Probing first-order spatial coherence of a Bose-Einstein condensate

Abstract

We probe the spatial coherence properties of a magnetically trapped Bose gas. Two matter wave beams are extracted from two spatially separated regions of the trap and overlap outside the trapping region. The visibility of the resulting interference pattern measures the phase coherence between the regions of extraction. By varying the spatial separation between the two regions the first-order spatial correlation function of the trapped Bose gas can be measured. The location of the minima of the interference pattern is reproducible, which experimentally confirms that the trapped Bose-Einstein condensate is not fragmented into individual condensates.     

Finite-temperature Effect in Phase Transition to Superfluidity for Bose–Einstein Condensates in a 1-D Optical Lattice

We experimentally study the phase transition of ⁸⁷Rb Bose–Einstein condensates adiabatically loaded to a combined trap of a 1D optical lattice and a magnetic trap. The phase coherence property of this system is probed by recording the interference pattern of the expanded atomic cloud suddenly released from the combined trap. We show that as the temperature is sufficiently low (below the critical temperature T _C ), an interference pattern has a “peak on a peak” feature which is a true signature of macroscopic superfluid states. The normal gas only contributes to the broad background and three wide peaks in an interference pattern. These observations qualitatively agree with the recent theoretical predictions (Diener et al. in Phys. Rev. Lett. 98:180404, 2007; Kato et al. in Nat. Phys. 4:617, 2008). We also computed both the critical temperature and the interference pattern for a practical combined trap as ours in the tight-binding limit, and the numerical results are consistent with our experimental observations.     

Nondiffracting interference patterns generated with programmable spatial light modulators

Nondiffracting beams are of interest for optical metrology applications because the size and shape of the beams do not change as the beams propagate. We have created a generating pattern consisting of a linear combination of two nondiffracting patterns. This pattern forms a nondiffracting interference pattern that appears as a circular array of nondiffracting spots. More complicated multiplexed arrays are also constructed that simultaneously yield two different nondiffracting patterns. We generate these Bessel function arrays with a programmable spatial light modulator. Such arrays would be useful for angular alignment and for optical interconnection applications.     

Multiscale patterning of plasmonic metamaterials

The interaction of light with surface plasmons--collective oscillations of free electrons--in metallic nanostructures has resulted in demonstrations of enhanced optical transmission, collimation of light through a subwavelength aperture, negative permeability and refraction at visible wavelengths, and second-harmonic generation from magnetic metamaterials. The structures that display these plasmonic phenomena typically consist of ordered arrays of particles or holes with sizes of the order of 100 nm. However, surface plasmons can interact with each other over much longer distances, so the ability to organize nanoscale particles or holes over multiple length scales could lead to new plasmonic metamaterials with novel optical properties. Here, we present a high-throughput nanofabrication technique-soft interference lithography-that combines the ability of interference lithography to produce wafer-scale nanopatterns with the versatility of soft lithography, and use it to create such plasmonic metamaterials. Metal films perforated with quasi-infinite arrays of 100-nm holes were generated over areas greater than 10 cm(2), exhibiting sharp spectral features that changed in relative amplitude and shifted to longer wavelengths when exposed to increased refractive index environments. Moreover, gold nanohole arrays patterned into microscale patches exhibited strikingly different transmission properties; for instance, patches of nanoholes displayed narrow resonances (<14.5 nm full-width-at-half-maximum) that resulted in high refractive index sensitivities far exceeding those reported previously. Soft interference lithography was also used to produce various infinite and finite-area arrays of nanoparticles, including patterns that contained optically distinct particles side by side and arrays that contained both metallic and dielectric materials.     

Laser control of the state of a plasma in a selective optical trap

Laser cooling of resonant ions is shown to be applicable to the effective control of the temperature of charged particles in a low-temperature electron-ion plasma confined in a magnetic trap. Pis’ma Zh. Tekh. Fiz. 23, 28–32 (January 26, 1997)     

TECHNIQUES FOR SELECTIVE MAGNETIC SEPARATION OF FINE PARTICLES

ABSTRACT

Magnetic separation as a particle-particle or particle-fluid separation technique has been extended to be effective for particulates with the smallest known magnetic susceptibility. Most commonly found materials are diamagnetic but the effectiveness of high magnetic field gradient separators for even these very weakly magnetic materials makes it difficult to separate more magnetic species of particles from them. The selectivity of such separations has been improved by matrix design and by several separation techniques. Regular arrays of matrix wires can be arranged according to the calculated field profile to exclude regions of capture for magnetic particulates of positive or negative susceptibility. The magnetic field orientation with respect to the array provides control over the competition between magnetic capture forces and those of fluid flow. The size of particle depletion regions in model arrays depends on particle size and susceptibility and suggests a method of measurement of these even for submicron particulates.     

Numerical simulation of chainlike cluster movement of feeble magnetic particles by induced magnetic dipole moment under high magnetic fields

Abstract

In this paper, the motion of a chainlike cluster of feeble magnetic particles induced by high magnetic field is discussed on the basis of the results of numerical simulations. The simulations were performed on glass particles with a diameter of 0.8 mm; and the viscosity, applied magnetic field and magnetic properties of the surrounding medium were changed. In addition to the magnetic field and the difference in magnetic susceptibility between the particles and the surrounding medium, the obtained results indicate that the viscosity is an essential factor for the formation of the chainlike alignment of feeble magnetic particles. We also carried out simulations using glass particles with a smaller diameter of 0.1 mm. Chainlike clusters were produced similar to those of ferromagnetic particles formed in a ferromagnetic fluid.     

Coherence of bose condensates

Abstract

We study the coherence of interacting Bose condensates in recent magnetic trap experiments. The coherent evolution manifests itself in the macroscopic interference of two independent Bose condensates. The theoretical predictions from the time-dependent Gross–Pitaevskii equation are in excellent agreement with the measured interference patterns. A coherent coupling of two condensates represents the atomic analogon of a Josephson junction. The dependence of the magnetic confinement on the nuclear spin orientation allows one to build a controllable beam splitter by magnetic resonance. The application of this beam splitter to realize an atom laser is studied theoretically. The coherence of the output beam is limited only by phase diffusion of the condensate.     

The Non-isoplanatic Image Equation and the Effect of Not Satisfying the Sine Condition in the Scanning Microscope

Abstract

By considering lack of agreement with the sine condition and using the concept of image formation by interference of plane waves, we derive a new equation for non-isoplanatic image formation. Moreover, applying this equation and considering alignment errors between optical elements, a new equation for the image formation of the object-scan type scanning microscope is derived. This type of microscope also includes laser-disc optical systems. Effects of the sine condition not being satisfied both for the illumination lens and for the collector lens are discussed.     

Strategies to obtain pattern fidelity in nanowire growth from large-area surfaces patterned using nanoimprint lithography

Position controlled nanowire growth is important for nanowire-based optoelectronic components which rely on light emission or light absorption. For solar energy harvesting applications, dense arrays of nanowires are needed; however, a major obstacle to obtaining dense nanowire arrays is seed particle displacement and coalescing during the annealing stage prior to nanowire growth. Here, we explore three different strategies to improve pattern preservation of large-area catalyst particle arrays defined by nanoimprint lithography for nanowire growth. First, we see that heat treating the growth substrate prior to nanoimprint lithography improves pattern preservation. Second, we explore the possibility of improving pattern preservation by fixing the seed particles in place prior to annealing by modifying the growth procedure. And third, we show that a SiN _x growth mask can fully prevent seed particle displacement. We show how these strategies allow us to greatly improve the pattern fidelity of grown InP nanowire arrays with dimensions suitable for solar cell applications, ultimately achieving 100% pattern preservation over the sampled area. The generic nature of these strategies is supported through the synthesis of GaAs and GaP nanowires.

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Rotation of microparticles with Bessel beams generated by diffractive elements

Abstract

We show that imaging a non-diverging Bessel beam by a spherical lens leads to the generation of a diverging Bessel beam. Expressions for the projections of the Umov-Poynting vector for a two-dimensional TE-polarized Bessel beam and a three-dimensional paraxial linearly polarized Bessel beam are derived. A fifth-order Bessel beam is produced using a single optical element-a 16-level phase-only diffractive helical axicon fabricated using electron beam lithography. This beam was successfully used to trap and rotate 5-10 μm diameter yeast particles and polystyrene beads of diameter 5 μm.     

Novel Polarimetric Technique Exploring Spatiotemporal Birefringent Response of an Anti-ferroelectric Liquid Crystal Cell

Abstract

This paper describes a novel polarimetric technique for mapping the spatiotemporal birefringent parameters characterizing an anti-ferroelectric liquid crystal cell. A linearly polarized beam of light transmitted by the liquid crystal cell turns into an elliptically polarized beam. Some birefringent irregularities existing over the cell make state of polarization of the elliptically polarized beam of light be spatiotemporal. This beam works as a signal beam to interfere with a reference beam consisting of two orthogonal linearly polarized components. The resultant interference pattern is taken by a charge-coupled device video camera and recorded in a computer. The computer gives the information required for determining the spatiotemporal birefringent parameters that characterize the liquid crystal cell. The major advantage is that the two-dimensional distribution of the birefringent axes as well as the two principal refractive indices can be determined simultaneously, and no use of any optical components for polarization alignment makes it possible to follow a rapid change in birefringent parameters within the maximum frame rate of the video camera. A change in time-dependent birefringent parameter is measured at every 0·1 ms for the demonstration experiment.     

Rapid,Controllable Fabrication of Regular Complex Microarchitectures by Capillary Assembly of Micropillars and Their Application in Selectively Trapping/Releasing Microparticles

A simple strategy to realize new controllable 3D microstructures and a novel method to reversibly trapping and releasing microparticles are reported. This technique controls the height, shape, width, and arrangement of pillar arrays and realizes a series of special microstructures from 2‐pillar‐cell to 12 cell arrays, S‐shape, chain‐shape and triangle 3‐cell arrays by a combined top down/bottom up method: laser interference lithography and capillary force‐induced assembly. Due to the inherent features of this method, the whole time is less than 3 min and the fabricated area determined by the size of the laser beam can reach as much as 1 cm², which shows this method is very simple, rapid, and high‐throughput. It is further demonstrated that the ‘mechanical hand’‐like 4‐cell arrays could be used to selectively trap/release microparticles with different sizes, e.g., 1.5, 2, or 3.5 μm, which are controlled by the period of the microstructures from 2.5 to 4 μm, and 6 μm. Finally, the ‘mechanical hand’‐like 4‐cell arrays are integrated into 100 μm‐width microfluidic channels prepared by ultraviolet photolithography, which shows that this technique is compatible with conventional microfabrication methods for on‐chip applications.     

Hyperboloid mass spectrometer with a truncated trap

A hyperboloid mass spectrometer is proposed in which the analyzer is a three-dimensional ion trap truncated by the plane z=0. The mass peaks for different operating regimes of the mass analyzer are constructed from the results of a numerical modeling of the electric field and a simulation of the process of sorting the charged particles. The results serve as a basis for the construction of a hyperboloid mass spectrometer with a simple electrode system and a high resolving power. Pis’ma Zh. Tekh. Fiz. 25, 51–56 (May 26, 1999)     

Realization of a mirror magneto-optical trap

Abstract

We present details for construction and the operation of a mirror magneto-optical trap for cooling and trapping rubidium atoms. For trap operation, only four input laser beams are needed in contrast to the normal six for a standard trap. In excess of 10⁸ atoms have been trapped with this arrangement, with the atomic ensemble only ～1mm from the surface of a reflective mirror. This trap is highly suited to studies of magnetic guiding and magnetic manipulation of cold atomic ensembles.     

Particle number fluctuations in an ideal Bose gas

Abstract

We analyse occupation number fluctuations of an ideal Bose gas in a trap which is isolated from the environment with respect to particle exchange (canonical ensemble). We show that in contrast to the predictions of the grandcanonical ensemble, the counting statistics of particles in the trap ground state changes from monotonously decreasing above the condensation temperature to single-peaked below that temperature. For the exactly solvable case of a harmonic oscillator trapping potential in one spatial dimension we extract a Landau–Ginzburg functional which–despite the non-interacting nature of the system–displays the characteristic behaviour of a weakly interacting Bose gas. We also compare our findings with the usual treatment which is based on the grand-canonical ensemble. We show that for an ideal Bose gas neither the grand-canonical and canonical ensemble thermodynamically equivalent, nor the grand-canonical ensemble can be viewed as a small system in diffusive contact with a particle reservoir.     

Measurement of the Optical Force and Trapping Range of a Single-beam Gradient Optical Trap for Micron-sized Latex Spheres

Abstract

A single-beam gradient optical trap was constructed using a 20 mW 632·8 nm He–Ne laser coupled to an optical microscope. Latex spheres were trapped in water at the focal point of a tightly-focused laser beam, which was generated using a 100 × objective. The efficiency of the trap was evaluated by determining the maximum speeds at which the trapped particles could be manipulated. Typical maximum speeds of tens of microns per second were recorded, at the maximum trapping power of 6·7 mW. The effective transverse trapping range for 1–7 μm diameter latex spheres was measured to be 1–3 μm, and the maximum transverse optical force on 1–12 μm diameter latex spheres varied in the range 0·4–4·5 pN.     

Vortex Lattices in Rotating Bose-Einstein Condensate in an Optical Lattice: Analogy to Uniformly Frustrated Josephson-Junction Arrays

We investigate the effect of rotation for two-dimensional Josephson junction arrays consisting of atomic Bose-Einstein condensates trapped by both a harmonic trap and an optical lattice. This system is analogous to the superconducting Josephson junction array to which a transverse magnetic field is applied, being described by the uniformly frustrated XY model. The frustration parameter f, defined by the rotation frequency of the condensate and the lattice constant of the optical lattice, is an important parameter to determine the ground state. The numerical simulations of the Gross-Pitaevskii equation reveal that for f=1/2 the ground state possesses the checkerboard pattern of vortices, and for f<1/2 the vortex configuration is characterized by the staircase form.      

In situ Interferometric alignment systems for the assembly of microchannel relay systems

An interferometric alignment technique developed for the assembly of microchannel relay systems is described. The method uses pairs of diffractive lenslets that are arranged to form compact in situ interferometers. The relative transverse, longitudinal, and rotational alignment of the two lenslet arrays can be quantitatively determined from the resulting interference patterns. The theoretical analysis is compared with the experimental performance.     

Rapid rotation of micron and submicron dielectric particles measured using optical tweezers

Abstract

We demonstrate the use of a laser trap (‘optical tweezers’) and back-focal-plane position detector to measure rapid rotation in aqueous solution of single particles with sizes in the vicinity of 1 μm. Two types of rotation were measured: electrorotation of polystyrene microspheres and rotation of the flagellar motor of the bacterium Vibrio alginolyticus. In both cases, speeds in excess of 1000 Hz (rev s^?1) were measured. Polystyrene beads of diameter about 1 μm labelled with smaller beads were held at the centre of a microelectrode array by the optical tweezers. Electrorotation of the labelled beads was induced by applying a rotating electric field to the solution using microelectrodes. Electrorotation spectra were obtained by varying the frequency of the applied field and analysed to obtain the surface conductance of the beads. Single cells of V. alginolyticus were trapped and rotation of the polar sodium-driven flagellar motor was measured. Cells rotated more rapidly in media containing higher concentrations of Na⁺, and photodamage caused by the trap was considerably less when the suspending medium did not contain oxygen. The technique allows single-speed measurements to be made in less than a second and separate particles can be measured at a rate of several per minute.