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New Journal of Physics

Collective transverse cavity cooling of a dense molecular beam

Thomas Salzburger, Helmut Ritsch

Published May 14, 2009• 24 citations
Publisher

Abstract

Based on a classical point particle description, we study light induced transverse collimation and phase space compression of a fast molecular beam traversing the crossover region of a high- Q optical cavity and a standing-wave laser beam. The molecules scatter pump laser light, far detuned from any molecular transition, into the resonant cavity mode. We show that despite a very small probability for this process for a single particle, collective enhancement can lead to significant transverse cooling and collimation above the self-organization threshold. The analytical formulae for this threshold derived from homogeneous one-dimensional (1D) models give surprisingly good estimates for the pulsed 3D case. We compare ring and standing wave cavity geometries and show that phase space compression can be achieved even for extremely small particle field coupling if compensated by a large density and pump power. In the vicinity of the critical point the compression time can be reduced by tailored seeding of the cavity mode or using a second buildup cavity for the pump field.

DOI
10.1088/1367-2630/11/5/055025

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Based on a classical point particle description, we study light induced transverse collimation and phase space compression of a fast molecular beam traversing the crossover region of a high- Q optical cavity and a standing-wave laser beam. The molecules scatter pump laser light, far detuned from any molecular transition, into the resonant cavity mode. We show that despite a very small probability for this process for a single particle, collective enhancement can lead to significant transverse cooling and collimation above the self-organization threshold. The analytical formulae for this threshold derived from homogeneous one-dimensional (1D) models give surprisingly good estimates for the pulsed 3D case. We compare ring and standing wave cavity geometries and show that phase space compression can be achieved even for extremely small particle field coupling if compensated by a large density and pump power. In the vicinity of the critical point the compression time can be reduced by tailored seeding of the cavity mode or using a second buildup cavity for the pump field.
We study the dynamics of a fast gaseous beam in a high Q ring cavity counter propagating a strong pump laser with large detuning from any particle optical resonance. As spontaneous emission is strongly suppressed the particles can be treated as polarizable point masses forming a dynamic moving mirror. Above a threshold intensity the particles exhibit spatial periodic ordering enhancing collective coherent backscattering which decelerates the beam. Based on a linear stability analysis in their accelerated rest frame we derive analytic bounds for the intensity threshold of this selforganization as a function of particle number, average velocity, kinetic temperature, pump detuning and resonator linewidth. The analytical results agree well with time dependent simulations of the N-particle motion including field damping and spontaneous emission noise. Our results give conditions which may be easily evaluated for stopping and cooling a fast molecular beam.
We study the dynamics of a multispecies mixture of laser-illuminated polarizable particles moving inside an optical resonator. Above a certain pump threshold the collective enhanced scattering of laser light into the cavity induces a phase transition from a homogeneous spatial distribution to a common crystalline order. We analytically show that adding particles of any mass and temperature always strictly lowers the minimum pump power required for self-ordering and trapping. This allows to capture and trap new species of atoms, molecules or even polarizable nanoparticles in combination with proven examples, for which a high phase-space density is readily available. Cooperative light scattering mediates effective energy exchange and thus sympathetic cooling between different species without the need for direct collisional interaction. The predicted ordering thresholds and cooling timescales are in the range of current technology for particles with a wide range of mass, polarizability and initial temperature.
We theoretically investigate the correlated dynamics of N coherently driven atoms coupled to a standing-wave cavity mode. For red detuning between the driving field and the cavity as well as the atomic resonance frequencies, we predict a light force induced self-organization of the atoms into one of two possible regular patterns, which maximize the cooperative scattering of light into the cavity field. Kinetic energy is extracted from the atoms by superradiant light scattering to reach a final kinetic energy related to the cavity linewidth. The self-organization starts only above a threshold of the pump strength and atom number. We find a quadratic dependence of the cavity mode intensity on the atom number, which demonstrates the cooperative effect.
Active atomic clocks are predicted to provide far better short-term stability and robustness against thermal fluctuations than typical feedback-based optical atomic clocks. However, continuous laser operation using an ensemble of clock atoms still remains an experimentally challenging task. We study spatial self-organization in a transversely driven ensemble of clock atoms inside an optical resonator and coherent light emission from the cavity. We focus on the spectral properties of the emitted light in the narrow atomic linewidth regime, where the phase coherence providing frequency stability is stored in the atomic dipoles rather than the cavity field. The atoms are off-resonantly driven by a standing-wave coherent laser transversely to the cavity axis, allowing for atomic motion along the cavity axis as well as along the pump. In order to treat larger atom numbers we employ a second-order cumulant expansion which allows us to calculate the spectrum of the cavity light field. We identify the self-organization threshold where the atoms align themselves in a checkerboard pattern, thus maximizing light scattering into the cavity, which simultaneously induces cooling. For a larger driving intensity, more atoms are transferred to the excited state, reducing cooling but increasing light emission from the excited atoms. This can be enhanced via a second cavity mode at the atomic frequency spatially shifted by a quarter wavelength. For large enough atom numbers we observe laser-like emission close to the bare atomic transition frequency.
We propose a cavity-based laser-cooling and trapping scheme, providing tight confinement and cooling to very low temperatures, without degradation at high particle densities. A bidirectionally pumped ring cavity builds up a resonantly enhanced optical standing wave that acts to confine polarizable particles in deep potential wells. The particle localization yields a coupling of the degenerate traveling wave modes via coherent photon redistribution. This induces a splitting of the cavity resonances with a high-frequency component, which is tuned to the anti-Stokes Raman sideband of the particles oscillating in the potential wells, yielding cooling due to excess anti-Stokes scattering.
Abstract A dilute atomic gas in an optical resonator exhibits a phase transition from a homogeneous density to crystalline order when laser illuminated orthogonal to the resonator axis. We study this well-known self-organization phenomenon for a generalized pumping scheme using a femtosecond pulse train with a frequency spectrum spanning a large bandwidth covering many cavity modes. We show that due to simultaneous scattering into adjacent longitudinal cavity modes the induced light forces and the atomic dynamics becomes nearly translation-invariant along the cavity axis. In addition the laser bandwidth introduces a new correlation length scale within which clustering of the atoms is energetically favorable. Numerical simulations allow us to determine the self-consistent ordering threshold power as function of bandwidth and atomic cloud size. We find strong evidence for a change from a second order to a first order self-ordering phase transition with growing laser bandwidth when the size of the atomic cloud gets bigger than the clustering length. An analysis of the cavity output reveals a corresponding transition from a single to a double pulse traveling within the cavity. This doubles the output pulse repetition rate and creates extra substructures in close analogy to a time crystal formation in the cavity output. Simulations also show that multi-mode operation significantly improves cavity cooling generating lower kinetic temperatures at a much faster cooling rate.