Dynamical Instability of Coreless Vortices in F=2 Spinor Bose-Einstein Condensates

We theoretically investigate the low-lying excitation spectra of coreless vortex states in Bose-Einstein condensates (BECs) with F=2 hyperfine spin degrees of freedom. Here, we extend the previous work in F=1 spinor BEC. In addition to the dynamical instabilities in F=1 coreless vortex states, we find an another set of dynamical instabilities due to different hyperfine spin interaction. The calculation is carried out in the possible parameter space of the F=2 ⁸⁷Rb atom. This study assists interpretation of experimental data and presents a general characteristics of the dynamical instability of F=2 hyperfine spin system. whether the ground state of the spin interaction is in the cyclic or polar phase. Our study can encourages the experiments to examine our results.     

A two species trap for chromium and rubidium atoms

Abstract

We realize a combined trap for bosonic chromium (⁵²Cr) and rubidium (⁸⁷Rb) atoms. Initial experiments focus on exploring a suitable loading scheme for the combined trap and on studies of new trap loss mechanisms originating from simultaneous trapping of two species. By comparing the trap loss from the ⁸⁷Rb magneto-optical trap (MOT) in the absence and presence of magnetically trapped ground state ⁵²Cr atoms we determine the scattering cross-section of σ _inel,RbCr = 5.0 ± 4.0 × 10^?18 m² for light-induced inelastic collisions between the two species. Studying the trap loss from the Rb magneto-optical trap induced by the Cr cooling-laser light, the photoionization cross-section of the excited 5P_3/1 state at an ionizing wavelength of 426 nm is measured to be σ _P = 1.1 ± 0.3 × 10^?21 m².     

Estimating Bounds on Collisional Relaxation Rates of Spin-Polarized 87Rb Atoms at Ultracold Temperatures

We present quantum scattering calculations for the collisional relaxation rate coefficient of spin-polarized ⁸⁷Rb(f = 2,m = 2) atoms, which determines the loss rate of cold Rb atoms from a magnetic trap. Unlike the lighter alkali atoms, spin-polarized ⁸⁷Rb atoms can undergo dipolar relaxation due to both the normal spin-spin dipole interaction and a second-order spin-orbit interaction with distant electronic states of the dimer. We present ab initio calculations for the second-order spin-orbit terms for both Rb₂ and Cs₂. The corrections lead to a reduction in the relaxation rate for ⁸⁷Rb. Our primary concern is to analyze the sensitivity of the ⁸⁷Rb trap loss to the uncertainties in the ground state molecular potentials. Since the scattering length for the a³Σ⁺_u state is already known, the major uncertainties are associated with the X¹Σ⁺_g potential. After testing the effect of systematically modifying the short-range form of the molecular potentials over a reasonable range, and introducing our best estimate of the second-order spin-orbit interaction, we estimate that in the low temperature limit the rate coefficient for loss of Rb atoms from the f = 2,m = 2 state is between 0.4 × 10⁻¹⁵ cm³/s and 2.4 × 10⁻¹⁵ cm³/s (where this number counts two atoms lost per collision). In a pure condensate the rate coefficient would be reduced by 1/2.     

Quantum non-demolition measurements using cold atoms in an optical cavity

Abstract

In this paper we present a theoretical analysis of a recent quantum non-demolition experiment in optics using cold atoms in a magneto-optical trap as a nonlinear medium. A signal beam and a meter beam from two independent lasers are coupled within a A-type three-level scheme in the D1 line of ⁸⁷Rb atoms. The experimental results for the relevant quantum correlations of the fields represent up to now the best achievement for a single back-action evading measurement. Moreover, they are found to be in remarkably good agreement with the theoretical predictions from a fully quantum model for three-level atoms in a doubly resonant cavity.     

Ground state cooling,quantum state engineering and study of decoherence of ions in Paul traps

Abstract

We investigate single ions of ⁴⁰Ca⁺ in Paul traps for quantum information processing. Superpositions of the S_½ electronic ground state and the metastable D_5/2; state are used to implement a qubit. Laser light on the S_½ ? D_5/2 transition is used for the manipulation of the ion's quantum state. We apply sideband cooling to the ion and reach the ground state of vibration with up to 99.9% probability. Starting from this Fock state (n = 0), we demonstrate coherent quantum state manipulation. A large number of Rabi oscillations and a ms-coherence time is observed. Motional heating is measured to be as low as one vibrational quantum in 190ms. We also report on ground state cooling of two ions.     

Production of full intensity,highly nuclear spin polarized alkali-metal (23Na) beams by a double resonance technique

Simultaneous optical pumping with a laser and induction of rf transitions within the hyperfine levels of alkali-metal (²³Na) ground states allow to pump all atoms of an atomic beam into one hyperfine component (F = 2, m_F = +2 or −2). The technique used is briefly described. The effect of coherent coupling between atomic states (Autler-Townes or dynamical Stark effect) is discussed in some detail, in particular how to avoid drawbacks of this effect on the optical pumping process.     

A Nonextensive Approach to Bose-Einstein Condensation of Trapped Interacting Boson Gas

In the Bose-Einstein condensation of interacting atoms or molecules such as ⁸⁷Rb, ²³Na and ⁷Li, the theoretical understanding of the transition temperature is not always obvious due to the interactions or zero point energy which cannot be exactly taken into account. The S-wave collision model fails sometimes to account for the condensation temperatures. In this work, we look at the problem within the nonextensive statistics which is considered as a possible theory describing interacting systems. The generalized energy U _q and the particle number N _q of boson gas are given in terms of the nonextensive parameter q. q>1 (q<1) implies repulsive (attractive) interaction with respect to the perfect gas. The generalized condensation temperature T _cq is derived versus T _c given by the perfect gas theory. Thanks to the observed condensation temperatures, we find q≈0.1 for ⁸⁷Rb atomic gas, q≈0.95 for ⁷Li and q≈0.62 for ²³Na. It is concluded that the effective interactions are essentially attractive for the three considered atoms, which is consistent with the observed temperatures higher than those predicted by the conventional theory.      

Trapping Fermionic 40K and Bosonic 87Rb on a Chip

We demonstrate the loading of a Bose–Fermi mixture into a microfabricated magnetic trap. In a single-chamber vacuum system, laser-cooled atoms are transported to the surface of a substrate on which gold wires have been microfabricated. The magnetic field minimum formed near these current-carrying wires is used to confine up to 6 × 10⁴ neutral ⁴⁰K atoms. In addition, we can simultaneously load 2 × 10^{5 87}Rb atoms, demonstrating the confinement of two distinct elements with such a trap. In a sequence optimized for ⁸⁷Rb alone, we observe up to 1 × 10⁷ trapped atoms. We describe in detail the experimental apparatus, and discuss prospects for evaporative cooling towards quantum degeneracy in both species.     

Interaction of a System of Initially Unexcited Two-level Atoms with a Weak Cavity Field

Abstract

Using a perturbation method, constructed in terms of SU(2) group representations, the interaction of N initially unexcited two-level atoms and a weak single-mode cavity field is studied. The field is assumed to be initially either in a Fock state with a number of photons equal to n or in a coherent state. In the case of the photon-number state with n  3, the pure phenomenon of collective collapses and revivals manifests itself. For the initially coherent field the phenomenon of collapses and revivals arising from the photon number distribution mechanism is additionally modulated by this collective mechanism. The problem of the interaction of excited atoms with an initially coherent field has already been solved numerically by Barnett and Knight. For n=1 2 and 3 the approximate solution is compared with the exact solutions also given in this paper and the limit of applicability of our approach is established.     

Properties of Spinor Bose Condensates

We analyze the ground state structure and low energy dynamics of an f=1 spinor condensate. We show that there are distinct time scales governing the spin-mixing process in spinor condensates and analyze them using algebraic, semiclassical, and numerical approaches. We find that the dynamics is sensitive to the relative phase, particle number distribution among the spin components, and the total particle number in the condensate. We further find that complicated structures develop in the densities during the evolution. We also investigate the dynamics under the action of external magnetic fields and uncover an intriguing set of phenomena like stochastization in spin populations, metastability in the spin component distribution, and dynamic localization in spin space.     

Cooperative Atomic Behaviour and Oscillator Formation in a Squeezed Vacuum

Abstract

Time-dependent (numerical) results are presented for super-radiant behaviour in the Dicke model of N _a = 2, 3 atoms in a broad band squeezed vacuum. This concerns the fluctuations and the intensity of the fluorescent radiation as well as the atomic population inversion of the system with atoms initially in an atomic coherent state. In the steady state, and in the N _a → ∞, we show that the ‘atomic’ Dicke model behaves like a ‘giant quantum oscillator’, in which the number of excited atoms asymptotically approaches the average number of photons in the resonant mode of the squeezed vacuum, just as in the thermally driven case.     

Periodic Squeezing in the Tavis-Cummings Model

Abstract

By utilizing our previous operator solution [17], we have investigated the squeezing in the radiation field of the Tavis-Cummings model (collective N ? 1 two-level atoms interacting with a resonant single cavity quantized mode). With field and atoms initially in coherent field state strong or weak and atomic coherent state (of few excited atoms), periodic time-dependent squeezing in the field and the macroscopic polarization is expressed in terms of Jacobian elliptic functions of the first kind. The statistical investigations are carried out for the quasiprobability distribution functions (Wigner function and Q function). The distribution function of the field quadrature has a variance less (greater) than that for a coherent state if this quadrature is squeezed (unsqueezed).     

Resonant nonlinearity enhancement in rubidium vapor with additional optical pumping

We investigate the enhancement of characteristic nonlinear phase shift in warm rubidium vapor for a signal beam using an additional pump laser at different frequency. A numerical model based on density matrix formalism is used. Experimental results of self-rotation and diffraction in a three-wave mixing process as well as beam amplification are shown. For ⁸⁷Rb transition D2 line with F_g?=?1, the nonlinearity to absorption ratio can be enhanced approximately two times with a pump beam tuned at F_g?=?2 transition in a co-propagating scheme, which produces strong nonlinear interaction for F_g?=?1 line at signal beam powers of ~10?mW.     

Making cold molecules by time-dependent feshbach resonances

Abstract

Pairs of trapped atoms can be associated to make a diatomic molecule using a time-dependent magnetic field to ramp the energy of a scattering resonance state from above to below the scattering threshold. A relatively simple model, parametrized in terms of the background scattering length and resonance width and magnetic moment, can be used to predict conversion probabilities from atoms to molecules. The model and its Landau-Zener interpretation are described and illustrated by specific calculations for ²³Na, ⁸⁷Rb and ¹³³Cs resonances. The model can be readily adapted to Bose-Einstein condensates. Comparison with full many-body calculations for the condensate case shows that the model is very useful for making simple estimates of molecule conversion efficiencies.     

Controlling decoherence of a two-level atom in a lossy cavity

Abstract

By use of external periodic driving sources, we demonstrate the possibility of controlling the coherent as well as the decoherent dynamics of a two-level atom placed in a lossy cavity. The control of the coherent dynamics is elucidated for the phenomenon of coherent destruction of tunnelling (CDT), i.e. the coherent dynamics of a driven two-level atom in a quantum superposition state can be brought practically to a complete standstill. We study this phenomenon for different initial preparations of the two-level atom. We then proceed to investigate the decoherence originating from the interaction of the two-level atom with a lossy cavity mode. The loss mechanism is described in terms of a microscopic model that couples the cavity mode to a bath of harmonic field modes. A suitably tuned external cw-laser field applied to the two-level atom slows down considerably the decoherence of the atom. We demonstrate the suppression of decoherence for two opposite initial preparations of the atomic state: a quantum superposition state as well as the ground state. These findings can be used to decrease the influence of decoherence in qubit manipulation processes.     

Higher-generation Schrödinger cat states in cavity QED

Abstract

Higher-generation Schrödinger cat states of the quantized electromagnetic field can be produced in a high-Q cavity, starting from a coherent state, through the passage of prepared Rydberg atoms interacting dispersively across it. These states are natural generalizations of the even and odd coherent states, the N ^th-generations corresponding to specific superpositions of 2 ^N states on a circle in phase space with well defined parity, and present very peculiar properties. Their photon statistics interchange between super- and sub-Poissonian behaviours and the nature of the photon bunching oscillates as the field intensity in the cavity is varied. For higher-generation even states, the minimum value of the Mandel factor almost reaches ?1.0 and the state represents the Fock state |2 ^N ). Squeezing properties and the Wigner function of these higher-generation Schrödinger cat states are also considered.     

Synthesis and structural studies of a new potassium uranyl selenate K(H5O2)[(UO2)2(SeO4)3(H2O)] with strongly deformed layers

Single crystals of a new uranyl selenate, K(H₅O₂)[(UO₂)₂(SeO₄)₃(H₂O)] (I), were prepared by isothermal evaporation at room temperature. The crystal structure of I was solved by the direct method (space group P2₁/c; a = 11.456(2), b = 10.231(1), c = 14.809(2) ?; β = 101.901(4)°, V = 1698.4(4) ?³; Z = 4) and refined to R ₁ = 0.0547 (wR ₂ = 0.0825) for 3375 reflections with |F _o| ≥ 4σ _F . The structure of I is based on layers of the composition [(UO₂)₂(SeO₄)₃(H₂O)]²⁻. The charge of the inorganic layer is compensated by potassium and oxonium ions located in the interlayer space. Each potassium ion is coordinated by seven oxygen atoms belonging to uranyl selenate layers, including uranyl oxygen atoms, which leads to bending of uranyl selenate structural elements.     

Vortices in a stirred Bose-Einstein condensate

Abstract

We stir with a focused laser beam a Bose-Einstein condensate of ⁸⁷Rb atoms confined in a magnetic trap. We observe the formation of a single vortex for a stirring frequency exceeding a critical value. At larger rotation frequencies we produce states of the condensate for which up to eleven vortices are simultaneously present. We present measurements of the decay of a vortex array once the stirring laser beam is removed.     

Stabilization of mode-locked trains,and dark resonance of two-photon lambda-level structures

Our ultimate objective is to design a combined frequency standard for optical as well as radio frequencies. A mode-locked laser provides frequency components that can be used as a ruler to measure any unknown optical source through direct beating. The frequency spacing of a pair of teeth of this comb is in itself a radio frequency reference. Fast control and correction for both the average frequency and the repetition rate of a mode-locked Ti : sapphire laser are achieved by locking the laser to a reference cavity of ultra-low expansion quartz with equal mode spacing. We measure an optical frequency with a mean square deviation of 700 Hz, instability limited by the radio-frequency sources used to count the repetition rate. As a reference standard to achieve absolute accuracy, we use the Λ transition 5S^1/2 (F = 1) → 5D^5/2 (F = 3) → 5S^1/2 (F = 2) of rubidium. The theory for this coherent interaction shows that, with one mode resonant with the two-photon 5S^1/2 (^F = 1) → 5D^5/2 (^F = 3) transition, the fluorescence goes through a resonance for a change in repetition rate of less than 10 kHz. These results suggest that, by locking to the peak of that resonant feature, optical stability and absolute accuracy better than 1 kHz can easily be achieved.     

Splitting of a Quadruply Quantized Vortex in the Rb Bose-Einstein Condensate

We observed the sudden deformation of a quadruply quantized vortex into a linear shape in a ⁸⁷Rb (F=2,m _F =2) Bose-Einstein condensate (BEC). Multiply quantized vortex is predicted to split into singly quantized vortices and the observed deformation is considered to be the onset of the splitting. The displacement of the vortex with respect to the center of the BEC would induce the observed splitting. Our theoretical simulation qualitatively supports these arguments.