Thomas Busch

Two Cold Atoms in a Harmonic Trap

Two ultracold atoms moving in a trap interact weakly at a very short distance. This interaction can be modeled by a properly regularized contact potential. We solve the corresponding time-independent Schrödinger equation under the assumption of a parabolic, spherically symmetric trapping potential.

Delay-induced excitability.

We analyze the stochastic dynamics of a bistable system under the influence of time-delayed feedback. Assuming an asymmetric potential, we show the existence of a regime in which the system dynamics displays excitability by calculating the relevant residence time distributions and power spectra. Experimentally we then observe this behavior in the polarization dynamics of a vertical cavity surface emitting laser with optoelectronic feedback. Extending these observations to two-dimensional systems with diffusive coupling, we finally show numerically that delay-induced excitability can lead to the appearance of propagating wave fronts and spirals.

Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin.

The nonlocalized case of the spatial density probability of the two-dimensional Grover walk can be obtained using only a two-dimensional coin space and a quantum walk in alternate directions. This significantly reduces the resources necessary for its feasible experimental realization. We present a formal proof of this correspondence and analyze the behavior of the coin-position entanglement as well as the x-y spatial entanglement in our scheme with respect to the Grover one. Our scheme allows us to entangle the two orthogonal directions of the walk more efficiently.

Criticality, factorization, and long-range correlations in the anisotropic XY model

We study the long-range quantum correlations in the anisotropic XY-model. By first examining the thermodynamic limit we show that employing the quantum discord as a figure of merit allows one to capture the main features of the model at zero temperature. Further, by considering suitably large site separations we find that these correlations obey a simple scaling behavior for finite temperatures, allowing for efficient estimation of the critical point. We also address ground-state factorization of this model by explicitly considering finite size systems, showing its relation to the energy spectrum and explaining the persistence of the phenomenon at finite temperatures. Finally, we compute the fidelity between finite and infinite systems in order to show that remarkably small system sizes can closely approximate the thermodynamic limit.

Alternate two-dimensional quantum walk with a single-qubit coin

We have recently proposed a two-dimensional quantum walk where the requirement of a higher dimensionality of the coin space is substituted with the alternance of the directions in which the walker can move [C. Di Franco, M. Mc Gettrick, and Th. Busch, Phys. Rev. Lett. 106, 080502 (2011)]. For a particular initial state of the coin, this walk is able to perfectly reproduce the spatial probability distribution of the nonlocalized case of the Grover walk. Here, we present a more detailed proof of this equivalence. We also extend the analysis to other initial states in order to provide a more complete picture of our walk. We show that this scheme outperforms the Grover walk in the generation of x-y spatial entanglement for any initial condition, with the maximum entanglement obtained in the case of the particular aforementioned state. Finally, the equivalence is generalized to wider classes of quantum walks and a limit theorem for the alternate walk in this context is presented.

Observing the profile of an atom laser beam

We report on an investigation of the beam profile of an atom laser extracted from a magnetically trapped

Spatial adiabatic passage: a review of recent progress.

^{87}\mathrm{Rb}

Measurement of collective excitations in a spin-orbit-coupled Bose-Einstein condensate

Bose-Einstein condensate. The transverse momentum distribution is magnified by a curved mirror for matter waves and a momentum resolution of

Gap Solitons in Spin-Orbit-Coupled Bose-Einstein Condensates in Optical Lattices

1∕60

Quenching small quantum gases: Genesis of the orthogonality catastrophe

of a photon recoil is obtained. We find the transverse momentum distribution to be determined by the mean-field potential of the residing condensate, which leads to a nonsmooth transverse density distribution. Our experimental data are compared with a full three-dimensional simulation of the output coupling process and we find good agreement.