Optical lattices and Quantum Information
A system of neural atoms stored in an optical lattice as shown in the figure below is a promising candidate for implementing scalable quantum computing. In this research project the leading European groups in the field conduct a concerted research effort towards making quantum information in optical lattices viable. Following their initial work, these groups have shown experimentally and theoretically that a quantum phase transition can be used to prepare exactly one atom per lattice site, where each atom can be considered as quantum bit. Based on this socalled MottInsulator state several schemes for quantum computation have been proposed, including proposals for the creation of entanglement, computation with cluster states and quantum simulations. In this project we use a Mott insulator composed of single atoms as a quantum register, in which one can encode qubits in the single atoms on each lattice site and quantum gates can be implemented acting on different atoms of the lattice. This setup is schematically shown in the figure. Atoms can be manipulated either at the single particle level or collectively. Crucial advantages are i) the simple quantumlevel structures of atoms; ii) the insulation of the neutral atoms from the environment which leads to a strong suppression of decoherence, and iii) the ability to trap and act on a very large ensemble of identical atoms. An impressive example of the flexibility of optical lattices is the use of the internal degrees of freedom of ground state neutral atoms in order to generate the quantum entanglement that is essential of many quantum information protocols. To generate entanglement, one requires an experimental system that can be prepared in a pure atomic state, with significant and coherently controlled interactions between the particles composing the pure state. Samples of BoseEinstein condensates, or of Fermi degenerate gases, fulfil these requirements, and, therefore, they could provide an ideal experimental system for studying quantum entanglement.
The goal of this work is to make quantum processing viable by using neutral atoms trapped in optical lattices. We focus on different challenges: preparation and initialisation of a quantum register; addressing, manipulating and measuring on single sites; twobit gates and compatible stable qubits; generation and characterisation of multiparticle entanglement states; strategies for minimising decoherence; quantum simulator; new theoretical strategies for quantum computers with optical lattices. The final objectives of the project will provide a persistent and longterm commitment to emerging applications.
Investigators:  D. Jaksch

Collaborators:  E. Arimondo (Coordinator) , I. Bloch, H.J. Briegel, T. Esslinger and P. Zoller

 
Home page:  http://olaqui.df.unipi.it/

Acronym:  OLAQUI

Funded by:  EU Specific Targeted Research Project; Call: FP62002ISTC, Fet Open; Contract No 013501

 
Start date:  20050201

End date:  20080731

 
Related Publications

S.W. Lee and D. Jaksch,
Maximal violation of tight Bell inequalities for maximal highdimensional entanglement,
Phys. Rev. A 80, 010103(R) (2009).
We propose a Bell inequality for highdimensional bipartite systems obtained by binning local measurement outcomes and show that it is tight. We find a binning method for even ddimensional measurement outcomes for which this Bell inequality is maximally violated by maximally entangled states. Furthermore, we demonstrate that the Bell inequality is applicable to continuous variable systems and yields strong violations for twomode squeezed states.
created: 20032008, last modified: 30072009

A. Klein and D. Jaksch,
Phononinduced artificial magnetic fields,
EuroPhys. Lett. 85, 13001 (2009).
We investigate the effect of a rotating BoseEinstein condensate on a system of immersed impurity atoms trapped by an optical lattice. We analytically show that for a onedimensional, ringshaped setup the coupling of the impurities to the Bogoliubov phonons of the condensate leads to a nontrivial 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 twomode BoseHubbard model. We also give analytical expressions for the occurring phase terms for a twodimensional 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.
created: 15082008, last modified: 19012009

B Vaucher, S.J. Thwaite and D. Jaksch,
Ultralarge Rydberg dimers in optical lattices,
Phys. Rev. A 78, 043415 (2008).
We investigate the dynamics of Rydberg electrons excited from the ground
state of ultracold atoms trapped in an optical lattice. We first consider a
lattice comprising an array of doublewell potentials, where each double well is occupied by two ultracold atoms. We demonstrate the existence of molecular states with equilibrium distances of the order of experimentally attainable interwell spacings and binding energies of the order of 103 GHz. We also consider the situation whereby groundstate atoms trapped in an optical lattice are collectively excited to Rydberg levels, such that the chargedensity distributions of neighbouring atoms overlap. We compute the hopping rate and interaction matrix elements between highlyexcited electrons separated by distances comparable to typical lattice spacings. Such systems have tunable interaction parameters and a temperature ~10^{4} times smaller than the Fermi temperature, making them potentially attractive for the study and simulation of strongly correlated electronic systems.
created: 16082008, last modified: 13072009

U. Dorner, A. Klein and D. Jaksch,
A quantum repeater based on decoherence free subspaces,
Quant. Inf. Comp. 8, 0468 (2008).
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.
created: 01062007, last modified: 17042008

M. Rodriguez, S.R. Clark and D. Jaksch,
Adiabatic melting of twocomponent Mottinsulator states,
Phys. Rev. A 77, 043613 (2008).
We analyze the outcome of a Mott insulator to superfluid
transition for a twocomponent Bose gas with two atoms per site in
an optical lattice in the limit of slow ramping down the lattice
potential. This manipulation of the initial Mott insulating state
transforms local correlations between hyperfine states of atom
pairs into multiparticle correlations extending over the whole
system. We show how to create macroscopic twin Fock states in this
way an that, in general, the obtained superfluid states are highly
depleted even for initial ground Mott insulator states.
created: 22012008, last modified: 11042008

M. Bruderer, A. Klein, S.R. Clark and D. Jaksch,
Transport of strongcoupling polarons in optical lattices,
New J. Phys. 10, 033015 (2008).
We study the transport of ultracold impurity atoms immersed in a BoseEinstein condensate (BEC) and trapped in a tight optical lattice. Within the strongcoupling regime, we derive an extended Hubbard model describing the dynamics of the impurities in terms of polarons, i.e. impurities dressed by a coherent state of Bogoliubov phonons. Using a generalized master equation based on this microscopic model we show that inelastic and dissipative phonon scattering results in (i) a crossover from coherent to incoherent transport of impurities with increasing BEC temperature and (ii) the emergence of a net atomic current across a tilted optical lattice. The dependence of the atomic current on the lattice tilt changes from ohmic conductance to negative differential conductance within an experimentally accessible parameter regime. This transition is accurately described by an EsakiTsutype relation with the effective relaxation time of the impurities as a temperaturedependent parameter.
created: 25102007, last modified: 11032008

B Vaucher, A Nunnenkamp and D. Jaksch,
Creation of robust entangled states and new resources for measurementbased quantum computation using optical superlattices,
New J. Phys. 10, 023005 (2008).
We investigate how to create robust entangled states of ultracold atoms trapped in optical lattices by dynamically manipulating the shape of the lattice potential. We consider an additional potential (the superlattice) that allows both the splitting of each site into a double well potential, and the control of the height of potential barrier between sites. We use superlattice manipulations to perform entangling operations between neighbouring qubits encoded on the Zeeman levels of the atoms without having to perform transfers between the different vibrational states of the atoms. We show how to use superlattices to engineer robust manybody entangled states. Also, we present a method to realize a 2D resource for measurementbased quantum computing via Bellpair measurements that is resilient to collective dephasing noise. We analyze measurement networks that allow the execution of quantum algorithms while maintaining the resilience properties of the system throughout the computation.
created: 26102007, last modified: 07022008

B Vaucher, S.R. Clark, U. Dorner and D. Jaksch,
Fast initialization of a highfidelity quantum register using optical superlattices,
New J. Phys. 9, 221 (2007).
We propose a method for the fast generation of a quantum register of
addressable qubits consisting of ultracold atoms stored in an
optical lattice. Starting with a half filled lattice we remove every
second lattice barrier by adiabatically switching on a superlattice
potential which leads to a long wavelength lattice in the Mott
insulator state with unit filling. The larger periodicity of the
resulting lattice could make individual addressing of the atoms via
an external laser feasible. The dynamics of the transition from a
half filled to a commensurately filled lattice is analyzed
numerically with the help of the Time Evolving Block Decimation
algorithm and analytically using the KibbleZurek theory. We show
that the time scale for the whole process, i.e. creating the half
filled lattice and subsequent doubling of the lattice periodicity, is
significantly faster than adiabatic direct quantum freezing of a
superfluid into a Mott insulator for large lattice periods. Our
method therefore provides a high fidelity quantum register of
addressable qubits on a fast time scale.
created: 27022007, last modified: 27112007

S.R. Clark, A. Klein, M. Bruderer and D. Jaksch,
Graph state generation with noisy mirrorinverting spin chains,
New J. Phys. 9, 202 (2007).
We investigate the influence of noise on a graph state generation
scheme which exploits a mirror inverting spin chain. Within this
scheme the spin chain is used repeatedly as an entanglement bus
(EB) to create multipartite entanglement. The model we consider
comprises of each spin of this EB being exposed to independent
local noise which degrades the capabilities of the EB. Here we
concentrate on quantifying its performance as a singlequbit
channel and as a mediator of a twoqubit entangling gate, since
these are basic operations necessary for graph state generation
using the EB. In particular, for the singlequbit case we
numerically calculate the average channel fidelity and whether the
channel becomes entanglement breaking, i.e., expunges any
entanglement the transferred qubit may have with other external
qubits. We find that neither local decay nor dephasing noise cause
entanglement breaking. This is in contrast to local thermal and
depolarizing noise where we determine a critical length and
critical noise coupling, respectively, at which entanglement
breaking occurs. The critical noise coupling for local
depolarizing noise is found to exhibit a powerlaw dependence on
the chain length. For two qubits we similarly compute the average
gate fidelity and whether the ability for this gate to create
entanglement is maintained. By considering the concatenation of
these noisy gates for the construction of a linear cluster state
we demonstrate that there are severe constraints on the level of
noise that can be tolerated for graph state generation.
created: 16022007, last modified: 26112007

A. Klein, M. Bruderer, S.R. Clark and D. Jaksch,
Dynamics, dephasing and clustering of impurity atoms in BoseEinstein condensates,
New J. Phys. 9, 411 (2007).
We investigate the influence of a BoseEinstein 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 (QME) for the lattice system. In the special case of fixed impurities with two internal states the atoms represent a quantum register and the QME reproduces the exact evolution of the qubits. We characterize 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.
created: 21112007, last modified: 26112007

A. Klein, D. Jaksch, Y Zhang and W. Bao,
Dynamics of vortices in weakly interacting BoseEinstein condensates,
Phys. Rev. A 76, 043602 (2007).
We study the dynamics of vortices in ideal and weakly interacting BoseEinstein condensates using a Ritz minimization method to solve the twodimensional GrossPitaevskii equation. For different initial vortex configurations we calculate the trajectories of the vortices. We find conditions under which a vortexantivortex 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 GrossPitaevskii equation confirming our analytical findings.
created: 03102007

M. Bruderer, A. Klein, S.R. Clark and D. Jaksch,
Polaron Physics in Optical Lattices,
Phys. Rev. A 76, 011605(R) (2007).
We investigate the effects of a nearly uniform BoseEinstein condensate (BEC) on the properties of immersed trapped impurity atoms. Using a weakcoupling expansion in the BECimpurity 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 phononmediated offsite attraction.
created: 06032007, last modified: 24072007

A. Griessner, A.J. Daley, S.R. Clark, D. Jaksch and P. Zoller,
Dark state cooling of atoms by superfluid immersion,
Phys. Rev. Lett. 97, 220403 (2006).
We propose and analyse a scheme to cool atoms in an optical lattice to ultralow temperatures within a Bloch band, and away from commensurate filling. The protocol is inspired by ideas from dark state laser cooling, but replaces electronic states with motional levels, and spontaneous emission of photons by emission of phonons into a BoseEinstein condensate, in which the lattice is immersed. In our model, achievable temperatures correspond to a small fraction of the Bloch band width, and are much lower than the reservoir temperature.
created: 10072006, last modified: 29112006

R.N. Palmer and D. Jaksch,
High field fractional quantum Hall effect in optical lattices,
Phys. Rev. Lett. 96, 180407 (2006).
We consider interacting bosonic atoms in an optical lattice
subject to a large simulated magnetic field. We develop a model
similar to a bilayer fractional quantum Hall system valid near
simple rational numbers of magnetic flux quanta per lattice cell.
Then we calculate its ground state, magnetic lengths, fractional
fillings, and find unexpected sign changes in the Hall current.
Finally we study methods for detecting these novel features via
shot noise and Hall current measurements.
created: 11042006, last modified: 30052006

A. Klein and D. Jaksch,
Simulating hightemperature superconductivity model Hamiltonians with atoms in optical lattices,
Phys. Rev. A 73, 053613 (2006).
We investigate the feasibility of simulating different model Hamiltonians used in hightemperature superconductivity. We briefly discuss the most common models and then focus on the simulation of the socalled tJU Hamiltonian using ultracold 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 Mottinsulator. Using ultracold 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.
created: 13012006, last modified: 29052006

A. Klein, U. Dorner, C. Moura Alves and D. Jaksch,
Robust implementations of Quantum Repeaters,
Phys. Rev. A 73, 012332 (2006).
We show how to efficiently exploit decoherence free subspaces,
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.
created: 08112005, last modified: 24012006

A.J. Daley, S.R. Clark, D. Jaksch and P. Zoller,
Numerical Analysis of Coherent ManyBody Currents in a Single Atom Transistor,
Phys. Rev. A 72, 043618 (2005).
We study the dynamics of many atoms in the recently proposed Single Atom Transistor setup [A. Micheli, A. J. Daley, D. Jaksch, and P. Zoller, Phys. Rev. Lett. 93, 140408 (2004)] using recently developed numerical methods. In this setup, a localised spin 1/2 impurity is used to switch the transport of atoms in a 1D optical lattice: in one state the impurity is transparent to probe atoms, but in the other acts as a single atom mirror. We calculate timedependent currents for bosons passing the impurity atom, and find interesting many body effects. These include substantially different transport properties for bosons in the strongly interacting (Tonks) regime when compared with fermions, and an unexpected decrease in the current when weakly interacting probe atoms are initially accelerated to a nonzero mean momentum. We also provide more insight into the application of our numerical methods to this system, and discuss open questions about the currents approached by the system on long timescales.
created: 02072005, last modified: 11072006

R.N. Palmer, C. Moura Alves and D. Jaksch,
Detection and characterization of multipartite entanglement in optical lattices,
Phys. Rev. A 72, 042335 (2005).
We investigate the detection and characterization of entanglement based on the quantum network introduced in [Phys. Rev. Lett. 93, 110501 (2004)] for different experimental scenarios. We first give a detailed discussion of the ideal scheme where no errors are present and full spatial resolution is available. Then we analyze the implementation of the network in an optical lattice. We find that even without any spatial resolution entanglement can be detected and characterized in various kinds of states including cluster states and macroscopic superposition states. We also study the effects of detection errors and imperfect dynamics on the detection network. For our scheme to be practical these errors have to be on the order of one over the number of investigated lattice sites. Finally, we consider the case of limited spatial resolution and conclude that significant improvement in entanglement detection and characterization compared to having no spatial resolution is only possible if single lattice sites can be resolved.
created: 02072005, last modified: 08112005