Multistate Markov models for systems with dependent units

A system that can be described by a homogeneous continuous-time discrete-state Markov process is treated. The case in which transition rates for each unit depend on the current state of the system is considered. The condition in which the transition-rate matrix of the system has the form of a modified Kronecker sum of transition-rate matrices of its units is investigated. An algorithm based on the Kronecker algebra is introduced for determining the transition-rate matrix of the system. its use is particularly efficient during construction of machines when reliability is evaluated for several systems with the same structure but different transition rates     

Digital quantum simulation with Rydberg atoms

We discuss in detail the implementation of an open-system quantum simulator with Rydberg states of neutral atoms held in an optical lattice. Our scheme allows one to realize both coherent as well as dissipative dynamics of complex spin models involving many-body interactions and constraints. The central building block of the simulation scheme is constituted by a mesoscopic Rydberg gate that permits the entanglement of several atoms in an efficient, robust and quick protocol. In addition, optical pumping on ancillary atoms provides the dissipative ingredient for engineering the coupling between the system and a tailored environment. As an illustration, we discuss how the simulator enables the simulation of coherent evolution of quantum spin models such as the two-dimensional Heisenberg model and Kitaev’s toric code, which involves four-body spin interactions. We moreover show that in principle also the simulation of lattice fermions can be achieved. As an example for zcontrolled dissipative dynamics, we discuss ground state cooling of frustration-free spin Hamiltonians.     

A Double Well Interferometer on an Atom Chip

Radio-Frequency coupling between magnetically trapped atomic states allows to create versatile adiabatic dressed state potentials for neutral atom manipulation. Most notably, a single magnetic trap can be split into a double well by controlling amplitude and frequency of an oscillating magnetic field. We use this to build an integrated matter wave interferometer on an atom chip. Transverse splitting of quasi one-dimensional Bose–Einstein condensates over a wide range from 3 to 80 μm is demonstrated, accessing the tunnelling regime as well as completely isolated sites. By recombining the two split BECs in time of flight expansion, we realize a matter wave interferometer. The observed interference pattern exhibits a stable relative phase of the two condensates, clearly indicating a coherent splitting process. Furthermore, we measure and control the deterministic phase evolution throughout the splitting process. RF induced potentials are especially suited for integrated micro manipulation of neutral atoms on atom chips: designing appropriate wire patterns enables control over the created potentials to the (nanometer) precision of the fabrication process. Additionally, hight local RF amplitudes can be obtained with only moderate currents. This new technique can be directly implemented in many existing atom chip experiments.