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Physical Review Letters

Quantum superpositions of atomic de Broglie waves by an atomic mirror

Weiping Zhang, Daniel F. Walls

Published Jun 1, 1992• 12 citations
Publisher

Abstract

We consider the reflection of de Broglie waves for a three-level atom from an atomic mirror using the evanescent wave at a vacuum dielectric interface. We show that in addition to state-selective reflection the atomic mirror in the near-field region can reflect the atom in a coherent superposition of different internal states entangled with different center-of-mass motion.

DOI
10.1103/physrevlett.68.3287

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We consider the reflection of de Broglie waves for a three-level atom from an atomic mirror using the evanescent wave at a vacuum dielectric interface. We show that in addition to state-selective reflection the atomic mirror in the near-field region can reflect the atom in a coherent superposition of different internal states entangled with different center-of-mass motion.
A detailed theoretical investigation of the reflection of an atomic de Broglie wave at an evanescent wave mirror is presented. The classical and the semiclassical descriptions of the reflection process are reviewed, and a full wave-mechanical approach based on the analytical soution of the corresponding Schrödinger equation is presented. The phase shift at reflection is calculated exactly and interpreted in terms of instantaneous reflection of the atom at an effective mirror. Besides the semiclassical regime of reflection describable by the WKB method, a pure quantum regime of reflection is identified in the limit where the incident de Broglie wavelength is large compared to the evanescent wave decay length.
The diffraction theory of a reflection grating for atoms based on a standing light wave is developed in a particular dressed-state approximation. The basis states take into account internal and external atomic degrees of freedom simultaneously and correspond to diffraction orders in the asymptotic region. In this basis the atom is described as an effective multilevel system. In an adiabatic approximation for the motion perpendicular to the grating, these levels serve as position-dependent potentials. An incoming de Broglie wave is coupled to higher diffraction orders by nonadiabatic transitions near avoided crossings of the potentials. Numerical results confirm the qualitative predictions following from the physical picture of the diffraction process and lead to an improved description of experiments.
We propose atom mirror schemes for a three-level atom of Λ-type interacting with two evanescent fields, which are generated as a result of the total internal reflection of two coherent Gaussian laser beams at the interface of a dielectric prism with vacuum. The forces acting on the atom are derived by means of optical Bloch equations, based on the atomic density matrix elements. The theory is illustrated by setting up the equations of motion for 23Na atom. Two types of excited schemes are examined, namely the cases in which the evanescent fields have polarization types of and . The equations are solved numerically and we get results for atomic trajectories for different parameters. The performance of the mirror for the two types of polarization schemes is quantified and discussed. The possibility of reflecting atoms at pre-determined directions is also discussed.
Cesium atoms prepared in a state of well-defined total energy have been reflected from a vibrating mirror, causing the matter waves to be phase modulated. The mirror is an evanescent light wave whose intensity is modulated in time at a frequency $\ensuremath{\nu}$ in the range 0 to 2 MHz; the atoms are reflected at normal incidence. The resulting beam consists of a ``carrier'' plus various sidebands corresponding to de Broglie waves propagating at different velocities. The precision and flexibility of this technique make it a promising tool in atom optics.
In the reflection of atoms by evanescent wave the amplitude of the light field can be changed not necessarily adiabatically slow in comparison with relaxation of internal atomic motion. An approach to describe the reflection of atoms by evanescent wave is the dressed state picture. An atomic mirror can be formed also by a focused elliptical laser beam, in which atoms intersect near the waist of the laser beam. A simple evanescent wave allows one to create a high homogeneous field along the surface of an atomic mirror, without a limitation on the intensity of the field in an evanescent wave. The size of an atomic mirror is usually restricted by the laser intensity required by the reflection. There are several processes at the reflection of atom by light which could lead to non ideal properties of the mirror. One of the remarkable properties of an atomic mirror is its ability to reflect atoms in a certain quantum state.
Cook and Hill suggested that the gradient of an optical field can be used to reflect atoms. To reflect atoms, the repulsive dipole force is used, which comes from the interaction between the electric dipole moment of atoms and the evanescent field. The evanescent wave is generated when light is totally reflected internally at the interface of different refractive indices. Later, the way to enhance the evanescent wave with a thin dielectric waveguide has been reported. We designed the atomic mirror for silicon atoms, whose structure enhances the evanescent field that is used to repel silicon atoms. We also set up the equations of motion for silicon atoms and derive trajectories of the atoms reflected by the atomic mirror. Optical intensity, incident angle of the light, and effective detuning are described in terms of controlling the trajectory of the atom.