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Atomic motion in longitudinally modulated light crystals

S. Meneghini, Igor Jex, K. A. H. van Leeuwen, M.R. Kasimov, Wolfgang P. Schleich, Yakovlev, VP

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

We study the dynamics of atomic waves in longitudinally modulated light crystals using an effective complex potential with time (space) dependent detuning. In the weak coupling regime we predict a sharp asymmetry of the scattering probability near the Bragg angle. In the strong coupling case we introduce the concept of a light crystal with "complex kick." We have found that the initially blue detuned crystal is much more transparent for atomic waves. Moreover, the probability distribution of the outgoing wave shows carpetlike interference structure.

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Physical Review A•Mar 1, 1993•27 citations
We study the dynamics of atomic waves in longitudinally modulated light crystals using an effective complex potential with time (space) dependent detuning. In the weak coupling regime we predict a sharp asymmetry of the scattering probability near the Bragg angle. In the strong coupling case we introduce the concept of a light crystal with "complex kick." We have found that the initially blue detuned crystal is much more transparent for atomic waves. Moreover, the probability distribution of the outgoing wave shows carpetlike interference structure.
We study the dynamics of atomic waves in a two-dimensional light crystal formed by two crossed standing laser fields. The longitudinal modulation of the crystal with the Doppler frequency significantly influences the transversal spatial modulation of the atomic wave. Near the doppleron resonance the atomic density shows a fractional space period. In this case a normally incident wave gives rise to an almost perfect conversion into the first momentum components and the light crystal acts as a highly efficient beamsplitter. The crossing angle, determining the Doppler frequency, is the easy-to-control parameter of the system.
Bragg diffraction of atoms at thick standing light waves requires that the wave-matching condition is fulfilled. This usually means that the atomic beam crosses the light wave exactly at the Bragg angle. Nevertheless, our experiments also demonstrate Bragg diffraction at detuned angles if the amplitude of the standing light wave is temporally modulated with an appropriate frequency. If, on the other hand, the phase of the light wave is modulated no diffraction is observed. Both modulation processes produce frequency sidebands which set up `slowly travelling standing waves' in front of a retro-reflection mirror. Atoms are diffracted at these `almost standing' light waves in a similar way to photons at the travelling sound waves in an acousto-optic modulator. The frequency of the diffracted de Broglie waves is assumed to be shifted by the intensity modulation frequency. The different results using amplitude- and phase-modulated light waves are due to interference between the diffraction contributions of the individual frequency sidebands contained in the standing light wave.
The diffraction of a coherent, stationary, beam of atoms from a standing wave of light is considered. Particular attention is paid to long interaction times for which the motion of the atoms inside the light field must be taken into account. This is the regime of dynamical diffraction, and is treated within the framework of a set of differential difference equations due to Raman and Nath. The popular Raman-Nath approximation, in which the kinetic energy imparted to the atoms by the light wave is ignored, is no longer valid and the full equations must be solved. When the interaction between the atoms and the light is very weak then few beams are produced. To describe spontaneous emission from the atom one can invoke a complex potential as a model for dissipation. If the atom beam is obliquely incident one finds anomalously high transmission close to the Bragg angles which is the physical manifestation of degeneracies in non-Hermitian matrices. The classical limit is approached when the atom-light interaction is strong, producing many beams. The classical dynamics (geometrical rays) reveal that the farfield intensity pattern is dominated by caustics. These proliferate with increasing interaction distance. Two methods are presented for analytically treating the semiclassical limit of the wave mechanics. The first begins with W.K.B. solutions to the continuised Raman-Nath equations. Mapping onto parabolic cylinder functions removes the spurious divergences of the W.K.B. solutions, giving eigenvectors which are uniformly valid for all scattering angles and may be summed to give the wavefunction. The second method transforms the original W.K.B. eigensum, using the Poisson summation formula, giving a new sum, each term of which has classical significance. This method shows that wave theory decorates the classical caustics with an Airy function intensity profile, as predicted by catastrophe theory.
Temporal light modulation methods which are of great practical importance in optical technology, are emulated with matter waves. This includes generation and tailoring of matter-wave sidebands, using amplitude and phase modulation of an atomic beam. In the experiments atoms are Bragg diffracted at standing light fields, which are periodically modulated in intensity or frequency. This gives rise to a generalized Bragg situation under which the atomic matter waves are both diffracted and coherently shifted in their de Broglie frequency. In particular, we demonstrate creation of complex and non-Hermitian matter-wave modulations. One interesting case is a potential with a time-dependent complex helicity $[V\ensuremath{\propto}\mathrm{exp}(i\ensuremath{\omega}t)],$ which produces a purely lopsided energy transfer between the atoms and the photons, and thus violates the usual symmetry between absorption and stimulated emission of energy quanta. Possible applications range from atom cooling over advanced atomic interferometers to a new type of mass spectrometer.
Superradiance has drawn increasing interest, motivated by the development of quantum technology. In general, a large number of atoms are favored for inducing a strong superradiance. However, our analytical and numerical calculations of light scattering from an atomic grating longitudinally pumped by a laser show that when the atom number is small, superradiant light scattering (SLS) is induced, that is, the reflected light intensity is proportional to the square of the atom number, whereas the SLS is saturated with the increase in the atom number. In our calculation, using the coupled-wave theory, we treat the atomic grating as a dynamical photonic crystal and find rich time-dependent optical properties due to collective atomic recoil motion, which is available within research under current experimental condition. Thus, our paper could also spark an investigation of the optical features of tunable photonic crystals in the time domain.
We have investigated the effect of the dipole force and its fluctuation on the motion of Li atoms in an intense, one-dimensional, near-resonant standing light wave. The duration of the interaction of the atoms with the standing wave was varied from several tens of spontaneous-emission lifetimes to several hundreds. For a standing-wave frequency blue detuned from resonance, diffusive heating can dominate the time-averaged dissipative dipole force so that there is no steady-state momentum distribution. However, for sufficiently large blue detunings, the rate of diffusion is so slow that the resulting distribution approaches a quasisteady state. For red detunings, the diffusion is balanced with the force and a true steady state is achieved. We apply a Monte Carlo method based on the density-matrix equations in the dressed-state representation to simulate the atomic motion. The dynamics of atom channeling is discussed.