Search

We construct a unified operator framework for quantum holonomies generated from bosonic systems. For a system whose Hamiltonian is bilinear in the creation and annihilation operators, we find a holonomy group determined only by a set of selected orthonormal modes obeying a stronger version of the adiabatic theorem. This photon-number independent description offers deeper insight as well as a computational advantage when compared to the standard formalism on geometric phases. In particular, a strong analogy between quantum holonomies and linear optical networks can be drawn. This relation provides an explicit recipe of how any linear optical quantum computation can be made geometrically robust in terms of adiabatic or nonadiabatic geometric phases.

Geometric phases, which are ubiquitous in quantum mechanics, are commonly more than only scalar quantities. Indeed, often they are matrix-valued objects that are connected with non-Abelian geometries. Here, we show how generalized non-Abelian geometric phases can be realized using electromagnetic waves traveling through coupled photonic waveguide structures. The waveguides implement an effective Hamiltonian possessing a degenerate dark subspace in which an adiabatic evolution can occur. The associated quantum metric induces the notion of a geodesic that defines the optimal adiabatic evolution. We exemplify the non-Abelian evolution of an Abelian gauge field by a Wilson loop.

We study the interaction of thermal rubidium atoms with the guided mode of slot waveguides integrated in a vapor cell. Slot waveguides provide strong confinement of the light field in an area that overlaps with the atomic vapor. We investigate the transmission of the atomic cladding waveguides depending on the slot width, which determines the fraction of transmitted light power interacting with the atomic vapor. An elaborate simulation method has been developed to understand the behavior of the measured spectra. This model is based on individual trajectories of the atoms and includes both line shifts and decay rates due to atom-surface interactions that we have calculated for our specific geometries using the discrete dipole approximation. Furthermore, we investigate density-dependent effects on the line widths and line shifts of the rubidium atoms in the subwavelength interaction region of a slot waveguide.

In this article, we analyze the Casimir-Polder interaction of atoms with a solid grating and the repulsive interaction between the atoms and the grating in the presence of an external laser source. The Casimir-Polder potential is evaluated exactly in terms of Rayleigh reflection coefficients and via an approximate Hamaker approach. The laser-tuned repulsive interaction is given in terms of Rayleigh transmission coefficients. The combined potential landscape above the solid grating is probed locally by diffraction of Bose-Einstein condensates. Measured diffraction efficiencies reveal information about the shape of the potential landscape in agreement with the theory based on Rayleigh decompositions.