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arXiv:2005.07790 · Physical Review Letters

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

R. J. C. Spreeuw

Published Dec 1, 2020• 13 citations
arXivHTMLPDF

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.

DOI
10.1103/physrevlett.125.233201

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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.
The insight that optical vortex beams carry orbital angular momentum (OAM), which emerged in Leiden about 30 years ago, has since led to an ever expanding range of applications and follow-up studies. This paper starts with a short personal account of how these concepts arose. This is followed by a description of some recent ideas where the coupling of transverse orbital and spin angular momentum (SAM) in tightly focused laser beams produces interesting new effects. The deflection of a focused light beam by an atom in the focus is reminiscent of the Magnus effect known from aerodynamics. Momentum conservation dictates an accompanying light force on the atom, transverse to the optical axis. As a consequence, an atom held in an optical tweezer will be trapped at a small distance of up to λ/2π away from the optical axis, which depends on the spin state of the atom and the magnetic field direction. This opens up new avenues to control the state of motion of atoms in optical tweezers as well as potential applications in quantum gates and interferometry.
We directly observe and spatially map an optical analog of the Magnus effect, where intrinsic spin-orbit-like coupling of light generates a spin-dependent transverse displacement of the atom-light interaction profile for a 40^{40}40Ca+^++ ion. Probed on a quadrupole transition using a tightly focused beam, we observe displacements of the maximum in the profile of the effective interaction by several 100 nm originating from intrinsic longitudinal electric field components beyond the paraxial approximation. The tight focus of the beam induces additional transverse polarization gradients, which we characterize through a phase-sensitive measurement and spatial maps for different beam configurations. The results establish the physical basis of polarization-gradient interactions relevant to optical tweezer-based quantum control.
Abstract The insight that optical vortex beams carry orbital angular momentum (OAM), which emerged in Leiden about 30 years ago, has since led to an ever expanding range of applications and follow‐up studies. This paper starts with a short personal account of how these concepts arose. This is followed by a description of some recent ideas where the coupling of transverse orbital and spin angular momentum (SAM) in tightly focused laser beams produces interesting new effects. The deflection of a focused light beam by an atom in the focus is reminiscent of the Magnus effect known from aerodynamics. Momentum conservation dictates an accompanying light force on the atom, transverse to the optical axis. As a consequence, an atom held in an optical tweezer will be trapped at a small distance of up to λ /2 π away from the optical axis, which depends on the spin state of the atom and the magnetic field direction. This opens up new avenues to control the state of motion of atoms in optical tweezers as well as potential applications in quantum gates and interferometry.
The time evolution of the radiation pressure forces due to the action of laser light on matter in the form of neutral molecules, atoms, and ions is considered when the frequency of the light is comparable to a dipole-allowed transition frequency. We find that the transient regime, applicable from the instant the laser is switched on, is important for the gross motion, provided that the upper-state lifetime ${\ensuremath{\Gamma}}^{\ensuremath{-}1}$ is relatively long, while the steady-state regime, formally such that $t⪢{\ensuremath{\Gamma}}^{\ensuremath{-}1}$, is appropriate for the evaluation of the forces and the dynamics for large $\ensuremath{\Gamma}$. With a focus on the orbital-angular-momentum-endowed laser light, the light-induced time-dependent forces and torques are determined and their full time dependence utilized to determine trajectories. Marked differences are found in both translational and rotational features in comparison with the results emerging when the steady-state forces are assumed from the outset. Intricate and detailed atom trajectories are plotted for Laguerre-Gaussian light at near resonance for a transition of Eu3+{\mathrm{Eu}}^{3+}Eu3+ that has a particularly small $\ensuremath{\Gamma}$. The implications of the results for trapping and manipulating atoms and ions using laser light are pointed out and discussed.
An atom placed in a focused laser beam will experience a dipole force due to the gradient in the interaction energy, which is analogous to the well-known optical tweezers effect. This force will be dependent on the velocity of the atom due to the Doppler effect, which could potentially be used to implement a Maxwell's demon. Photon scattering and other forms of dissipation can be negligibly small, which would seem to contradict quantum information proofs that a Maxwell's demon must dissipate a minimum amount of energy. We show that the velocity dependence of the dipole force is cancelled out by another force that is related to the gradient in the phase of the laser beam. As a result, a Maxwell's demon cannot be implemented in this way.