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Physical Review A

Stability diagram of the collective atomic recoil laser with thermal atoms

H. Tomczyk, Dag Schmidt, Christoph Georges, Sebastian Slama, Claus Zimmermann

Published Jun 29, 2015• 3 citations
Publisher

Abstract

We experimentally investigate cold thermal atoms in a single sidedly pumped optical ring resonator for temperatures between 0.4 and $9\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$. The threshold for collective atomic recoil lasing (CARL) is recorded for various pump-cavity detunings. The resulting stability diagram is interpreted by simulating the classical CARL equations. We find that the stability diagram for thermal atoms shows the same asymmetry as observed for Bose-Einstein condensates in previous experiments. Whereas for condensates the asymmetry is well explained by a Dicke-type quantum model we here discuss a simplified classical model. It complements the quantum model and provides an intuitive explanation based on the change in the long-range atomic interaction with pump-cavity detuning.

DOI
10.1103/physreva.91.063837

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We experimentally investigate cold thermal atoms in a single sidedly pumped optical ring resonator for temperatures between 0.4 and 9\ensuremathμK9\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}9\ensuremathμK. The threshold for collective atomic recoil lasing (CARL) is recorded for various pump-cavity detunings. The resulting stability diagram is interpreted by simulating the classical CARL equations. We find that the stability diagram for thermal atoms shows the same asymmetry as observed for Bose-Einstein condensates in previous experiments. Whereas for condensates the asymmetry is well explained by a Dicke-type quantum model we here discuss a simplified classical model. It complements the quantum model and provides an intuitive explanation based on the change in the long-range atomic interaction with pump-cavity detuning.
Cold atoms in optical high‐Q cavities are an ideal model system for long‐range interacting particles. The position of two arbitrary atoms is, independent on their distance, coupled by the back‐scattering of photons within the cavity. This mutual coupling can lead to collective instability and self‐organization of a cloud of cold atoms interacting with the cavity fields. This phenomenon (CARL, i.e. Collective Atomic Recoil Lasing) has been discussed theoretically for years, but was observed only recently in our lab. The CARL‐effect is closely linked to superradiant Rayleigh scattering, which has been intensely studied with Bose‐Einstein condensates in free space. By adding a resonator the coherence time of the system, in which the instability occurs, can be strongly enhanced. This enables us to observe cavity‐enhanced superradiance with both Bose‐Einstein condensates and thermal clouds and allows us to close the discussion about the role of quantum statistics in superradiant scattering.
We experimentally investigate the dynamical instability of a Bose-Einstein condensate in an optical ring resonator for various cavity detuning and pump powers. The resulting stability diagram is asymmetric with respect to the cavity detuning and can be described by the coupling of two atomic modes with one optical mode. We compare the experimental data to a numerical simulation and to an analytic expression of the phase boundary. For positive and negative pump cavity detuning, different coupling mechanisms are identified explaining the asymmetry of the stability diagram. We present a physical interpretation and discuss the connection to the Dicke quantum phase transition.
Summary form only given. The collective atomic recoil laser (CARL) was proposed as an atomic analog of the free electron laser. Recently, there has been an increased interest in the CARL primarily because it can be regarded as a parametric amplifier for the momentum side modes. Our CARL model consists of a cavity CARL signal of wave number k/sub 1/, and an opposing non-depletion pump field of k/sub 2/, and a steady flow of an ultra-cold two-level atomic beam along a direction normal to the propagation of the fields. Both fields are assumed to be far-off resonance. A momentum change of /spl planck/K, where K = k/sub 1/ + k/sub 2/, takes place in each virtual two-photon process. This allows us to divide the total momentum space into different momentum families, and each momentum family into different diffraction groups.
A cloud of ultra-cold atoms is loaded into the attractive potential of a light wave that is generated by two counter-propagating modes of a high-finesse ring resonator. The two modes are coupled by the atoms due to coherent Rayleigh scattering and generate a potential which acts back on the motion of the atoms. This feedback leads to a new frequency component and can be described in terms of the long time proposed collective atomic recoil laser (CARL). This model is investigated experimentally and extended by introducing an optical friction force acting on the atoms. This allows for steady state operation of the CARL. Furthermore, it leads to a threshold behaviour of the CARL that translates into a novel type of phase transition: while passing the threshold the initially homogeneous atomic distribution is bunched in space and velocity. With this behaviour the system turns out to acquire some of the main features of the so-called Kuramoto model which provides a very general description of a network of limit cycle oscillators.