Standing-wave Laser Field Research Articles

Two-atom resonance fluorescence in running- and standing-wave laser fields.

Resonance fluorescence of two two-level atoms driven by a coherent laser field propagating parallel to the interatomic axis is examined, taking into account the dipole-dipole interaction. We show that the number of peaks in the fluorescence intensity depends on the direction of observation with respect to the interatomic axis and on whether the system is driven by a standing-wave or a running-wave laser field. When the system is driven by the standing-wave field the fluorescence intensity shows two peaks and a dip for an observation direction perpendicular to the interatomic axis and three peaks in the direction parallel to it. When the system is driven by the running-wave field only two peaks are observed for the perpendicular direction. We explain these features in terms of the collective states of the system and show that the directional effect can be attributed to the fact that the antisymmetric state of the system does not radiate in the direction perpendicular to the interatomic axis. Photon statistics also demonstrate the directional effect for the standing-wave field. Frequency regimes are found where sub-Poissonian photon statistics occur. Depending on the direction of the observation, a state close to a Fock state can occur for one or two frequencies of the driving field, corresponding to zero-photon-number fluctuations or maximum sub-Poissonian behavior. The fluorescence spectrum is found to depend on the direction of observation and the interatomic separation. For small interatomic separations and a standing-wave driving field the spectrum exhibits seven lines for the perpendicular direction and 13 lines in the direction parallel to the interatomic axis. For the running-wave field the spectrum shows 13 lines independent of the direction of observation. Moreover, we show that for particular interatomic separations dark regimes appear in the spectrum. We discuss the effect of the dipole-dipole interaction on the dark states and explain the spectral features in terms of the dressed-atom model. We also consider the absorption spectrum of a weak probe beam illuminating the two-atom system. We show that apart from a weak dispersion structure, the spectrum shows large peaks as one of the atoms is moved to successive nodes of the field.

Quantum dynamics and cooling of atoms in one-dimensional standing-wave laser fields: Anomalous effects in Doppler cooling.

We report computational results for the time evolution of the velocity distribution P(V,t) for two-level and multilevel ``Doppler'' laser cooling. We compare results obtained from the semiclassical (SC) Fokker-Planck equation and from generalized optical Bloch equations applied to density matrices over a basis of products of internal and quantized translational states (QDM). Computer memory requirements are optimized to make large-scale QDM calculations feasible. QDM and SC agree well except for two cases: (a) atoms in the wells of the light-shift potential (with kinetic energy less than the well depth, ${\mathit{U}}_{0}$), and (b) atoms with recoil energy ${\mathit{E}}_{\mathit{R}}$ comparable to or greater than the natural linewidth \ensuremath{\Elzxh}\ensuremath{\Gamma}. Transient dips occur in P(V,t) at V=0 in QDM results due to slow cooling of atoms in the light-shift potential wells. Dips in P(V,t) occur at velocity-tuned-resonance (Doppleron) velocities but disappear over long interaction times as atoms accumulate near points where the force is zero. When ${\mathit{E}}_{\mathit{R}}$\ensuremath{\approxeq}\ensuremath{\Elzxh}\ensuremath{\Gamma}, sharp peaks occur in P(V,T) at V=\ifmmode\pm\else\textpm\fi{}${\mathit{V}}_{\mathit{R}}$ from velocity-selective population quasitrapping not previously found in a two-level transition. Sharp features in P(V,t) occur also for J\ensuremath{\rightarrow}J+1 transitions with J>0, small ${\mathit{U}}_{0}$/${\mathit{E}}_{\mathit{R}}$, and sufficiently large detuning, from transitions between individual quantum states in the periodic potential.

Crystallization of dielectric spheres in laser standing wave field

Experimental study on crystallization of polystyrene spheres and SrTiO3 particles in laser standing wave field is presented. The diameter of polystyrene, which are able to be trapped, is 7 times smaller than that reported by Burns, the corresponding lattice constant is reduced to 1.5 μm. The crystallization effect of SrTiO3 particles with a refractive constant of 2.5 in the visible range is observed for the first time. Based on the results above we believe that it is possible to construct photonic crystal with lattice constant extended to visible wave range by this method.

Creating and probing subwavelength atomic gratings using spatially separated fields.

The interaction of an atomic beam with three spatially separated linearly polarized standing-wave fields is considered, taking into account the magnetic degeneracy and hyperfine splitting of the atomic levels. A spatial modulation of the ground-state density matrix occurs, and is not washed out as a result of spontaneous decay from the upper states. The interaction with fields separated by a distance L results in a focusing of harmonics at distances L'=(m/n)L, where m and n are integers; the period of the matter gratings is \ensuremath{\lambda}/2n, where \ensuremath{\lambda} is the wavelength of the radiation field. For a beam having angular divergence \ensuremath{\theta}, one can observe these higher harmonics independently from each other if L\ensuremath{\gg}\ensuremath{\lambda}/\ensuremath{\theta}. The gratings can be probed using a third standing-wave laser field in the focal plane of the harmonic under investigation. General expressions that allow one to calculate the probe absorption for atoms having arbitrary fine and hyperfine structure are derived. Explicit calculations for the alkali metals are presented. It is predicted that spatial modulations having periods 30--500 nm and modulation depths 2.5--50 % can be produced in this manner. The focusing of the spatial harmonics is interpreted in terms of a shadow effect.

THE MECHANICAL ACTION OF LASER LIGHT ON RYDBERG ATOMS

The momentum exchange between a standing wave laser field and an atomic center-of-mass is dominated by the internal dynamics of an atomic electron in the exciting laser field. Rydberg atoms are one of the simplest physical systems where the dependence of this radiative force on the electronic dynamics can be investigated in detail. The characteristics of the momentum transfer between an atomic center-of-mass and a standing wave laser field strongly depend on whether the “particle” or the “wave” aspect of the electronic dynamics prevail. In this review recent theoretical advances in the description of the mechanical action of laser light on Rydberg atoms are discussed. These advances have become possible by the application of semiclassical path integral techniques with respect to the electronic dynamics which clearly exhibit the “particle” and “wave” aspects of this momentum transfer.

Quantum field theory of interaction of ultracold atoms with a light wave: Bragg scattering in nonlinear atom optics.

A vector quantum field theory is developed to describe the interaction of an ultracold atomic ensemble with a laser field. The ultracold atomic ensemble is composed of either bosonic atoms or fermionic atoms. The photon exchanges between different ultracold atoms result in a long-range interatom interaction. Under appropriate conditions, such a many-body interaction leads to an effective ``Kerr-type'' nonlinearity of atomic waves. In terms of the nonlinearity, we construct a general formalism of nonlinear atom optics for an ultracold atomic beam. Applying the formalism to the diffraction of an ultracold atomic beam composed of bosonic atoms by a standing-wave laser field, we find that the many-body nonlinearity induces self-phase and cross-phase modulation of diffracted atomic waves. As a result, a standing-wave laser acts as a nonlinear atomic grating which diffracts atoms in the same way as a nonlinear periodic medium diffracts photons.

Effect of virtual Compton scattering on electron propagation in a laser field

Volkov wave functions describe the motion of an electron in a plane-wave laser field and are widely used in the treatment of multiphoton ionization and laser-assisted scattering. These functions are not applicable for fields of a more general type in which the various modes propagate in different directions. Recent work on the development of generalized Volkov solutions, applicable when the field is not a plane wave, is extended here to account for the effect of virtual Compton scattering involving photon pairs that transfer only a small amount of momentum. When such processes occur as initial- or final-state interactions in which the energy of the electron is nearly conserved, near degeneracies are introduced requiring special care in the solution of the wave equation. Methods for constructing approximate solutions that treat these effects accurately are described here for both nonrelativistic and relativistic wave equations. The solutions are used in an analysis of the Kapitza-Dirac effect---the scattering of an electron in a standing-wave laser field---and more general results are obtained than have been in earlier treatments of this problem. In a different class of applications, the generalized Volkov solutions are adopted in a study of the (relativistic) potential scattering of an electron in the presence of a two-mode laser field. A variational formulation, evaluated in the weak-field limit, is used to generate a low-frequency approximation for two-photon bremsstrahlung. A sum rule is derived that provides a simple relation between the true cross section and that obtained with the omission of virtual Compton scattering effects.

Kinetic effects of 3-13-photon velocity-tuned resonances investigated by a time-of-flight technique.

We have investigated the change in the transverse-velocity distribution of a beam of metastable argon atoms when crossed by an intense, near-resonant, standing-wave laser field. A time-of-flight technique that provides a better resolution at low velocity than the Doppler fluorescence technique used in earlier experiments has been utilized. The effect of 3--13-photon velocity-tuned (doppleron) resonances in the mean force acting on the atoms has been studied for various laser-frequency detunings and truncations of a Gaussian light beam. The experimental results have been compared with semiclassical laser cooling theory.

Laser-Focused Atomic Deposition

The ability to fabricate nanometer-sized structures that are stable in air has the potential to contribute significantly to the advancement of new nanotechnologies and our understanding of nanoscale systems. Laser light can be used to control the motion of atoms on a nanoscopic scale. Chromium atoms were focused by a standing-wave laser field as they deposited onto a silicon substrate. The resulting nanostructure consisted of a series of narrow lines covering 0.4 millimeter by 1 millimeter. Atomic force microscopy measurements showed a line width of 65 +/- 6 nanometers, a spacing of 212.78 nanometers, and a height of 34 +/-+ 10 nanometers. The observed line widths and shapes are compared with the predictions of a semiclassical atom optical model.

Correlation-function approach to the momentum diffusion of atoms moving in standing waves.

We consider the momentum diffusion of atoms moving in a standing-wave laser field. We show how the correlation-function approach as originally applied to atoms at rest can be generalized to derive the velocity dependence of the momentum diffusion coefficient in standing waves, and that it gives results in agreement with the transport-equation approach to laser cooling. As an example we apply our calculations to determine the achievements of laser cooling in intense fields where cooling may occur around a nonvanishing velocity. Here we obtain temperatures which are 30% lower than the corresponding minimum obtained around zero velocity. Our explicit calculations involve usage of the optical Bloch equations, the quantum regression theorem, and the matrix continued-fraction method.

Separation and superposition of atomic wave packets by reflection and transmission by an optical ripple mirror.

In this paper, we investigate the reflection and transmission of an atomic wave by an optical ripple mirror which may be realized by a standing-wave laser field. We show that the ripple mirror can operate as a separator of the incident atomic waves corresponding to different internal states by reflection and transmission. For different laser parameters, the atomic ripple mirror can reflect one linear combination of two ground states and transmit the orthogonal linear combination. The transmitted superposition state corresponds to the well-known ``dark'' state. The atomic wave function is a coherent superposition of reflected and transmitted waves entangled with different internal states.

Momentum diffusion of atoms moving in laser fields

The momentum diffusion coefficient, as a function of position and velocity, is discussed for two-state atoms travelling through a standing-wave laser field. Equations leading to the force and diffusion coefficient have been obtained by Minogin. The authors present an alternative derivation, based on moments of the Wigner function and give numerical solutions in terms of matrix continued fractions. In strong fields, the discussion is supplemented by a derivation of the diffusion coefficient within the dressed-atom basis, and a picture of the diffusion mechanism emerges which is quite different from the one at low intensities. Calculated forces and diffusion coefficients are used in a Fokker-Planck equation to obtain stationary atomic velocity distributions.

Spontaneous emission in the near-resonant kapitza-dirac effect

We study the influence of spontaneous emission on atom diffraction by a standing wave laser field. We characterize, analytically, the major regimes of the near-resonant Kapitza-Dirac effect and study, numerically, the influence of spontaneous emission. In particular, we discuss in some detail two important classes of two-beam resonances which are major candidates to develop effective atom beam splitters, the so-called Bragg and Doppleron resonances.

The force on atoms in intense standing wave laser fields: dipole force with doppleron structure

The dressed atom approach is used to investigate the evolution of atoms moving in an intense standing wave laser field. When coherences between the dressed states can be neglected, a simple expression is obtained for the radiative force acting on the atoms. The Landau-Zener model, well-known in the theory of slow atomic collisions, is here used to include coherences in an analytic treatment. At high velocities, where the simplest approach breaks down, the results are in good agreement with exact numerical calculations. Applications outside the field of laser cooling are discussed.

Dynamical localization of atomic-beam deflection by a modulated standing light wave.

The deflection of an atomic beam passing a standing-wave laser field in front of an oscillating mirror occurs by chaotic diffusive momentum transfer in a classical description and, as we show, is limited by dynamical localization quantum mechanically. An experiment to observe this quantum effect in an atomic beam is proposed.

Laser cooling in a squeezed vacuum

In this paper, the use of squeezed light in laser cooling is investigated. We find that in a traveling-wave laser field, a two-level atom in a squeezed vacuum cannot be cooled to a lower temperature than in normal vacuum. For a two-level atom in a standing-wave laser field, if it is tuned from the resonant region, the conclusion is the same as in the traveling-wave case. However, near the resonant region, the atom in a standing-wave field can achieve a lower temperature than Doppler limit.

Slowing and cooling an atomic beam using an intense optical standing wave.

We have demonstrated a new slowing and cooling technique which uses a standing-wave laser field collinear with a thermal Na atomic beam to produce a continuous supply of slow atoms, with most probable velocities ranging from -40 to + 80 m/sec. The velocity spread can be \ensuremath{\sim}10 m/sec (150 mK), the density ${>10}^{8}$, and the peak density in phase space \ensuremath{\sim}100 times that at the peak of the original Maxwell-Boltzmann distribution.

Deflection of barium atoms by a standing-wave light field

Experimental results are reported for the deflection of barium atoms from a collimated atomic beam (divergence⩽0.35 mrad) at nonorthogonal incidence to a standing-wave laser field. A deflection along the axis of the standing-wave laser cavity was observed, which is proportional to the average velocity-dependent light pressure force projected along the propagating direction of the laser light field. These results demonstrate that cooling and heating of atoms along the propagating direction of laser field depend not only on frequency detuning from resonance but also on the initial velocity in the direction of the laser light field.

Asymmetric line shapes for weak transitions in strong standing-wave fields.

We have observed the resonance line shape for a very weak atomic transition excited when an atomic beam intersects a strong standing-wave laser field. The line shape has a dramatic intensity-dependent distortion which is Doppler free and independent of the excitation rate. We have calculated the line shape predicted by optical Bloch equations that include a spatially varying ac Stark shift, and find good agreement with our experimental results.

Ultrahigh-resolution two-photon optical Ramsey spectroscopy of an atomic fountain.

We present a semiclassical analysis of ultrahigh-resolution two-photon optical Ramsey spectroscopy of cold neutral atoms falling freely in a fountain. Considering atoms which interact with the same standing-wave laser field twice on their parabolic trajectories and averaging over a broad atomic velocity distribution, we predict a nearly Lorentzian line shape whose width is just the natural linewidth. We have investigated a number of systematic corrections to the atomic resonance frequency, including first-order and second-order Doppler shifts, gravitational red shifts, and ac Stark shifts. First-order Doppler shifts due to vertical motion cancel even if the counterpropagating beams are slightly misaligned, and resolutions below 1 Hz appear feasible with a fountain of modest dimensions.