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arXiv:1401.7165 · Journal of the Korean Physical Society

Temperature and phase-space density of a cold atom cloud in a quadrupole magnetic trap

Surjya Prakash Ram, Satya Ram Mishra, S. K. Tiwari, H. S. Rawat

Published Aug 1, 2014• 4 citations
arXivHTMLPDF

Abstract

We present studies on modifications in the temperature, number density and phase-space density when a laser-cooled atom cloud from optical molasses is trapped in a quadrupole magnetic trap. Theoretically, for a given temperature and size of the cloud from the molasses, the phase-space density in the magnetic trap is shown first to increase with increasing magnetic field gradient and then to decrease with it after attaining a maximum value at an optimum value of the magnetic-field gradient. The experimentally-measured variation in the phase-space density in the magnetic trap with changing magnetic field gradient is shown to exhibit a similar trend. However, the experimentally-measured values of the number density and the phase-space density are much lower than the theoretically-predicted values. This is attributed to the experimentally-observed temperature in the magnetic trap being higher than the theoretically-predicted temperature. Nevertheless, these studies can be useful for setting a higher phase-space density in the trap by establishing an optimal value of the field gradient for a quadrupole magnetic trap.

DOI
10.3938/jkps.65.462

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We present studies on modifications in the temperature, number density and phase-space density when a laser-cooled atom cloud from optical molasses is trapped in a quadrupole magnetic trap. Theoretically, for a given temperature and size of the cloud from the molasses, the phase-space density in the magnetic trap is shown first to increase with increasing magnetic field gradient and then to decrease with it after attaining a maximum value at an optimum value of the magnetic-field gradient. The experimentally-measured variation in the phase-space density in the magnetic trap with changing magnetic field gradient is shown to exhibit a similar trend. However, the experimentally-measured values of the number density and the phase-space density are much lower than the theoretically-predicted values. This is attributed to the experimentally-observed temperature in the magnetic trap being higher than the theoretically-predicted temperature. Nevertheless, these studies can be useful for setting a higher phase-space density in the trap by establishing an optimal value of the field gradient for a quadrupole magnetic trap.
We present an investigation of the cesium magneto-optical trap, with particular regard to the best combination of atomic density and temperature that can be produced. Conditions in the trap depend on four independent parameters: the detuning and intensity of the light, the gradient of the magnetic field, and the number of atoms trapped. We have varied all these parameters and measured the temperature and density distribution of the trapped cloud. Both the nonlinear variation with position of the restoring force and the reabsorption of photons scattered in the cloud limit the maximum density, and we present an empirical model that takes this into account. This in turn limits the density in phase space \ensuremath{\rho} (defined as the number of atoms in a box with sides of one thermal de Broglie wavelength). We have observed a maximum \ensuremath{\rho}=(1.5\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$, with a spatial density of about 2\ifmmode\times\else\texttimes\fi{}1011{10}^{11}1011 atoms/cm3{\mathrm{cm}}^{3}cm3.
Sodium atoms have been loaded from a slowed beam into a dark magneto-optical trap which confines atoms mostly in the non-absorbing F=1 ground state. This method has allowed us to achieve samples of more than 10{sup 10} atoms with optical densities in excess of 150. Temperatures around 1.2 mK and densities around 10{sup 12} cm{sup -3} have been measured using weak probe absorption. At this density an elastic collisions rate is already approximately 100 Hz. Our goal is to reach the regime where the rate is high enough to allow evaporative cooling of the trapped sample enroute to Bose-Einstein Condensation, for which yet higher densities and lower temperatures are required. We report the current status of experiments underway to further increase the phase space density of the trapped atoms by cooling with polarization-gradient molasses and reloading them into a magnetic trap with a spherical quandrupole field.
 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 ( 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.
We have studied the temperature scaling laws for the conditions under which a cloud of trapped ^85Rb atoms in the sigma+/sigma- configuration makes the transition from the temperature-limited regime to the multiple-scattering regime. Our experimental technique for measuring temperature relies on measuring the ballistic expansion of the cloud after turning off the confining forces and imaging the cloud size as a function of time with two CCD cameras. In the transition regime, the temperature T is shown to depend on the number of atoms N and the peak density n as (T-T_0) proportional N^1/3 and as (T-T_0) proportional n^2/3, in a manner consistent with theoretical predictions. Here T_0 is defined as the equilibrium temperature of a low-density optical molasses. In the multiple-scattering regime we find that T proportional Omega^2/(delta Gamma), where Omega and delta are the Rabi frequency and the detuning of the trapping laser, respectively, and Gamma is the natural linewidth of the cycling transition. We have also measured the ratio of temperatures along the axial and radial directions of the magnetic field gradient coils and find that the temperature is isotropic only if the intensities of the three orthogonal trapping beams are equal, and that the ratio is generally independent of trapping laser intensity and magnetic field gradient. Finally we demonstrate a measurement of the gravitational acceleration precise to approximately 0.1% by tracking the center of the cloud during ballistic expansion.
We investigate the behavior of a cloud of atoms in a magneto-optical trap, which—after collection—is compressed when the field gradients of the trap magnetic field are increased. We measure sizes and shapes of the atom cloud as a function of laser detuning, magnetic field gradient, and number of trapped atoms. A transient density increase of more than an order of magnitude has been achieved. Moreover, reproducible Gaussian density distributions are observed at large detunings and intermediate magnetic-field gradients, permitting an accurate determination of density.
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.