Quantum Vortex States Research Articles

Two-mode superposition coherent states with spatial vortex structure for the quantized radiation field

Through superposing M two-mode coherent state a two-mode superposition coherent state with a spatial vortex structure in configuration space is constructed. Such quantum vortex state is an eigenstate of sum of squared two-mode annihilation operators and is always entangled. In the limiting condition of large M the quantum vortex state has a modified Bessel–Gaussian vortex structure with topological charge index n. Experimentally, such two-mode vortex states may be prepared by virtue of a multimode coherent state with currently available technology.

Non-Gaussian state with vortex structure of quantized radiation field

A new kind of quantum non-Gaussian state with vortex structure termed as a modified Bessel–Gaussian vortex state is constructed, and it is an eigenstate of sum of squared annihilation operator a2+b2. The quantum vortex state exhibits a rich variety of nonclassical signatures and is always entangled. The dependence of its statistical properties on state parameters is analyzed, and the non-Gaussianity is investigated in detail. It is found that, for sufficient small values of α, the properties clearly depend on the topological charge index n. Moreover, a scheme for generating such quantized vortex states is proposed.

Vortex configuration and vortex–vortex interaction in nano-structured superconductors

We study the vortex structures and quasi-particle structures in nano-structured superconductors. We used the Bogoliubov–de Gennes equation and the finite element method and obtained stable magnetic flux structures and the quasi-particle states. We found the vortex configurations are affected by the interference of the quasi-particle bound states around the vortices. In order to clarify the interference between the quasi-particle wave-functions around two vortices we have developed a numerical method using the elliptic coordinates and the Mathieu functions. We apply this method to two singly quantized vortex state in a conventional s-wave superconductor and a pair of half-quantum vortices in a chiral p-wave superconductor.

Pair coherent state evolutions through parametric frequency conversion and the realization of quantized vortex states

The pair coherent state evolution during a parametric frequency conversion is analyzed. And the wavefunction of the evolving pair coherent state in configuration space is obtained. It is found that the state may become a modified Bessel-Gaussian vortex state with topological charge index q which is a new non-Gaussian state. In coherent state representation such a modified Bessel-Gaussian vortex state is an eigenstate of sum of squared two-mode annihilation operators a2 + b2. The result obtained in this paper provides a new scheme for generating quantized vortex states in experiment with currently available technology.

Rotating Fulde-Ferrell-Larkin-Ovchinnikov state in cold Fermi gases

We study an effect of rotation on the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of two component Fermi superfluid gases in a toroidal trap. We investigate a stability of the FFLO states in the quasi-one-dimensional regime on the basis of the Bogoliubov-de Gennes equation. We find that two novel FFLO phases, i.e., the half quantum vortex state and the intermediate state of Fulde-Ferrell (FF) state and Larkin-Ovchinnikov (LO) state, are stabilized by the rotation. The phase diagram for the FF state, LO state, intermediate state, and half quantum vortex state is shown in both T-P plane and T-h plane. We demonstrate characteristic features of these states, such as the order parameter, flux quantization, and local polarization. Several related works are discussed, and the advantages of cold Fermi gases are indicated.

Giant vortex and multivortex states under local supercurrent injection in a mesoscopic superconducting square

We experimentally study giant vortex states (GVSs) and multivortex states (MVSs) in a mesoscopic superconducting square under local supercurrent injection. By using the multiple-small-tunnel-junction measurement, we find that the magnetic field for the transition between a GVS and an MVS with a fixed vorticity depends on the magnitude of the injected supercurrent. This result indicates the possibility of manipulating quantum vortex states with supercurrent injection.

Creating vortices in dipolar spinor condensates via rapid adiabatic passage

We propose to create vortices in spin-1 condensates via magnetic dipole-dipole interaction. Starting with a polarized condensate prepared under large axial magnetic field, we show that by gradually inverting the field, population transfer among different spin states can be realized in a controlled manner. Under optimal condition, we generate a doubly quantized vortex state containing nearly all atoms in the condensate. The resulting vortex state is a direct manifestation of the dipole-dipole interaction and spin textures in spinor condensates. We also point out that the whole process can be qualitatively described by a simple three-level rapid adiabatic passage model.

Stability of quantized vortices in a Bose-Einstein condensate confined in an optical lattice

We investigate the existence and especially the linear stability of single- and multiple-charge quantized vortex states of nonlinear Schr\"odinger equations in the presence of a periodic and a parabolic potential in two spatial dimensions. The study is motivated by an examination of pancake-shaped Bose-Einstein condensates in the presence of magnetic and optical confinement. A two-parameter space of the condensate's chemical potential versus the periodic potential's strength is scanned for both single- and double-quantized vortex states located at a local minimum or a local maximum of the lattice. Triple-charged vortices are also briefly discussed. Single-charged vortices are found to be stable for cosinusoidal potentials and unstable for sinusoidal ones above a critical strength. Higher-charge vortices are more unstable for both types of potentials, and their dynamical evolution leads to a breakup into single-charged vortices.

Quantized vortex states of strongly interacting bosons in a rotating optical lattice

Bose gases in rotating optical lattices combine two important topics in quantum physics: superfluid rotation and strong correlations. In this paper, we examine square two-dimensional systems at zero temperature comprised of strongly repulsive bosons with filling factors of less than one atom per lattice site. The entry of vortices into the system is characterized by jumps of 2 pi in the phase winding of the condensate wavefunction. A lattice of size L X L can have at most L-1 quantized vortices in the lowest Bloch band. In contrast to homogeneous systems, angular momentum is not a good quantum number since the continuous rotational symmetry is broken by the lattice. Instead, a quasi-angular momentum captures the discrete rotational symmetry of the system. Energy level crossings indicative of quantum phase transitions are observed when the quasi-angular momentum of the ground-state changes.

Collective oscillations in a two-dimensional Bose-Einstein condensate with a quantized vortex state

We study the effect of lower dimensional geometry on the frequency splitting of the quadrupole oscillations of a harmonically trapped Bose-Einstein condensate due to the presence of a quantized vortex. To study the effect of two-dimensional geometry we consider a pancake-shaped condensate and employ various models for the coupling parameter depending on the thickness of the condensate relative to the value of the scattering length. Using these models and the sum-rule approach we obtain analytical expressions for the frequency splitting. These expressions are valid for positive scattering length and large $N$. We show that the frequency splitting of the quadrupole oscillations are significantly altered by the reduced dimensionality and also study the evolution of the splitting as the system makes transition from one scattering regime to the other.

Vortices and hysteresis in a rotating Bose-Einstein condensate with anharmonic confinement

We examine an effectively repulsive Bose-Einstein condensate of atoms that rotates in a quadratic-plus-quartic trapping potential. We investigate the phase diagram of the system as a function of the angular frequency of rotation and of the coupling constant, demonstrating that there are phase transitions between multiply and singly quantized vortex states. We also show that states of different circulation can be metastable and, as a result, the gas can exhibit hysteresis as the angular frequency of rotation of the trap is varied. The simplicity of the picture that emerges for small coupling strengths suggests that this system may be attractive for studies of phase transitions.

Split-merge cycle, fragmented collapse, and vortex disintegration in rotating Bose-Einstein condensates with attractive interactions

The dynamical instabilities and ensuing dynamics of singly and doubly quantized vortex states of Bose-Einstein condensates with attractive interactions are investigated using full three-dimensional numerical simulations of the Gross-Pitaevskii equation. With increasing the strength of attractive interactions, a series of dynamical instabilities such as quadrupole, dipole, octupole, and monopole instabilities emerge. The most prominent instability depends on the strength of interactions, the geometry of the trapping potential, and deviations from the axisymmetry due to external perturbations. Singly quantized vortices split into two clusters and subsequently undergo split-merge cycles in a pancake-shaped trap, whereas the split fragments immediately collapse in a spherical trap. Doubly quantized vortices are always unstable to disintegration of the vortex core. If we suddenly change the strength of interaction to within a certain range, the vortex splits into three clusters, and one of the clusters collapses after a few split-merge cycles. The vortex split can be observed using a current experimental setup of Leanhardt et al. [Phys. Rev. Lett. 89, 190403 (2002)].

Superfluidity and quantized vortex studies under rotation up to [formula omitted] at mK and [formula omitted] at sub-mK temperatures

Two new high-speed rotating cryostats at the ISSP, University of Tokyo, capable of operating at mK temperatures, are currently employed for studies of superfluidity and quantized vortex states in 4 He and 3 He . A stable high- Q torsional oscillator is used for the study of superfluidity in low-density 4 He films adsorbed on 3-D connected porous substrates. At T c, the critical phenomena of 3-D Bose superfluids is seen. Under rotation a new type of vortex state is observed. High-resolution NMR studies of superfluid 3 He , contained in capillary arrays of two different diameters, are made as a function of rotational speed. In these experiments, single vortex intrusion events as well as texural modification under rotation are clearly resolved.

Planck Mass Plasma Vacuum Conjecture

As an alternative to string field theories in R10 (or M theory in R11) with a large group and a very large number of possible vacuum states, we propose SU2 as the fundamental group, assuming that nature works like a computer with a binary number system. With SU2 isomorphic to SO3, the rotation group in R3, explains why R3 is the natural space. Planck’s conjecture that the fundamental equations of physics should contain as free parameters only the Planck length, mass and time, requires to replace differentials by rotation - invariant finite difference operators in R3. With SU2 as the fundamental group, there should be negative besides positive Planck masses, and the freedom in the sign of the Planck force permits to construct in a unique way a stable Planck mass plasma composed of equal numbers of positive and negative Planck mass particles, with each Planck length volume in the average occupied by one Planck mass particle, with Planck mass particles of equal sign repelling and those of opposite sign attracting each other by the Planck force over a Planck length. From the thusly constructed Planck mass plasma one can derive quantum mechanics and Lorentz invariance, the latter for small energies compared to the Planck energy. In its lowest state the Planck mass plasma has dilaton and quantized vortex states, with Maxwell’s and Einstein’s field equations derived from the antisymmetric and symmetric modes of a vortex sponge. In addition, the Planck mass plasma has excitonic quasiparticle states obeying Dirac’s equation with a maximum of four such states, and a mass formula of the lowest state in terms of the Planck mass, permitting to compute the value of the finestructure constant at the Planck length, in surprisingly good agreement with the empirical value.

Collapse of attractive Bose-Einstein condensed vortex states in a cylindrical trap.

The quantized vortex states of a weakly interacting Bose-Einstein condensate of atoms with attractive interatomic interaction in an axially symmetric harmonic oscillator trap are investigated using the numerical solution of the time-dependent Gross-Pitaevskii equation obtained by the semi-implicit Crank-Nicholson method. The collapse of the condensate is studied in the presence of deformed traps with the larger frequency along either the radial or the axial direction. The critical number of atoms for collapse is calculated as a function of the vortex quantum number L. The critical number increases with increasing angular momentum L of the vortex state but tends to saturate for large L.

Vortices in Bose-Einstein condensates confined in a multiply connected Laguerre-Gaussian optical trap

The quantized vortex state is investigated in a Bose-Einstein condensate, confined in a multiply connected geometry formed by a Laguerre-Gaussian optical trap. Solving the Gross-Pitaevskii equation variationally, we show that the criterium for vortex stability is that the interatomic interaction strength must exceed a critical interaction strength. The time evolution of a freely expanding Laguerre-Gaussian condensate with a vortex is calculated, and used to derive the interference pattern of such a condensate overlapping with a parabolically trapped condensate.

Vortex Stabilization in Dilute Bose-Einstein Condensate Under Rotation

The stability of a quantized vortex state in Bose-Einstein condensation is examined within Bogoliubov theory for alkali atom gases confined in a harmonic potential under forced rotation. By solving the non-linear Bogoliubov equations coupled with the Gross-Pitavskii equation, the elementary excitations and the total energy of the systems are calculated as a function of rotation velocity. There are two distinct criteria of vortex stability; The position of the excitation energy levels relative to the condensate energy level yields the local stability criterion, and the total energy relative to that of the non-vortex state yields the global stability criterion. The vortex stability phase diagram in the rotation velocity vs the particle density of the system is obtained, allowing one to locate the appropriate region to observe the singly quantized vortex.

Massive Quantum Vortex Excitations in a Pure Gauge Abelian Theory in 2 + 1D

We introduce and study a pure gauge Abelian theory in 2 + 1D in which massive quantum vortex states do exist in the spectrum of excitations. This theory can be mapped in a three-dimensional gas of point particles with a logarithmic interaction, in the grand-canonical ensemble. We claim that this theory is the 2 + 1D analog of the sine–Gordon, the massive vortices being the counterparts of sine–Gordon solitons. We show that a symmetry breaking, order parameter, similar to the vacuum expectation value of a Higgs field does exist.

Orbitally quantized vortex states of laser radiation and photonic superfluidity

The existence of the phenomenon of photonic superfluidity in certain laser systems is demonstrated as is the identity of orbitally quantized excitations of the photonic Bose condensate to vortex lines in superfluid He and Abrikosov’s vortex lines in type-II superconductors.

Andreev bound states in unconventional vortices

We present isolated vortex solutions of the quasiclassical equations in weak coupling for an unconventional superconductor that belongs to the E1g representation of the hexagonal symmetry group. We discuss the structure of the single flux quantum vortex states and the dispersion of Andreev bound states.