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Physical Review A

Quantum reflection engineering: The bichromatic evanescent-wave mirror

Robin Côté, B. Segev

Published Apr 22, 2003• 20 citations
Publisher

Abstract

We explore the design of atom-optic components, such as mirrors, to manipulate ultracold atoms. We show that it is possible to enhance significantly quantum effects by engineering sharp features in the interaction potential between atoms and the component. We illustrate the concept by calculating the reflection probability for ultracold sodium atoms incident on a bichromatic evanescent-wave atomic mirror created by lasers red and blue detuned from resonance with intensities and detunings chosen to enhance quantum reflection of a purely attractive potential. With realistic parameters for sodium atoms incident on glass at 10 cm/s, up to 30% reflection can be obtained.

DOI
10.1103/physreva.67.041604

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We explore the design of atom-optic components, such as mirrors, to manipulate ultracold atoms. We show that it is possible to enhance significantly quantum effects by engineering sharp features in the interaction potential between atoms and the component. We illustrate the concept by calculating the reflection probability for ultracold sodium atoms incident on a bichromatic evanescent-wave atomic mirror created by lasers red and blue detuned from resonance with intensities and detunings chosen to enhance quantum reflection of a purely attractive potential. With realistic parameters for sodium atoms incident on glass at 10 cm/s, up to 30% reflection can be obtained.
We calculate the reflection probability for ultracold atoms incident on an evanescent-wave atomic mirror, and analyze the optimum conditions to observe quantum reflection. We find that averaging over the Gaussian profile of the laser beam dramatically reduces the quantum signature, and consider the effects of an appropriate aperture that limits the variation of beam intensity. We show that quantum reflection is particularly sensitive to details of the atom-surface potential, and could be used to resolve retardation effects.
We show that an attractive potential created by an evanescent wave quantum mechanically reflects an atom with nonzero probability if the atom’s incident de Broglie wavelength is larger than the decay length of the evanescent wave. The amplitude reflection coefficient is calculated by use of an analytical solution of the corresponding Schrödinger equation. We also discuss electromagnetic wave analog of the effect, the partial reflection of light at an exponentially increasing index. We interpret the quantum reflection in terms of a virtual turning point, by means of a complex stationary phase approximation. If the potential remains exponential until it becomes as deep as several hundred recoil energies, the reflection coefficient for a low-energy de Broglie wave is independent of the details of the potential far from the virtual turning point. This means that, if the evanescent wave is strong enough, interactions between the atom and the glass surface at which the evanescent wave is created can be neglected.
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.
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.
We describe the interaction of an ultracold diatomic polar molecule with an evanescent-wave mirror. Several features of this system are explored, such as the coupling between internal rovibrational states of the molecule and the laser field. Numerical simulations show quantum reflection and state selection under attainable physical conditions. Such molecular optics components will facilitate the manipulation and trapping of ultracold molecules, and might serve in future applications in several fields, e.g., as devices to filter and select a state for ultracold chemistry, to measure extremely low temperatures of molecules, or to manipulate states for quantum information processing.