Abstract:
We present a general analysis of the state obtained by subjecting the output from a continuous-wave (cw) Gaussian field to non-Gaussian measurements. The generic multimode state of cw Gaussian fields is characterized by an infinite dimensional covariance matrix involving the noise correlations of the source. Our theory extracts the information relevant for detection within specific temporal output modes from these correlation functions . The formalism is applied to schemes for production of non-classical light states from a squeezed beam of light.

Abstract:
Two independently prepared condensates can be combined into a single larger condensate by detection of their relative phase in an intereference measurement.

Abstract:
We propose to subject two Bose-Einstein condensates to a periodic potential, so that one condensate undergoes the Mott insulator transition to a state with precisely one atom per lattice site. We show that photoassociation of heteronuclear molecules within each lattice site is described by the quantum optical Jaynes-Cummings Hamiltonian. In analogy with studies of this Hamiltonian with cavity fields and trapped ions, we are thus able to engineer quantum optical states of atomic matter wave fields and we are able to reconstruct these states by quantum state tomography.

Abstract:
This paper deals with the conversion between atoms and molecules in optical lattices. We show that in the absence of collisional interaction, the atomic and molecular components in different lattice wells combine into states with macroscopic condensate fractions, which can be observed as a strong diffraction signal, if the particles are abruptly released from the lattice. The condensate population, and the diffraction signal are governed not only by the mean number of atoms or molecules in each well, but by the precise amplitudes on state vector components with different numbers of particles. We discuss ways to control these amplitudes and to maximize the condensate fraction in the molecular formation process.

Abstract:
A recent analysis [quant-ph/0104062] suggests that weak measurements can be used to give observational meaning to counterfactual reasoning in quantum physics. A weak measurement is predicted to assign a negative unit population to a specific state in an interferometric Gedankenexperiment proposed by Hardy. We propose an experimental implementation with trapped ions of the Gedankenexperiment and of the weak measurement. In our standard quantum mechanical analysis of the proposal no states have negative population, but we identify the registration of a negative population by particles being displaced on average in the direction opposite to a force acting upon them.

Abstract:
We present an analysis of the cooling of a micro-mechanical resonator by means of measurements and back action. The measurements are performed via the coupling to a Cooper-pair box, and although the coupling does not lead to net cooling, the extraction of information and hence entropy from the system leads to a pure quantum state. Under suitable circumstances, the states become very close to coherent states, conditioned on the measurement record, and can hence be displaced to the oscillator ground state.

Abstract:
We propose to encode quantum information in rotational excitations in a molecular ensemble. Using a stripline cavity field for quantum state transfer between the molecular ensemble and a Cooper pair box two-level system, our proposal offers a linear scaling of the number of qubits in our register with the number of rotationally excited states available in the molecules.

Abstract:
We propose an efficient method to produce multi-particle entangled states of ions in an ion trap for which a wide range of interesting effects and applications have been suggested. Our preparation scheme exploits the collective vibrational motion of the ions, but it works in such a way that this motion need not be fully controlled in the experiment. The ions may, e.g., be in thermal motion and exchange mechanical energy with a surrounding heat bath without detrimental effects on the internal state preparation. Our scheme does not require access to the individual ions in the trap.

Abstract:
We propose an implementation of quantum logic gates via virtual vibrational excitations in an ion trap quantum computer. Transition paths involving unpopulated, vibrational states interfere destructively to eliminate the dependence of rates and revolution frequencies on vibrational quantum numbers. As a consequence quantum computation becomes feasible with ions whos vibrations are strongly coupled to a thermal reservoir.

Abstract:
We propose an approach to quantum computing in which quantum gate strengths are parametrized by quantum degrees of freedom, and the capability of the quantum computer to perform desired tasks is monitored and gradually improved by successive feedback modifications of the coupling strength parameters. Our proposal aims at experimental implementation, scalable to computational problems too large to be simulated theoretically, and we demonstrate feasibility of our proposal with simulations on search and factoring algorithms.