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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Imaging of phase-space evolution of trapped atoms

Dmitry Strekalov, Andrey V. Turlapov, Anantharaman Kumarakrishnan, Andreas Karpf, Tycho Sleator

Published Jul 19, 1999• 0 citations
Publisher

Abstract

Experimental results on phase-space imaging of a laser- cooled atomic cloud are presented. Both position and velocity information are encoded in the frequency of the signal coherently radiated from the cloud. This encoding is achieved by application of a position-dependent magnetic field. Fourier transformation of the signal yields a projection of the phase-space density of the atoms. Imprinting a structure on the cloud we observe its time `sheering' evolution in the phase-space. Since the projection direction is determined by the imposed field gradient, we can reconstruct the phase-space structure of the cloud.

DOI
10.1117/12.354727

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Experimental results on phase-space imaging of a laser- cooled atomic cloud are presented. Both position and velocity information are encoded in the frequency of the signal coherently radiated from the cloud. This encoding is achieved by application of a position-dependent magnetic field. Fourier transformation of the signal yields a projection of the phase-space density of the atoms. Imprinting a structure on the cloud we observe its time `sheering' evolution in the phase-space. Since the projection direction is determined by the imposed field gradient, we can reconstruct the phase-space structure of the cloud.
Experimental results on phase-space imaging of a laser- cooled atomic cloud are presented. Both position and velocity information are encoded in the frequency of the signal coherently radiated from the cloud. This encoding is achieved by application of a position-dependent magnetic field. Fourier transformation of the signal yields a projection of the phase-space density of the atoms. Since the projection direction is determined by the imposed field gradient, we can reconstruct the phase-space structure of the cloud and trace its time evolution.
We describe a simple time-of-flight technique for measuring the magnetic moment of an optically pumped magneto-optical trap. The technique relies on free-expansion imaging of a cold atom cloud in a small magnetic field gradient without the need to detect spatial separation between magnetic sublevels. We find that the effective acceleration of the cloud can be used to characterize extreme state optical pumping. In the general case, we show that the integrated displacement of the falling cloud can be accurately modeled using rate equation simulations of magnetic sublevel populations, and knowledge of local magnetic fields, field gradients, and light intensities. The agreement between the model and the data allows the reconstruction of magnetic moments and suggests that this technique may be suitable for the measurement of population distributions over a range of optical pumping conditions.
We present a simple review of the basic physical processes allowing one to control, with laser beams, the velocity and the position of neutral atoms. The control of the velocity corresponds to a cooling of atoms, that is, a reduction of the atomic velocity spread around a given value. The control of the position means a trapping of atoms in real space. The best present performances will be given, in terms of the lowest temperatures and the highest densities. The corresponding highest quantum degeneracy will also be estimated. It is imposed by fundamental limits, which will be described briefly. We also give the general trends in this field of research and outline the new directions which look promising for observing quantum statistical effects in laser cooled atomic samples, but which are for the moment restricted by unsolved problems. Introducing the Simple Schemes The radiative forces acting on atoms in a light field can be split into two parts, a reactive one and a dissipative one. The dissipative force (radiation pressure), which basically involves scattering processes, is velocity dependent. We will see that this dependence leads to the Doppler cooling scheme and to the concept of optical molasses, and we will give the corresponding minimal achievable temperature. The dissipative force can be made position dependent, through a gradient of the magnetic field, so that the atoms are also trapped in the so-called magneto-optical trap.
A transparent polarisation-sensitive phase pattern changes the phase of transmitted light without absorption, whereas this change of phase depends on the polarisation of incident light. A position-localised polarisation-dependent phase pattern is imprinted onto the phase-space of atoms by using atomic state dependent velocity-selective hole burning. A phase-space localised pattern is a higher dimensional generalisation of patterns localised in the position-space. Such a pattern cannot be imaged with a lens. The imprinted pattern is localised in a unique three-dimensional subspace of the six-dimensional phase-space of atoms. The phase-space localised pattern transforms the polarisation of light transmitting through it. This pattern is tomographically imaged at room temperature by measuring the intensity of the transmitted imaging laser beam of variable frequency with a camera after its polarisation analysis. Two sub-tomographs of the imprinted phase-space localised pattern are constructed. This paper presents a concept and experiment of imprinting and imaging of a polarisation-sensitive phase pattern localised in the phase-space.
We demonstrate a technique for imaging magnetic fields using velocity-selective two-photon resonances in a cold atom cloud. Freely expanding (85)Rb atoms released from a magneto-optical trap are exposed to a brief (approximately 1 ms), off-resonant, retro-reflected laser pulse in a lin-perp-lin configuration. Two-photon resonance between magnetic sublevels occurs only for atoms in narrow velocity classes dependent on the magnetic field strength. The momentum of resonant atoms is altered by the pulse, and this two-photon momentum change is easily visible after further ballistic expansion. When the momentum pulse is applied to an atom cloud with finite size, magnetic field variations across the sample result in position-dependent features in images of the expanded cloud. We demonstrate the technique by imaging magnetic field variations over approximately 5 mm with approximately 250 microm spatial resolution.