Research ArticlePHYSICS

Rotational Doppler cooling and heating

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Science Advances  06 Jan 2021:
Vol. 7, no. 2, eabd6705
DOI: 10.1126/sciadv.abd6705
  • Fig. 1 Comparison between translational and rotational Doppler cooling and heating.

    (A and B) Illustration of translational Doppler cooling. In the laboratory frame [(A), top], a particle is moving with velocity v in the presence of two counter-propagating light waves (wavy curves) of frequency ω. In the frame moving with the particle [(A), bottom], the extinction cross section (σext) of these two waves [see (B)] is affected by Doppler shifts to ω(1 ± v/c), leading to an optical force that pushes the particle to the left, thus causing particle deceleration in the laboratory frame. (C) We consider a particle rotating with angular velocity Ω and illuminated by linearly polarized light of frequency ω (top). The incident light can be decomposed into right circularly polarized (RCP) and left circularly polarized (LCP) components, which are Doppler-shifted to ω ∓ Ω in the frame rotating with the particle (bottom). Black circular arrows denote the directions of the electric field rotation on the plane perpendicular to the wave vector.

  • Fig. 2 Optical torque acting on rotating particles.

    (A to C) Optical response of rotating particles of different geometries, namely, nanorod (A), nanocross (B), and nanodisk (C), to RCP (red) and LCP (blue) incident light. We plot the imaginary part of the polarizability, which is related to the extinction cross section according to σext = (4πω/c) Im {α}. A solid particle such as the nanodisk (C) exhibits different circular dichroism relative to particles with confined electron motion, such as the nanorod (A) and nanocross (B). (D to F) Time-averaged torque Mdr acting on the rotating particles considered in (A) to (C) under linearly polarized illumination. Insets: Mdr versus particle rotating frequency Ω for two typical light frequencies in the cooling and heating regimes. In all cases, damping rates are assumed to be γ = 0.2ω0 and τ−1 = 0.02ω0. Apart from the insets, particles are rotating with angular velocity Ω = 0.1ω0. All frequencies are normalized to the particle resonance frequency ω0, the polarizability is normalized to α0=Q2/mω02, and the torque is normalized to M0 = α0E±2/2. We assume a large resonance linewidth for illustration.

  • Fig. 3 Rotational dynamics of particles under linearly polarized illumination.

    (A) Stability of the nanocross considered in Fig. 2 (B and E) at rest under linearly polarized illumination of frequency ω = 1.1ω0 (solid curve) and 1.3ω0 (dashed curve), as a function of vacuum and particle temperatures T0 and T1 normalized to Θ0 = ħω0/kB. For each value of T0, a steady particle temperature T1 is reached at a laser intensity I(T1). The black solid and dashed curves denote phase boundaries for frequencies ω = 1.1ω0 and 1.3ω0, respectively. (B and C) Evolution of the nanocross at arbitrary initial T1 and Ω for light frequency ω = 1.1ω0, with vacuum temperature T0 = 0.4Θ0 and laser intensities I(0.41Θ0) (B) or I(0.5Θ0) (C), which correspond to the black dots I and II in (A). (D) Illustration of the particle state in different phases. Top: The equilibrium state at Ω = 0 is stable [black dot, also in (B)]. Middle: The equilibrium state at Ω = 0 is unstable for high light intensity [gray dot, also in (C)]. Bottom: A metastable configuration (see below). (E) Driving torque acting on the particle rotating at different velocities Ω for light frequencies ω = 1.1ω0 and 1.3ω0. (F) Same as (C) for light frequency ω = 1.3ω0. Two metastable configurations are observed, yielding the equilibrium at Ω = 0 stable [point II in (A) is in the normal phase for ω = 1.3ω0], which is intuitively illustrated in the bottom panel of (D).

Supplementary Materials

  • Supplementary Materials

    Rotational Doppler cooling and heating

    Deng Pan, Hongxing Xu, F. Javier García de Abajo

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