arXiv subjects

Eite Tiesinga

Publications and source records attributed to Eite Tiesinga.

At least 37 records · Page 2Linked to original sources

arXiv2017

Above threshold scattering about a Feshbach resonance for ultracold atoms in an optical collider

Ultracold atomic gases have realised numerous paradigms of condensed matter physics where control over interactions has crucially been afforded by tunable Feshbach resonances. So far, the characterisation of these Feshbach resonances has almost exclusively relied on experiments in the threshold regime near zero energy. Here we use a laser-based collider to probe a narrow magnetic Feshbach resonance of rubidium above threshold. By measuring the overall atomic loss from colliding clouds as a function of magnetic field, we track the energy-dependent resonance position. At higher energy, our collider scheme broadens the loss feature, making the identification of the narrow resonance challenging. However, we observe that the collisions give rise to shifts in the centre-of-mass positions of outgoing clouds. The shifts cross zero at the resonance and this allows us to accurately determine its location well above threshold. Our inferred resonance positions are in excellent agreement with theory.

cond-mat.quant-gas↗

arXiv2017

Dispersive optical detection of magnetic Feshbach resonances in ultracold gases

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 $^{87}$Rb, between the $|\rm{F} = 1, \rm{m_F}=1 \rangle$ and $|\rm{F} = 2, \rm{m_F}=0 \rangle$ states. Despite the loss features being $\lesssim0.1$ G wide, we require only 21 experimental runs to explore a magnetic field range >18 G, where $1~\rm{G}=10^{-4}$ T. 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.

cond-mat.quant-gas↗

arXiv2017

Phase-space mixing in dynamically unstable, integrable few-mode quantum systems

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.

cond-mat.quant-gas↗

arXiv2017

Pendular trapping conditions for ultracold polar molecules enforced by external electric fields

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 $^{23}$Na$^{40}$K 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 $54.7^\circ$ between this field and the polarization of the optical laser lead to a trapping design for $^{23}$Na$^{40}$K 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.

quant-ph↗

arXiv2017

Investigation of Feshbach Resonances in ultra-cold 40 K spin mixtures

Magnetically-tunable Feshbach resonances are an indispensable tool for experiments with atomic quantum gases. We report on twenty thus far unpublished Feshbach resonances and twenty one further probable Feshbach resonances in spin mixtures of ultracold fermionic 40 K with temperatures well below 100 nK. In particular, we locate a broad resonance at B=389.6 G with a magnetic width of 26.4 G. Here 1 G=10^-4 T. Furthermore, by exciting low-energy spin waves, we demonstrate a novel means to precisely determine the zero crossing of the scattering length for this broad Feshbach resonance. Our findings allow for further tunability in experiments with ultracold 40 K quantum gases.

cond-mat.quant-gas↗

arXiv2016

Wannier functions using a discrete variable representation for optical lattices

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 Kivelson \cite{kivelson_wannier_1982}, for a symmetric lattice with inversion symmetry, we construct Wannier functions as eigen states of the position operators $\hat x$, $\hat y$ and $\hat z$ 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 eigen states 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 ten 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 (BH) model, and show the dependence of these energies on lattice asymmetry.

cond-mat.quant-gas↗

arXiv2016

Sudden-quench dynamics of Bardeen-Cooper-Schrieffer states in deep optical lattices

We determine the exact dynamics of an initial Bardeen-Cooper-Schrieffer (BCS) state of ultra-cold atoms in a deep hexagonal optical lattice. The dynamical evolution is triggered by a quench of the lattice potential, such that the interaction strength $U_f$ is much larger than the hopping amplitude $J_f$. The quench initiates collective oscillations with frequency $|U_f|/(2π)$ in the momentum occupation numbers and imprints an oscillating phase with the same frequency on the BCS order parameter $Δ$. The oscillation frequency of $Δ$ is not reproduced by treating the time evolution in mean-field theory. In our theory, the momentum noise (i.e. density-density) correlation functions oscillate at frequency $|U_f|/2π$ as well as at its second harmonic. For a very deep lattice, with zero 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. The damping occurs even for a finite-temperature initial BCS state, but not for a non-interacting Fermi gas. Furthermore, damping is stronger for larger order parameter and may therefore be used as a signature of the BCS state. Finally, our theory shows that the noise correlation functions in a honeycomb lattice will develop strong anti-correlations near the Dirac point.

cond-mat.quant-gas↗

arXiv2016

Multiple scattering dynamics of fermions at an isolated p-wave resonance

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 $\rm^{40}K$ 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 $90^\circ$ 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 $\rm^{40}K$ 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.

cond-mat.quant-gas↗

arXiv2016

A Hubbard model for ultracold bosonic atoms interacting via zero-point-energy induced three-body interactions

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 $^{88}$Sr 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.

cond-mat.quant-gas↗

arXiv2015

Photoassociation of spin polarized Chromium

We report the homonuclear photoassociation (PA) of ultracold ${}^{52}\mathrm{Cr}$ atoms in an optical dipole trap. This constitutes the first measurement of PA in an element with total electron spin $\tilde{S}>1$. Although Cr, with its ${}^{7}\mathrm{S}_{3}$ ground and ${}^{7}\mathrm{P}_{4,3,2}$ 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 ${}^{7}\mathrm{P}_{3}$ asymptote we observe two distinct vibrational series each following a LeRoy-Bernstein law for a $C_3 / R^{3}$ potential with excellent agreement. We determine the $C_3$ coefficients of the Hund's case c) relativistic adiabatic potentials to be -1.83$\pm$0.02 a.u. and -1.46$\pm$0.01a.u.. Theoretical non-rotating Movre-Pichler calculations enable a first assignment of the series to $Ω=6_u$ and $5_g$ 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.

physics.atom-ph↗

arXiv2015

Self-heterodyne detection of the {\it in-situ} phase of an atomic-SQUID

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.

quant-ph↗

arXiv2015

Large effective three-body interaction in a double-well optical lattice

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.

cond-mat.quant-gas↗

arXiv2014

Optimization of collisional Feshbach cooling of an ultracold nondegenerate gas

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.

cond-mat.quant-gas↗

arXiv2014

Spin-orbit-coupled topological Fulde-Ferrell states of fermions in a harmonic trap

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.

cond-mat.quant-gas↗

arXiv2013

Controlling the group velocity of colliding atomic Bose-Einstein condensates with Feshbach resonances

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, $δ$, 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 $δ$ 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.

cond-mat.quant-gas↗

arXiv2013

Formation and decay of Bose-Einstein condensates in an excited band of a double-well optical lattice

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.

cond-mat.quant-gas↗

arXiv2013

Spinor dynamics in an antiferromagnetic spin-1 thermal Bose gas

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.

physics.atom-ph↗

arXiv2013

Quadrature interferometry for nonequilibrium ultracold bosons in optical lattices

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.

cond-mat.quant-gas↗