A Vlasov approach to bunching and selfordering of particles in optical resonators

T. Griesser, H. Ritsch, M. Hemmerling, G. R. M. Robb

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We develop a Vlasov type continuum density description for the coupled nonlinear dynamics of polarizable particles moving in the light field of a high Q optical resonator. The intracavity light field, which exerts optical forces on the particles, depends itself on the dynamics of the particle density, which constitutes a time dependent refractive index. This induces mode frequency shifts, losses and coupling. For typical geometries we find solid analytic criteria for the stability of an initial homogeneous particle density for a wide class of initial velocity distributions including thermal distributions. These agree with previously found bunching and self-ordering instabilities but are extended to a wider range of parameters and initial conditions. Using a linear perturbation expansion we calculate the growth exponents of small density perturbations in the parameter region beyond this instability threshold. Numerical solutions of the full equations as well as simulations of the underlying many particle trajectories confirm these results. In addition the equations allow to extract analytical scaling laws to extrapolate cavity cooling and selfordering dynamics to higher particle numbers.

LanguageEnglish
Pages349-368
Number of pages20
JournalEuropean Physical Journal D: Atomic, Molecular, Optical and Plasma Physics
Volume58
Issue number3
DOIs
Publication statusPublished - Jun 2010

Fingerprint

optical resonators
bunching
perturbation
particle trajectories
scaling laws
frequency shift
Q factors
velocity distribution
exponents
refractivity
continuums
cooling
cavities
expansion
thresholds
geometry
simulation

Keywords

  • collective atomic recoil
  • self-organization
  • ring cavity
  • threshold
  • slow
  • gas

Cite this

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A Vlasov approach to bunching and selfordering of particles in optical resonators. / Griesser, T.; Ritsch, H.; Hemmerling, M.; Robb, G. R. M.

In: European Physical Journal D: Atomic, Molecular, Optical and Plasma Physics, Vol. 58, No. 3, 06.2010, p. 349-368.

Research output: Contribution to journalArticle

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AU - Hemmerling, M.

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AB - We develop a Vlasov type continuum density description for the coupled nonlinear dynamics of polarizable particles moving in the light field of a high Q optical resonator. The intracavity light field, which exerts optical forces on the particles, depends itself on the dynamics of the particle density, which constitutes a time dependent refractive index. This induces mode frequency shifts, losses and coupling. For typical geometries we find solid analytic criteria for the stability of an initial homogeneous particle density for a wide class of initial velocity distributions including thermal distributions. These agree with previously found bunching and self-ordering instabilities but are extended to a wider range of parameters and initial conditions. Using a linear perturbation expansion we calculate the growth exponents of small density perturbations in the parameter region beyond this instability threshold. Numerical solutions of the full equations as well as simulations of the underlying many particle trajectories confirm these results. In addition the equations allow to extract analytical scaling laws to extrapolate cavity cooling and selfordering dynamics to higher particle numbers.

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