Abstract
A cold dilute atomic gas in an optical resonator can be radiatively cooled by coherent scattering processes when the driving laser frequency is tuned close to but below the cavity resonance. When the atoms are sufficiently illuminated, their steady state undergoes a phase transition from a homogeneous distribution to a spatially organized Bragg grating. We characterize the dynamics of this self-ordering process in the semi-classical regime when distinct cavity modes with commensurate wavelengths are quasi-resonantly driven by laser fields via scattering by the atoms. The lasers are simultaneously applied and uniformly illuminate the atoms; their frequencies are chosen so that the atoms are cooled by the radiative processes, and their intensities are either suddenly switched or slowly ramped across the self-ordering transition. Numerical simulations for different ramp protocols predict that the system will exhibit long-lived metastable states, whose occurrence strongly depends on the initial temperature, ramp speed, and the number of atoms.
Highlights
Laser light creates an attractive optical potential for cold atoms when far detuned below an optical transition
In this work we have studied the semi-classical dynamics of atoms interacting with two cavity modes after quenches of the intensity and/or frequency of the pumping lasers
We could verify numerically that the states reached at the asymptotics of the dynamics correspond to the minima of the free energy of a corresponding thermodynamic description developed in Ref. [13]
Summary
Laser light creates an attractive optical potential for cold atoms when far detuned below an optical transition. The interference contrast, and the trapping depends on the relative positions of the scattering atoms This phenomenon can be understood in terms of an effective long-range force, which is mediated by the collectively scattered photons [5,6,7,8,9]. In our example the particles can order in a lattice at a given length scale λ and/or on a lattice with half the period λ/2 For these settings we numerically analyze the semi-classical dynamics following sudden quenches or slow ramps of the laser intensities across.
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