One- and Two-Dimensional Arrays of Double-Well Optical Traps for Cold Atoms or Molecules

We propose a novel scheme to form one- and two-dimensional arrays of double-well optical dipole traps for cold atoms (or molecules) by using an optical system composed of a binary π-phase grating and a lens illuminated by a plane light wave, and study the relationship between the maximum intensity Imax of each optical well (or the maximum trapping potential Umax for ^85Rb atoms) and the relative aperture β (= α/f) of the lens. We also calculate the intensity gradients of each optical well and their curvatures, and estimate the spontaneous photon-scattering rate of trapped atom in each well, including Rayleigh and Raman scattering rates. Our study shows that the proposed 1D and 2D arrays of double-well traps can be used to prepare 1D and 2D novel optical lattices with cold atoms (or molecules), or form an all-optically integrated atom optical chip, or even to realize an array of all-optical double-well atomic (or molecular) Bose-Einstein condensates by optical-potential evaporative cooling, and so on.     

2D dark optical surface lattice with an efficient intensity-gradient cooling of atoms by evanescent wave interference

We propose a novel scheme to form a 2D dark optical surface lattice (DOSL) for cold atoms on the surface of the dense flint glass by using two sets of blue-detuned evanescent wave interference fields and a blue-detuned evanescent wave field. In the 2D DOSL, cold atoms will be trapped in the vicinity of minimum intensity and suffered the minimal light shift as well as the lowest coherence loss. The total potential and trap-depth of the individual optical micro-trap in the 2D DOSL are high enough to trap cold atoms (T = 120 μK) released from the standard magneto-optical trap (MOT), and atoms trapped in the 2D DOSL can be cooled to several μK with the efficient intensity-gradient Sisyphus cooling. The lattice constant of the DOSL can be controllable by changing the incident angles of lights.     

Writing a superlattice with light forces

In atom lithography the conventional roles played by light and matter are reversed. Instead of using a solid mask to pattern a light beam, a mask of light is used to pattern a beam of neutral atoms. In this paper we report the production of different chromium dot arrays with quadratic symmetry. The lattice period depends on the relative polarization and the phase of the two standing waves generating the light mask. A small angular misalignment of the laser beams breaks the high symmetry and a chromium superlattice is written, that is a continuous periodic change between two different quadratic lattices. The structures exhibit lines with a FWHM below 50 nm and clearly separated chromium dots with a FWHM below 70 nm. Received: 30 September 1999 / Revised version: 14 February 2000 / Published online: 5 April 2000     

Observation of collimation and decollimation of an atomic beam in a misaligned standing wave

This paper reports an experimental study on the collimation and decollimation of an atomic beam in a misaligned standing wave, in which the effective detuning caused by the Doppler effect is affected by the longitudinal velocity of the atomic beam. The experiment shows that in a strong field with red detuning between laser field and atomic transition frequency, laser heating in a normal standing wave becomes laser cooling in a misaligned standing wave for an approriate misalignment angle. For blue detuning, laser cooling in a standing wave can also become laser heating in a misaligned standing wave for an appropriate condition. These results ca be used in controling atomic motion.     

Laser collimation of an Fe atomic beam on a leaky transition

We report results of the first laser collimation of a thermal beam of Fe atoms on the leaky ⁵D₄ ⁵F₅ transition, with both parallel linear ^xx and crossed linear ^xy laser polarization configurations. The measured atomic beam divergence is compared to a rate-equation model and a quantum Monte Carlo model. The experimental values for the divergence are limited by the finite laser line width, which is comparable to the natural line width of the Fe atom. In general, flux decreases with higher intensities, showing the effect of the leaky transition. At the best beam collimation _RMS = 0.17 mrad, which is for a detuning of = – and a saturation parameter of s = 6, the flux decreased to approximately 70%. Highest flux was measured for a detuning of = –2 and s = 4, reaching 135% of the uncooled value. From our measurements we estimate the total leak rate to be 1/(240 ± 40), which is in good agreement with the literature value of 1/244. The crossed linear polarization configuration is the better choice, with a slightly better collimation but the same atomic beam flux. Plugging of the largest leak would increase the flux to at least 80% of the closed transition value, resulting in better contrast for atom lithography.     

Two dimension selective coherent population trapping controlled by a phase shift

Two-dimensional laser cooling based on velocity-selective coherent population trapping is investigated theoretically for the J _g=1J _e=0 atomic transition. Wavevectors and polarizations of three laser beams are chosen to realize a coherent superposition of three degenerate ground states. For the first time in laser cooling, use is made of the electric field phases to realize coherent population trapping selective in two dimensions. Numerical solutions and analytic estimates are presented for laser cooling of helium atoms.     

Simulation of Chromium Atom Deposition Pattern in a Gaussain Laser Standing Wave with Different Laser Power

One-dimensional deposition of a neutral chromium atomic beam focused by a near-resonant Gaussian standing- laser field is discussed by using a fourth-order Runge-Kutta type algorithm. The deposition pattern of neutral chromium atoms in a laser standing wave with different laser power is discussed and the simulation result shows that the full width at half maximum （FWHM） of a nanometer stripe is 115nm and the contrast is 2.5：1 with laser power 3.93mW; the FWHM is 0.8nm and the contrast is 27：1 with laser power 16mW, the optimal laser power; but with laser power increasing to 50mW, the nanometer structure forms multi-crests and the quality worsens quickly with increasing laser power.     

Controllable Photonic Band Gap and Defect Mode in a 1D CO2-Laser Optical Lattice

We propose a new method to form a novel controfiable photonic crystal with cold atoms and study the photonic band gap （PBG） of an infinite 1D CO2-laser optical lattice of SSRb atoms under the condition of quantum coherence. A significant gap generated near the resonant frequency of the atom is founded and its dependence on physical parameters is also discussed. Using the eigenquation of defect mode, we calculate the defect mode when a defect is introduced into such a lattice. Our study shows that the proposed new method can be used to optically probe optical lattice in situ and to design some novel and controllable photonic crystals.     

Novel 1D optical molasses composed of two elliptical Gaussian beams with an ultrahigh orbital angular-momentum

We propose a novel scheme to form a 1D optical molasses by using two counter-propagating red-detuned elliptical Gaussian beams possessing an ultrahigh orbital angular-momentum. In this optical molasses, atoms will suffer both an axial and an azimuthal Doppler cooling, and their temperature can be far below the conventional Doppler cooling limit, which provides a new opportunity for the laser cooling of the most abundant bosonic isotopes of alkaline-earth atoms. Because these atoms lack the hyperfine structure, they cannot be cooled by the well-known sub-Doppler cooling schemes.     

Optical forces acting on Rayleigh particle placed into interference field

We describe a general way how to calculate optical forces acting on Rayleigh particles or colloids placed into general interference field. In this paper, we focus on a configuration with three interfering beams laying in one plane and we present a comprehensive analysis of trap properties and particle behaviour. We found that this arrangement can be used for simultaneous 2D/3D confinement or sorting of particles having refractive index higher or lower comparing to the surrounding immersion medium.     

Realization of a single-beam mini magneto-optical trap: A candidate for compact CPT cold atom-clocks

We have demonstrated the experimental realization of a single-beam mini magneto-optical trap of ⁸⁷Rb atoms, originally designed for a cold atom-clock with coherent population trapping (CPT). Only one beam is used as cooling, trapping and repumping beams rather than the three pairs of orthogonal beams of the standard magneto-optical trap. The core optics, which consists of a modified pyramidal funnel type mirror, a quarter-wave plate and a retroreflect mirror, is installed inside a mini titanium cubic chamber. The vacuum system, rubidium source, magnetic field coils and beam expander are designed in a compact geometry. As many as 1.1 × 10⁷ rubidium atoms are cooled and trapped, and thus the mini trap is ready for the implementation of a novel compact coherent population trapping cold atom-clock.     

Localization of atoms in light fields: Optical molasses,adiabatic compression and squeezing

We present a theoretical study of the localization1 of atoms with an angular momentumJ _g=3 toJ _e=4 transition (e.g., chromium atoms) in quantized optical molasses created by two counterpropagating linearly polarized laser beams. We study the localization as a function of the potential depth, the angle between the polarizations and the interaction time with the molasses in the low-intensity limit, and discuss the possibility of adiabatic compression and squeezing of the atomic distribution.Dedicated to H. Walther on the occasion of his 60th birthday     

Sympathetic cooling rate of gas-phase ions in a radio-frequency-quadrupole ion trap

We theoretically investigated the mass dependence of the sympathetic cooling rate of gas-phase ions trapped in a linear radio-frequency-quadrupole ion trap. Using an a priori molecular dynamical calculation, tracing numerically with Newtonian equations of motion, we found that ions with a mass greater than 0.54±0.04 times that of the laser-cooled ions are sympathetically cooled; otherwise, they are heated. To understand the mass dependence obtained using the molecular-dynamical calculation, we made a heat-exchange model of sympathetic cooling, which shows that the factor of 0.54±0.04 is a consequence of absence of micro-motion along the axis of the linear ion trap. Received: 10 December 2001 / Revised version: 28 January 2002 / Published online: 14 March 2002     

Collisional effects on the collective laser cooling . of trapped bosonic gases

We analyse the effects of atom–atom collisions on a collective laser cooling scheme. We derive a quantum master equation which describes the laser cooling in presence of atom–atom collisions in the weak-condensation regime. Using such equation, we perform Monte Carlo simulations of the population dynamics in one and three dimensions. We observe that the ground-state laser-induced condensation is maintained in the presence of collisions. Laser cooling causes a transition from a Bose–Einstein distribution describing collisionally induced equilibrium, to a distribution with an effective zero temperature. We analyse also the effects of atom–atom collisions on the cooling into an excited state of the trap. Received: 18 June 1999 / Revised version: 24 September 1999 / Published online: 10 November 1999     

One atom in an optical cavity: Spatial resolution beyond the standard diffraction limit

The position of a slow atom passing through a standing-wave light field in an ultrahigh-finesse optical resonator can be measured by observing either the intensity of the light transmitted through the cavity or its phase. Apart from the periodicity of the standing wave, both techniques allow to determine the position of the particle with a resolution much better than the standard classical diffraction limit /2. Position measurements with uncertainty </20 seem to be possible with all-optical techniques.These notes were prepared to celebrate H. Walther's 60th birthday and to honour his pioneering contributions to some of the most lively fields of quantum optics     

Decoding the dynamics of a single trapped atom from photon correlations

Received: 4 September 1998     

Nonlinear resonances and phase transitions of two-ion Coulomb clusters in a Paul trap: Calculations without laser cooling

The mechanism responsible for transitions of laser-cooled trapped ions from an ordered crystal state to an irregular cloud state has been discussed controversially. A numeric and analytic study of the relative motion of two trapped ions without laser cooling is performed and compared with the results of previous simulations involving the laser. It turns out that the system without laser, in spite of its simplicity, already exhibits a non-monotonic dependence of crystal stability on trap parameters, which is linked to the presence of low-order nonlinear resonances.     

Partially coherent matter wave and its evolution

The evolution and propagation of a partially coherent matter wave (PCMW) is investigated theoretically by the correlation function method. The ABCD matrix formalism previously used for a fully coherent matter wave is extended to make it applicable for the PCMW. A new tensor ABCD law is derived, which makes the propagation and evolution of a PCMW very simple and clear. As an example, the evolution of the coherence of a PCMW in a gravitational field is calculated.     

Measurement of the gravitational acceleration of an atom with a light-pulse atom interferometer

Velocity sensitive stimulated Raman transitions have been used to measure the gravitational acceleration, g, of laser cooled sodium atoms in an atomic fountain geometry. By using an improved scheme to drive the Raman transitions, we have demonstrated a resolution of 3×10^–8 g after 2×10³ seconds of integration time. In addition to presenting recent experimental results, we review the theory of stimulated Raman transitions as it applies to atom interferometers and discuss the prospects of an atom interferometer-based gravimeter with better than 10^–10 g absolute accuracy.     

Nanoscale focusing of atoms with a pulsed standing wave

We have theoretically and experimentally investigated the focusing properties of a detuned pulsed standing wave onto a beam of neutral atoms. In close analogy to the continuous-wave situation the dipole force leads to a periodic focusing of atoms with a period of λ/2, provided an adiabatic condition is fulfilled. Pulsed laser light is conveniently converted to short wavelengths and hence offers advantages in the application of atom lithography with elements of technological interest having blue or UV resonance lines. Received: 6 October 1999 / Revised version: 3 February 2000 / Published online: 5 April 2000