Liouvillian of the Open STIRAP Problem.

With the corresponding Liouvillian as a starting point, we demonstrate two seemingly new phenomena of the STIRAP problem when subjected to irreversible losses. It is argued that both of these can be understood from an underlying Zeno effect, and in particular both can be viewed as if the environment assists the STIRAP population transfer. The first of these is found for relative strong dephasing, and, in the language of the Liouvillian, it is explained from the explicit form of the matrix generating the time-evolution; the coherence terms of the state decay off, which prohibits further population transfer. For pure dissipation, another Zeno effect is found, where the presence of a non-zero Liouvillian gap protects the system's (adiabatic) state from non-adiabatic excitations. In contrast to full Zeno freezing of the evolution, which is often found in many problems without explicit time-dependence, here, the freezing takes place in the adiabatic basis such that the system still evolves but adiabatically.

XYZ quantum Heisenberg models with p-orbital bosons.

We demonstrate how the spin-1/2 XYZ quantum Heisenberg model can be realized with bosonic atoms loaded in the p band of an optical lattice in the Mott regime. The combination of Bose statistics and the symmetry of the p-orbital wave functions leads to a nonintegrable Heisenberg model with antiferromagnetic couplings. Moreover, the sign and relative strength of the couplings characterizing the model are shown to be experimentally tunable. We display the rich phase diagram in the one-dimensional case and discuss finite size effects relevant for trapped systems. Finally, experimental issues related to preparation, manipulation, detection, and imperfections are considered.

Absence of vacuum induced Berry phases without the rotating wave approximation in cavity QED.

We revisit earlier studies on Berry phases suggested to appear in certain cavity QED settings. It has been especially argued that a nontrivial geometric phase is achievable even in the situation of no cavity photons. We, however, show that such results hinge on imposing the rotating wave approximation (RWA), while without the RWA no Berry phases occur in these schemes. A geometrical interpretation of our results is obtained by introducing semiclassical energy surfaces which in a simple way brings out the phase-space dynamics. With the RWA, a conical intersection between the surfaces emerges and encircling it gives rise to the Berry phase. Without the RWA, the conical intersection is absent and therefore the Berry phase vanishes. It is believed that this is a first example showing how the application of the RWA in the Jaynes-Cummings model may lead to false conclusions, regardless of the mutual strengths between the system parameters.

Effective Abelian and non-Abelian gauge potentials in cavity QED.

Cavity QED models are analyzed in terms of field quadrature operators. We demonstrate that in such representation, the problem can be formulated in terms of effective gauge potentials. In this respect, it presents a completely new system in which gauge fields arise, possessing the advantages of purity, high control of system parameters as well as preparation and detection methods. Studying three well-known models, it is shown that either Abelian or non-Abelian gauge potentials can be constructed. The non-Abelian characteristics are confirmed via numerical simulations utilizing experimental parameters.

Mott-insulator States of ultracold atoms in optical resonators.

We study the low temperature physics of an ultracold atomic gas in the potential formed inside a pumped optical resonator. Here, the height of the cavity potential, and hence the quantum state of the gas, depends not only on the pump parameters, but also on the atomic density through a dynamical ac-Stark shift of the cavity resonance. We derive the Bose-Hubbard model in one dimension and use the strong coupling expansion to determine the parameter regime in which the system is in the Mott-insulator state. We predict the existence of overlapping, competing Mott-insulator states, and bistable behavior in the vicinity of the shifted cavity resonance, controlled by the pump parameters. Outside these parameter regions, the state of the system is in most cases superfluid.