Standing-wave Light Field Research Articles

Bistability and macroscopic quantum coherence in BECs: the two cases of attractive and repulsive interactions

We consider Bose-Einstein condensates (BECs) in situations where the density undergoes a symmetry breaking, either in real space or in momentum space. This occurs for a suitable number of condensed atoms in a double well potential, obtained in real space for a BEC of lithium atoms by adding a standing wave light field to the trap potential, or in momentum space for rubidium atoms by Raman coupling two BECs in different magnetic states with two tilted light fields. Evidence of bistability results from the solution of the Gross-Pitaevskii equation. By second quantization, we show that the classical bistable situation is in fact a Schrödinger cat (SC) and we evaluate the macroscopic quantum coherence between the two SC states.

High-resolution atomic channeling using. velocity-selected atomic beam

High-resolution atomic channeling using velocity-controlled atoms may be able to overcome precision limitations of the conventional atom lithography. We have experimentally clarified the dependence of line width and contrast of atomic patterns in the channeling region on the velocity spread of the atomic source for the first time. Thermal or velocity-selected atomic beams prepared with a one-dimensional magneto-optical trap were employed as the atomic sources. We investigated the channeling characteristics by measuring the frequency shifts of the atomic absorption spectra in an intense standing wave light field. As a result, we can show that narrower line width and higher contrast atomic patterns are obtained as the velocity spread becomes narrower. An atomic pattern with an estimated line width of 57 nm was generated when the velocity spread of the atomic source was almost 50 m/s, that is, 1/6 that of the thermal beam.

Quantum theory of a micromaser operating on the atomic scattering from a resonant standing wave

We study the amplification of a resonant standing-wave light field due to the interaction with a beam of monovelocity two-level atoms moving in the Raman-Nath regime and in the Bragg regime. The atomic density is low so that, at most, one atom is inside the cavity at a time. This system is very similar to the well-known micromaser but it is operating in the optical region of the field frequencies. Therefore, the situation corresponds to a microlaser. Unlike the micromaser system, the momentum transfer between the atoms and photons in the microlaser essentially effects the center-of-mass motion of the atoms and the evolution of the field.

Realization of bichromatic optical superlattices

We present the experimental realization of optical superlattices created by exposing laser cooled ${}^{85}\mathrm{Rb}$ atoms to a bichromatic standing-wave light field. The two light frequencies are tuned close to the ${D}_{1}$ and ${D}_{2}$ lines of ${}^{85}\mathrm{Rb}.$ The total optical potential seen by the atoms exhibits a modulation at the spatial beat period of the two light fields in addition to the typical periodicity on the scale of an optical wavelength. The bichromatic light field cools the atoms into the superlattice potential, resulting in a density modulation on a macroscopic scale. We have observed the density modulation directly in one- and three-dimensional superlattice configurations using an absorption imaging technique.

Ponderomotive optical lattice for Rydberg atoms.

We propose to use the ponderomotive energy of Rydberg electrons in standing-wave light fields to form an optical lattice for Rydberg atoms. Application of the Born-Oppenheimer approximation shows that, with readily achievable experimental parameters, atoms in any Rydberg state can be trapped. Realization of this scheme would extend the benefits of atom trapping to highly excited atoms.

How to catch an atom with single photons

We report on trapping a single neutral atom in the standing-wave light field of a high-finesse optical cavity containing one photon on average, a single-photon optical trap, or SPOT for short. This trap has the novel feature that the light field is also used to observe the atom in real time. The oscillatory motion of the trapped atom induces well-resolved oscillations of the light intensity. Periodic structure is visible in the fourth-order intensity correlation function, attributed to long-distance flights of the atom along the standing wave. The finite duration of those flights provides evidence for cavity-mediated cooling of atoms. We discuss the various mechanisms determining the trapping time and compare the results with a quantum-jump Monte Carlo simulation to interpret the observed signals.

Atomic beam guide by a one-dimensional magneto-optical trap

The fine control of a neutral atomic beam by radiation pressure has opened a new field called atom lithography. In particular, a direct writing method, which focuses an atomic beam with a standing-wave light field into narrow lines, has been demonstrated. A velocity-controlled and isotope-selected atomic beam is essential for improving the performance of this lithography method. An atomic deflection technique using radiation pressure is indispensable for producing such an atomic beam. Here we report on an atomic beam guide using a one-dimensional magneto-optical trap (1D-MOT). First we decelerate atoms whose velocities lie in the range between 250 and 320 m/s. A diode laser (780 nm) is used as the light source for deceleration and its injection current is modulated at 2 MHz. Then the decelerated beam is deflected by a tilted 1D-MOT, which consists of four copper rods and four rectangular mirrors.

Correlation between momenta of two atoms deflected from an off-resonant quantized standing-wave light field

Correlation between momenta of two atoms deflected from an off-resonant quantized standing-wave light field

A virtual amplitude grating for atomic optics

We propose an atom optical amplitude grating formed by a standing wave light field. The standing wave optically pumps all atoms except those localized near the nodes of the light field into an undetected internal state. The distribution of atoms near the nodes in the detected internal state can approach that of a minimum uncertainty wavepacket. The periodicity of the spatial localization results in a well resolved diffraction pattern. We also explore the spatial coherence of atomic wavepackets following the interaction with the virtual grating.

Quantum conversion between laser fields and vibrational wave-packets of particles in a three-dimensional quantized trap

Raman transitions between vibrational states of the center-of-mass motions of single particles confined in a three-dimensional quantized trap are investigated in nonresonant standing-wave light fields, which can be used to observe quantum features transferred from laser fields to vibrational wave-packets of motion.

Band gaps for atoms in light-based waveguides.

The energy spectrum for a system of atoms in a periodic potential can exhibit a gap in the band structure. We describe a system in which a laser is used to produce a mechanical potential for the atoms, and a standing wave light field is used to shift the atomic levels using the Autler-Townes effect, which produces a periodic potential. The band structure for atoms guided by a hollow optical fiber waveguide is calculated in three dimensions with quantised external motion. The size of the band gap is controlled by the light guided by the fiber. This variable band structure may allow the construction of devices which can cool atoms. The major limitation on this device would be the spontaneous emission losses.

Atom-optical properties of a standing-wave light field

The focusing of atoms to nanometer-scale dimensions by a near-resonant standing-wave light field is examined from a particle optics perspective. The classical equation of motion for atoms traveling through the lens formed by a node of the standing wave is derived and converted to a spatial trajectory equation. A paraxial solution is obtained, which results in simple expressions for the focal properties of the lens, useful for estimating its behavior. Aberrations are also discussed, and an exact numerical solution of the trajectory equation is presented. The effects on focal linewidth of angular collimation and velocity spread in the atomic beam are investigated, and it is shown that angular collimation has a much more significant effect than velocity spread, even when the velocity spread is thermal.

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 limitΔϰ ≥ λ/2. Position measurements with uncertainty <λ/20 seem to be possible with all-optical techniques.

Anisotropic velocity-dependent vortex forces: two-level atoms in two-dimensional standing waves

We consider the velocity-dependent light pressure force on a two-level atom interacting with a two-dimensional nearly resonant standing-wave light field. We show that there can be anisotropic cooling-heating forces that will cool the atoms along one field axis while heating them along the perpendicular axis. The force is identified as a spontaneous vortex force associated with the local traveling-wave character of the two-dimensional field. We provide a simple interpretation of this anomalous force in terms of the interplay between the vortical momentum flow of the light field and a motion-induced population transfer between the ground and excited atomic states.

Quantum collapse and revival in the motion of a single trapped ion.

Within certain limits, the dynamics of a single trapped ion oscillating about the node of a standing-wave light field is described by the Jaynes-Cummings model, which is routinely used for cavity-QED experiments. We propose a technique to measure quantum collapse and revival in the population inversion of a single trapped ion, and show that this method is uniquely suited for the measurement of final temperatures of the trapped ion as well as for the analysis of nonclassical states of the ion motion, such as Fock and squeezed states. The results are discussed with particular consideration given to the effects of a finite laser bandwidth.

Theory of the light-force technique for measuring polarizabilities.

The theory of a method to measure electric-dipole polarizabilities is presented. The method uses two-stage laser ablation to produce a pulsed beam of atoms from a solid target. A pair of slits makes the velocity distribution of the atomic beam nonuniform in a way that is well characterized. The light-force technique uses the polarization forces experienced by an atom in the intense, inhomogeneous electromagnetic field of a standing-wave laser to change the velocity distribution of the atomic beam. The large forces cause measurable Doppler shifts in the resonant frequency of the atoms. These frequency shifts change the amount of absorption of resonant light, yielding information about the change in the velocity distribution of the atoms. The detailed shape of the final absorption distribution is polarizability dependent. In the classical picture of the light force, the standing-wave [ital electric] field induces a time-varying dipole moment in each atom. Each atom then experiences a Lorentz force due to coherent interaction of the oscillating dipole moment with the time-varying [ital magnetic] field. The quantum-mechanical picture corresponds to the Kapitza-Dirac effect for atoms: an atom absorbs a photon from one of the two beams which form the standing wave, and is then stimulated tomore » emit this photon by the other, counterpropagating beam. This paper provides a classical treatment of the light force experienced by an atom in a standing-wave light field; the polarizability is treated quantum mechanically. The theory presented here can be applied to atoms with a scalar polarizability, such as rubidium, and to atoms with significant tensor components, such as uranium. Experimental results from application of the light-force technique to a measurement of the polarizability of rubidium are also presented.« less

"Dark" squeezed states of the motion of a trapped ion.

We propose a scheme for preparing coherent squeezed states of motion in an ion trap based on the multichromatic excitation of a trapped ion by standing- and traveling-wave light fields. The squeezed state is produced when the beat frequency between two standing-wave light fields is equal to twice the trap frequency, and is indicated by a ``dark resonance'' in the fluorescence emitted by the ion.

Deflection of resonant multilevel particles in a standing wave light field

We study the deflection of an atomic system with a resonant multilevel energy structure in classical and quantized wave light fields. We obtain that the shape of the momentum distribution is very sensitive to the energy level structure, whereas its moments are not. Comparison with a two-level case is made.

Numerical simulation of atomic diffraction in the Raman-Nath regime

The theory of atomic diffraction from a classical standing wave light field in the presence of spontaneous emission in the Raman-Nath regime was developed by Tanguy et al. [6]. We describe the basis of computationally efficient methods for performing calculations in this regime and show their agreement with recent experimental results of Gould et al. [4].

Atomic deflection in the transition between diffractive and diffusive regimes: A numerical simulation.

The transition between diffractive and diffusive regimes in the deflection of atoms by a standing-wave light field has recently been observed experimentally by Gould et al, [Phys. Rev. A 43, 585 (1991)]. We describe and present the results of a numerical simulation which allows these results to be understood in terms of the theory developed by Tanguy, Reynaud, and Cohen-Tannoudji [J. Phys. B 17, 4623 (1984)].