Force pattern on atoms in a monochromatic light field with arbitrary polarization

Bezverbnyĭ, A. V.; Nienhuis, G.; Tumaĭkin, A. M.

doi:10.1016/s0030-4018(97)00697-4

Cited by 12 publications

(4 citation statements)

References 21 publications

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“…The steady-state solution discussed in this paper can be viewed as the zeroth-order approximation with respect to the atomic velocity. This solution is needed for an explicit calculation of radiative forces [19,22,41,46] and geometrical potentials [42,47], which also affect the dynamics of atoms in optical lattices.…”

Section: Discussionmentioning

confidence: 99%

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Steady state of atoms in a resonant field with elliptical polarization

et al. 2004

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We present a complete set of analytical and invariant expressions for the steady-state density matrix of atoms in a resonant radiation field with arbitrary intensity and polarization. The field drives the closed dipole transition with arbitrary values of the angular momenta $J_{g}$ and $J_{e}$ of the ground and excited state. The steady-state density matrix is expressed in terms of spherical harmonics of a complex direction given by the field polarization vector. The generalization to the case of broad-band radiation is given. We indicate various applications of these results.Comment: revtex, 26 pages, including 3 eps figures; PRA accepted for publication;v2 three typos are fixe

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Section: Discussionmentioning

confidence: 99%

“…The plane of this circular vector is normal to the direction of the orientation of the spin vector represented by the spinor. Conversely, any circular vector can be represented in the form (46) for some spinor χ. Now for a given polarization vector e, the two circular vectors (43) correspond to two spinors χ (1,2) so that…”

Section: Dark Statesmentioning

confidence: 99%

Steady state of atoms in a resonant field with elliptical polarization

et al. 2004

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“…However, even for low velocities and monochromatic fields, a general theoretical description of radiative forces is very complex [10,[28][29][30]. We thus study the simplest relevant case: the 1D J ′′ = 1 → J ′ = 0 transition.…”

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Bichromatic magneto-optical trapping forJ→J,J−1configurations

et al. 2016

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A magneto-optical trap (MOT) of atoms or molecules is studied when two lasers of different detunings and polarization are used. Especially for J → J, J − 1 transitions, a scheme using more than one frequency per transition and different polarization is required to create a significant force. Calculations have been performed with the simplest forms of the J → J − 1 case (i.e. J ′′ = 1 → J ′ = 0) and J → J case (i.e. J ′′ = 1/2 → J ′ = 1/2). A one dimensional (1D) model is presented and a complete 3D simulation using rate equations confirm the results. Even in the absence of Zeeman effect in the excited state, where no force is expected in the single laser field configuration, we show that efficient cooling and trapping forces are restored in our configuration. We study this mechanism for the C − 2 molecular anion as a typical example of the interplay between the two simple transitions J → J, J − 1. Laser cooling and magneto-optical trapping of atoms typically involves J → J + 1 closed transitions driven by counter-propagating circularly polarized laser fields (J is the total angular momentum). On the contrary laser forces on molecule, a more recent subject despite the pioneer experiments [1,2], typically involve N ′′ = 1 → N ′ = 0 transitions (N is the rotational quantum number) between X 2 Σ(v ′′ = 0) and A 2 Π 1/2 (v ′ = 0) vibronic levels [3][4][5]. Including the electron spin leads to J ′′ = 1/2, 3/2 → J ′ = 1/2 transitions. Theoretical study of the correct choice of circular polarization for magnetooptical trapping depending on the angular momenta, J ′′ and J ′ , and on the g-factors, g ′′ and g ′ (respectively of the lower and upper states) has been performed in Ref [6]. It has been found heuristically that the trapping force is weak whenever g ′ is small compared to g ′′ . This is a serious limitation because in pure Hund's case (a) or (b), A 2 Π 1/2 does not present any Zeeman effect [7], so g ′ = 0 prevents any force. However experiments, such as that on SrF [8], were possible because of rotational and spin-orbit Π − Σ mixing allowing a small non zero value for g ′ (∼ 0.1 [6]). In addition to this weak force, J ′′ = 1/2, 3/2 → J ′ = 1/2 transitions present one or two dark states [9, 10] which leads to experimental difficulties if a stronger confining force is desired. Yet stronger force can be produced by rapidly switching the magnetic field gradient and laser beam polarization on a timescale (typically in the sub-microsecond range which is not a simple experimental task) preventing the adiabatic following of the atomic states as done in reference [3] .In this letter we suggest that efficient magneto-optical forces can be restored in all J ′′ → J ′ cases, even for g ′ = 0, in a very simple way, by simply adding one laser field of opposite polarization with a different detuning. We treat the simplest J → J − 1 case (that * Corresponding author: anne.cournol@u-psud.fr is J ′′ = 1 → J ′ = 0) and J → J case (that is J ′′ = 1/2 → J ′ = 1/2). An analytical one dimensional (1D) model is presented and help get t...

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“…This is an essential ingredient of the description of sub-Doppler laser cooling [3], and of the formation of optical lattices [9]. A study of the force pattern in the case of transitions F → F , with half-integer F values has recently been given [10]. ***…”

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Steady state of atoms in a monochromatic elliptically polarized light field

Nienhuis¹,

Тайченачев

Tumaĭkin

et al. 1998

Europhys. Lett.

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An analytical and invariant expression is given for the steady-state density matrix of free atoms in a monochromatic radiation field with arbitrary intensity and arbitrary elliptical polarization. The field drives the closed transition F → F + 1, with arbitrary values of F . This is the only class of transitions where a closed analytical expression for the steady state was lacking. Some applications of this result are indicated.

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Force pattern on atoms in a monochromatic light field with arbitrary polarization

Cited by 12 publications

References 21 publications

Steady state of atoms in a resonant field with elliptical polarization

Steady state of atoms in a resonant field with elliptical polarization

Bichromatic magneto-optical trapping forJ→J,J−1configurations

Steady state of atoms in a monochromatic elliptically polarized light field

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