Magnetic Trapping Potential Research Articles

Uniform L∞-bounds for energy-conserving higher-order time integrators for the Gross–Pitaevskii equation with rotation

Abstract In this paper, we consider an energy-conserving continuous Galerkin discretization of the Gross–Pitaevskii equation with a magnetic trapping potential and a stirring potential for angular momentum rotation. The discretization is based on finite elements in space and time and allows for arbitrary polynomial orders. It was first analyzed by O. Karakashian and C. Makridakis (SIAM J. Numer. Anal., 36(6),1779–1807, 1999) in the absence of potential terms and corresponding a priori error estimates were derived in $2D$. In this work we revisit the approach in the generalized setting of the Gross–Pitaevskii equation with rotation and we prove uniform $L^{\infty }$-bounds for the corresponding numerical approximations in $2D$ and $3D$ without coupling conditions between the spatial mesh size and the time step size. With this result at hand, we are particularly able to extend the previous error estimates to the $3D$ setting while avoiding artificial CFL conditions.

Performance bounds of magnetic traps for neutral particles

Knowledge of the fundamental limitations on a magnetic trap for neutral particles is of paramount interest to designers as it allows for the rapid assessment of the feasibility of specific trap requirements or the quality of a given design. In this paper, performance limitations are defined for convexity of magnetic trapping potential and bias field using a local approximation in the trapping center. As an example, the fundamental bounds are computed for current supporting regions in the form of a spherical shell, a cylindrical region, and a box. A Pareto-optimal set considering both objectives is found and compared with known designs of the Baseball trap and Ioffe-Pritchard trap. The comparison reveals a significant gap in the performance of classical trap designs from the fundamental limitations. This indicates a possibility of improved trap designs and modern techniques of shape synthesis are applied in order to prove their existence. The topologically optimized traps perform almost two times better as compared to conventional designs. Last, but not least, the developed framework might serve as a prototype for the formulation of fundamental limitations on plasma confinement in a wider sense.

Coherent splitting of two-dimensional Bose gases in magnetic potentials

Investigating out-of-equilibrium dynamics with two-dimensional (2D) systems is of widespread theoretical interest, as these systems are strongly influenced by fluctuations and there exists a superfluid phase transition at a finite temperature. In this work, we realise matter-wave interference for degenerate Bose gases, including the first demonstration of coherent splitting of 2D Bose gases using magnetic trapping potentials. We improve the fringe contrast by imaging only a thin slice of the expanded atom clouds, which will be necessary for subsequent studies on the relaxation of the gas following a quantum quench.

Sensitivity of ultracold atoms to quantized flux in a superconducting ring.

We report on the magnetic trapping of an ultracold ensemble of (87)Rb atoms close to a superconducting ring prepared in different states of quantized magnetic flux. The niobium ring of 10 μm radius is prepared in a flux state n Φ(0), where Φ(0)=h/2e is the flux quantum and n varying between ±6. An atomic cloud of 250 nK temperature is positioned with a harmonic magnetic trapping potential at ∼18 μm distance below the ring. The inhomogeneous magnetic field of the supercurrent in the ring contributes to the magnetic trapping potential of the cloud. The induced deformation of the magnetic trap impacts the shape of the cloud, the number of trapped atoms, as well as the center-of-mass oscillation frequency of Bose-Einstein condensates. When the field applied during cooldown of the chip is varied, the change of these properties shows discrete steps that quantitatively match flux quantization.

Bose–Einstein condensate on a persistent-supercurrent atom chip

A Bose–Einstein condensate was achieved in a stable magnetic trap on a persistent-supercurrent atom chip with a superconducting closed-loop circuit. We determined precisely the shape of the magnetic trapping potential by systematically controlling the persistent supercurrent. The condensation was verified by time-of-flight imaging and by atom number decay measurements. The measured decay rates agreed quantitatively with numerical simulations on the three-body loss process assuming all of the atoms to be a condensate. We also discuss the feasibility of creating a quasi-one-dimensional Bose gas on our atom chip.

Rapid Coherent Optical Modulation of Atomic Momenta via Pseudoresonances

We show that modulation of an optical field injected into a cavity containing a dilute Bose-Einstein condensate is transformed into a modulation of the population of the atomic momentum states due to pseudoresonances of the resolvent which describes the linearized evolution of the atom-cavity system. This effect is related to the way the atomic momentum states and the cavity optical field are dynamically coupled. The results presented offer new possibilities for rapid modulation of atomic momentum state populations up to 3 orders of magnitude faster than modulation of magnetic trapping potentials.

Dynamical Creation of Fractionalized Vortices and Vortex Lattices

We investigate the dynamic creation of fractionalized half-quantum vortices in Bose-Einstein condensates of sodium atoms. Our simulations show that both individual half-quantum vortices and vortex lattices can be created in rotating optical traps when additional pulsed magnetic trapping potentials are applied. We also find that a distinct periodically modulated spin-density-wave spatial structure is always embedded in square half-quantum vortex lattices. This structure can be conveniently probed by taking absorption images of ballistically expanding cold atoms in a Stern-Gerlach field.

Magnetic interactions of cold atoms with anisotropic conductors

We analyze atom-surface magnetic interactions on atom chips where the magnetic trapping potentials are produced by current carrying wires made of electrically anisotropic materials. We discuss a theory for time dependent fluctuations of the magnetic potential, arising from thermal noise originating from the surface. It is shown that using materials with a large electrical anisotropy results in a considerable reduction of heating and decoherence rates of ultra-cold atoms trapped near the surface, of up to several orders of magnitude. The trap loss rate due to spin flips is expected to be significantly reduced upon cooling the surface to low temperatures. In addition, the electrical anisotropy significantly suppresses the amplitude of static spatial potential corrugations due to current scattering within imperfect wires. Also the shape of the corrugation pattern depends on the electrical anisotropy: the preferred angle of the scattered current wave fronts can be varied over a wide range. Materials, fabrication, and experimental issues are discussed, and specific candidate materials are suggested.

Averaging out magnetic forces with fast rf sweeps in an optical trap for metastable chromium atoms

We introduce a time-averaged trap in which the internal state of the atoms is rapidly modulated to modify the magnetic trapping potential. In our experiment, fast radio-frequency linear sweeps flip the spins of atoms at a fast rate, which averages out the magnetic forces. We use this procedure to optimize the accumulation of metastable chromium atoms in an optical dipole trap from a magneto-optical trap. The potential experienced by the metastable atoms is identical to the bare optical dipole potential, so that this procedure allows for trapping all magnetic sublevels, hence increasing by up to 80% the final number of accumulated atoms.

Atom trapping with a thin magnetic film

We have created a $^{87}$Rb Bose-Einstein condensate in a magnetic trapping potential produced by a hard disk platter written with a periodic pattern. Cold atoms were loaded from an optical dipole trap and then cooled to BEC on the surface with radiofrequency evaporation. Fragmentation of the atomic cloud due to imperfections in the magnetic structure was observed at distances closer than 40 $\mu$m from the surface. Attempts to use the disk as an atom mirror showed dispersive effects after reflection.

Trapping cold atoms near carbon nanotubes: Thermal spin flips and Casimir-Polder potential

We investigate the possibility to trap ultracold atoms near the outside of a metallic carbon nanotube (CN) which we imagine to use as a miniaturized current-carrying wire. We calculate atomic spin flip lifetimes and compare the strength of the Casimir-Polder potential with the magnetic trapping potential. Our analysis indicates that the Casimir-Polder force is the dominant loss mechanism and we compute the minimum distance to the carbon nanotube at which an atom can be trapped.

Designing potentials by sculpturing wires

Magnetic trapping potentials for atoms on atom chips are determined by the current flow in the chip wires. By modifying the shape of the conductor we can realize specialized current flow patterns and therefore microdesign the trapping potentials. We have demonstrated this by nano-machining an atom chip using the focused ion beam technique. We built a trap, a barrier, and using a Bose-Einstein Condensate as a probe we showed that by polishing the conductor edge the potential roughness on the selected wire can be reduced. Furthermore, we give different other designs and discuss the creation of a one-dimensional magnetic lattice on an atom chip.

Radiofrequency-dressed-state potentials for neutral atoms

Potentials for atoms can be created by external fields acting on properties such as magnetic moment, charge, polarizability, or by oscillating fields that couple internal states. The most prominent realization of the latter is the optical dipole potential formed by coupling ground and electronically excited states of an atom with light. Here, we present an extensive experimental analysis of potentials derived from radiofrequency (RF) coupling of electronic ground states. The coupling is magnetic and the vector character allows the design of versatile microscopic state-dependent potential landscapes. Compared with standard magnetic trapping, we find no additional heating or (collisional) loss up to densities of 1015 atoms cm−3. We demonstrate robust evaporative cooling in RF potentials, which allows easy production of Bose–Einstein condensates in complex potentials. Altogether, this makes RF dressing a new powerful tool for manipulating ultracold atoms complementary to magnetic trapping and optical dipole potentials.

Time domain de Broglie wave interferometry along a magnetic guide

Time domain deBroglie wave interferometry [Cahn et al, Phys. Rev. Lett. 79, 784] is applied to Rb87 atoms in a magnetic guide. A standing wave light field is carefully aligned along the guiding direction of the magnetic trapping potential from a soft-ferromagnetic 4-foil structure. A sequence of two standing wave pulses is applied to the magnetically trapped atoms. The backscattered light at the atomic density grating revival time is collected and detected via a heterodyning technique. In addition to the observed recoil oscillations that fit the interferometer theory for atoms in free space, we observe a decay of the interferometer contrast on a millisecond time scale with unexpected millisecond-scale oscillations. We find that the oscillating decay is explained by a residual variation of the linear trapping potential along the standing wave direction.

Scalable register initialization for quantum computing in an optical lattice

The Mott insulator state created by loading an atomic Bose–Einstein condensate (BEC) into an optical lattice may be used as a means to prepare a register of atomic qubits in a quantum computer. Such architecture requires a lattice commensurately filled with atoms, which corresponds to the insulator state only in the limit of zero inter-well tunnelling. We show that a lattice with spatial inhomogeneity created by a quadratic magnetic trapping potential can be used to isolate a subspace in the centre which is impervious to hole-hoping. Components of the wavefunction with more than one atom in any well can be projected out by selective measurement on a molecular photo-associative transition. Maintaining the molecular coupling can sustain a commensurately filled register for the duration of a quantum computation.

Evolution of spin-dependent atomic wave packets in a harmonic potential

We have investigated theoretically the evolution of spin-dependent atomic wave packets in a harmonic magnetic trapping potential. For a Bose-condensed gas, which undergoes a Mott insulator transition and a spin-dependent transport, the atomic wavefunction can be described by an entangled single-atom state. Due to the confinement of the harmonic potential, the density distributions exhibit periodic decay and revival, which is different from the case of free expansion after switching off the combined harmonic and optical lattice potential.

Cold atoms near surfaces: designing potentials by sculpturing wires

The magnetic trapping potentials for atoms on atom chips are determined by the current flow pattern in the chip wires. By modifying the wire shape using focused ion beam nano-machining we can design specialized current flow patterns and therefore micro-design the magnetic trapping potentials. We give designs for a barrier, a quantum dot, and a double well or double barrier and show preliminary experiments with ultra cold atoms in these designed potentials.

Alkali-metal adsorbate polarization on conducting and insulating surfaces probed with Bose-Einstein condensates

A magnetically trapped $^{87}\mathrm{Rb}$ Bose-Einstein condensate is used as a sensitive probe of short-range electrical forces. In particular, the electric polarization of, and the subsequent electric field generated by, $^{87}\mathrm{Rb}$ adsorbates on conducting and insulating surfaces is measured by characterizing perturbations to the magnetic trapping potential using high quality factor condensate excitations. The nature of the alterations to the electrical properties of $\mathrm{Rb}$ adsorbates is studied on titanium (metal) and silicon (semiconductor) surfaces, which exhibit nearly identical properties, and on glass (insulator), which displays a smaller transitory electrical effect. The limits of this technique in detecting electrical fields and ramifications for measurements of short-range forces near surfaces are discussed.

Modulational Instability in Bose–Einstein Condensates under Feshbach Resonance Management

We investigate the modulational instability of nonlinear Schrödinger equations with periodic variation of their coefficients. In particular, we focus on the case of the recently proposed, experimentally realizable protocol of Feshbach Resonance Management for Bose–Einstein condensates. We derive the corresponding linear stability equation analytically and we show that it can be reduced to a Kronig–Penney model, which allows the determination of the windows of instability. The results are tested numerically in the absence, as well as in the presence of the magnetic trapping potential.

Experimental observation of Beliaev coupling in a Bose-Einstein condensate.

We report the first experimental observation of Beliaev coupling between collective excitations of a Bose-Einstein condensed gas. Beliaev coupling is not predicted by the Gross-Pitaevskii equation and so this experiment tests condensate theory beyond the mean field approximation. Measurements of the amplitude of a high frequency scissors mode show that the Beliaev process transfers energy to a lower-lying mode and then back and forth between these modes, unlike Landau processes which lead to a monotonic decrease in amplitude. To enhance the Beliaev process we adjusted the geometry of the magnetic trapping potential to give a frequency ratio of 2 to 1 between the two scissors modes.