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Journal of Physics B Atomic Molecular and Optical Physics

Atom optics with magnetic surfaces: II. Microscopic analysis of the `floppy disk' mirror

Ifan G. Hughes, P A Barton, Timothy Roach, Edward A. Hinds

Published May 14, 1997• 46 citations
Publisher

Abstract

In a recent experiment we studied cold rubidium atoms bouncing on a magnetic mirror made from a flexible computer disk with sinusoidal magnetization. The motion was well described by a model in which the mirror was a perfect specular reflector, but complete agreement with the data required the reflecting surface to be slightly corrugated. Here we explore the physical origins of the corrugation both theoretically and experimentally. First, we develop a theory relating the reflecting force on the atoms to the magnetization of the mirror, taking into account the finite thickness of the magnetic film. We find that if the signal on the floppy disk is not harmonic the atoms appear to have been reflected from a corrugated surface, as observed in our recent experiment. Next, we describe magnetic force microscope measurements which allow us to determine the distortion on the disk and hence to quantify its effect on the reflected atoms. We show that recording nonlinearity is indeed a major cause of the mirror roughness. We also consider other sources of roughness and identify an important effect associated with the boundaries between recorded tracks. Agreement between our experiment and theory suggests that we have identified the limiting factors in a real atom-optical element made from a floppy disk. At present the angular resolution of the mirror is approximately 35 mrad for atoms dropped from a height of 4 cm. We discuss how this can be improved to reach a level of 5 mrad or better.

DOI
10.1088/0953-4075/30/9/013

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In a recent experiment we studied cold rubidium atoms bouncing on a magnetic mirror made from a flexible computer disk with sinusoidal magnetization. The motion was well described by a model in which the mirror was a perfect specular reflector, but complete agreement with the data required the reflecting surface to be slightly corrugated. Here we explore the physical origins of the corrugation both theoretically and experimentally. First, we develop a theory relating the reflecting force on the atoms to the magnetization of the mirror, taking into account the finite thickness of the magnetic film. We find that if the signal on the floppy disk is not harmonic the atoms appear to have been reflected from a corrugated surface, as observed in our recent experiment. Next, we describe magnetic force microscope measurements which allow us to determine the distortion on the disk and hence to quantify its effect on the reflected atoms. We show that recording nonlinearity is indeed a major cause of the mirror roughness. We also consider other sources of roughness and identify an important effect associated with the boundaries between recorded tracks. Agreement between our experiment and theory suggests that we have identified the limiting factors in a real atom-optical element made from a floppy disk. At present the angular resolution of the mirror is approximately 35 mrad for atoms dropped from a height of 4 cm. We discuss how this can be improved to reach a level of 5 mrad or better.
We have demonstrated that a suitably magnetized surface can be used to retroreflect cold atoms for applications in atom optics. This has some advantages relative to evanescent wave mirrors because no light is involved. Multiple bounces of cold rubidium atoms have been observed for times up to 1 s in a trap formed by gravity and a 2 cm diameter spherical mirror made from a flexible computer disk (`floppy disk'). We have studied the dynamics of the atoms bouncing in this trap from several different heights up to 40.5 mm and we conclude that the atoms are reflected specularly and with reflectivity 1.01(3). The performance of this mirror is limited at present by collisions with the background gas and by unwanted harmonics in the magnetization of the surface. This is the first in a series of papers concerning the use of magnetized surfaces in atom optics.
Multiple bounces of cold rubidium atoms have been observed for times up to one second in a trap formed by gravity and a 2 cm-diameter spherical mirror made from a sinusoidally magnetized floppy disk. We have studied the dynamics of the atoms bouncing in this trap from several different heights up to 40.5 mm and we conclude that the atoms are reflected specularly and with reflectivity 1.01(3). Slight roughness of the mirror is caused by harmonics in the magnetization of the surface and by discontinuities at the boundaries between recorded tracks. As the next step in this atom optics program we propose using a magnetic mirror to create a 2D atomic gas. We discuss how cold atoms can be loaded into the ground state of a static magnetic potential well that exists above the surface of the mirror as a consequence of the intermediate-field Zeeman effect.
For the last decade it has been possible to cool atoms to microkelvin temperatures (~1 cm s -1 ) using a variety of optical techniques. Light beams provide the very strong frictional forces required to slow atoms from room temperature (~500 m s -1 ). However, once the atoms are cold, the relatively weak conservative forces of static electric and magnetic fields play an important role. In our group we have been studying the interaction of cold rubidium atoms with periodically magnetized data storage media. Here we review the underlying principles of the forces acting on atoms above a suitably magnetized substrate or near current-carrying wires. We also summarize the status of experiments. These structures can be used as smooth or corrugated reflectors for controlling the trajectories of cold atoms. Alternatively, they may be used to confine atoms to a plane, a line, or a dot and in some cases to reach the quantum limit of confinement. Atoms levitated above a magnetized surface can be guided electrostatically by wires deposited on the surface. The flow and interaction of atoms in such a structure may form the basis of a new technology, `integrated atom optics' which might ultimately be capable of realizing a quantum computer.
We have measured the magnitude and roughness of the reflecting potential produced by a current-carrying magnetic mirror from which cold rubidium atoms have been bounced at normal incidence. By varying the current in the mirror, a study of the potential barrier from which the atoms in different magnetic substates bounce has been made. A combination of time-of-flight and imaging techniques allowed us to study the roughness of the reflecting potential. We have demonstrated that the observed roughness can be reduced by additional wires to compensate for the finite-size effects, and by careful control of the direction of the magnetic bias field.
We have demonstrated that cold atoms can be retroflected from a ferromagnetic surface by the Stern-Gerlach effect. When the surface is magnetized periodically, the reflectivity for suitably polarized atoms is $(94\ifmmode\pm\else\textpm\fi{}8)%$ and the reflection is specular. A demagnetized surface is also highly reflecting but the reflections are diffuse. These magnetic processes are of interest for atom optics because they permit the manipulation of cold atoms without the use of laser beams. In our experiments, Rb atoms released from a magneto-optic trap (MOT) fall under gravity until they are reflected, after which they are recaptured in the MOT. Multiple bounces of these atoms have been studied for times up to 600 ms.
We have imaged an $18\ensuremath{\mu}\mathrm{K}$ cloud of 85Rb{}^{85}\mathrm{Rb}85Rb atoms bouncing freely on a horizontal, concave magnetic atom mirror (radius of curvature RRR). A high-quality image is observed even after 14 reflections. Initially compact, the cloud is alternately collimated (odd bounces) and brought back to a focus (even bounces) when dropped from a height R/4R/4R/4. This multiple reconstruction of a thermally expanding cloud hinges on the microscopic reversal of the atomic motion. We discuss the factors limiting the resolution of the mirror and describe the method of construction.