Self ordering threshold and superradiant backscattering to slow a fast gas beam in a ring cavity with counter propagating pump

Abstract

Abstract:We study the threshold conditions of spatial self organization combined with collective coherent optical backscattering of a thermal gaseous beam moving in a high Q ring cavity with counter propagating pump. We restrict ourselves to the limit of large detuning between the particles optical resonances and the light field, where spontaneous emission is negligible and the particles can be treated as polarizable point masses. Using a linear stability analysis in the accelerated rest frame of the particles we derive an analytic bounds for the selforganization as a function of particle number, average velocity, temperature and resonator parameters. We check our results by a numerical iteration procedure as well as by direct simulations of the N-particle dynamics. Due to momentum conservation the backscattered intensity determines the average force on the cloud, which gives the conditions for stopping and cooling a fast molecular beam.

Atomic self-ordering in a ring cavity with counterpropagating pump fields

“…Two counterpropagating, orthogonally polarized modes f + α and f − β are pumped with amplitudes η 1 ≡ η + and η 4 ≡ η − , while the other two modes f − α and f + β are only populated by scattered photons. This configuration represents only a slight change as compared to standard ring cavity cooling scheme [15][16][17], but constitutes a very different situation physically. As the two counterpropagating pump fields do not interfere, no prescribed optical lattice is formed and the system is inherently translation invariant.…”

“…While we have started from a particle ensemble at rest up to now and found a moving gas in a steady state, one can turn the idea around and use this setup to efficiently slowing down a cold atomic or molecular beam by collective scattering, improving a similar approach which has already been presented in [16] (see the red curve in fig. 4).…”

Cavity-induced phase stability to decelerate a fast molecular beam via feedback-controlled time-varying optical pumps

“…In the ring cavity, which is the simplest multimode cavity supporting two counter-propagating modes, the locations of the antinodes are collectively determined by the particles moving in the cavity, instead of self-emergent as in the standing-wave cavity, so the translational symmetry breaking of the system is continuous rather than discrete as in the standing-wave cavity. This collective determination of the antinodes results in a shift of the peak density position of the particles from the optical field minima in the cavity and thus the system cannot reach a time-independent self-consistent particle-field steady state [43]. In the present study, we expect a self-consistent molecule-field steady state because of the use of a standing-wave cavity where the antinodes are fixed by the cavity geometry and such a steady state is also expected to be achieved in the bad cavity regime where there is no dissipative factor to destroy its stability.…”

“…When a fast-moving molecular beam is considered instead of the stationary cold atomic cloud, a new parameter, the central velocity of the beam v 0 , is introduced into the system, which brings in new physics that has no counterpart as in the case of the stationary cold atomic cloud. The phase transition of a fast-moving gas beam in a ring cavity pumped by two counter-propagating laser fields through the cavity mirrors has been studied [43]. It is shown to occur only when the frequency shift induced by the particles is larger than the cavity linewidth, which implies a large ensemble of particles or a high-Q cavity.…”

Microscopic dynamics of ultracold particles in a ring-cavity optical lattice

“…A ring geometry offers a wider capture range, faster cooling times [6], as well as lower temperatures [17], including even the idea of stopping and cooling a fast molecular beam [18]. An ultimate goal here is the development of an all-optical route to a BEC of polarizable point objects replacing evaporative cooling by cavity cooling which involves no particle loss.…”