arXiv subjects

Dieter Jaksch

Publications and source records attributed to Dieter Jaksch.

121 records · Page 7Linked to original sources

arXiv2009

Parameter estimation with cluster states

We propose a scheme for parameter estimation with cluster states. We find that phase estimation with cluster states under a many-body Hamiltonian and separable measurements leads to a precision at the Heisenberg limit. As noise models we study the dephasing, depolarizing, and pure damping channels. Decoherence reduces the sensitivity but our scheme remains superior over several reference schemes with states such as maximally entangled states and product states. For small cluster states and fixed evolution times it remains at the Heisenberg limit for approximately 2 times as many qubits than alternative schemes.

quant-ph↗

arXiv2009

Phonon-induced artificial magnetic fields

We investigate the effect of a rotating Bose-Einstein condensate on a system of immersed impurity atoms trapped by an optical lattice. We analytically show that for a one-dimensional, ring-shaped setup the coupling of the impurities to the Bogoliubov phonons of the condensate leads to a non-trivial phase in the impurity hopping. The presence of this phase can be tested by observing a drift in the transport properties of the impurities. These results are quantitatively confirmed by a numerically exact simulation of a two-mode Bose-Hubbard model. We also give analytical expressions for the occurring phase terms for a two-dimensional setup. The phase realises an artificial magnetic field and can for instance be used for the simulation of the quantum Hall effect using atoms in an optical lattice.

quant-ph↗

arXiv2008

Optical lattice quantum Hall effect

We explore the behavior of interacting bosonic atoms in an optical lattice subject to a large artificial magnetic field. We extend earlier investigations of this system where the number of magnetic flux quanta per unit cell alpha is close to a simple rational number [Phys. Rev. Lett. 96, 180407 (2006)]. Interesting topological states such as the Laughlin and Read-Rezayi states can occur even if the atoms experience a weak trapping potential in one direction. An explicit numerical calculation near alpha = 1/2 shows that the system exhibits a striped vortex lattice phase of one species, which is analogous to the behavior of a two-species system for small alpha. We also investigate methods to probe the encountered states. These include spatial correlation functions and the measurement of noise correlations in time of flight expanded atomic clouds. Characteristic differences arise which allow for an identification of the respective quantum Hall states. We furthermore discuss that a counterintuitive flow of the Hall current occurs for certain values of alpha.

cond-mat.mes-hall↗

arXiv2007

Dynamics, dephasing and clustering of impurity atoms in Bose-Einstein condensates

We investigate the influence of a Bose-Einstein condensate (BEC) on the properties of immersed impurity atoms, which are trapped in an optical lattice. Assuming a weak coupling of the impurity atoms to the BEC, we derive a quantum master equation for the lattice system. In the special case of fixed impurities with two internal states the atoms represent a quantum register and the quantum master equation reproduces the exact evolution of the qubits. We characterise the qubit dephasing which is caused by the interspecies coupling and show that the effect of sub- and superdecoherence is observable for realistic experimental parameters. Furthermore, the BEC phonons mediate an attractive interaction between the impurities, which has an important impact on their spatial distribution. If the lattice atoms are allowed to move, there occurs a sharp transition with the impurities aggregating in a macroscopic cluster at experimentally achievable temperatures. We also investigate the impact of the BEC on the transport properties of the impurity atoms and show that a crossover from coherent to diffusive behaviour occurs with increasing interaction strength.

quant-ph↗

arXiv2007

A quantum repeater based on decoherence free subspaces

We study a quantum repeater which is based on decoherence free quantum gates recently proposed by Klein et al. [Phys. Rev. A 73, 012332 (2006)]. A number of operations on the decoherence free subspace in this scheme makes use of an ancilla qubit, which undergoes dephasing and thus introduces decoherence to the system. We examine how this decoherence affects entanglement swapping and purification as well as the performance of a quantum repeater. We compare the decoherence free quantum repeater with a quantum repeater based on qubits that are subject to decoherence and show that it outperforms the latter when decoherence due to long waiting times of conventional qubits becomes significant. Thus, a quantum repeater based on decoherence free subspaces is a possibility to greatly improve quantum communication over long or even intercontinental distances.

quant-ph↗

arXiv2007

Dynamics of vortices in weakly interacting Bose-Einstein condensates

We study the dynamics of vortices in ideal and weakly interacting Bose-Einstein condensates using a Ritz minimization method to solve the two-dimensional Gross-Pitaevskii equation. For different initial vortex configurations we calculate the trajectories of the vortices. We find conditions under which a vortex-antivortex pair annihilates and is created again. For the case of three vortices we show that at certain times two additional vortices may be created, which move through the condensate and annihilate each other again. For a noninteracting condensate this process is periodic, whereas for small interactions the essential features persist, but the periodicity is lost. The results are compared to exact numerical solutions of the Gross-Pitaevskii equation confirming our analytical findings.

quant-ph↗

arXiv2007

Polaron Physics in Optical Lattices

We investigate the effects of a nearly uniform Bose-Einstein condensate (BEC) on the properties of immersed trapped impurity atoms. Using a weak-coupling expansion in the BEC-impurity interaction strength, we derive a model describing polarons, i.e., impurities dressed by a coherent state of Bogoliubov phonons, and apply it to ultracold bosonic atoms in an optical lattice. We show that, with increasing BEC temperature, the transport properties of the impurities change from coherent to diffusive. Furthermore, stable polaron clusters are formed via a phonon-mediated off-site attraction.

quant-ph↗

arXiv2006

Convergence rate of dimension reduction in Bose-Einstein condensates

In this paper, we study dimension reduction of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) modelling Bose-Einstein condensation under different limiting interaction and trapping frequencies parameter regimes. Convergence rates for the dimension reduction of 3D ground state and dynamics of the GPE in the case of disk-shaped condensation and cigar-shaped condensation are reported based on our asymptotic and numerical results. In addition, the parameter regimes in which the 3D GPE cannot be reduced to lower dimensions are identified.

cond-mat.mtrl-sci↗

arXiv2006

Simulating high-temperature superconductivity model Hamiltonians with atoms in optical lattices

We investigate the feasibility of simulating different model Hamiltonians used in high-temperature superconductivity. We briefly discuss the most common models and then focus on the simulation of the so-called t-J-U Hamiltonian using ultra-cold atoms in optical lattices. For this purpose, previous simulation schemes to realize the spin interaction term J are extended. We especially overcome the condition of a filling factor of exactly one, which otherwise would restrict the phase of the simulated system to a Mott-insulator. Using ultra-cold atoms in optical lattices allows simulation of the discussed models for a very wide range of parameters. The time needed to simulate the Hamiltonian is estimated and the accuracy of the simulation process is numerically investigated for small systems.

quant-ph↗

arXiv2006

Robust implementations of Quantum Repeaters

We show how to efficiently exploit decoherence free subspaces (DFSs), which are immune to collective noise, for realizing quantum repeaters with long lived quantum memories. Our setup consists of an assembly of simple modules and we show how to implement them in systems of cold, neutral atoms in arrays of dipole traps. We develop methods for realizing robust gate operations on qubits encoded in a DFS using collisional interactions between the atoms. We also give a detailed analysis of the performance and stability of all required gate operations and emphasize that all modules can be realized with current or near future experimental technology.

quant-ph↗

arXiv2004

Could Energy Decoherence due to Quantum Gravity be observed?

It has recently been proposed that quantum gravity might lead to the decoherence of superpositions in energy, corresponding to a discretization of time at the Planck scale. At first sight the proposal seems amenable to experimental verification with methods from quantum optics and atomic physics. However, we argue that the predicted decoherence is unobservable in such experiments if it acts globally on the whole experimental setup. This is related to the unobservability of the global phase in interference. We also show how local energy decoherence, which acts separately on system and phase reference, could be detected with remarkable sensitivity and over a wide range of length scales by long-distance Ramsey interferometry with metastable atomic states. The sensitivity of the experiments can be further enhanced using multi-atom entanglement.

quant-ph↗

arXiv2003

An explicit unconditionally stable numerical method for solving damped nonlinear Schrödinger equations with a focusing nonlinearity

This paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schrödinger equations (NLS). The method is explicit, unconditionally stable and time transversal invariant. Moreover, it preserves the exact decay rate for the normalization of the wave function if linear damping terms are added to the NLS. Extensive numerical tests are presented for cubic focusing nonlinear Schrödinger equations in 2d with a linear, cubic or a quintic damping term. Our numerical results show that quintic or cubic damping always arrests blowup, while linear damping can arrest blowup only when the damping parameter $\dt$ is larger than a threshold value $\dt_{\rm th}$. We note that our method can also be applied to solve the 3d Gross-Pitaevskii equation with a quintic damping term to model the dynamics of a collapsing and exploding Bose-Einstein condensate (BEC).

math.NA↗

arXiv2003

Numerical Solution of the Gross-Pitaevskii Equation for Bose-Einstein Condensation

We study the numerical solution of the time-dependent Gross-Pitaevskii equation (GPE) describing a Bose-Einstein condensate (BEC) at zero or very low temperature. In preparation for the numerics we scale the 3d Gross-Pitaevskii equation and obtain a four-parameter model. Identifying `extreme parameter regimes', the model is accessible to analytical perturbation theory, which justifies formal procedures well known in the physical literature: reduction to 2d and 1d GPEs, approximation of ground state solutions of the GPE and geometrical optics approximations. Then we use a time-splitting spectral method to discretize the time-dependent GPE. Again, perturbation theory is used to understand the discretization scheme and to choose the spatial/temporal grid in dependence of the perturbation parameter. Extensive numerical examples in 1d, 2d and 3d for weak/strong interactions, defocusing/focusing nonlinearity, and zero/nonzero initial phase data are presented to demonstrate the power of the numerical method and to discuss the physics of Bose-Einstein condensation.

cond-mat↗