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The Dicke model is of fundamental importance in quantum mechanics for understanding the collective behaviour of atoms coupled to a single electromagnetic mode. In this paper, we demonstrate a Dicke-model simulation using cavity-assisted Raman transitions in a configuration using counter-propagating laser beams. The observations indicate that motional effects should be included to fully account for the results and these results are contrasted with the experiments using single-beam and co-propagating configurations. A theoretical description is given that accounts for the beam geometries used in the experiments and indicates the potential role of motional effects. In particular a model is given that highlights the influence of Doppler broadening on the observed thresholds.
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Squeezing ensemble of spins provides a way to surpass the standard quantum limit (SQL) in quantum metrology and test the fundamental physics as well, and therefore attracts broad interest. Here we propose an experimentally accessible protocol to squeeze a giant ensemble of spins via the geometric phase control. Using the cavity-assisted Raman transitions in a double $Lambda$-type system, we realize an effective Dicke model. Under the condition of vanishing effective spin transition frequency, we find a particular evolution time where the cavity decouples from the spins and the spin ensemble is squeezed considerably. Our scheme has the potential to improve the sensitivity in quantum metrology with spins by about two orders.
We present two schemes for driving Raman transitions between the ground state hyperfine manifolds of a single atom trapped within a high-finesse optical cavity. In both schemes, the Raman coupling is generated by standing-wave fields inside the cavity, thus circumventing the optical access limitations that free-space Raman schemes must face in a cavity system. These cavity-based Raman schemes can be used to coherently manipulate both the internal and the motional degrees of freedom of the atom, and thus provide powerful tools for studying cavity quantum electrodynamics. We give a detailed theoretical analysis of each scheme, both for a three-level atom and for a multi-level cesium atom. In addition, we show how these Raman schemes can be used to cool the axial motion of the atom to the quantum ground state, and we perform computer simulations of the cooling process.
A new optical pumping scheme is presented that uses incoherent Raman transitions to prepare a trapped Cesium atom in a specific Zeeman state within the 6S_{1/2}, F=3 hyperfine manifold. An important advantage of this scheme over existing optical pumping schemes is that the atom can be prepared in any of the F=3 Zeeman states. We demonstrate the scheme in the context of cavity quantum electrodynamics, but the technique is equally applicable to a wide variety of atomic systems with hyperfine ground-state structure.
Two-level atoms interacting with a one mode cavity field at zero temperature have order parameters which reflect the presence of a quantum phase transition at a critical value of the atom-cavity coupling strength. Two popular examples are the number of photons inside the cavity and the number of excited atoms. Coherent states provide a mean field description, which becomes exact in the thermodynamic limit. Employing symmetry adapted (SA) SU(2) coherent states (SACS) the critical behavior can be described for a finite number of atoms. A variation after projection treatment, involving a numerical minimization of the SA energy surface, associates the finite number phase transition with a discontinuity in the order parameters, which originates from a competition between two local minima in the SA energy surface.
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