Low dimensional manifolds for exact representation of open quantum systems

Weakly nonlinear degrees of freedom in dissipative quantum systems tend to localize near manifolds of quasi-classical states. We present a family of analytical and computational methods for deriving optimal unitary model transformations based on representations of finite dimensional Lie groups. The transformations are optimal in that they minimize the quantum relative entropy distance between a given state and the quasi-classical manifold. This naturally splits the description of quantum states into quasi-classical coordinates that specify the nearest quasi-classical state and a transformed quantum state that can be represented in fewer basis levels. We derive coupled equations of motion for the coordinates and the transformed state and demonstrate how this can be exploited for efficient numerical simulation. Our optimization objective naturally quantifies the non-classicality of states occurring in some given open system dynamics. This allows us to compare the intrinsic complexity of different open quantum systems.Comment: Added section on semi-classical SR-latch, added summary of method, revised structure of manuscrip

Specification of photonic circuits using Quantum Hardware Description Language

Following the simple observation that the interconnection of a set of quantum optical input-output devices can be specified using structural mode VHSIC Hardware Description Language (VHDL), we demonstrate a computer-aided schematic capture workflow for modeling and simulating multi-component photonic circuits. We describe an algorithm for parsing circuit descriptions to derive quantum equations of motion, illustrate our approach using simple examples based on linear and cavity-nonlinear optical components, and demonstrate a computational approach to hierarchical model reduction.Comment: 20 pages, 6 figures, 1 table, 6 code listing

Spectral properties of finite laser-driven lattices of ultracold Rydberg atoms

We investigate the spectral properties of a finite laser-driven lattice of ultracold Rydberg atoms exploiting the dipole blockade effect in the frozen Rydberg gas regime. Uniform one-dimensional lattices as well as lattices with variable spacings are considered. In the case of a weak laser coupling, we find a multitude of many-body Rydberg states with well-defined excitation properties which are adiabatically accessible starting from the ground state. A comprehensive analysis of the degeneracies of the spectrum as well as of the single and pair excitations numbers of the eigenstates is performed. In the strong laser regime, analytical solutions for the pseudo-fermionic eigenmodes are derived. Perturbative energy corrections for this approximative approach are provided.Comment: 17 pages, 12 figure