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arXiv:0706.1052 · Physical Review Letters

Cavity Nonlinear Optics at Low Photon Numbers from Collective Atomic Motion

Subhadeep Gupta, Kevin L. Moore, Kater W. Murch, Dan Stamper-Kurn

Published Nov 20, 2007• 266 citations
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Abstract

We report on Kerr nonlinearity and dispersive optical bistability of a Fabry-Perot optical resonator due to the displacement of ultracold atoms trapped within. In the driven resonator, such collective motion is induced by optical forces acting upon up to 10(5) 87Rb atoms prepared in the lowest band of a one-dimensional intracavity optical lattice. The longevity of atomic motional coherence allows for strongly nonlinear optics at extremely low cavity photon numbers, as demonstrated by the observation of both branches of optical bistability at photon numbers below unity.

DOI
10.1103/physrevlett.99.213601

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We report on Kerr nonlinearity and dispersive optical bistability of a Fabry-Perot optical resonator due to the displacement of ultracold atoms trapped within. In the driven resonator, such collective motion is induced by optical forces acting upon up to 10(5) 87Rb atoms prepared in the lowest band of a one-dimensional intracavity optical lattice. The longevity of atomic motional coherence allows for strongly nonlinear optics at extremely low cavity photon numbers, as demonstrated by the observation of both branches of optical bistability at photon numbers below unity.
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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
We study the collective motion of atoms confined in an optical lattice operating inside a high-finesse ring cavity. A simplified theoretical model for the dynamics of the system is developed upon the assumption of adiabaticity of the atomic motion. We show that in a regime where the light shift per photon times the number of atoms exceeds the linewidth of the cavity resonance, the otherwise tiny retroaction of the atoms upon the light field becomes a significant feature of the system. As a result dispersive optical bistability can arise and the lattice positions is determined by the strength of the atom-cavity coupling rather than by the phases of the incoupled light beams. Solving the complete set of classical equations of motion confirms these findings, however, additional nonadiabatic phenomena are predicted, such as, for example, self-induced radial breathing oscillations. We compare these results with experiments involving laser-cooled 85Rb^{85}\mathrm{Rb}85Rb atoms trapped in an optical lattice inside a ring cavity with a finesse of $1.8\ifmmode\times\else\texttimes\fi{}{10}^{5}$. Our observations are in excellent agreement with our theoretical predictions.
We report on studies on optical bistability from coherently driven $\ensuremath{\Lambda}$-type three-level atoms in a Fabry-Perot resonator. The nonlinear mechanism relies on transverse optical pumping and is due to population trapping in a coherent superposition of the ground-state sublevels. If, under appropriate conditions, a zero-field level-crossing resonance (Hanle resonance) occurs in the atomic system, the optical device is shown to display dispersive or absorptive bistability. Our theoretical studies are based on numerical solutions of the corresponding three-level Bloch equations in the presence of optical feedback. Experiments are performed on the D1{D}_{1}D1​ line in a sodium-filled Fabry-Perot resonator using transverse optical Zeeman pumping of the 2S12^{2}S_{\frac{1}{2}}2S21​​ ground state. The measurements are found to be in fair agreement with the theoretical predictions from our simple model.