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arXiv:1607.07941 · Physical Review Letters

Cavity-Assisted Measurement and Coherent Control of Collective Atomic Spin Oscillators

Jonathan Kohler, Nicolas Spethmann, Sydney Schreppler, Dan Stamper-Kurn

Published Feb 8, 2017• 25 citations
arXivHTMLPDF

Abstract

We demonstrate continuous measurement and coherent control of the collective spin of an atomic ensemble undergoing Larmor precession in a high-finesse optical cavity. The coupling of the precessing spin to the cavity field yields phenomena similar to those observed in cavity optomechanics, including cavity amplification, damping, and optical spring shifts. These effects arise from autonomous optical feedback onto the atomic spin dynamics, conditioned by the cavity spectrum. We use this feedback to stabilize the spin in either its high- or low-energy state, where, in equilibrium with measurement backaction heating, it achieves a steady-state temperature, indicated by an asymmetry between the Stokes and the anti-Stokes scattering rates. For sufficiently large Larmor frequency, such feedback stabilizes the spin ensemble in a nearly pure quantum state, in spite of continuous measurement by the cavity field.

DOI
10.1103/physrevlett.118.063604

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We demonstrate continuous measurement and coherent control of the collective spin of an atomic ensemble undergoing Larmor precession in a high-finesse optical cavity. The coupling of the precessing spin to the cavity field yields phenomena similar to those observed in cavity optomechanics, including cavity amplification, damping, and optical spring shifts. These effects arise from autonomous optical feedback onto the atomic spin dynamics, conditioned by the cavity spectrum. We use this feedback to stabilize the spin in either its high- or low-energy state, where, in equilibrium with measurement backaction heating, it achieves a steady-state temperature, indicated by an asymmetry between the Stokes and the anti-Stokes scattering rates. For sufficiently large Larmor frequency, such feedback stabilizes the spin ensemble in a nearly pure quantum state, in spite of continuous measurement by the cavity field.
We report out-of-equilibrium stabilization of the collective spin of an atomic ensemble through autonomous feedback by a driven optical cavity. For a magnetic field applied at an angle to the cavity axis, dispersive coupling to the cavity provides sensitivity to a combination of the longitudinal and transverse spin. Coherent backaction by cavity light onto the atoms, conditioned by the cavity susceptibility, stabilizes the spin state at an arbitrary energy. The setpoint tracking and closed-loop gain spectrum of the feedback system are characterized and found to agree closely with analytic predictions.
The quantum nature of light makes it a basic component for models of quantum measurement and information exchange between disparate quantum modes, pioneered in the field of cavity quantum electrodynamics. The interaction of atomic ensembles with the mode of an optical cavity provides a flexible platform for exploring the coherent interaction of light with diverse macroscopic dynamics, such as collective motion and spin. This dissertation presents experimental results and theoretical models for continuous measurement and control of the center of mass motion and collective spin precession of an atomic ensemble, mediated by coupling to a high-finesse optical cavity. First, the theory of dispersive coupling between the cavity mode and the collective motion and spin of an atomic ensemble is derived, and then a general time-domain formalism is developed for theoretical analysis of multi-mode optodynamical systems. Single-mode optodynamical effects are introduced through experimental demonstrations of measurement and control of the collective atomic spin, providing a close analogy to cavity optomechanics.Next, multiple collective atomic modes are considered within a single cavity, in order to assemble optically mediated interactions within multi-mode optodynamical systems. A demonstration of optodynamical interactions between the center of mass motion of two atomic ensembles is presented, coupled through an optical spring mediated by the cavity mode. Then simultaneous coupling of the center of mass motion and total spin precession of a single ensemble of atoms is described, yielding an experimental realization of a negative-mass instability, facilitated by the novel resource of the spin ensembles inverted state. A theoretical analysis of the negative-mass instability is presented, which indicates the possibility of generating two-mode squeezed states in the absence of excess incoherent noise. Finally, linear state retrodiction from the optodynamical signals is discussed, providing background and supplemental material for a forthcoming manuscript.
We study a hybrid system composed of a three-level atomic ensemble inside an optomechanical cavity. The mechanical oscillator is coupled to the internal state of the atomic ensemble via electromagnetically induced transparency (EIT), created by the intra-cavity field and an off-resonance control laser. The fluctuation in the output-coupled cavity field is fed back to the mechanical oscillator. We use a combination of feedback and EIT-assisted cooling of the oscillator to its quantum ground state and then establish coherent coupling between the oscillator and the atomic spin. The superposition of the atomic state and oscillator is studied in different regimes of optomechanical and light–atom coupling strengths and the conditions for creating a single atom-phonon polaron is identified. We observe coherent superposition of fluctuations in a range of optomechanical and atomic cooperativities.
We realize a spin-orbit interaction between the collective spin precession and center-of-mass motion of a trapped ultracold atomic gas, mediated by spin- and position-dependent dispersive coupling to a driven optical cavity. The collective spin, precessing near its highest-energy state in an applied magnetic field, can be approximated as a negative-mass harmonic oscillator. When the Larmor precession and mechanical motion are nearly resonant, cavity mediated coupling leads to a negative-mass instability, driving exponential growth of a correlated mode of the hybrid system. We observe this growth imprinted on modulations of the cavity field and estimate the full covariance of the resulting two-mode state by observing its transient decay during subsequent free evolution.
We directly measure the quantized collective motion of a gas of thousands of ultracold atoms, coupled to light in a high-finesse optical cavity. We detect strong asymmetries, as high as 3:1, in the intensity of light scattered into low- and high-energy motional sidebands. Owing to high cavity-atom cooperativity, the optical output of the cavity contains a spectroscopic record of the energy exchanged between light and motion, directly quantifying the heat deposited by a quantum position measurement's backaction. Such backaction selectively causes the phonon occupation of the observed collective modes to increase with the measurement rate. These results, in addition to providing a method for calibrating the motion of low-occupation mechanical systems, offer new possibilities for investigating collective modes of degenerate gases and for diagnosing optomechanical measurement backaction.
A common goal of recent research is the elucidation and control over quantum mechanical behavior in ever-larger physical systems. In this thesis I present an alternative target for investigating the quantum motion of macroscopic bodies: the collective motion of an ultracold atomic gas trapped within a high-finesse Fabry-Perot optical cavity in the single-atom strong-coupling regime of cavity quantum electrodynamics (CQED). When ultracold atoms are trapped in the Lamb-Dicke regime, the cavity-mode structure selects a single collective degree of freedom that is at once actuated by the optical forces from cavity probe light and measured by the cavity’s optical properties. Dispersive optical bistability arising from collective motion of the atomic medium was observed. Measurement of the collective motion was subject to quantum measurement backaction by the quantum force fluctuations of the cavity optical field. The strength and spectrum of these backaction force fluctuations was measured by quantifying the cavity-light-induced heating rate of the intracavity atomic ensemble, finding quantitative agreement with the expected heating rate from quantum optical fluctuations. Dynamical phenomena in the optomechanical system were explored experimentally and theoretically. Quantum limited measurements are discussed and were