arXiv subjects

C. J. Williams

Publications and source records attributed to C. J. Williams.

30 records · Page 2Linked to original sources

arXiv2004

Loading Bose condensed atoms into the ground state of an optical lattice

We optimize the turning on of a one-dimensional optical potential, V_L(x,t) = S(t) V_0 cos^2(kx) to obtain the optimal turn-on function S(t) so as to load a Bose-Einstein condensate into the ground state of the optical lattice of depth V_0. Specifically, we minimize interband excitations at the end of the turn-on of the optical potential at the final ramp time t_r, where S(t_r) = 1, given that S(0) = 0. Detailed numerical calculations confirm that a simple unit cell model is an excellent approximation when the turn-on time t_r is long compared with the inverse of the band excitation frequency and short in comparison with nonlinear time \hbar/μwhere μis the chemical potential of the condensate. We demonstrate using the Gross-Pitaevskii equation with an optimal turn-on function S(t) that the ground state of the optical lattice can be loaded with very little excitation even for times t_r on the order of the inverse band excitation frequency.

cond-mat.other↗

arXiv2004

Precise determination of $^6$Li cold collision parameters by radio-frequency spectroscopy on weakly bound molecules

We employ radio-frequency spectroscopy on weakly bound $^6$Li$_2$ molecules to precisely determine the molecular binding energies and the energy splittings between molecular states for different magnetic fields. These measurements allow us to extract the interaction parameters of ultracold $^6$Li atoms based on a multi-channel quantum scattering model. We determine the singlet and triplet scattering lengths to be $a_s=45.167(8)a_0$ and $a_t=-2140(18)a_0$ (1 $a_0$ = 0.0529177 nm), and the positions of the broad Feshbach resonances in the energetically lowest three $s-$wave scattering channels to be 83.41(15) mT, 69.04(5) mT, and 81.12(10) mT.

cond-mat.other↗

arXiv2004

Feshbach Resonances in Fermionic Lithium-6

Feshbach resonances in lithium-6 were experimentally studied and theoretically analyzed. In addition to two previously known s-wave resonances, we found three p-wave resonances. Four of these resonances are narrow and yield a precise value of the singlet scattering length, but do not allow us to accurately predict the location of the broad resonance near 83 mT. Its position was previously measured in a molecule-dissociation experiment for which we, here, discuss systematic shifts.

cond-mat.soft↗

arXiv2004

Four-Wave Mixing In BEC Systems With Multiple Spin States

We calculate the four-wave mixing (FWM) in a Bose-Einstein condensate system having multiple spin wave packets that are initially overlapping in physical space, but have nonvanishing relative momentum that cause them to recede from one another. Three receding condensate atom wave packets can result in production of a fourth wave packet by the process of FWM due to atom-atom interactions. We consider cases where the four final wave packets are composed of 1, 2, 3 and 4 different internal spin components. FWM with 1- or 2-spin state wave packets is much stronger than 3- or 4-spin state FWM, wherein two of the coherent moving BEC wave packets form a polarization-grating that rotates the spin projection of the third wave into that of fourth diffracted wave (as opposed to the 1- or 2-spin state case where a regular density-grating is responsible for the diffraction). Calculations of FWM for $^{87}$Rb and $^{23}$Na condensate systems are presented.

cond-mat.soft↗

arXiv2003

Effects of Inhomogeneity on the Spectrum of the Mott-Insulator State

We investigate the existence of quantum {\it quasi} phase transitions for an ensemble of ultracold bosons in a one-dimensional optical lattice, performing exact diagonalizations of the Bose-Hubbard Hamiltonian. When an external parabolic potential is added to the system {\it quasi} phase transitions are induced by the competition of on-site mean-field energy, hopping energy, and energy offset among lattice sites due to the external potential and lead to the coexistence of regions of particle localization and delocalization in the lattice. We clarify the microscopic mechanisms responsible for these {\it quasi} phase transitions as a function of the depth of the external potential when the on-site mean-field energy is large compared to the hopping energy. In particular, we show that a model Hamiltonian involving a few Fock states can describe the behavior of energy gap, mean particle numbers per site, and number fluctuations per site almost quantitatively. The role of symmetry on the gap as a function of the depth of the external trapping potential is elucidated. We discuss possible experimental signatures of {\it quasi} phase transitions studying the single particle density matrix and explain microscopically the occurrence of local maxima in the momentum distribution. The role of a thermal population of the excited states on the momentum distribution is discussed.

cond-mat↗

arXiv2003

Purely-long-range bound states of He$(2s ^3S)+$He$(2p ^3P)$

We predict the presence and positions of purely-long-range bound states of $^4$He$(2s ^3S)+{}^4$He$(2p ^3P)$ near the $2s ^3S_1+2p ^3P_{0,1}$ atomic limits. The results of the full multichannel and approximate models are compared, and we assess the sensitivity of the bound states to atomic parameters characterizing the potentials. Photoassociation to these purely-long-range molecular bound states may improve the knowledge of the scattering length associated with the collisions of two ultracold spin-polarized $^4$He$(2s ^3S)$ atoms, which is important for studies of Bose-Einstein condensates.

physics.atom-ph↗

arXiv2002

Excitation and damping of collective modes of a Bose-Einstein condensate in a one-dimensional lattice

The mode structure of a Bose-Einstein condensate non-adiabatically loaded into a one-dimensional optical lattice is studied by analyzing the visibility of the interference pattern as well as the radial profile of the condensate after a time-of-flight. A simple model is proposed that predicts the short-time decrease of the visibility as a function of the condensate parameters. In the radial direction, heavily damped oscillations are observed, as well as an increase in the condensate temperature. These findings are interpreted as a re-thermalization due to dissipation of the initial condensate excitations into high-lying modes.

cond-mat.soft↗

arXiv2002

Measurement of the Zero Crossing in a Feshbach Resonance of Fermionic 6-Li

We measure a zero crossing in the scattering length of a mixture of the two lowest hyperfine states of 6-Li. To locate the zero crossing, we monitor the decrease in temperature and atom number arising from evaporation in a CO2 laser trap as a function of magnetic field B. The temperature decrease and atom loss are minimized for B=528(4) G, consistent with no evaporation. We also present preliminary calculations using potentials that have been constrained by the measured zero crossing and locate a broad Feshbach resonance at approximately 860 G, in agreement with previous theoretical predictions. In addition, our theoretical model predicts a second and much narrower Feshbach resonance near 550 G.

cond-mat.soft↗

arXiv2002

Creation of a molecular condensate by dynamically melting a Mott-insulator

We propose creation of a molecular Bose-Einstein condensate (BEC) by loading an atomic BEC into an optical lattice and driving it into a Mott insulator (MI) with exactly two atoms per site. Molecules in a MI state are then created under well defined conditions by photoassociation with essentially unit efficiency. Finally, the MI is melted and a superfluid state of the molecules is created. We study the dynamics of this process and photoassociation of tightly trapped atoms.

cond-mat.soft↗

arXiv2001

Quantum Logic for Trapped Atoms via Molecular Hyperfine Interactions

We study the deterministic entanglement of a pair of neutral atoms trapped in an optical lattice by coupling to excited-state molecular hyperfine potentials. Information can be encoded in the ground-state hyperfine levels and processed by bringing atoms together pair-wise to perform quantum logical operations through induced electric dipole-dipole interactions. The possibility of executing both diagonal and exchange type entangling gates is demonstrated for two three-level atoms and a figure of merit is derived for the fidelity of entanglement. The fidelity for executing a CPHASE gate is calculated for two 87Rb atoms, including hyperfine structure and finite atomic localization. The main source of decoherence is spontaneous emission, which can be minimized for interaction times fast compared to the scattering rate and for sufficiently separated atomic wavepackets. Additionally, coherent couplings to states outside the logical basis can be constrained by the state dependent trapping potential.

quant-ph↗

arXiv2000

Atom loss and the formation of a molecular Bose-Einstein condensate by Feshbach resonance

In experiments conducted recently at MIT on Na Bose-Einstein condensates [S. Inouye et al, Nature 392, 151 (1998); J. Stenger et al, Phys. Rev. Lett. 82, 2422 (1999)], large loss rates were observed when a time-varying magnetic field was used to tune a molecular Feshbach resonance state near the state of a pair of atoms in the condensate. A collisional deactivation mechanism affecting a temporarily formed molecular condensate [see V. A. Yurovsky, A. Ben-Reuven, P. S. Julienne and C. J. Williams, Phys. Rev. A 60, R765 (1999)], studied here in more detail, accounts for the results of the slow-sweep experiments. A best fit to the MIT data yields a rate coefficient for deactivating atom-molecule collisions of 1.6e-10 cm**3/s. In the case of the fast sweep experiment, a study is carried out of the combined effect of two competing mechanisms, the three-atom (atom-molecule) or four-atom (molecule-molecule) collisional deactivation vs. a process of two-atom trap-state excitation by curve crossing [F. H. Mies, P. S. Julienne, and E. Tiesinga, Phys. Rev. A 61, 022721 (2000)]. It is shown that both mechanisms contribute to the loss comparably and nonadditively.

cond-mat↗

arXiv1999

Atom loss from Bose-Einstein condensates due to Feshbach resonance

In recent experiments on Na Bose-Einstein condensates [S. Inouye et al, Nature 392, 151 (1998); J. Stenger et al, Phys. Rev. Lett. 82, 2422 (1999)], large loss rates were observed when a time-varying magnetic field was used to tune a molecular Feshbach resonance state near the state of pairs of atoms belonging to the condensate many-body wavefunction. A mechanism is offered here to account for the observed losses, based on the deactivation of the resonant molecular state by interaction with a third condensate atom.

cond-mat↗