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Physical Review A

Magneto-optical trap operating on a magnetically induced level-mixing effect

K. A. Nasyrov, V. Biancalana, A. Burchianti, R. Calabrese, C. Marinelli, E. Mariotti, L. Moi

Published Jul 6, 2001• 10 citations
Publisher

Abstract

In this work we point out a theoretical picture accounting for some unpredicted trapping conditions that have been observed---but not satisfactorily explained---in the past and have been recently confirmed by our experiments. We have realized a sodium magneto-optical trap working on the ${3}^{2}{S}_{1/2}(F=1)\ensuremath{\rightarrow}{3}^{2}{P}_{3/2}{(F}^{\ensuremath{'}}=0)$ transition that, according to the usually accepted model, should not work. Our results, with respect to the previous unexplained observations, support more stringent conclusions because our experimental setup gives us the possibility to repump atoms from the $F=2$ state using ${D}_{1}$ transitions. This definitely excludes that the repumping frequency may play a role in the trap dynamics. A peculiar perturbation approach allows us to demonstrate that the confinement force originates, in this case, from a magnetically induced level-mixing effect. Moreover, we describe separately the nature of damping and confining forces and we recognize that in this case they are due to different transitions. Trap simulations based on a dynamical three-dimensional model are presented, which quantitatively reproduce our experimental results.

DOI
10.1103/physreva.64.023412

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In this work we point out a theoretical picture accounting for some unpredicted trapping conditions that have been observed---but not satisfactorily explained---in the past and have been recently confirmed by our experiments. We have realized a sodium magneto-optical trap working on the 32S1/2(F=1)\ensuremath→32P3/2(F\ensuremath′=0){3}^{2}{S}_{1/2}(F=1)\ensuremath{\rightarrow}{3}^{2}{P}_{3/2}{(F}^{\ensuremath{'}}=0)32S1/2​(F=1)\ensuremath→32P3/2​(F\ensuremath′=0) transition that, according to the usually accepted model, should not work. Our results, with respect to the previous unexplained observations, support more stringent conclusions because our experimental setup gives us the possibility to repump atoms from the F=2F=2F=2 state using D1{D}_{1}D1​ transitions. This definitely excludes that the repumping frequency may play a role in the trap dynamics. A peculiar perturbation approach allows us to demonstrate that the confinement force originates, in this case, from a magnetically induced level-mixing effect. Moreover, we describe separately the nature of damping and confining forces and we recognize that in this case they are due to different transitions. Trap simulations based on a dynamical three-dimensional model are presented, which quantitatively reproduce our experimental results.
The role of repumping in the magneto-optical trap (MOT) has often been seen as a necessary evil, requiring the introduction of either an electro-optical modulator or extra laser.1,2 However, repumping can be exploited to improve the performance of the MOT,3 or to study further the behavior of such a trap. We report results of a modified MOT using for repumping the D1 transitions 3S1/2 F = 1 to 3Pl/2 F = 1 and F = 2. Because these wavelengths are well displaced from the usual (D2) repump wavelengths, the direct repump influence on the trapping and cooling laser interaction should be significantly reduced. We also expect further possibilities for cold-atom spectroscopy within the MOT. The possibility of a dark trap with this repumping transition has been suggested.3
We present a rate equation model to account for the trapping mechanism in the sodium type-II magneto-optical trap (MOT). A key feature of the model is that excitation from the ground F=1 state to both excited states F∣IH{\mathrm{F}}^{|\mathrm{I}\mathrm{H}}F∣IH=1 and F∣IH{\mathrm{F}}^{|\mathrm{I}\mathrm{H}}F∣IH=0---possible in sodium because of the small excited state separation---is confirmed to be crucial in avoiding the optical pumping that otherwise inhibits steady-state trapping. Furthermore, we calculate that the mixed polarization typically present in a three-dimensional trapping arrangement gives substantially better one-dimensional trapping performance than pure circular polarization, and that the active role of repumping in the trapping process is important. The model is also applied to the type-I (F=2 to F∣IH{\mathrm{F}}^{|\mathrm{I}\mathrm{H}}F∣IH=3) MOT and comparisons are made with experiment in both cases. The possibility of blue-detuned Sisyphus cooling in the F=1 to F∣IH{\mathrm{F}}^{|\mathrm{I}\mathrm{H}}F∣IH=1 and 0 transition scheme is considered.
Our study indicates that the number of trapped Rb atoms in a magneto-optical trap (MOT) strongly depends on the trapping laser intensity and detuning, the repumping laser intensity and the magnetic gradient. We estimate the trapped-atom numbers changing with the trapping laser intensity and detuning, using a two-level system model. The theoretical results are in qualitative agreement with the experimental results. The experimental results also show an obvious dependence of the trapped-atom numbers on repumping laser intensity and the magnetic gradient, which the simple theory cannot account for. These studies are helpful for selecting suitable experimental parameters to achieve larger numbers of cold atoms.
The influence of the magnetic field gradient on the number of Cs atoms captured in a three-dimensional magneto-optical trap is investigated both theoretically and experimentally. Two one-dimensional models of the capture process are proposed, which differ only by the nature of the assumptions on the effect of Zeeman optical pumping. Transverse cooling beams are accounted for by a mere modification of the scattering rate. Comparison with experiment shows that the number of trapped atoms versus laser detuning, laser intensity, laser beam diameter and magnetic field gradient is best predicted by a model including all Zeeman substates of the Cs atoms. Quantitative agreement is within a factor of three in most cases of interest.
We have observed periodic structures of atoms when a bichromatic laser combination, with frequencies near the D1D1D1 and D2D2D2 lines, is used to produce a magneto-optical trap of sodium atoms. These periodic spatial distributions could not be explained on the basis of rectified force. Our interpretation relies on a possible spatial modulation of the damping and spring constants, resulting from the interference between the two atomic transitions.
An overview of the theory of the magneto-optical trap is presented, along with measurements of the effect of an imbalance in the intensities of the trapping beams. This investigation tests the theory of the spring constant of the trap and confirms that the confining force at the center of the trap results from an induced orientation of the atomic ground state. The experimental results give the magnitude of this force, which has not yet been calculated accurately. We calculate the radiation field in the three-dimensional molasses, finding that the relative time phase of the orthogonal standing waves is significant, and we give some insight into the phenomenon of interference fringes when the beams are misaligned. We also discuss the limitation of the trapped atomic density resulting from photon scattering within the cloud, predicting that densities above 1013 atoms/cm3 could be achieved in a trap operating at low saturation of the atomic transition. Finally, we briefly consider collisional loss at low densities, finding an especially large contribution from resonant dipole–dipole scattering.