Niklas Teichmann

Differences between mean-field dynamics and N-particle quantum dynamics as a signature of entanglement.

A Bose-Einstein condensate in a tilted double-well potential under the influence of time-periodic potential differences is investigated in the regime where the mean-field (Gross-Pitaevskii) dynamics become chaotic. For some parameters near stable regions, even averaging over several condensate oscillations does not remove the differences between mean-field and N-particle results. While introducing decoherence via piecewise deterministic processes reduces those differences, they are due to the emergence of mesoscopic entangled states in the chaotic regime.

Coherently controlled entanglement generation in a binary Bose-Einstein condensate

Considering a two-component Bose-Einstein condensate in a double-well potential, a method to generate a Bell state consisting of two spatially separated condensates is suggested. For repulsive interactions, the required tunnelling control is achieved numerically by varying the amplitude of a sinusoidal potential difference between the wells. Both numerical and analytical calculations reveal the emergence of a highly entangled mesoscopic state.

Fractional photon-assisted tunneling for Bose-Einstein condensates in a double well

Half-integer photon-resonances in a periodically shaken double well are investigated on the level of the N-particle quantum dynamics. Contrary to non-linear mean-field equations, the linear N-particle Schrodinger equation does not contain any non-linearity which could be the origin of such resonances. Nevertheless, analytic calculations on the N-particle level explain why such resonances can be observed even for particle numbers as low as N = 2. These calculations also demonstrate why fractional photon resonances are not restricted to half-integer values.

Process-chain approach to the Bose-Hubbard model: Ground-state properties and phase diagram

We carry out a perturbative analysis, of high order in the tunneling parameter, of the ground state of the homogeneous Bose-Hubbard model in the Mott insulator phase. This is made possible by a diagrammatic process-chain approach, derived from Katos representation of the many-body perturbation series, which can be implemented numerically in a straightforward manner. We compute ground-state energies, atom-atom correlation functions, density-density correlations, and occupation number fluctuations, for one-, two-, and three-dimensional lattices with arbitrary integer filling. A phenomenological scaling behavior is found which renders the data almost independent of the filling factor. In addition, the process-chain approach is employed for calculating the boundary between the Mott insulator phase and the superfluid phase with high accuracy. We also consider systems with dimensionalities d>3, thus monitoring the approach to the mean-field limit. The versatility of the method suggests further applications to other systems which are less well understood.

Bose-Hubbard phase diagram with arbitrary integer filling

We study the transition from a Mott insulator to a superfluid in both the two- and the three-dimensional Bose-Hubbard model at zero temperature, employing the method of the effective potential. Converting Katos perturbation series into an algorithm capable of reaching high orders, we obtain accurate critical parameters for any integer filling factor. Our technique allows us to monitor both the approach to the mean-field limit by considering spatial dimensionalities d>3 and to the quantum rotor limit of high filling, which refers to an array of Josephson junctions.

Reproducible mesoscopic superpositions of Bose-Einstein condensates and mean-field chaos

In a parameter regime for which the mean-field (Gross-Pitaevskii) dynamics becomes chaotic, mesoscopic quantum superpositions in phase space can occur in a double-well potential, which is shaken periodically. For experimentally realistic initial states, such as the ground state of some 100 atoms, the emergence of mesoscopic quantum superpositions in phase space is investigated numerically. It is shown to be reproducible, even if the initial conditions change slightly. Although the final state is not a perfect superposition of two distinct phase states, the superposition is reached an order of magnitude faster than in the case of the collapse-and-revival phenomenon. Furthermore, a generator of entanglement is identified.

Fractional-photon-assisted tunneling in an optical superlattice: Large contribution to particle transfer

Fractional-photon-assisted tunneling is investigated both analytically and numerically for few interacting ultracold atoms in the double wells of an optical superlattice. This can be realized experimentally by adding periodic shaking to an existing experimental setup [Cheinet et al., Phys. Rev. Lett. 101, 090404 (2008)]. Photon-assisted tunneling is visible in the particle transfer between the wells of the individual double wells. In order to understand the physics of the photon-assisted tunneling, an effective model based on the rotating-wave approximation is introduced. The validity of this effective approach is tested for wide parameter ranges that are accessible to experiments in double-well lattices. The effective model goes well beyond previous perturbation theory approaches and is useful for investigating in particular the fractional-photon-assisted tunneling resonances. Analytic results on the level of the experimentally realizable two-particle quantum dynamics show very good agreement with the numerical solution of the time-dependent Schroedinger equation. Far from being a small effect, both the one-half-photon and the one-third-photon resonances are shown to have large effects on the particle transfer.

Reference data for phase diagrams of triangular and hexagonal bosonic lattices

We investigate systems of bosonic particles at zero temperature in triangular and hexagonal optical lattice potentials in the framework of the Bose-Hubbard model. Employing the process-chain approach, we obtain accurate values for the boundaries between the Mott insulating phase and the superfluid phase. These results can serve as reference data for both other approximation schemes and upcoming experiments. Since arbitrary integer filling factors g are amenable to our technique, we are able to monitor the behavior of the critical hopping parameters with increasing filling. We also demonstrate that the g-dependence of these exact parameters is described almost perfectly by a scaling relation inferred from the mean-field approximation.

Signatures of chaos-induced mesoscopic entanglement

For a Bose–Einstein condensate in a double-well potential, time-periodic shaking can lead to the emergence of non-classical mesoscopic superpositions on very short timescales. It is suggested to experimentally detect these deviations from mean-field (Gross–Pitaevskii) behaviour by investigating both the variance of the particle number and the interference pattern. The disappearance of the interference pattern followed by its reappearance a short time later could serve as an experimental signature of mesoscopic entanglement.

Generation of mesoscopic superpositions of a binary Bose-Einstein condensate in a slightly asymmetric double well

A previous publication [1] suggested to coherently generate mesoscopic superpositions of a two-component Bose-Einstein condensate in a double well under perfectly symmetric conditions. However, already tiny asymmetries can destroy the entanglement properties of the ground state. Nevertheless, even under more realistic conditions, the scheme is demonstrated numerically to generate mesoscopic superpositions.