Tunneling, self-trapping and manipulation of higher modes of a BEC in a double well

We consider an atomic Bose-Einstein condensate trapped in a symmetric one-dimensional double well potential in the four-mode approximation and show that the semiclassical dynamics of the two ground state modes can be strongly influenced by a macroscopic occupation of the two excited modes. In particular, the addition of the two excited modes already unveils features related to the effect of dissipation on the condensate. In general, we find a rich dynamics that includes Rabi oscillations, a mixed Josephson-Rabi regime, self-trapping, chaotic behavior, and the existence of fixed points. We investigate how the dynamics of the atoms in the excited modes can be manipulated by controlling the atomic populations of the ground states.Comment: 12 pages, 5 figure

Protecting subspaces by acting on the outside

Many quantum control tasks aim at manipulating the state of a quantum mechanical system within a finite subspace of states. However, couplings to the outside are often inevitable. Here we discuss strategies which keep the system in the controlled subspace by applying strong interactions onto the outside. This is done by drawing analogies to simple toy models and to the quantum Zeno effect. Special attention is paid to the constructive use of dissipation in the protection of subspaces.Comment: 16 pages, 10 figure

Approximate joint measurement of qubit observables through an Arthur-Kelly type model

We consider joint measurement of two and three unsharp qubit observables through an Arthur-Kelly type joint measurement model for qubits. We investigate the effect of initial state of the detectors on the unsharpness of the measurement as well as the post-measurement state of the system. Particular emphasis is given on a physical understanding of the POVM to PVM transition in the model and entanglement between system and detectors.Two approaches for characterizing the unsharpness of the measurement and the resulting measurement uncertainty relations are considered.The corresponding measures of unsharpness are connected for the case where both the measurements are equally unsharp. The connection between the POVM elements and symmetries of the underlying Hamiltonian of the measurement interaction is made explicit and used to perform joint measurement in arbitrary directions. Finally in the case of three observables we derive a necessary condition for the approximate joint measurement and use it show the relative freedom available when the observables are non-orthogonal.Comment: 22 pages; Late

Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures

A limitation on simultaneous measurement of two arbitrary positive operator valued measures is discussed. In general, simultaneous measurement of two noncommutative observables is only approximately possible. Following Werner's formulation, we introduce a distance between observables to quantify an accuracy of measurement. We derive an inequality that relates the achievable accuracy with noncommutativity between two observables. As a byproduct a necessary condition for two positive operator valued measures to be simultaneously measurable is obtained.Comment: 7 pages, 1 figure. To appear in Phys. Rev.

Cold Power Tests of the sc 325 MHz CH-Cavity

At the Institute for Applied Physics (IAP), Frankfurt University, a superconducting 325 MHz CH-Cavity has been designed, built and first tests have successfully been performed. The cavity is determined for a 11.4 AMeV, 10 mA ion beam at the GSI UNILAC. Consisting of 7 gaps this resonator is envisaged to deliver a gradient of 5 MV/m. Novel features of this structure are a compact design, low peak fields, improved surface processing and power coupling. Furthermore a tuner system based on bellow tuners driven by a stepping motor and a piezo actuator and attached inside the resonator will control the frequency. In this contribution measurements executed at 4 K and 2 K at the cryo lab in Frankfurt will be presented

Simultaneous measurement of two non-commuting quantum variables: Solution of a dynamical model

The possibility of performing simultaneous measurements in quantum mechanics is investigated in the context of the Curie-Weiss model for a projective measurement. Concretely, we consider a spin-$\frac{1}{2}$ system simultaneously interacting with two magnets, which act as measuring apparatuses of two different spin components. We work out the dynamics of this process and determine the final state of the measuring apparatuses, from which we can find the probabilities of the four possible outcomes of the measurements. The measurement is found to be non-ideal, as (i) the joint statistics do not coincide with the one obtained by separately measuring each spin component, and (ii) the density matrix of the spin does not collapse in either of the measured observables. However, we give an operational interpretation of the process as a generalised quantum measurement, and show that it is fully informative: The expected value of the measured spin components can be found with arbitrary precision for sufficiently many runs of the experiment.Comment: 24 pages, 9 figures; close to published versio