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Journal of the Optical Society of America B

Quantum reflection of atoms from a periodic dipole potential

N. Friedman, Roee Ozeri, Nir Davidson

Published Jun 1, 1998• 21 citations
Publisher

Abstract

Quantum reflection of neutral atoms from a periodic far-detuned dipole potential is proposed and analyzed. This periodic atom mirror relies on constructive interference of small reflections from each cell to yield a high reflection coefficient even for very weak potentials. The reflected energy spectrum is calculated as a function of the potential height and the number of cells for both positive and negative potentials, and its relation to the reflection from one potential cell is derived. Two ways of increasing the reflection bandwidth, one based on changing the envelope of the potential and the other on changing its period gradually (chirp), are investigated. The phase of the reflected atoms and its dependence on experimental parameters are calculated, as well as the interaction time of the atoms with the potential and the spontaneous-emission rate during the reflection. Finally, it is shown that atoms with velocities of a few tens mm/s can be coherently reflected from a negative periodic potential with readily available laser diodes.

DOI
10.1364/josab.15.001749

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Quantum reflection of neutral atoms from a periodic far-detuned dipole potential is proposed and analyzed. This periodic atom mirror relies on constructive interference of small reflections from each cell to yield a high reflection coefficient even for very weak potentials. The reflected energy spectrum is calculated as a function of the potential height and the number of cells for both positive and negative potentials, and its relation to the reflection from one potential cell is derived. Two ways of increasing the reflection bandwidth, one based on changing the envelope of the potential and the other on changing its period gradually (chirp), are investigated. The phase of the reflected atoms and its dependence on experimental parameters are calculated, as well as the interaction time of the atoms with the potential and the spontaneous-emission rate during the reflection. Finally, it is shown that atoms with velocities of a few tens mm/s can be coherently reflected from a negative periodic potential with readily available laser diodes.
We propose a laser arrangement that can allow a multipeaked laser profile with periodicity of the order of the laser wavelength. We analyse the reflection properties of atoms dropped onto this periodical laser. This periodicity produces bands in the reflection spectrum of the atoms. We have studied the case of repulsive and attractive laser potential. In particular we prove the feasibility of constructing an atom mirror with an attractive potential, i.e. a potential without turning points. We include in our calculations the gravitational effects. The spontaneous emission is also analysed as a lossy mechanism, and we have proved that for sufficiently large detuning the bands remain.
All existing atomic mirrors are conceptually similar to metallic mirrors in standard optics in the sense that they are constructed with repulsive potentials and thus produce an imaginary ``refraction index.'' Here a different kind of mirror for atoms that is similar to a multilayer dielectric mirror in standard optics is proposed. We show that a periodic attractive laser potential can reflect atoms of certain momenta due to the presence of gaps in the spectrum of energies, as in the photonic band-gap structures in light optics. Spontaneous emission and gravitational effects are also analyzed.
A research project at the “Laboratoire d’électronique quantique” consists in a theoretical study of the reflection and diffraction phenomena via an atomic mirror. This poster presents the principle of an atomic mirror. Many groups in the world have constructed this type of atom optics experiments such as in Paris‐Orsay‐Villetaneuse (France), Stanford‐Gaithersburg (USA), Munich‐Heidelberg (Germany), etc. A laser beam goes into a prism with an incidence bigger than the critical incidence. It undergoes a total reflection on the plane face of the prism and then exits. The transmitted resulting wave out of the prism is evanescent and repulsive as the frequency detuning of the laser beam compared to the atomic transition δ = ωL−ω0 is positive. The cold atomic sample interacts with this evanescent wave and undergoes one or more elastic bounces by passing into backward points in its trajectory because the atoms’ kinetic energy (of the order of the μeV) is less than the maximum of the dipolar potential barrier ℏΩ2/Δ where Ω is the Rabi frequency [1]. In fact, the atoms are cooled and captured in a magneto‐optical trap placed at a distance of the order of the cm above the prism surface. The dipolar potential with which interact the slow atoms is obtained for a two level atom in a case of a dipolar electric transition (D2 Rubidium transition at a wavelength of 780nm delivered by a Titane‐Saphir laser between a fundamental state Jf = l/2 and an excited state Je = 3/2). This potential is corrected by an attractive Van der Waals term which varies as 1/z3 in the Lennard‐Jones approximation (typical atomic distance of the order of λ0/2π where λ0 is the laser wavelength) and in 1/z4 if the distance between the atom and its image in the dielectric is big in front of λ0/2π. This last case is obtained in a quantum electrodynamic calculation by taking into account an orthornormal base [2]. We’ll examine the role of spontaneous emission for which the rate is inversely proportional to the detuning δ and is responsible of the non specular aspect of the atomic reflection (atomic diffusion). In the contrary, we note that the specularity of the reflection preserve the coherence of the atomic wave packet. The atoms will constitute a probe of the rugosity of the prism surface which can be imperfect or super‐polished.
In order to further investigate the non-reciprocity of light propagation in the defective atomic lattices, and due to its effective application in designing novel photonic devices, such as all-optical diodes and isolators, which are powerful tools for information processing and quantum simulation, we innovatively propose to use the Fibonacci sequence to modulate the arrangement of empty lattice cells that form a quasi periodic defective atomic lattices. In the electromagnetically induced transparency window, the probe light is almost not absorbed under the control of a strong coupling field (see Fig. 1). The numerical simulation indicates that a wide nonreciprocal reflection band can be achieved by modulating the number of filled lattice cells, Fibonacci sequence, the period number in a single quasi period (see Fig. 2). These results provide more degrees of freedom for regulating nonreciprocal reflection with wide bandwidth and high contrast, and have potential applications in quantum computing and information processing.
In this thesis, the use of pulsed laser fields to control the center-of-mass motion of neutral atoms and molecules is studied both numerically and experimentally. In particular, we consider the use of a pulsed standing wave for the deflection of atomic beams, and develop novel types of mirrors for applications in atom and molecule optics. The research work shows that pulsed laser fields can be applied to form efficient mirrors for neutral particles regardless of the details of their internal energy-level structure. Moreover, it is shown that pulsed standing waves can also be utilized to efficiently deflect atomic beams. In the first part of the thesis, we study the effects of phase fluctuations of the laser field on the momentum distribution of atoms after interaction with a standing wave. Our numerical simulations show that the coherence properties of the laser field play a major role in diffraction of atoms, especially when using pulsed lasers. It turns out that the effects caused by the limited coherence time of the optical field are clearly observable as a transfer of atoms in momentum space to the region around zero momentum rather than to high momentum states. The numerical analysis of the pulsed standing-wave diffraction was complemented by experimental measurements of the deflection profiles of a beam of thermal sodium atoms. The experimental distributions were measured for a value of the coherence time intermediate between the Rabi period and the interaction time. A comparison of the results with an expected distribution calculated for a fully coherent interaction shows that the phase fluctuations of the light field drastically affect the achievable transverse momentum values. Based on our theoretical and experimental analysis of the diffraction profiles, we conclude that large deflection angles can be reached only when laser pulses with a Fourier-limited bandwidth are applied. The second part of the thesis concentrates on the development of pulsed mirrors for neutral atoms and molecules. In particular, we consider the use of an evanescent wave, formed in total internal reflection of light on a vacuum-dielectric interface, and of a standing wave as possible mirror configurations. Our numerical simulations of the pulsed evanescent-wave mirror show that atoms with initial velocities up to several tens of meters per second can be reflected already at the moderate field intensities of a few tens of MW/cm2. This allows pulsed evanescent waves to be applied in a compact setup to control the motion of thermal atomic beams, for which the traditional atom mirrors are suited only at grazing incidence. However, since the effective interaction volume of the atomic beam and the laser field is limited by the short decay length of the evanescent wave, only a relatively small number of atoms can be reflected with a single laser pulse. Furthermore, the reflection is always inelastic, since the force exerted on the atoms varies as a function of the initial position of the particles. To solve the above problem we consider the use of a standing wave as a pulsed mirror for atoms. Our numerical simulations show that with a proper choice of the pulse duration and field intensity, each period of the standing-wave pattern functions as an elastic mirror for particles with an initial kinetic energy below the depth of the standing-wave potential. Hence, the standing-wave pattern acts as a long row of independent atom mirrors, which provides a novel route to controlling large volumes of fast atoms even with a single laser pulse. As a second application for the pulsed standing-wave mirror we consider the reflection of slow molecules, for which no efficient mirror configuration previously has been available. It is shown that pulsed standing waves of nonresonant frequencies can be used to efficiently manipulate large volumes of rotationally cold molecules. With a suitable choice of the parameter values, the molecules can be reflected nearly elastically, or with a tailored momentum distribution. This opens up a possibility to use the pulsed standing-wave mirror to control the motion of particles in various applications of atomic and molecular physics. Such a mirror could be applied, for example, to steer and image molecular beams, separate molecular species, and to form pulsed molecular beams.