TY - JOUR T1 - Collisions of room-temperature helium with ultracold lithium and the van der Waals bound state of HeLi JF - Phys. Rev. A Y1 - 2020 A1 - Constantinos Makrides A1 - Daniel S Barker A1 - James A Fedchak A1 - Julia Scherschligt A1 - Stephen Eckel A1 - Eite Tiesinga AB -

We have computed the thermally averaged total, elastic rate coefficient for the collision of a room-temperature helium atom with an ultracold lithium atom. This rate coefficient has been computed as part of the characterization of a cold-atom vacuum sensor based on laser-cooled Li 6 or Li 7 atoms that will operate in the ultrahigh-vacuum (p< 10− 6 Pa) and extreme-high-vacuum (p< 10− 10 Pa) regimes. The analysis involves computing the X 2 Σ+ HeLi Born-Oppenheimer potential followed by the numerical solution of the relevant radial Schrödinger equation. The potential is computed using a single-reference-coupled-cluster electronic-structure method with basis sets of different completeness in order to characterize our uncertainty budget. We predict that the rate coefficient for a 300 K helium gas and a 1 μ K Li gas is 1.467 (13)× 10− 9 cm 3/s for He 4+ Li 6 and 1.471 (13)× 10− 9 cm 3/s for He 4+ Li 7, where the …

VL - 101 CP - 012702 U5 - https://doi.org/10.1103/PhysRevA.101.012702 ER - TY - JOUR T1 - Feshbach resonances in p-wave three-body recombination within Fermi-Fermi mixtures of open-shell 6Li and closed-shell 173Yb atoms Y1 - 2019 A1 - Alaina Green A1 - Hui Li A1 - Jun Hui See Toh A1 - Xinxin Tang A1 - Katherine McCormick A1 - Ming Li A1 - Eite Tiesinga A1 - Svetlana Kotochigova A1 - Subhadeep Gupta AB -

We report on observations and modeling of interspecies magnetic Feshbach resonances in dilute ultracold mixtures of open-shell alkali-metal 6Li and closed-shell 173Yb atoms with temperatures just above quantum degeneracy for both fermionic species. Resonances are located by detecting magnetic-field-dependent atom loss due to three-body recombination. We resolve closely-located resonances that originate from a weak separation-dependent hyperfine coupling between the electronic spin of 6Li and the nuclear spin of 173Yb, and confirm their magnetic field spacing by ab initio electronic-structure calculations. Through quantitative comparisons of theoretical atom-loss profiles and experimental data at various temperatures between 1 μK and 20 μK, we show that three-body recombination in fermionic mixtures has a p-wave Wigner threshold behavior leading to characteristic asymmetric loss profiles. Such resonances can be applied towards the formation of ultracold doublet ground-state molecules and quantum simulation of superfluid p-wave pairing.

UR - https://arxiv.org/abs/1912.04874 ER - TY - JOUR T1 - Fractal Universality in Near-Threshold Magnetic Lanthanide Dimers JF - Science Advances Y1 - 2018 A1 - Constantinos Makrides A1 - Ming Li A1 - Eite Tiesinga A1 - Svetlana Kotochigova AB -

Ergodic quantum systems are often quite alike, whereas nonergodic, fractal systems are unique and display characteristic properties. We explore one of these fractal systems, weakly bound dysprosium lanthanide molecules, in an external magnetic field. As recently shown, colliding ultracold magnetic dysprosium atoms display a soft chaotic behavior with a small degree of disorder. We broaden this classification by investigating the generalized inverse participation ratio and fractal dimensions for large sets of molecular wave functions. Our exact close-coupling simulations reveal a dynamic phase transition from partially localized states to totally delocalized states and universality in its distribution by increasing the magnetic field strength to only a hundred Gauss (or 10 mT). Finally, we prove the existence of nonergodic delocalized phase in the system and explain the violation of ergodicity by strong coupling between near-threshold molecular states and the nearby continuum.

VL - 4 U4 - eaap8308 UR - https://arxiv.org/abs/1802.09586 CP - 2 U5 - https://doi.org/10.1126/sciadv.aap8308 ER - TY - JOUR T1 - Observation of bound state self-interaction in a nano-eV atom collider JF - Nature Communications Y1 - 2018 A1 - Ryan Thomas A1 - Matthew Chilcott A1 - Eite Tiesinga A1 - Amita B. Deb A1 - Niels Kjærgaard AB -

Quantum mechanical scattering resonances for colliding particles occur when a continuum scattering state couples to a discrete bound state between them. The coupling also causes the bound state to interact with itself via the continuum and leads to a shift in the bound state energy, but, lacking knowledge of the bare bound state energy, measuring this self-energy via the resonance position has remained elusive. Here, we report on the direct observation of self-interaction by using a nano-eV atom collider to track the position of a magnetically-tunable Feshbach resonance through a parameter space spanned by energy and magnetic field. Our system of potassium and rubidium atoms displays a strongly non-monotonic resonance trajectory with an exceptionally large self-interaction energy arising from an interplay between the Feshbach bound state and a different, virtual bound state at a fixed energy near threshold.

VL - 9 UR - https://arxiv.org/abs/1807.01174 CP - 4895 U5 - https://doi.org/10.1038/s41467-018-07375-8 ER - TY - JOUR T1 - Orbital quantum magnetism in spin dynamics of strongly interacting magnetic lanthanide atoms Y1 - 2018 A1 - Ming Li A1 - Eite Tiesinga A1 - Svetlana Kotochigova AB -

Laser cooled lanthanide atoms are ideal candidates with which to study strong and unconventional quantum magnetism with exotic phases. Here, we use state-of-the-art closed-coupling simulations to model quantum magnetism for pairs of ultracold spin-6 erbium lanthanide atoms placed in a deep optical lattice. In contrast to the widely used single-channel Hubbard model description of atoms and molecules in an optical lattice, we focus on the single-site multi-channel spin evolution due to spin-dependent contact, anisotropic van der Waals, and dipolar forces. This has allowed us to identify the leading mechanism, orbital anisotropy, that governs molecular spin dynamics among erbium atoms. The large magnetic moment and combined orbital angular momentum of the 4f-shell electrons are responsible for these strong anisotropic interactions and unconventional quantum magnetism. Multi-channel simulations of magnetic Cr atoms under similar trapping conditions show that their spin-evolution is controlled by spin-dependent contact interactions that are distinct in nature from the orbital anisotropy in Er. The role of an external magnetic field and the aspect ratio of the lattice site on spin dynamics is also investigated.

UR - https://arxiv.org/abs/1804.10102 ER - TY - JOUR T1 - A semiclassical theory of phase-space dynamics of interacting bosons Y1 - 2018 A1 - Ranchu Mathew A1 - Eite Tiesinga AB -

We study the phase-space representation of dynamics of bosons in the semiclassical regime where the occupation number of the modes is large. To this end, we employ the van Vleck-Gutzwiller propagator to obtain an approximation for the Green's function of the Wigner distribution. The semiclassical analysis incorporates interference of classical paths and reduces to the truncated Wigner approximation (TWA) when the interference is ignored. Furthermore, we identify the Ehrenfest time after which the TWA fails. As a case study, we consider a single-mode quantum nonlinear oscillator, which displays collapse and revival of observables. We analytically show that the interference of classical paths leads to revivals, an effect that is not reproduced by the TWA or a perturbative analysis.

UR - https://arxiv.org/abs/1803.05122 ER - TY - JOUR T1 - Above threshold scattering about a Feshbach resonance for ultracold atoms in an optical collider JF - Nature Communications Y1 - 2017 A1 - Milena S. J. Horvath A1 - Ryan Thomas A1 - Eite Tiesinga A1 - Amita B. Deb A1 - Niels Kjærgaard AB -

Studies of magnetically tunable Feshbach resonances in ultracold atomic gases have predominantly been carried out in the zero collision-energy limit. Here, we explore above threshold collisions at well-defined energies in the vicinity of a narrow magnetic Feshbach resonance by means of a laser-based collider. Our experiment focuses on collisions between ground-state 87Rb atoms in the |F = 2,mF = 0i and |F = 1,mF = 1i hyperfine states, which have a known s-wave resonance at 9.040(7) G at threshold that strongly couples to inelastic channels, where 1 G = 10−4 T. Using our collider we can track the magnetic field shift in resonance position as the energy is tuned. This presents a challenge due to the narrow width of the resonance in conjunction with inherent broadening mechanisms of the collider. We find, however, that the narrow Feshbach scattering feature becomes imprinted on the spatial distribution of atoms in a fashion that allows for an accurate determination of resonance position as a function of collision energy through a shift in center-of-mass position of the outgoing clouds. This shift has a dispersive line shape with a zero value at the resonance position. We obtain excellent agreement with theory on the resonance position.

VL - 8 UR - https://arxiv.org/abs/1704.07109 CP - 452 U5 - 10.1038/s41467-017-00458-y ER - TY - JOUR T1 - Development of a new UHV/XHV pressure standard (cold atom vacuum standard) JF - Metrologia Y1 - 2017 A1 - Julia Scherschligt A1 - James A Fedchak A1 - Daniel S Barker A1 - Stephen Eckel A1 - Nikolai Klimov A1 - Constantinos Makrides A1 - Eite Tiesinga AB -

The National Institute of Standards and Technology has recently begun a program to develop a primary pressure standard that is based on ultra-cold atoms, covering a pressure range of 1 x 10-6 to 1 x 10-10 Pa and possibly lower. These pressures correspond to the entire ultra-high vacuum range and extend into the extreme-high vacuum. This cold-atom vacuum standard (CAVS) is both a primary standard and absolute sensor of vacuum. The CAVS is based on the loss of cold, sensor atoms (such as the alkali-metal lithium) from a magnetic trap due to collisions with the background gas (primarily H2) in the vacuum. The pressure is determined from a thermally-averaged collision cross section, which is a fundamental atomic property, and the measured loss rate. The CAVS is primary because it will use collision cross sections determined from ab initio calculations for the Li + H2 system. Primary traceability is transferred to other systems of interest using sensitivity coefficients.

VL - 54 UR - https://arxiv.org/abs/1801.10120 CP - 6 U5 - https://doi.org/10.1088/1681-7575/aa8a7b ER - TY - JOUR T1 - Dispersive optical detection of magnetic Feshbach resonances in ultracold gases JF - Physical Review A Y1 - 2017 A1 - Bianca J. Sawyer A1 - Milena S. J. Horvath A1 - Eite Tiesinga A1 - Amita B. Deb A1 - Niels Kjærgaard AB -

Magnetically tunable Feshbach resonances in ultracold atomic systems are chiefly identified and characterized through time consuming atom loss spectroscopy. We describe an off-resonant dispersive optical probing technique to rapidly locate Feshbach resonances and demonstrate the method by locating four resonances of 87Rb, between the |F=1,mF=1 and |F=2,mF=0 states. Despite the loss features being 100 mG wide, we require only 21 experimental runs to explore a magnetic field range >18 G. The resonances consist of two known s-wave features in the vicinity of 9 G and 18 G and two previously unobserved p-wave features near 5 G and 10 G. We further utilize the dispersive approach to directly characterize the two-body loss dynamics for each Feshbach resonance.

VL - 96 U4 - 022705 UR - https://arxiv.org/abs/1702.02216 CP - 2 U5 - 10.1103/PhysRevA.96.022705 ER - TY - JOUR T1 - Pendular trapping conditions for ultracold polar molecules enforced by external electric fields JF - Physical Review A Y1 - 2017 A1 - Ming Li A1 - Alexander Petrov A1 - Constantinos Makrides A1 - Eite Tiesinga A1 - Svetlanta Kotochigova AB -

We theoretically investigate trapping conditions for ultracold polar molecules in optical lattices, when external magnetic and electric fields are simultaneously applied. Our results are based on an accurate electronic-structure calculation of the polar 23Na40K polar molecule in its absolute ground state combined with a calculation of its rovibrational-hyperfine motion. We find that an electric field strength of 5.26(15) kV/cm and an angle of 54.7 between this field and the polarization of the optical laser lead to a trapping design for 23Na40K molecules where decoherences due laser-intensity fluctuations and fluctuations in the direction of its polarization are kept to a minimum. One standard deviation systematic and statistical uncertainties are given in parenthesis. Under such conditions pairs of hyperfine-rotational states of v=0 molecules, used to induce tunable dipole-dipole interactions between them, experience ultrastable, matching trapping forces.

VL - 95 U4 - 063422 UR - https://arxiv.org/abs/1703.03839 CP - 6 U5 - 10.1103/PhysRevA.95.063422 ER - TY - JOUR T1 - Phase-space mixing in dynamically unstable, integrable few-mode quantum systems JF - Physical Review A Y1 - 2017 A1 - Ranchu Mathew A1 - Eite Tiesinga AB -

Quenches in isolated quantum systems are currently a subject of intense study. Here, we consider quantum few-mode systems that are integrable in their classical mean-field limit and become dynamically unstable after a quench of a system parameter. Specifically, we study a Bose-Einstein condensate (BEC) in a double-well potential and an antiferromagnetic spinor BEC constrained to a single spatial mode. We study the time dynamics after the quench within the truncated Wigner approximation (TWA) and find that system relaxes to a steady state due to phase-space mixing. Using the action-angle formalism and a pendulum as an illustration, we derive general analytical expressions for the time evolution of expectation values of observables and their long-time limits. We find that the deviation of the long-time expectation value from its classical value scales as 1/O(ln N), where N is the number of atoms in the condensate. Furthermore, the relaxation of an observable to its steady state value is a damped oscillation and the damping is Gaussian in time. We confirm our results with numerical TWA simulations.

VL - 96 U4 - 013604 UR - https://arxiv.org/abs/1705.01702 CP - 1 U5 - 10.1103/PhysRevA.96.013604 ER - TY - JOUR T1 - A Hubbard model for ultracold bosonic atoms interacting via zero-point-energy induced three-body interactions JF - Physical Review A Y1 - 2016 A1 - Saurabh Paul A1 - P. R. Johnson A1 - Eite Tiesinga AB -

We show that for ultra-cold neutral bosonic atoms held in a three-dimensional periodic potential or optical lattice, a Hubbard model with dominant, attractive three-body interactions can be generated. In fact, we derive that the effect of pair-wise interactions can be made small or zero starting from the realization that collisions occur at the zero-point energy of an optical lattice site and the strength of the interactions is energy dependent from effective-range contributions. We determine the strength of the two- and three-body interactions for scattering from van-der-Waals potentials and near Fano-Feshbach resonances. For van-der-Waals potentials, which for example describe scattering of alkaline-earth atoms, we find that the pair-wise interaction can only be turned off for species with a small negative scattering length, leaving the 88Sr isotope a possible candidate. Interestingly, for collisional magnetic Feshbach resonances this restriction does not apply and there often exist magnetic fields where the two-body interaction is small. We illustrate this result for several known narrow resonances between alkali-metal atoms as well as chromium atoms. Finally, we compare the size of the three-body interaction with hopping rates and describe limits due to three-body recombination.

VL - 93 U4 - 043616 UR - http://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.043616 CP - 4 U5 - 10.1103/PhysRevA.93.043616 ER - TY - JOUR T1 - Multiple scattering dynamics of fermions at an isolated p-wave resonance JF - Nature Communications Y1 - 2016 A1 - Ryan Thomas A1 - Kris O. Roberts A1 - Eite Tiesinga A1 - Andrew C.J. Wade A1 - P. Blair Blakie A1 - Amita B. Deb A1 - Niels Kjærgaard AB -

The wavefunction for indistinguishable fermions is anti-symmetric under particle exchange, which directly leads to the Pauli exclusion principle, and hence underlies the structure of atoms and the properties of almost all materials. In the dynamics of collisions between two indistinguishable fermions this requirement strictly prohibits scattering into 90 degree angles. Here we experimentally investigate the collisions of ultracold clouds fermionic 40K atoms by directly measuring scattering distributions. With increasing collision energy we identify the Wigner threshold for p-wave scattering with its tell-tale dumb-bell shape and no 90 yield. Above this threshold effects of multiple scattering become manifest as deviations from the underlying binary p-wave shape, adding particles either isotropically or axially. A shape resonance for 40K facilitates the separate observation of these two processes. The isotropically enhanced multiple scattering mode is a generic p-wave threshold phenomenon, while the axially enhanced mode should occur in any colliding particle system with an elastic scattering resonance.

VL - 7 U4 - 12069 UR - http://www.nature.com/articles/ncomms12069 U5 - 10.1038/ncomms12069 ER - TY - JOUR T1 - Photoassociation of spin polarized Chromium JF - Physical Review A Y1 - 2016 A1 - Jahn Rührig A1 - Tobias Bäuerle A1 - Paul S. Julienne A1 - Eite Tiesinga A1 - Tilman Pfau AB - We report the homonuclear photoassociation (PA) of ultracold 52Cr atoms in an optical dipole trap. This constitutes the first measurement of PA in an element with total electron spin S~>1. Although Cr, with its 7S3 ground and 7P4,3,2 excited states, is expected to have a complicated PA spectrum we show that a spin polarized cloud exhibits a remarkably simple PA spectrum when circularly polarized light is applied. Over a scan range of 20 GHz below the 7P3 asymptote we observe two distinct vibrational series each following a LeRoy-Bernstein law for a C3/R3 potential with excellent agreement. We determine the C3 coefficients of the Hund's case c) relativistic adiabatic potentials to be -1.83±0.02 a.u. and -1.46±0.01a.u.. Theoretical non-rotating Movre-Pichler calculations enable a first assignment of the series to Ω=6u and 5g potential energy curves. In a different set of experiments we disturb the selection rules by a transverse magnetic field which leads to additional PA series. VL - 93 U4 - 021406 UR - http://arxiv.org/abs/1512.04378 CP - 2 U5 - 10.1103/PhysRevA.93.021406 ER - TY - JOUR T1 - Sudden-quench dynamics of Bardeen-Cooper-Schrieffer states in deep optical lattices JF - Physical Review A Y1 - 2016 A1 - Marlon Nuske A1 - L. Mathey A1 - Eite Tiesinga AB -

We determine the exact time evolution of an initial Bardeen-Cooper-Schrieffer (BCS) state of ultra-cold atoms in a hexagonal optical lattice. The dynamical evolution is triggered by ramping the lattice potential up, such that the interaction strength Uf is much larger than the hopping amplitude Jf. The quench initiates collective oscillations with frequency |Uf|/(2π) in the momentum occupation numbers and imprints an oscillating phase with the same frequency on the order parameter Δ. The latter is not reproduced by treating the time evolution in mean-field theory. The momentum density-density or noise correlation functions oscillate at frequency |Uf|/2π as well as its second harmonic. For a very deep lattice, with negligible tunneling energy, the oscillations of momentum occupation numbers are undamped. Non-zero tunneling after the quench leads to dephasing of the different momentum modes and a subsequent damping of the oscillations. This occurs even for a finite-temperature initial BCS state, but not for a non-interacting Fermi gas. We therefore propose to use this dephasing to detect a BCS state. Finally, we predict that the noise correlation functions in a honeycomb lattice will develop strong anti-correlations near the Dirac point.

VL - 94 U4 - 023607 UR - http://arxiv.org/abs/1602.00979 CP - 2 U5 - http://dx.doi.org/10.1103/PhysRevA.94.023607 ER - TY - JOUR T1 - Wannier functions using a discrete variable representation for optical lattices JF - Physical Review A Y1 - 2016 A1 - Saurabh Paul A1 - Eite Tiesinga AB -

We propose a numerical method using the discrete variable representation (DVR) for constructing real-valued Wannier functions localized in a unit cell for both symmetric and asymmetric periodic potentials. We apply these results to finding Wannier functions for ultracold atoms trapped in laser-generated optical lattices. Following S. Kivelson [Phys. Rev. B 26, 4269 (1982)], for a symmetric lattice with inversion symmetry, we construct Wannier functions as eigenstates of the position operators xˆ, yˆ, and zˆ restricted to single-particle Bloch functions belonging to one or more bands. To ensure that the Wannier functions are real-valued, we numerically obtain the band structure and real-valued eigenstates using a uniform Fourier grid DVR. We then show, by a comparison of tunneling energies, that the Wannier functions are accurate for both inversion-symmetric and asymmetric potentials to better than 10 significant digits when using double-precision arithmetic. The calculations are performed for an optical lattice with double-wells per unit cell with tunable asymmetry along the x axis and a single sinusoidal potential along the perpendicular directions. Localized functions at the two potential minima within each unit cell are similarly constructed, but using a superposition of single-particle solutions from the two lowest bands. We finally use these localized basis functions to determine the two-body interaction energies in the Bose-Hubbard model and show the dependence of these energies on lattice asymmetry.

VL - 94 U4 - 033606 UR - http://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.033606 CP - 3 U5 - http://dx.doi.org/10.1103/PhysRevA.94.033606 ER - TY - JOUR T1 - Large effective three-body interaction in a double-well optical lattice JF - Phys. Rev. A 92, 023602 Y1 - 2015 A1 - Saurabh Paul A1 - Eite Tiesinga AB - We study ultracold atoms in an optical lattice with two local minima per unit cell and show that the low energy states of a multi-band Bose-Hubbard (BH) Hamiltonian with only pair-wise interactions is equivalent to an effective single-band Hamiltonian with strong three-body interactions. We focus on a double-well optical lattice with a symmetric double well along the $x$ axis and single well structure along the perpendicular directions. Tunneling and two-body interaction energies are obtained from an exact band-structure calculation and numerically-constructed Wannier functions in order to construct a BH Hamiltonian spanning the lowest two bands. Our effective Hamiltonian is constructed from the ground state of the $N$-atom Hamiltonian for each unit cell obtained within the subspace spanned by the Wannier functions of two lowest bands. The model includes hopping between ground states of neighboring unit cells. We show that such an effective Hamiltonian has strong three-body interactions that can be easily tuned by changing the lattice parameters. Finally, relying on numerical mean-field simulations, we show that the effective Hamiltonian is an excellent approximation of the two-band BH Hamiltonian over a wide range of lattice parameters, both in the superfluid and Mott insulator regions. VL - 92 U4 - 023602 UR - http://journals.aps.org/pra/abstract/10.1103/PhysRevA.92.023602 CP - 2 ER - TY - JOUR T1 - Optimization of collisional Feshbach cooling of an ultracold nondegenerate gas JF - Physical Review A Y1 - 2015 A1 - Marlon Nuske A1 - Eite Tiesinga A1 - L. Mathey AB - We optimize a collision-induced cooling process for ultracold atoms in the nondegenerate regime. It makes use of a Feshbach resonance, instead of rf radiation in evaporative cooling, to selectively expel hot atoms from a trap. Using functional minimization we analytically show that for the optimal cooling process the resonance energy must be tuned such that it linearly follows the temperature. Here, optimal cooling is defined as maximizing the phase-space density after a fixed cooling duration. The analytical results are confirmed by numerical Monte-Carlo simulations. In order to simulate more realistic experimental conditions, we show that background losses do not change our conclusions, while additional non-resonant two-body losses make a lower initial resonance energy with non-linear dependence on temperature preferable. VL - 91 U4 - 043626 UR - http://arxiv.org/abs/1412.8473v1 CP - 4 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.91.043626 ER - TY - JOUR T1 - Self-heterodyne detection of the \it in-situ phase of an atomic-SQUID JF - Physical Review A Y1 - 2015 A1 - Ranchu Mathew A1 - Avinash Kumar A1 - Stephen Eckel A1 - Fred Jendrzejewski A1 - Gretchen K. Campbell A1 - Mark Edwards A1 - Eite Tiesinga AB - We present theoretical and experimental analysis of an interferometric measurement of the {\it in-situ} phase drop across and current flow through a rotating barrier in a toroidal Bose-Einstein condensate (BEC). This experiment is the atomic analog of the rf-superconducting quantum interference device (SQUID). The phase drop is extracted from a spiral-shaped density profile created by the spatial interference of the expanding toroidal BEC and a reference BEC after release from all trapping potentials. We characterize the interferometer when it contains a single particle, which is initially in a coherent superposition of a torus and reference state, as well as when it contains a many-body state in the mean-field approximation. The single-particle picture is sufficient to explain the origin of the spirals, to relate the phase-drop across the barrier to the geometry of a spiral, and to bound the expansion times for which the {\it in-situ} phase can be accurately determined. Mean-field estimates and numerical simulations show that the inter-atomic interactions shorten the expansion time scales compared to the single-particle case. Finally, we compare the mean-field simulations with our experimental data and confirm that the interferometer indeed accurately measures the {\it in-situ} phase drop. VL - 92 U4 - 033602 UR - http://arxiv.org/abs/1506.09149v2 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.92.033602 ER - TY - JOUR T1 - Spin-orbit-coupled topological Fulde-Ferrell states of fermions in a harmonic trap JF - Physical Review A Y1 - 2014 A1 - Lei Jiang A1 - Eite Tiesinga A1 - Xia-Ji Liu A1 - Hui Hu A1 - Han Pu AB - Motivated by recent experimental breakthroughs in generating spin-orbit coupling in ultracold Fermi gases using Raman laser beams, we present a systematic study of spin-orbit-coupled Fermi gases confined in a quasi-one-dimensional trap in the presence of an in-plane Zeeman field (which can be realized using a finite two-photon Raman detuning). We find that a topological Fulde-Ferrell state will emerge, featuring finite-momentum Cooper pairing and zero-energy Majorana excitations localized near the edge of the trap based on the self-consistent Bogoliubov-de Genes (BdG) equations. We find analytically the wavefunctions of the Majorana modes. Finally using the time-dependent BdG we show how the finite-momentum pairing field manifests itself in the expansion dynamics of the atomic cloud. VL - 90 UR - http://arxiv.org/abs/1404.6211v1 CP - 5 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.90.053606 ER - TY - JOUR T1 - Controlling the group velocity of colliding atomic Bose-Einstein condensates with Feshbach resonances JF - Physical Review A Y1 - 2013 A1 - Ranchu Mathew A1 - Eite Tiesinga AB - We report on a proposal to change the group velocity of a small Bose Einstein Condensate (BEC) upon collision with another BEC in analogy to slowing of light passing through dispersive media. We make use of ultracold collisions near a magnetic Feshbach resonance, which gives rise to a sharp variation in scattering length with collision energy and thereby changes the group velocity. A generalized Gross-Pitaveskii equation is derived for a small BEC moving through a larger stationary BEC. We denote the two condensates by laser and medium BEC, respectively, to highlight the analogy to a laser pulse travelling through a medium. We derive an expression for the group velocity in a homogeneous medium as well as for the difference in distance, $\delta$, covered by the laser BEC in the presence and absence of a finite-sized medium BEC with a Thomas-Fermi density distribution. For a medium and laser of the same isotopic species, the shift $\delta$ has an upper bound of twice the Thomas-Fermi radius of the medium. For typical narrow Feshbach resonances and a medium with number density $10^{15}$ cm$^{-3}$ up to 85% of the upper bound can be achieved, making the effect experimentally observable. We also derive constraints on the experimental realization of our proposal. VL - 87 UR - http://arxiv.org/abs/1301.4234v2 CP - 5 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.87.053608 ER - TY - JOUR T1 - Formation and decay of Bose-Einstein condensates in an excited band of a double-well optical lattice JF - Physical Review A Y1 - 2013 A1 - Saurabh Paul A1 - Eite Tiesinga AB - We study the formation and collision-aided decay of an ultra-cold atomic Bose-Einstein condensate in the first excited band of a double-well 2D-optical lattice with weak harmonic confinement in the perpendicular $z$ direction. This lattice geometry is based on an experiment by Wirth et al. The double well is asymmetric, with the local ground state in the shallow well nearly degenerate with the first excited state of the adjacent deep well. We compare the band structure obtained from a tight-binding (TB) model with that obtained numerically using a plane wave basis. We find the TB model to be in quantitative agreement for the lowest two bands, qualitative for next two bands, and inadequate for even higher bands. The band widths of the excited bands are much larger than the harmonic oscillator energy spacing in the $z$ direction. We then study the thermodynamics of a non-interacting Bose gas in the first excited band. We estimate the condensate fraction and critical temperature, $T_c$, as functions of lattice parameters. For typical atom numbers, the critical energy $k_BT_c$, with $k_B$ the Boltzmann constant, is larger than the excited band widths and harmonic oscillator energy. Using conservation of total energy and atom number, we show that the temperature increases after the lattice transformation. Finally, we estimate the time scale for a two-body collision-aided decay of the condensate as a function of lattice parameters. The decay involves two processes, the dominant one in which both colliding atoms decay to the ground band, and the second involving excitation of one atom to a higher band. For this estimate, we have used TB wave functions for the lowest four bands, and numerical estimates for higher bands. The decay rate rapidly increases with lattice depth, but stays smaller than the tunneling rate between the $s$ and $p$ orbitals in adjacent wells. VL - 88 UR - http://arxiv.org/abs/1308.4449v1 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.88.033615 ER - TY - JOUR T1 - Quadrature interferometry for nonequilibrium ultracold bosons in optical lattices JF - Physical Review A Y1 - 2013 A1 - Eite Tiesinga A1 - Philip R. Johnson AB - We develop an interferometric technique for making time-resolved measurements of field-quadrature operators for nonequilibrium ultracold bosons in optical lattices. The technique exploits the internal state structure of magnetic atoms to create two subsystems of atoms in different spin states and lattice sites. A Feshbach resonance turns off atom-atom interactions in one spin subsystem, making it a well-characterized reference state, while atoms in the other subsystem undergo nonequilibrium dynamics for a variable hold time. Interfering the subsystems via a second beam-splitting operation, time-resolved quadrature measurements on the interacting atoms are obtained by detecting relative spin populations. The technique can provide quadrature measurements for a variety of Hamiltonians and lattice geometries (e.g., cubic, honeycomb, superlattices), including systems with tunneling, spin-orbit couplings using artificial gauge fields, and higher-band effects. Analyzing the special case of a deep lattice with negligible tunneling, we obtain the time evolution of both quadrature observables and their fluctuations. As a second application, we show that the interferometer can be used to measure atom-atom interaction strengths with super-Heisenberg scaling n^(-3/2) in the mean number of atoms per lattice site n, and standard quantum limit scaling M^(-1/2) in the number of lattice sites M. In our analysis, we require M >> 1 and for realistic systems n is small, and therefore the scaling in total atom number N = nM is below the Heisenberg limit; nevertheless, measurements testing the scaling behaviors for interaction-based quantum metrologies should be possible in this system. VL - 87 UR - http://arxiv.org/abs/1212.1193v2 CP - 1 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.87.013423 ER - TY - JOUR T1 - Soliton dynamics of an atomic spinor condensate on a Ring Lattice JF - Physical Review A Y1 - 2013 A1 - Indubala I Satija A1 - Carlos L. Pando A1 - Eite Tiesinga AB - We study the dynamics of macroscopically-coherent matter waves of an ultra-cold atomic spin-one or spinor condensate on a ring lattice of six sites and demonstrate a novel type of spatio-temporal internal Josephson effect. Using a discrete solitary mode of uncoupled spin components as an initial condition, the time evolution of this many-body system is found to be characterized by two dominant frequencies leading to quasiperiodic dynamics at various sites. The dynamics of spatially-averaged and spin-averaged degrees of freedom, however, is periodic enabling an unique identification of the two frequencies. By increasing the spin-dependent atom-atom interaction strength we observe a resonance state, where the ratio of the two frequencies is a characteristic integer multiple and the spin-and-spatial degrees of freedom oscillate in "unison". Crucially, this resonant state is found to signal the onset to chaotic dynamics characterized by a broad band spectrum. In a ferromagnetic spinor condensate with attractive spin-dependent interactions, the resonance is accompanied by a transition from oscillatory- to rotational-type dynamics as the time evolution of the relative phase of the matter wave of the individual spin projections changes from bounded to unbounded. VL - 87 UR - http://arxiv.org/abs/1301.5851v1 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.87.033608 ER - TY - JOUR T1 - Spinor dynamics in an antiferromagnetic spin-1 thermal Bose gas JF - Physical Review Letters Y1 - 2013 A1 - Hyewon K. Pechkis A1 - Jonathan P. Wrubel A1 - Arne Schwettmann A1 - Paul F. Griffin A1 - Ryan Barnett A1 - Eite Tiesinga A1 - Paul D. Lett AB - We present experimental observations of coherent spin-population oscillations in a cold thermal, Bose gas of spin-1 sodium-23 atoms. The population oscillations in a multi-spatial-mode thermal gas have the same behavior as those observed in a single-spatial-mode antiferromagnetic spinor Bose Einstein condensate. We demonstrate this by showing that the two situations are described by the same dynamical equations, with a factor of two change in the spin-dependent interaction coefficient, which results from the change to particles with distinguishable momentum states in the thermal gas. We compare this theory to the measured spin population evolution after times up to a few hundreds of ms, finding quantitative agreement with the amplitude and period. We also measure the damping time of the oscillations as a function of magnetic field. VL - 111 UR - http://arxiv.org/abs/1306.4255v1 CP - 2 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.111.025301 ER - TY - JOUR T1 - Anisotropy induced Feshbach resonances in a quantum dipolar gas of magnetic atoms JF - Physical Review Letters Y1 - 2012 A1 - Alexander Petrov A1 - Eite Tiesinga A1 - Svetlana Kotochigova AB - We explore the anisotropic nature of Feshbach resonances in the collision between ultracold magnetic submerged-shell dysprosium atoms, which can only occur due to couplings to rotating bound states. This is in contrast to well-studied alkali-metal atom collisions, where most Feshbach resonances are hyperfine induced and due to rotation-less bound states. Our novel first-principle coupled-channel calculation of the collisions between open-4f-shell spin-polarized bosonic dysprosium reveals a striking correlation between the anisotropy due to magnetic dipole-dipole and electrostatic interactions and the Feshbach spectrum as a function of an external magnetic field. Over a 20 mT magnetic field range we predict about a dozen Feshbach resonances and show that the resonance locations are exquisitely sensitive to the dysprosium isotope. VL - 109 UR - http://arxiv.org/abs/1203.4172v1 CP - 10 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.109.103002 ER - TY - JOUR T1 - Resonant control of polar molecules in an optical lattice JF - Physical Review A Y1 - 2012 A1 - Thomas M. Hanna A1 - Eite Tiesinga A1 - William F. Mitchell A1 - Paul S. Julienne AB - We study the resonant control of two nonreactive polar molecules in an optical lattice site, focussing on the example of RbCs. Collisional control can be achieved by tuning bound states of the intermolecular dipolar potential, by varying the applied electric field or trap frequency. We consider a wide range of electric fields and trapping geometries, showing that a three-dimensional optical lattice allows for significantly wider avoided crossings than free space or quasi-two dimensional geometries. Furthermore, we find that dipolar confinement induced resonances can be created with reasonable trapping frequencies and electric fields, and have widths that will enable useful control in forthcoming experiments. VL - 85 UR - http://arxiv.org/abs/1111.0227v1 CP - 2 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.85.022703 ER - TY - JOUR T1 - Detecting paired and counterflow superfluidity via dipole oscillations JF - Physical Review A Y1 - 2011 A1 - Anzi Hu A1 - L. Mathey A1 - Eite Tiesinga A1 - Ippei Danshita A1 - Carl J. Williams A1 - Charles W. Clark AB - We suggest an experimentally feasible procedure to observe paired and counterflow superfluidity in ultra-cold atom systems. We study the time evolution of one-dimensional mixtures of bosonic atoms in an optical lattice following an abrupt displacement of an additional weak confining potential. We find that the dynamic responses of the paired superfluid phase for attractive inter-species interactions and the counterflow superfluid phase for repulsive interactions are qualitatively distinct and reflect the quasi long-range order that characterizes these states. These findings suggest a clear experimental procedure to detect these phases, and give an intuitive insight into their dynamics. VL - 84 UR - http://arxiv.org/abs/1103.3513v3 CP - 4 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.84.041609 ER - TY - JOUR T1 - Spatial separation in a thermal mixture of ultracold $^174$Yb and $^87$Rb atoms JF - Physical Review A Y1 - 2011 A1 - Florian Baumer A1 - Frank Münchow A1 - Axel Görlitz A1 - Stephen E. Maxwell A1 - Paul S. Julienne A1 - Eite Tiesinga AB - We report on the observation of unusually strong interactions in a thermal mixture of ultracold atoms which cause a significant modification of the spatial distribution. A mixture of $^{87}$Rb and $^{174}$Yb with a temperature of a few $\mu$K is prepared in a hybrid trap consisting of a bichromatic optical potential superimposed on a magnetic trap. For suitable trap parameters and temperatures, a spatial separation of the two species is observed. We infer that the separation is driven by a large interaction strength between $^{174}$Yb and $^{87}$Rb accompanied by a large three-body recombination rate. Based on this assumption we have developed a diffusion model which reproduces our observations. VL - 83 UR - http://arxiv.org/abs/1104.1722v1 CP - 4 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.83.040702 ER - TY - JOUR T1 - Superradiance of cold atoms coupled to a superconducting circuit JF - Physical Review A Y1 - 2011 A1 - Daniel Braun A1 - Jonathan Hoffman A1 - Eite Tiesinga AB - We investigate superradiance of an ensemble of atoms coupled to an integrated superconducting LC-circuit. Particular attention is paid to the effect of inhomogeneous coupling constants. Combining perturbation theory in the inhomogeneity and numerical simulations we show that inhomogeneous coupling constants can significantly affect the superradiant relaxation process. Incomplete relaxation terminating in "dark states" can occur, from which the only escape is through individual spontaneous emission on a much longer time scale. The relaxation dynamics can be significantly accelerated or retarded, depending on the distribution of the coupling constants. On the technical side, we also generalize the previously known propagator of superradiance for identical couplings in the completely symmetric sector to the full exponentially large Hilbert space. VL - 83 UR - http://arxiv.org/abs/1101.5300v1 CP - 6 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.83.062305 ER - TY - JOUR T1 - Creation and manipulation of Feshbach resonances with radio-frequency radiation JF - New Journal of Physics Y1 - 2010 A1 - Thomas M. Hanna A1 - Eite Tiesinga A1 - Paul S. Julienne AB - We present a simple technique for studying collisions of ultracold atoms in the presence of a magnetic field and radio-frequency radiation (rf). Resonant control of scattering properties can be achieved by using rf to couple a colliding pair of atoms to a bound state. We show, using the example of 6Li, that in some ranges of rf frequency and magnetic field this can be done without giving rise to losses. We also show that halo molecules of large spatial extent require much less rf power than deeply bound states. Another way to exert resonant control is with a set of rf-coupled bound states, linked to the colliding pair through the molecular interactions that give rise to magnetically tunable Feshbach resonances. This was recently demonstrated for 87Rb [Kaufman et al., Phys. Rev. A 80:050701(R), 2009]. We examine the underlying atomic and molecular physics which made this possible. Lastly, we consider the control that may be exerted over atomic collisions by placing atoms in superpositions of Zeeman states, and suggest that it could be useful where small changes in scattering length are required. We suggest other species for which rf and magnetic field control could together provide a useful tuning mechanism. VL - 12 U4 - 083031 UR - http://arxiv.org/abs/1004.0636v1 CP - 8 J1 - New J. Phys. U5 - 10.1088/1367-2630/12/8/083031 ER - TY - JOUR T1 - Feshbach Resonances in Ultracold Gases JF - Reviews of Modern Physics Y1 - 2010 A1 - Cheng Chin A1 - Rudolf Grimm A1 - Paul Julienne A1 - Eite Tiesinga AB - Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This Review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules. VL - 82 U4 - 1225 - 1286 UR - http://arxiv.org/abs/0812.1496v2 CP - 2 J1 - Rev. Mod. Phys. U5 - 10.1103/RevModPhys.82.1225 ER - TY - JOUR T1 - Collisional cooling of ultra-cold atom ensembles using Feshbach resonances JF - Physical Review A Y1 - 2009 A1 - L. Mathey A1 - Eite Tiesinga A1 - Paul S. Julienne A1 - Charles W. Clark AB - We propose a new type of cooling mechanism for ultra-cold fermionic atom ensembles, which capitalizes on the energy dependence of inelastic collisions in the presence of a Feshbach resonance. We first discuss the case of a single magnetic resonance, and find that the final temperature and the cooling rate is limited by the width of the resonance. A concrete example, based on a p-wave resonance of $^{40}$K, is given. We then improve upon this setup by using both a very sharp optical or radio-frequency induced resonance and a very broad magnetic resonance and show that one can improve upon temperatures reached with current technologies. VL - 80 UR - http://arxiv.org/abs/0903.2568v1 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.80.030702 ER - TY - JOUR T1 - Counterflow and paired superfluidity in one-dimensional Bose mixtures in optical lattices JF - Physical Review A Y1 - 2009 A1 - Anzi Hu A1 - L. Mathey A1 - Ippei Danshita A1 - Eite Tiesinga A1 - Carl J. Williams A1 - Charles W. Clark AB - We study the quantum phases of mixtures of ultra-cold bosonic atoms held in an optical lattice that confines motion or hopping to one spatial dimension. The phases are found by using Tomonaga-Luttinger liquid theory as well as the numerical method of time evolving block decimation (TEBD). We consider a binary mixture with repulsive intra-species interactions, and either repulsive or attractive inter-species interaction. For a homogeneous system, we find paired- and counterflow-superfluid phases at different filling and hopping energies. We also predict parameter regions in which these types of superfluid order coexist with charge density wave order. We show that the Tomonaga-Luttinger liquid theory and TEBD qualitatively agree on the location of the phase boundary to superfluidity. We then describe how these phases are modified and can be detected when an additional harmonic trap is present. In particular, we show how experimentally measurable quantities, such as time-of-flight images and the structure factor, can be used to distinguish the quantum phases. Finally, we suggest applying a Feshbach ramp to detect the paired superfluid state, and a $\pi/2$ pulse followed by Bragg spectroscopy to detect the counterflow superfluid phase. VL - 80 UR - http://arxiv.org/abs/0906.2150v1 CP - 2 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.80.023619 ER - TY - JOUR T1 - Multi-channel modelling of the formation of vibrationally cold polar KRb molecules JF - New Journal of Physics Y1 - 2009 A1 - Svetlana Kotochigova A1 - Eite Tiesinga A1 - Paul S. Julienne AB - We describe the theoretical advances that influenced the experimental creation of vibrationally and translationally cold polar $^{40}$K$^{87}$Rb molecules \cite{nphys08,science08}. Cold molecules were created from very-weakly bound molecules formed by magnetic field sweeps near a Feshbach resonance in collisions of ultra-cold $^{40}$K and $^{87}$Rb atoms. Our analysis include the multi-channel bound-state calculations of the hyperfine and Zeeman mixed X$^1\Sigma^+$ and a$^3\Sigma^+$ vibrational levels. We find excellent agreement with the hyperfine structure observed in experimental data. In addition, we studied the spin-orbit mixing in the intermediate state of the Raman transition. This allowed us to investigate its effect on the vibrationally-averaged transition dipole moment to the lowest ro-vibrational level of the X$^1\Sigma^+$ state. Finally, we obtained an estimate of the polarizability of the initial and final ro-vibrational states of the Raman transition near frequencies relevant for optical trapping of the molecules. VL - 11 U4 - 055043 UR - http://arxiv.org/abs/0901.1486v1 CP - 5 J1 - New J. Phys. U5 - 10.1088/1367-2630/11/5/055043 ER - TY - JOUR T1 - Number Fluctuations and Energy Dissipation in Sodium Spinor Condensates JF - Physical Review Letters Y1 - 2009 A1 - Yingmei Liu A1 - Eduardo Gomez A1 - Stephen E. Maxwell A1 - Lincoln D. Turner A1 - Eite Tiesinga A1 - Paul D. Lett AB - We characterize fluctuations in atom number and spin populations in F=1 sodium spinor condensates. We find that the fluctuations enable a quantitative measure of energy dissipation in the condensate. The time evolution of the population fluctuations shows a maximum. We interpret this as evidence of a dissipation-driven separatrix crossing in phase space. For a given initial state, the critical time to the separatrix crossing is found to depend exponentially on the magnetic field and linearly on condensate density. This crossing is confirmed by tracking the energy of the spinor condensate as well as by Faraday rotation spectroscopy. We also introduce a phenomenological model that describes the observed dissipation with a single coefficient. VL - 102 UR - http://arxiv.org/abs/0906.2110v1 CP - 22 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.102.225301 ER - TY - JOUR T1 - Prediction of Feshbach resonances from three input parameters JF - Physical Review A Y1 - 2009 A1 - Thomas M. Hanna A1 - Eite Tiesinga A1 - Paul S. Julienne AB - We have developed a model of Feshbach resonances in gases of ultracold alkali metal atoms using the ideas of multichannel quantum defect theory. Our model requires just three parameters describing the interactions - the singlet and triplet scattering lengths, and the long range van der Waals coefficient - in addition to known atomic properties. Without using any further details of the interactions, our approach can accurately predict the locations of resonances. It can also be used to find the singlet and triplet scattering lengths from measured resonance data. We apply our technique to $^{6}$Li--$^{40}$K and $^{40}$K--$^{87}$Rb scattering, obtaining good agreement with experimental results, and with the more computationally intensive coupled channels technique. VL - 79 UR - http://arxiv.org/abs/0903.0884v2 CP - 4 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.79.040701 ER - TY - JOUR T1 - Quantum Phase Transitions and Continuous Observation of Spinor Dynamics in an Antiferromagnetic Condensate JF - Physical Review Letters Y1 - 2009 A1 - Yingmei Liu A1 - Sebastian Jung A1 - Stephen E. Maxwell A1 - Lincoln D. Turner A1 - Eite Tiesinga A1 - Paul. D. Lett AB - Condensates of spin-1 sodium display rich spin dynamics due to the antiferromagnetic nature of the interactions in this system. We use Faraday rotation spectroscopy to make a continuous and minimally destructive measurement of the dynamics over multiple spin oscillations on a single evolving condensate. This method provides a sharp signature to locate a magnetically tuned separatrix in phase space which depends on the net magnetization. We also observe a phase transition from a two- to a three-component condensate at a low but finite temperature using a Stern-Gerlach imaging technique. This transition should be preserved as a zero-temperature quantum phase transition. VL - 102 UR - http://arxiv.org/abs/0902.3189v1 CP - 12 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.102.125301 ER - TY - JOUR T1 - Avoided crossings between bound states of ultracold Cesium dimers JF - Physical Review A Y1 - 2008 A1 - Jeremy M. Hutson A1 - Eite Tiesinga A1 - Paul S. Julienne AB - We present an efficient new computational method for calculating the binding energies of the bound states of ultracold alkali-metal dimers in the presence of magnetic fields. The method is based on propagation of coupled differential equations and does not use a basis set for the interatomic distance coordinate. It is much more efficient than the previous method based on a radial basis set and allows many more spin channels to be included. This is particularly important in the vicinity of avoided crossings between bound states. We characterize a number of different avoided crossings in Cs_2 and compare our converged calculations with experimental results. Small but significant discrepancies are observed in both crossing strengths and level positions, especially for levels with l symmetry (rotational angular momentum L=8). The discrepancies should allow the development of improved potential models in the future. VL - 78 UR - http://arxiv.org/abs/0806.2583v1 CP - 5 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.78.052703 ER - TY - JOUR T1 - Multilevel effects in the Rabi oscillations of a Josephson phase qubit JF - Physical Review B Y1 - 2008 A1 - S. K. Dutta A1 - Frederick W. Strauch A1 - R. M. Lewis A1 - Kaushik Mitra A1 - Hanhee Paik A1 - T. A. Palomaki A1 - Eite Tiesinga A1 - J. R. Anderson A1 - Alex J. Dragt A1 - C. J. Lobb A1 - F. C. Wellstood AB - We present Rabi oscillation measurements of a Nb/AlOx/Nb dc superconducting quantum interference device (SQUID) phase qubit with a 100 um^2 area junction acquired over a range of microwave drive power and frequency detuning. Given the slightly anharmonic level structure of the device, several excited states play an important role in the qubit dynamics, particularly at high power. To investigate the effects of these levels, multiphoton Rabi oscillations were monitored by measuring the tunneling escape rate of the device to the voltage state, which is particularly sensitive to excited state population. We compare the observed oscillation frequencies with a simplified model constructed from the full phase qubit Hamiltonian and also compare time-dependent escape rate measurements with a more complete density-matrix simulation. Good quantitative agreement is found between the data and simulations, allowing us to identify a shift in resonance (analogous to the ac Stark effect), a suppression of the Rabi frequency, and leakage to the higher excited states. VL - 78 UR - http://arxiv.org/abs/0806.4711v2 CP - 10 J1 - Phys. Rev. B U5 - 10.1103/PhysRevB.78.104510 ER - TY - JOUR T1 - Quantum behavior of the dc SQUID phase qubit JF - Physical Review B Y1 - 2008 A1 - Kaushik Mitra A1 - F. W. Strauch A1 - C. J. Lobb A1 - J. R. Anderson A1 - F. C. Wellstood A1 - Eite Tiesinga AB - We analyze the behavior of a dc Superconducting Quantum Interference Device (SQUID) phase qubit in which one junction acts as a phase qubit and the rest of the device provides isolation from dissipation and noise in the bias leads. Ignoring dissipation, we find the two-dimensional Hamiltonian of the system and use numerical methods and a cubic approximation to solve Schrodinger's equation for the eigenstates, energy levels, tunneling rates, and expectation value of the currents in the junctions. Using these results, we investigate how well this design provides isolation while preserving the characteristics of a phase qubit. In addition, we show that the expectation value of current flowing through the isolation junction depends on the state of the qubit and can be used for non-destructive read out of the qubit state. VL - 77 UR - http://arxiv.org/abs/0805.3680v1 CP - 21 J1 - Phys. Rev. B U5 - 10.1103/PhysRevB.77.214512 ER - TY - JOUR T1 - Tunneling phase gate for neutral atoms in a double-well lattice JF - Physical Review A Y1 - 2008 A1 - Frederick W. Strauch A1 - Mark Edwards A1 - Eite Tiesinga A1 - Carl J. Williams A1 - Charles W. Clark AB - We propose a new two--qubit phase gate for ultra--cold atoms confined in an experimentally realized tilted double--well optical lattice [Sebby--Strabley et al., Phys. Rev. A {\bf 73} 033605 (2006)]. Such a lattice is capable of confining pairs of atoms in a two--dimensional array of double--well potentials where control can be exercised over the barrier height and the energy difference of the minima of the two wells (known as the ``tilt''). The four lowest single--particle motional states consist of two pairs of motional states in which each pair is localized on one side of the central barrier, allowing for two atoms confined in such a lattice to be spatially separated qubits. We present a time--dependent scheme to manipulate the tilt to induce tunneling oscillations which produce a collisional phase gate. Numerical simulations demonstrate that this gate can be performed with high fidelity. VL - 77 UR - http://arxiv.org/abs/0712.1856v1 CP - 5 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.77.050304 ER - TY - JOUR T1 - Two-body transients in coupled atomic-molecular BECs JF - Physical Review Letters Y1 - 2008 A1 - Pascal Naidon A1 - Eite Tiesinga A1 - Paul S. Julienne AB - We discuss the dynamics of an atomic Bose-Einstein condensate when pairs of atoms are converted into molecules by single-color photoassociation. Three main regimes are found and it is shown that they can be understood on the basis of time-dependent two-body theory. In particular, the so-called rogue dissociation regime [Phys. Rev. Lett., 88, 090403 (2002)], which has a density-dependent limit on the photoassociation rate, is identified with a transient regime of the two-atom dynamics exhibiting universal properties. Finally, we illustrate how these regimes could be explored by photoassociating condensates of alkaline-earth atoms. VL - 100 UR - http://arxiv.org/abs/0707.2963v2 CP - 9 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.100.093001 ER - TY - JOUR T1 - Coherent, adiabatic and dissociation regimes in coupled atomic-molecular Bose-Einstein condensates Y1 - 2007 A1 - Pascal Naidon A1 - Eite Tiesinga A1 - Paul S. Julienne AB - We discuss the dynamics of a Bose-Einstein condensate of atoms which is suddenly coupled to a condensate of molecules by an optical or magnetic Feshbach resonance. Three limiting regimes are found and can be understood from the transient dynamics occuring for each pair of atoms. This transient dynamics can be summarised into a time-dependent shift and broadening of the molecular state. A simple Gross-Pitaevskii picture including this shift and broadening is proposed to describe the system in the three regimes. Finally, we suggest how to explore these regimes experimentally. UR - http://arxiv.org/abs/0711.0397v2 ER - TY - JOUR T1 - Effective-range description of a Bose gas under strong one- or two-dimensional confinement JF - New Journal of Physics Y1 - 2007 A1 - Pascal Naidon A1 - Eite Tiesinga A1 - William F. Mitchell A1 - Paul S. Julienne AB - We point out that theories describing s-wave collisions of bosonic atoms confined in one- or two-dimensional geometries can be extended to much tighter confinements than previously thought. This is achieved by replacing the scattering length by an energy-dependent scattering length which was already introduced for the calculation of energy levels under 3D confinement. This replacement accurately predicts the position of confinement-induced resonances in strongly confined geometries. VL - 9 U4 - 19 - 19 UR - http://arxiv.org/abs/physics/0607140v2 CP - 1 J1 - New J. Phys. U5 - 10.1088/1367-2630/9/1/019 ER - TY - JOUR T1 - Multichannel quantum-defect theory for slow atomic collisions JF - Physical Review A Y1 - 2005 A1 - Bo Gao A1 - Eite Tiesinga A1 - Carl J. Williams A1 - Paul S. Julienne AB - We present a multichannel quantum-defect theory for slow atomic collisions that takes advantages of the analytic solutions for the long-range potential, and both the energy and the angular-momentum insensitivities of the short-range parameters. The theory provides an accurate and complete account of scattering processes, including shape and Feshbach resonances, in terms of a few parameters such as the singlet and the triplet scattering lengths. As an example, results for $^{23}$Na-$^{23}$Na scattering are presented and compared close-coupling calculations. VL - 72 UR - http://arxiv.org/abs/physics/0508060v1 CP - 4 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.72.042719 ER - TY - JOUR T1 - Sodium Bose-Einstein Condensates in an Optical Lattice JF - Physical Review A Y1 - 2005 A1 - K. Xu A1 - Y. Liu A1 - J. R. Abo-Shaeer A1 - T. Mukaiyama A1 - J. K. Chin A1 - D. E. Miller A1 - W. Ketterle A1 - Kevin M. Jones A1 - Eite Tiesinga AB - The phase transition from a superfluid to a Mott insulator has been observed in a $^{23}$Na Bose-Einstein condensate. A dye laser detuned $\approx 5$nm red of the Na $3^2$S$ \to 3^2$P$_{1/2}$ transition was used to form the three dimensional optical lattice. The heating effects of the small detuning as well as the three-body decay processes constrained the timescale of the experiment. Certain lattice detunings were found to induce a large loss of atoms. These loss features were shown to be due to photoassociation of atoms to vibrational levels in the Na$_2$ $(1) ^3\Sigma_g^+$ state. VL - 72 UR - http://arxiv.org/abs/cond-mat/0507288v1 CP - 4 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.72.043604 ER - TY - JOUR T1 - Spontaneous dissociation of long-range Feshbach molecules JF - Physical Review Letters Y1 - 2005 A1 - Thorsten Koehler A1 - Eite Tiesinga A1 - Paul S. Julienne AB - We study the spontaneous dissociation of diatomic molecules produced in cold atomic gases via magnetically tunable Feshbach resonances. We provide a universal formula for the lifetime of these molecules that relates their decay to the scattering length and the loss rate constant for inelastic spin relaxation. Our universal treatment as well as our exact coupled channels calculations for $^{85}$Rb dimers predict a suppression of the decay over several orders of magnitude when the scattering length is increased. Our predictions are in good agreement with recent measurements of the lifetime of $^{85}$Rb$_2$. VL - 94 UR - http://arxiv.org/abs/cond-mat/0408387v2 CP - 2 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.94.020402 ER - TY - JOUR T1 - Adiabatic association of ultracold molecules via magnetic field tunable interactions JF - Journal of Physics B: Atomic, Molecular and Optical Physics Y1 - 2004 A1 - Krzysztof Goral A1 - Thorsten Koehler A1 - Simon A. Gardiner A1 - Eite Tiesinga A1 - Paul S. Julienne AB - We consider in detail the situation of applying a time dependent external magnetic field to a 87Rb atomic Bose-Einstein condensate held in a harmonic trap, in order to adiabatically sweep the interatomic interactions across a Feshbach resonance to produce diatomic molecules. To this end, we introduce a minimal two-body Hamiltonian depending on just five measurable parameters of a Feshbach resonance, which accurately determines all low energy binary scattering observables, in particular, the molecular conversion efficiency of just two atoms. Based on this description of the microscopic collision phenomena, we use the many-body theory of T. Koehler and K. Burnett [Phys. Rev. A 65, 033601 (2002)] to study the efficiency of the association of molecules in a 87Rb Bose-Einstein condensate during a linear passage of the magnetic field strength across the 100 mT Feshbach resonance. We explore different, experimentally accessible, parameter regimes, and compare the predictions of Landau-Zener, configuration interaction, and two level mean field calculations with those of the microscopic many-body approach. Our comparative studies reveal a remarkable insensitivity of the molecular conversion efficiency with respect to both the details of the microscopic binary collision physics and the coherent nature of the Bose-Einstein condensed gas, provided that the magnetic field strength is varied linearly. We provide the reasons for this universality of the molecular production achieved by linear ramps of the magnetic field strength, and identify the Landau-Zener coefficient determined by F.H. Mies et al. [Phys. Rev. A 61, 022721 (2000)] as the main parameter that controls the efficiency. VL - 37 U4 - 3457 - 3500 UR - http://arxiv.org/abs/cond-mat/0312178v5 CP - 17 J1 - J. Phys. B: At. Mol. Opt. Phys. U5 - 10.1088/0953-4075/37/17/006 ER - TY - JOUR T1 - Ultracold collision properties of metastable alkaline-earth atoms JF - Physical Review Letters Y1 - 2003 A1 - Andrei Derevianko A1 - Sergey G. Porsev A1 - Svetlana Kotochigova A1 - Eite Tiesinga A1 - Paul S. Julienne AB - Ultra-cold collisions of spin-polarized 24Mg,40Ca, and 88Sr in the metastable 3P2 excited state are investigated. We calculate the long-range interaction potentials and estimate the scattering length and the collisional loss rate as a function of magnetic field. The estimates are based on molecular potentials between 3P2 alkaline-earth atoms obtained from ab initio atomic and molecular structure calculations. The scattering lengths show resonance behavior due to the appearance of a molecular bound state in a purely long-range interaction potential and are positive for magnetic fields below 50 mT. A loss-rate model shows that losses should be smallest near zero magnetic field and for fields slightly larger than the resonance field, where the scattering length is also positive. VL - 90 UR - http://arxiv.org/abs/physics/0210076v1 CP - 6 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.90.063002 ER - TY - JOUR T1 - Ultracold Cs$_2$ Feshbach Spectroscopy Y1 - 2003 A1 - Cheng Chin A1 - Vladan Vuletic A1 - Andrew J. Kerman A1 - Steven Chu A1 - Eite Tiesinga A1 - Paul J. Leo A1 - Carl J. Williams AB - We have observed and located more than 60 magnetic field-induced Feshbach resonances in ultracold collisions of ground-state $^{133}$Cs atoms. These resonances are associated with molecular states with up to four units of rotational angular momentum, and are detected through variations in the elastic, inelastic, and radiative collision cross sections. These observations allow us to greatly improve upon the interaction potentials between two cesium atoms and to reproduce the positions of most resonances to accuracies better than 0.5%. Based on the relevant coupling scheme between the electron spin, nuclear spin, and orbital angular momenta of the nuclei, quantum numbers and energy structure of the molecular states beneath the dissociation continuum are revealed. Finally, we predict the relevant collision properties for cesium Bose-Einstein condensation experiments. UR - http://arxiv.org/abs/cond-mat/0312613v2 ER -