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Journal of the Optical Society of America B

Technique for magnetic moment reconstruction of laser-cooled atoms using direct imaging and prospects for measuring magnetic sublevel distributions

Gehrig Carlse, Alexander Pouliot, Thomas Vacheresse, Adam C. Carew, Hermina C. Beica, Shoshana Winter, Anantharaman Kumarakrishnan

Published Mar 18, 2020• 10 citations
Publisher

Abstract

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.

DOI
10.1364/josab.388995

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•Jan 1, 1995•0 citations
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 discuss a simple time of flight technique for measurement of temperature of a cold cloud in a magneto-optical trap (MOT). The technique is based on spatiotemporal fluorescence imaging of the cloud that is allowed to undergo one-dimensional expansion in the presence of the orthogonal two-dimensional configuration of laser beams by temporal modulation of a pair of counterpropagating trapping beams in the MOT. We show that, in the time scale 0< or =t<5 ms, the expansion of the cloud is ballistic and the temperature can be extracted from the time variation of the rms size of the cloud in the expansion direction. The reliability of the technique has been established by comparing the results with release and recapture method, and also by fitting them to the known temperature scaling law.
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.
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 have studied velocity-selective resonances in the presence of a uniform magnetic field and shown how they can be used for rapid, single-shot assessment of the ground state magnetic sublevel spectrum in a cold atomic vapor. Cold atoms are released from a magneto-optical trap in the presence of a small bias magnetic field ( approximately 300 mG) and exposed to a laser field comprised of two phase-locked counterpropagating beams connecting the two ground state hyperfine manifolds. An image of the expanded cloud shows the velocity-selected resonances as distinct features, each corresponding to specific magnetic sublevel, in a direct, intuitive manner. We demonstrate the technique with both 87Rb and 85Rb, and show the utility of the technique by optically pumping into particular magnetic sublevels. The results are shown to agree with a theoretical model, and are compared to traditional Raman spectroscopy.
A detailed experimental and theoretical investigation of a magneto-optical trap for caesium atoms is presented. Particular emphasis has been placed on achieving high spatial number densities and low temperatures. Optimizing both of these together enables efficient evaporative cooling from a conservative trap, a procedure which has recently led to the first observations of Bose-Einstein condensation in a dilute atomic vapour. The behaviour of a magneto-optical trap is nominally determined by four independent parameters: the detuning and intensity of the light field, the magnetic field gradient and the number of trapped atoms. A model is presented which incorporates previous treatments into a single description of the trap that encompasses a wide range of its behaviour. This model was tested quantitatively by measuring the temperature of the cloud and its spatial distribution as a function of the four parameters. The maximum density was found to be limited both by the reabsorption of photons scattered within the cloud and by a reduction of the confining force at small light shifts. The nonlinear variation with position of the restoring force was found to be significant in limiting the number of atoms confined to a high density. A maximum density in phase space (defined as the number of atoms in a box with sides of dimension one thermal de Broglie wavelength) of (1.5 ± 0.5) x 10-5 was observed, with a spatial density of 1.5 x 1011 atoms per cm3. Cold collision losses from a caesium magneto-optical trap have been studied with the purpose of assessing their influence on spatial densities. In contrast to previous measurements of similar quantities, these measurements did not require the use of an ultra-low (< 10-10 Torr) background vapour pressure. The dependence of the cold collision loss coefficient β on the trapping intensity was measured to permit identification of the different cold collision processes. The largest loss rates observed were those due to hyperfine structure-changing collisions, with a coefficient β = (2±1) x 10-10cm3s-1. A study is presented of a modified magneto-optical trap in which a fraction of the population is shelved into a hyperfine level that does not interact with the trapping light. In this so-called "dark" magneto-optical trap, improved densities of nearly 1012cm-3 have been previously reported for sodium. The application of the technique to caesium is not straightforward due to the larger excited state hyperfine splittings. A simple theory for caesium is presented and its main predictions verified by measurements of density, number and temperature. A density of nearly 1012cm,-3 was indeed obtained but at a temperature substantially higher than in the conventional magneto-optical trap.