Abstract
It is shown that a circular dipole can deflect the focused laser beam that induces it and will experience a corresponding transverse force. Quantitative expressions are derived for Gaussian and angular top hat beams, while the effects vanish in the plane wave limit. The phenomena are analogous to the Magnus effect, pushing a spinning ball onto a curved trajectory. The optical case originates in the coupling of spin and orbital angular momentum of the dipole and the light. In optical tweezers the force causes off-axis displacement of the trapping position of an atom by a spin-dependent amount up to λ/2π, set by the direction of a magnetic field. This suggests direct methods to demonstrate and explore these effects, for instance, to induce spin-dependent motion.
Highlights
Published by the American Physical SocietyDisplacement of an emitting circular dipole [2,3]. Tweezer trap displacements have previously been calculated numerically, for specific beam shapes, in terms of vector and tensor light shifts [14,31]
A common practice in many branches of sports is to send a ball onto a curved trajectory by giving it a spin
We predict that an atomic circular dipole can deflect the centered focused laser beam that induces it
Summary
Displacement of an emitting circular dipole [2,3]. Tweezer trap displacements have previously been calculated numerically, for specific beam shapes, in terms of vector and tensor light shifts [14,31]. A comparison of a Gaussian beam with an angular top hat beam illustrates this This profound insight provides the basis for state-dependent manipulation of atomic motion within the tweezer. We describe these effects in terms of interference between the focused incident beam with the wave scattered by the circular dipole, see Fig. 1. We tune the laser close to the Δmj 1⁄4 þ1 transition, with a detuning Δ 1⁄4 ωL − ω0 small compared to the Zeeman shift, so that the Δmj 1⁄4 0; −1 transitions can be neglected (for example, Δ=2π ∼ 10 and μBB=h ∼ 100 MHz.) The emission by the induced circular dipole has a spiral wave front in the xz plane, tilted with respect to the forward zdirection of the incident beam. Combining Eqs. (1) and (2), the total radiant intensity is the sum of three terms, JðΩÞ 1⁄4 JinðΩÞ þ JscðΩÞ þ JifðΩÞ: ð4Þ
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