Quantum walks and quantum simulations with Bloch oscillating spinor atoms

We propose a scheme for the realization of a quantum walker and a quantum simulator for the Dirac equation with ultracold spinor atoms in driven optical lattices. A precise control of the dynamics of the atomic matter wave can be realized using time-dependent external forces. If the force depends on the spin state of the atoms, the dynamics will entangle the inner and outer degrees of freedom which offers unique opportunities for quantum information and quantum simulation. Here, we introduce a method to realize a quantum walker based on the state-dependent transport of spinor atoms and a coherent driving of the internal state. In the limit of weak driving the dynamics is equivalent to that of a Dirac particle in 1+1 dimensions. Thus it becomes possible to simulate relativistic effects such as Zitterbewegung and Klein tunneling.Comment: published version, 7 figure

Stochastic resonance driven by quantum shot noise in superradiant Raman scattering

We discuss the effects of noise on the timing and strength of superradiant Raman scattering from a small dense sample of atoms. We demonstrate a genuine quantum stochastic resonance effect, where the atomic response is largest for an appropriate quantum noise level. The peak scattering intensity per atom assumes its maximum for a specific non-zero value of quantum noise given by the square root of the number of atoms.Comment: 10 pages, 4 figure

Photon sorters and QND detectors using single photon emitters

We discuss a new method for realizing number-resolving and non-demolition photo detectors by strong coupling of light to individual single photon emitters, which act as strong optical non-linearities. As a specific application we show how these elements can be integrated into an error-proof Bell state analyzer, whose efficiency exceeds the best possible performance with linear optics even for a modest atom-field coupling. The methods are error-proof in the sense that every detection event unambiguously projects the photon state onto a Fock or Bell state.Comment: revised and enlarged version, 6+ pages, 5 figure

Photon scattering by a three-level emitter in a one-dimensional waveguide

We discuss the scattering of photons from a three-level emitter in a one-dimensional waveguide, where the transport is governed by the interference of spontaneously emitted and directly transmitted waves. The scattering problem is solved in closed form for different level structures. Several possible applications are discussed: The state of the emitter can be switched deterministically by Raman scattering, thus enabling applications in quantum computing such as a single photon transistor. An array of emitters gives rise to a photonic band gap structure, which can be tuned by a classical driving laser. A disordered array leads to Anderson localization of photons, where the localization length can again be controlled by an external driving.Comment: 17 pages, 8 figure

Dissipation induced macroscopic entanglement in an open optical lattice

We introduce a method for the dissipative preparation of strongly correlated quantum states of ultracold atoms in an optical lattice via localized particle loss. The interplay of dissipation and interactions enables different types of dynamics. This ushers a new line of experimental methods to maintain the coherence of a Bose-Einstein condensate or to deterministically generate macroscopically entangled quantum states.Comment: 4 figure

Dissipation induced coherence of a two-mode Bose-Einstein condensate

We discuss the dynamics of a Bose-Einstein condensate in a double-well trap subject to phase noise and particle loss. The phase coherence of a weakly-interacting condensate as well as the response to an external driving show a pronounced stochastic resonance effect: Both quantities become maximal for a finite value of the dissipation rate matching the intrinsic time scales of the system. Even stronger effects are observed when dissipation acts in concurrence with strong inter-particle interactions, restoring the purity of the condensate almost completely and increasing the phase coherence significantly.Comment: 10 pages, 5 figure

Quantum transport and localization in biased periodic structures under bi- and polychromatic driving

We consider the dynamics of a quantum particle in a one-dimensional periodic potential (lattice) under the action of a static and time-periodic field. The analysis is based on a nearest-neighbor tight-binding model which allows a convenient closed form description of the transport properties in terms of generalized Bessel functions. The case of bichromatic driving is analyzed in detail and the intricate transport and localization phenomena depending on the communicability of the two excitation frequencies and the Bloch frequency are discussed. The case of polychromatic driving is also discussed, in particular for flipped static fields, i.e. rectangular pulses, which can support an almost dispersionless transport with a velocity independent of the field amplitude.Comment: 18 pages, 11 figur

Beyond mean-field dynamics of small Bose-Hubbard systems based on the number-conserving phase space approach

The number-conserving quantum phase space description of the Bose-Hubbard model is discussed for the illustrative case of two and three modes, as well as the generalization of the two-mode case to an open quantum system. The phase-space description based on generalized SU(M) coherent states yields a Liouvillian flow in the macroscopic limit, which can be efficiently simulated using Monte Carlo methods even for large systems. We show that this description clearly goes beyond the common mean-field limit. In particular it resolves well-known problems where the common mean-field approach fails, like the description of dynamical instabilities and chaotic dynamics. Moreover, it provides a valuable tool for a semi-classical approximation of many interesting quantities, which depend on higher moments of the quantum state and are therefore not accessible within the common approach. As a prominent example, we analyse the depletion and heating of the condensate. A comparison to methods ignoring the fixed particle number shows that in this case artificial number fluctuations lead to ambiguities and large deviations even for quite simple examples.Comment: Significantly enhanced and revised version (20 pages, 20 figures