Per Kristian Rekdal

Optimal quantum control of Bose-Einstein condensates in magnetic microtraps

Transport of Bose-Einstein condensates in magnetic microtraps, controllable by external parameters such as wire currents or radio-frequency fields, is studied within the framework of optimal control theory (OCT). We derive from the Gross-Pitaevskii equation the optimality system for the OCT fields that allow efficient channeling of the condensate between given initial and desired states. For a variety of magnetic confinement potentials we study transport and wave-function splitting of the condensate, and demonstrate that OCT drastically outperforms simpler schemes for the time variation of the microtrap control parameters.

Quantum Dynamics of Non-Degenerate Parametric Amplification

A simple model of a two-mode non-resonant parametric amplifier is studied with special regard to non-classical features such as revivals and squeezing. The methods used apply for an arbitrary pump parameter. Detailed analytical and explicit expressions are given when the coupling of the two modes has a harmonic time-dependence. Despite its simplicity the model exhibits a very broad range of intricate physical effects. We show that quantum revivals are possible for a broad continuous range of physical parameters in the case of initial Fock states. For coherent states we find that such revivals are possible only for certain discrete rational number combinations of the ratio of frequency detuning and pump parameters. Correlation effects are shown to be very sensitive to the initial state of the system.

Theory of Casimir-Polder forces

We consider the energy shift for an atom close to a nonmagnetic body with a magnetic moment coupled to a quantized magnetic field. The corresponding repulsive Casimir-Polder force is obtained for a perfect conductor, a metal, a dielectric medium, with dielectric properties modeled by a Drude formula, and a superconductor at zero temperature. The dielectric properties of the superconductor are obtained by making use of the Mattis-Bardeen linear-response theory and we present some useful expressions for the low-frequency conductivity. The quantum dynamics with a given initial state is discussed in terms of the well-known Weisskopf-Wigner theory and is compared with corresponding results for a electric-dipole coupling. The results obtained are compatible with a conventional master-equation approach. In order to illustrate the dependence on geometry and material properties, numerical results are presented for the ground state using a two-level approximation.

Decay processes in the presence of thin superconducting films

In a recent paper [Phys. Rev. Lett. 97, 070401 (2006)] the transition rate of magnetic spin-flip of a neutral two-level atom trapped in the vicinity of a thick superconducting body was studied. In the present paper we will extend these considerations to a situation with an atom at various distances from a dielectric film. Rates for the corresponding electric dipole-flip transition will also be considered. The rates for these atomic flip transitions can be reduced or enhanced, and in some situations they can even be completely suppressed. For a superconducting film or a thin film of a perfect conducting material various analytical expressions are derived that reveals the dependence of the physical parameters at hand.

On the phase structure of the micromaser system

Abstract We investigate, in an exact manner, the phase structure of the micromaser system in terms of the physical parameters at hand, such as the atom cavity transit time, τ , the atom–photon frequency detuning, Δω , the number of thermal photons, n b and the probability, a , for a pump atom to be in its excited state. Phase diagrams are mapped out for various values of the physical parameters. At sufficiently large values of the detuning, we find a “twinkling” mode of the micromaser system. A correlation length is used to study fluctuations close to the various phase transitions.

Memory effects in spontaneous emission processes

We consider a quantum-mechanical analysis of spontaneous emission in terms of an effective two-level system with a vacuum decay rate

Noise and order in cavity quantum electrodynamics

\Gamma_0

Theory of the microscopic maser phase transitions

and transition angular frequency

Macroscopic Interference Effects in Resonant Cavities

\omega_A

Collective two-atom effects and trapping states in the micromaser

. Our analysis is in principle exact, even though presented as a numerical solution of the time-evolution including memory effects. The results so obtained are confronted with previous discussions in the literature. In terms of the {\it dimensionless} lifetime