Imprinting vortices in a Bose-Einstein condensate using topological phases

Vortices were imprinted in a Bose-Einstein condensate using topological phases. Sodium condensates held in a Ioffe-Pritchard magnetic trap were transformed from a nonrotating state to one with quantized circulation by adiabatically inverting the magnetic bias field along the trap axis. Using surface wave spectroscopy, the axial angular momentum per particle of the vortex states was found to be consistent with 2 variant Planck's over 2pi or 4 variant Planck's over 2pi, depending on the hyperfine state of the condensate.     

Semiclassical dynamics of electron wave packet states with phase vortices

We consider semiclassical higher-order wave packet solutions of the Schr?dinger equation with phase vortices. The vortex line is aligned with the propagation direction, and the wave packet carries a well-defined orbital angular momentum (OAM) variant Planck's over 2pil (l is the vortex strength) along its main linear momentum. The probability current coils around the momentum in such OAM states of electrons. In an electric field, these states evolve like massless particles with spin l. The magnetic-monopole Berry curvature appears in momentum space, which results in a spin-orbit-type interaction and a Berry/Magnus transverse force acting on the wave packet. This brings about the OAM Hall effect. In a magnetic field, there is a Zeeman interaction, which, can lead to more complicated dynamics.     

Fractional variant Planck's over 2pi scaling for quantum kicked rotors without Cantori

Previous studies of quantum delta-kicked rotors have found momentum probability distributions with a typical width (localization length L) characterized by fractional variant Planck's over 2pi scaling; i.e., L approximately variant Planck's over 2pi;{2/3} in regimes and phase-space regions close to "golden-ratio" cantori. In contrast, in typical chaotic regimes, the scaling is integer, L approximately variant Planck's over 2pi;{-1}. Here we consider a generic variant of the kicked rotor, the random-pair-kicked particle, obtained by randomizing the phases every second kick; it has no Kol'mogorov-Arnol'd-Moser mixed-phase-space structures, such as golden-ratio cantori, at all. Our unexpected finding is that, over comparable phase-space regions, it also has fractional scaling, but L approximately variant Planck's over 2pi;{-2/3}. A semiclassical analysis indicates that the variant Planck's over 2pi;{2/3} scaling here is of quantum origin and is not a signature of classical cantori.     

Quantized rotation of atoms from photons with orbital angular momentum

We demonstrate the coherent transfer of the orbital angular momentum of a photon to an atom in quantized units of variant Planck's over 2pi, using a 2-photon stimulated Raman process with Laguerre-Gaussian beams to generate an atomic vortex state in a Bose-Einstein condensate of sodium atoms. We show that the process is coherent by creating superpositions of different vortex states, where the relative phase between the states is determined by the relative phases of the optical fields. Furthermore, we create vortices of charge 2 by transferring to each atom the orbital angular momentum of two photons.     

Canonical momentum,angular momentum,and helicity of circularly polarized Airy beams

We report a study of the momentum, angular momentum, and helicity of circularly polarized Airy beams propagating in free space. By using the vector angular spectrum representation, the explicit analytical expressions for the electric and magnetic field components of circularly polarized Airy beams are derived in detail. To overcome the drawbacks of classical kinematics formulae when applied to structured light beams, a general canonical approach is introduced to describe the momentum, angular momentum and helicity of Airy beams. Numerical simulation results for the spatial distributions of the canonical momentum, spin and orbital angular momentum, as well as the helicity densities are presented and discussed. This study may provide useful insights into the dynamical properties of Airy beams that may be important in several applications, including the optical control, micromanipulation, and information processing.     

Ehrenfest-time-dependent excitation gap in a chaotic Andreev billiard

A semiclassical theory is developed for the appearance of an excitation gap in a ballistic chaotic cavity connected by a point contact to a superconductor. Diffraction at the point contact is a singular perturbation in the limit variant Planck's over 2pi -->0, which opens up a gap E(gap) in the excitation spectrum. The time scale variant Planck's over 2pi /E(gap) proportional, variant alpha(-1)ln( variant Planck's over 2pi (with alpha the Lyapunov exponent) is the Ehrenfest time, the characteristic time scale of quantum chaos.     

Observation of persistent flow of a Bose-Einstein condensate in a toroidal trap

We have observed the persistent flow of Bose-condensed atoms in a toroidal trap. The flow persists without decay for up to 10 s, limited only by experimental factors such as drift and trap lifetime. The quantized rotation was initiated by transferring one unit variant Planck's over 2pi of the orbital angular momentum from Laguerre-Gaussian photons to each atom. Stable flow was only possible when the trap was multiply connected, and was observed with a Bose-Einstein condensate fraction as small as 20%. We also created flow with two units of angular momentum and observed its splitting into two singly charged vortices when the trap geometry was changed from multiply to simply connected.     

Observation of high-order quantum resonances in the kicked rotor

Quantum resonances in the kicked rotor are characterized by a dramatically increased energy absorption rate, in stark contrast to the momentum localization generally observed. These resonances occur when the scaled Planck's constant Planck's [over ]=r/s 4pi, for any integers r and s. However, only the variant Planck's [over ]=r2pi resonances are easily observable. We have observed high-order quantum resonances (s>2) utilizing a sample of low energy, noncondensed atoms and a pulsed optical standing wave. Resonances are observed for variant Planck's [over ]=r/16 4pi for integers r=2-6. Quantum numerical simulations suggest that our observation of high-order resonances indicate a larger coherence length (i.e., coherence between different wells) than expected from an initially thermal atomic sample.     

Breakup of ring beams carrying orbital angular momentum in sodium vapor

We have observed filamentation due to azimuthal modulational instabilities in spinning ring solitons with orbital angular momentum m variant Planck's over 2pi in sodium vapor. We show experimentally that vortex beams with m values of 1, 2, and 3 tend to break into two, four, and six filaments, respectively. Treating the sodium vapor as a Doppler broadened two-level atomic system, we find that we can accurately model the propagation and breakup of these beams with numerical simulations.     

Measurement of the angular momentum of a rotating bose-einstein condensate

We study the quadrupole oscillation of a Bose-Einstein condensate of 87Rb atoms confined in an axisymmetric magnetic trap, after it has been stirred by an auxiliary laser beam. The stirring may lead to the nucleation of one or more vortices, whose presence is revealed unambiguously by the precession of the axes of the quadrupolar mode. For a stirring frequency Omega below the single vortex nucleation threshold Omega(c), no measurable precession occurs. Just above Omega(c), the angular momentum deduced from the precession is approximately Planck's over 2pi. For stirring frequencies above Omega(c) the angular momentum is a smooth and increasing function of Omega, until an angular frequency is reached at which the vortex lattice disappears.     

Nonmonotonicity in the quantum-classical transition: chaos induced by quantum effects

The classical-quantum transition for chaotic systems is understood to be accompanied by the suppression of chaotic effects as the relative variant Planck's over 2pi is increased. We show evidence to the contrary in the behavior of the quantum trajectory dynamics of a dissipative quantum chaotic system, the double-well Duffing oscillator. The classical limit in the case considered has regular behavior, but as the effective variant Planck's over 2pi is increased we see chaotic behavior. This chaos then disappears deeper into the quantum regime, which means that the quantum-classical transition in this case is nonmonotonic in variant Planck's over 2pi.     

Entry distribution, fission barrier, and formation mechanism of 254102No

The entry distribution in angular momentum and excitation energy for the formation of 254No has been measured after the 208Pb(48Ca,2n) reaction at 215 and 219 MeV. This nucleus is populated up to spin 22Planck's over 2pi and excitation energy greater, similar6 MeV above the yrast line, with the half-maximum points of the energy distributions at approximately 5 MeV for spins between 12Planck's over 2pi and 22Planck's over 2pi. This suggests that the fission barrier is greater, similar5 MeV and that the shell-correction energy persists to high spin.     

Quantum chaos of atoms in a resonant cavity

A system of atoms interacting with a radiation field in a resonant cavity is studied under conditions when the dynamics in the classical limit is stochastic. This situation is called quantum chaos. Equations of motion are obtained for the quantum-mechanical expectation values which take into account the quantum correlation functions. It is shown that in a situation corresponding to quantum chaos, the quantum corrections grow exponentially, making the evolution of the system essentially quantal after a certain time tau( variant Planck's over 2pi ) has elapsed. Analytical and numerical analysis show that in this regime the time tau( variant Planck's over 2pi ) obeys the logarithmic law tau( variant Planck's over 2pi ) approximately ln N (N is the number of atoms), and not the law tau( variant Planck's over 2pi ) approximately N(alpha) (alpha is a certain constant of order unity), as would be the case in the absence of chaos.     

Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity

Localization to the ground state of axial motion is demonstrated for a single, trapped atom strongly coupled to the field of a high finesse optical resonator. The axial atomic motion is cooled by way of coherent Raman transitions on the red vibrational sideband. An efficient state detection scheme enabled by strong coupling in cavity QED is used to record the Raman spectrum, from which the state of atomic motion is inferred. We find that the lowest vibrational level of the axial potential with zero-point energy variant Planck's over 2 h omega a/2kB = 13 microK is occupied with probability P0 approximately 0.95.     

Experimental observation of a superfluid gyroscope in a dilute Bose-Einstein condensate

We have observed a three-dimensional gyroscopic effect associated with a vortex in a dilute Bose-Einstein condensed gas. A condensate with a vortex possesses a single quantum of circulation, and this causes the plane of oscillation of the scissors mode to precess around the vortex line. We have measured the precession rate of the scissors oscillation. From this we deduced the angular momentum associated with the vortex line and found a value close to Planck's over 2pi per particle, as predicted for a superfluid.     

Tensor operators in noncommutative quantum mechanics

Some consequences of promoting the object of noncommutativity theta(ij) to an operator in Hilbert space are explored. Its canonical conjugate momentum is also introduced. Consequently, a consistent algebra involving the enlarged set of canonical operators is obtained, which permits us to construct theories that are dynamically invariant under the action of the rotation group. In this framework it is also possible to give dynamics to the noncommutativity operator sector, resulting in new features.     

Proposal for generating brilliant x-ray beams carrying orbital angular momentum

We consider use of a variable polarizing undulator for generating brilliant x-ray beams carrying orbital angular momentum. We find that higher harmonics of the radiation correspond to Laguerre-Gaussian modes with azimuthal mode indices l equal to one less than the harmonic number when the undulator is operated to produce circularly polarized light. Beams with nonzero l carry orbital angular momentum quantized in units of lvariant Planck's over 2pi per photon. When operated to produce linear polarization, the harmonics correspond to Hermite-Gaussian modes. Selection of these modes with conventional monochromator optics opens the door for new research with x-ray synchrotron and free-electron laser sources.     

Effect of the diamagnetic interaction on the intensity of the radiation lines of an atom in a magnetic field

Under the conditions of the total Paschen-Back effect the diamagnetic interaction determines the dependence of the intensity of the Zeeman components of atomic radiation lines on a magnetic field. The change in the matrix elements of the radiative transitions is due to the magnetically induced corrections to the wavefunctions of the initial and final states, whose contributions are of the same order of magnitude for the head lines of the optical series. For the high-frequency lines the positive corrections to the matrix element from the wavefunction of the upper level dominate. A magnetic field also induces dipole radiative transitions with selection rules for the orbital angular momentum | Δl| ≥ 3. The matrix elements of such transitions increase rapidly with the energy of the upper level, making possible efficient single-photon population of the dipole-inaccessible Rydberg states in moderate magnetic fields.     

Semiclassical structure of chaotic resonance eigenfunctions

We study the resonance (or Gamow) eigenstates of open chaotic systems in the semiclassical limit, distinguishing between left and right eigenstates of the nonunitary quantum propagator and also between short-lived and long-lived states. The long-lived left (right) eigenstates are shown to concentrate as variant Planck's over 2pi-->0 on the forward (backward) trapped set of the classical dynamics. The limit of a sequence of eigenstates [psi(variant Planck's over)] 2pi-->0 is found to exhibit a remarkably rich structure in phase space that depends on the corresponding limiting decay rate. These results are illustrated for the open baker's map, for which the probability density in position space is observed to have self-similarity properties.     

Fission barriers at high angular momentum and the ground state rotational band of the nucleus 254No

We study the superheavy nucleus 254No in the framework of the Hartree-Fock-Bogoliubov approximation with the finite-range density-dependent Gogny force, at zero and high angular momentum. The properties of the ground state rotational band and the fission barriers are discussed as a function of angular momentum. We found a two-humped barrier up to spin values of (30-40)Planck's over 2pi and a one-humped barrier for higher spins. We reproduce fairly well with the binding energy, the ground state deformation, the gamma-ray energies, and the bound on the fission barrier height measured at high spin.