NPSE) is derived in this setting, for the models with both repulsive and attractive interatomic interactions. Analytical formulas for the density profiles are obtained from the NPSE in the case of self-repulsion within the Thomas-Fermi approximation, and in the case of the self-attraction as exact solutions (bright solitons). A crucially important ingredient of the analysis is the comparison of these predictions with direct numerical solutions for the vortex states in the underlying 3D Gross-Pitaevskii equation. The comparison demonstrates that the NPSE provides for a very accurate approximation, in all the cases, including the prediction of the stability of the bright solitons and collapse threshold for them. In addition to the straight cigar-shaped trap, we also consider a torus-shaped configuration. In that case, we find a threshold for the transition from the axially uniform state, with the transverse intrinsic vorticity, to a symmetry-breaking pattern, due to the instability in the self-attractive BEC filling the circular trap.

Three-dimensional matter-wave vortices in optical lattices

We predict the existence of spatially localized nontrivial vortex states of a Bose-Einstein condensate with repulsive atomic interaction confined by a three-dimensional optical lattice. Such vortex-like structures include planar vortices, their co- and counter-rotating bound states, and distinctly three-dimensional non-planar vortex states. We demonstrate numerically that many of these vortex structures are remarkably robust, and therefore can be generated and observed in experiment.