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Off-Axis Dipole Forces in Optical Tweezers by an Optical Analog of the Magnus Effect

Robert J. C. Spreeuw
Phys. Rev. Lett. 125, 233201 – Published 1 December 2020
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    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.

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    • Received 15 May 2020
    • Accepted 2 November 2020

    DOI:https://doi.org/10.1103/PhysRevLett.125.233201

    Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

    Published by the American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Angular momentum of lightAtomic & molecular processes in external fieldsCooling & trappingQuantum opticsSpin-orbit coupling
    Atomic, Molecular & Optical

    Authors & Affiliations

    Robert J. C. Spreeuw*

    • Van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam, P.O. Box 94485, 1090 GL Amsterdam, The Netherlands

    • *r.j.c.spreeuw@uva.nl

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    Issue

    Vol. 125, Iss. 23 — 4 December 2020

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    • Figure 1
      Figure 1

      Optical analog of the Magnus effect. (a) A linearly polarized (E∥x), focused laser induces a circular dipole (xz plane) on a j=0→j′=1 (Δmj=1) transition, with a magnetic field B∥y setting the quantization axis. The spiral wave scattered by the circular dipole interferes with the incident wave, producing two effects: (b) The incident beam is deflected in the xz plane, with corresponding reaction force on the atom, transverse to the beam. The direction changes sign with the detuning from the atomic resonance. (c) In an optical tweezer (“red” detuning, Δ<0), the transverse force shifts the trapping position away from the optical axis by an amount ƛ=λ/2π. See Fig. 3 for a far off-resonance case.

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    • Figure 2
      Figure 2

      Beam deflection: radiant intensities in the plane of the u+ dipole, for (a) a Gaussian incident beam with wθ=0.6 and (b) an angular top hat incident beam with rθ=0.6. In both cases, the gray dotted curve shows Jin(θ,ϕ=0) of the incident beam, normalized to 1 for θ=0; red solid and blue dashed curves show the outgoing, or total J(θ,0), for Δ=−γ and +γ, respectively. For clarity, we identify (θ,0)≡(−θ,π). Curves remain the same upon switching simultaneously the signs of the detuning and the spin of the dipole.

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    • Figure 3
      Figure 3

      Optical tweezer operating on a j=1→j′=0 transition, leading to ±ƛ off-axis displacements for the (mj)y=∓1 sublevels (upper left). The four panels show, in clockwise order, the effect of a rotation of the quantization axis (B), through a cycle y→z→−y→−z. While the B-referenced (mj)B of an atom is conserved, the space-referenced (mj)y is not. The locations of the (mj)B=±1 traps move up and down along the x axis, in antiphase. If B is rotated at the trap frequency, spin-dependent oscillatory motion in the tweezer can be induced.

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