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arXiv:quant-ph/0512121 · Physical Review Letters

Normal Mode Splitting and Mechanical Effects of an Optical Lattice in a Ring Cavity

Julian Klinner, M. Lindholdt, Boris Nagorny, Andreas Hemmerich

Published Jan 19, 2006• 94 citations
arXivHTMLPDF

Abstract

A novel regime of atom-cavity physics is explored, arising when large atom samples dispersively interact with high-finesse optical cavities. A stable far-detuned optical lattice of several million rubidium atoms is formed inside an optical ring resonator by coupling equal amounts of laser light to each propagation direction of a longitudinal cavity mode. An adjacent longitudinal mode, detuned by about 3 GHz, is used to perform probe transmission spectroscopy of the system. The atom-cavity coupling for the lattice beams and the probe is dispersive and dissipation results only from the finite photon-storage time. The observation of two well-resolved normal modes demonstrates the regime of strong cooperative coupling. The details of the normal mode spectrum reveal mechanical effects associated with the retroaction of the probe upon the optical lattice.

DOI
10.1103/physrevlett.96.023002

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A novel regime of atom-cavity physics is explored, arising when large atom samples dispersively interact with high-finesse optical cavities. A stable far-detuned optical lattice of several million rubidium atoms is formed inside an optical ring resonator by coupling equal amounts of laser light to each propagation direction of a longitudinal cavity mode. An adjacent longitudinal mode, detuned by about 3 GHz, is used to perform probe transmission spectroscopy of the system. The atom-cavity coupling for the lattice beams and the probe is dispersive and dissipation results only from the finite photon-storage time. The observation of two well-resolved normal modes demonstrates the regime of strong cooperative coupling. The details of the normal mode spectrum reveal mechanical effects associated with the retroaction of the probe upon the optical lattice.
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 collective nonlinear dynamics in an optical lattice formed inside a high finesse ring cavity in a so far unexplored regime, where the light shift per photon times the number of trapped atoms exceeds the cavity resonance linewidth. We observe bistability and self-induced squeezing oscillations resulting from the retroaction of the atoms upon the optical potential wells. We can well understand most of our observations within a simplified model assuming adiabaticity of the atomic motion. Nonadiabatic aspects of the atomic motion are reproduced by solving the complete system of coupled nonlinear equations of motion.
The electromagnetic mode density of the vacuum can be dramatically \nmodified by the presence of an optical resonator. In the strong coupling \nregime, spontaneous emission in a cavity becomes a reversible process and \nthe intracavity photon number undergoes Rabi oscillations. We load up \nto 200x10^3 ^133Cs atoms into a nearly confocal lossy cavity and reach the \ncollective strong coupling regime. Normal mode splitting, the hallmark of this regime, is observed and cooperativities up to C_coll = (186±5) are measured. In a second experiment we investigate for the first time \nthe multi-mode character of the coupled cavity-atom system. In a confocal \ncavity the higher-order transverse cavity modes are degenerate in frequency and accessible to the spontaneous emission of the atomic ensemble. \nWe observe an increase of the coupling constant measured via modal decomposed transmission analysis, which could be attributed to \nthe presence of the higher-order modes. Normal mode splitting proportional to the square root of the atom number was visible for all of the \ndifferent mode components. Furthermore, we observe a redistribution of the relative weights in the modal transmission composition, which scales with the atom number in the cavity mode. \nIn a second set of experiments, ^87Rb atoms were loaded into a dissipative \nlin ⊥ lin lattice. By driving the lattice with a biharmonic force, transport can be observed when the systems symmetries are broken: the so called ratchet effect. Research in this area is concerned with the appearance \nof current reversals. We were able to identify dissipation related symmetry breaking as the underlying cause of an observed current reversal, which occurs as a function of the driving frequency. Furthermore, in a \nsecond experiment, we use the ratchet effect as a probe of the optical potential depths. We show that an oscillating force with a frequency far above any other system-inherent timescale, can be used to renormalize \nthe optical potential. The ^87Rb atoms experience an average position dependent force, which becomes controllable over the amplitude of the \napplied driving.
Summary form only given. We report on the observation of the many-atom dipole-dipole interaction in an ensemble of ultracold rubidium atoms strongly coupled to the standing-wave field of a weakly driven high-finesse optical cavity. The atoms split the cavity resonance into two normal modes. The many-atom light force changes the spatial distribution of the atoms, creating an asymmetry in the usually symmetric normal-mode spectrum, for intracavity photon numbers much less than one. This asymmetry is investigated as a function of the number of atoms and as a function of the intracavity photon number. Moreover, analytical expressions have been derived for the dipole force and the diffusion coefficient for an atom in presence of other atoms. These expressions allow us to simulate the trajectories of several atoms simultaneously. The calculated and measured spectra agree only if the full motional dynamics of all atoms is taken into account.
Strong collective interaction of atoms with an optical cavity causes normal mode splitting of the cavity's resonances, whose width is given by the collective coupling strength. At low optical density of the atomic cloud the intensity distribution of light in the cavity is ruled by the cavity's mode function, which is solely determined by its geometry. In this regime the dynamics of the coupled atom-cavity system is conveniently described by the open Dicke model, which we apply to calculating normal mode splitting generated by periodically ordered clouds in linear and ring cavities. We also show how to use normal mode splitting as witness for Wannier-Bloch oscillations in the tight-binding limit. At high optical density the atomic distribution contributes to shaping the mode function. This regime escapes the open Dicke model, but can be treated by a transfer matrix model provided the saturation parameter is low. Applying this latter model to an atomic cloud periodically ordered into a one-dimensional lattice, we observe the formation of photonic bands gaps competing with the normal mode splitting. We discuss the limitations of both models and point out possible pathways to generalized theories.
The strong collective interaction of atoms with an optical cavity causes normal mode splitting of the cavity's resonances, whose width is given by the collective coupling strength. At low optical density of the atomic cloud, the intensity distribution of light in the cavity is ruled by the cavity's mode function, which is determined solely by its geometry. In this regime the dynamics of the coupled atom-cavity system is conveniently described by the open Dicke model, which we apply to calculating normal mode splitting generated by periodically ordered clouds in linear and ring cavities. We also show how to use normal mode splitting as a witness for Wannier-Bloch oscillations in the tight-binding limit. At high optical density the atomic distribution contributes to shaping the mode function. This regime escapes the open Dicke model, but can be treated by a transfer matrix model provided the saturation parameter is low. Applying this latter model to an atomic cloud periodically ordered into a one-dimensional lattice, we observe the formation of photonic bands gaps competing with the normal mode splitting. We discuss the limitations of both models and point out possible pathways to generalized theories.