Quantum simulation using optical lattices
Our aim is to engineer the properties of ultracold atoms, and molecules, in optical lattices and so use these precisely controlled manybody systems to model important stronglycorrelated systems from Condensed Matter Physics (CMP). Opticallattice experiments thus function as analogue quantum computers, and allow exploration of physical regimes inaccessible in CMP systems themselves. The ultimate vision is to develop a complete 'toolbox' of methods for the direct quantum simulation (DQS) of stronglycorrelated systems. The intense current interest in this powerful interdisciplinary approach to fundamental quantum manybody problems has been stimulated, in part, by work carried out by members of this Collaboration. For example, Professor Bloch played a leading role in the first experimental observation of the superfluid to Mott Insulator transition in an optical lattice, a prime example of modelling CMP in such systems. This was predicted theoretically by Dr Jaksch (while working with Professor Zoller in Innsbruck). These ideas were recently extended in Florence to controlled disorder in optical lattices, and production of a Bose glass phase. This Collaboration will stimulate further work and collaborations between theory and experiment. The groundbreaking work on disorder will be continued by Dr Fort, using both bosons and fermions, and including timedependent studies. Professor Foot's team (Oxford) will create a rotating optical lattice to simulate the application of a magnetic field to the analogous Condensed Matter system, and test predictions of Dr Jaksch on the highfield Fractional Quantum Hall effect. Professor Bloch's group in Mainz will create heteronuclear dipolar molecules in an optical lattice and exploit their strong electrostatic interactions for DQS of spin systems. The theory groups of Dr Jaksch in Oxford and Dr Daley in Innsbruck, will use stateoftheart techniques to model the experimental systems, e.g. studying timedependent transport phenomena and methods for preparing specialised manybody states via controlled addition of noise.
Related Publications

T.H. Johnson, T. Elliot, S.R. Clark and D. Jaksch,
Capturing Exponential Variance Using Polynomial Resources: Applying Tensor Networks to Nonequilibrium Stochastic Processes,
Phys. Rev. Lett. 114, 090602 (2015).
Estimating the expected value of an observable appearing in a nonequilibrium stochastic process usually involves sampling. If the observable`s variance is high, many samples are required. In contrast, we show that performing the same task without sampling, using tensor network compression, efficiently captures high variances in systems of various geometries and dimensions. We provide examples for which matching the accuracy of our efficient method would require a sample size scaling exponentially with system size. In particular, the high variance observable exp(beta W, with W the work done quenching from equilibrium at inverse temperature beta, is exactly and efficiently captured by tensor networks.
created: 17112014, last modified: 09032015
 S. AlAssam, R. A. Williams, and C. J. Foot,
Ultracold atoms in an optical lattice with dynamically variable periodicity,
Phys. Rev. A 82, 021604(R) (2010).
The use of a dynamic 'accordion' lattice with ultracold atoms is demonstrated. Ultracold atoms of 87Rb are trapped in a twodimensional optical lattice, and the spacing of the lattice is then increased in both directions from 2.2 to 5.5 microns. Atoms remain bound for expansion times as short as a few milliseconds, and the experimentally measured minimum ramp time is found to agree well with numerical calculations. This technique allows an experiment such as quantum simulations to be performed with a lattice spacing smaller than the resolution limit of the imaging system, while allowing imaging of the atoms at individual lattice sites by subsequent expansion of the optical lattice.
created: 25092010

S. Broadfoot, U. Dorner and D. Jaksch,
Singlet Generation in Mixed State Quantum Networks,
Phys. Rev. A 81, 042316 (2010).
created: 27012010, last modified: 09052010
 R. A. Williams, S. AlAssam, and C. J. Foot,
Observation of Vortex Nucleation in a Rotating TwoDimensional Lattice of BoseEinstein Condensates,
Phys. Rev. Lett. 104, 050404 (2010).
We report the observation of vortex nucleation in a rotating optical lattice. A 87Rb BoseEinstein condensate was loaded into a static twodimensional lattice and the rotation frequency of the lattice was then increased from zero. We studied how vortex nucleation depended on optical lattice depth and rotation frequency. For deep lattices above the chemical potential of the condensate we observed a linear dependence of the number of vortices created with the rotation frequency, even below the thermodynamic critical frequency required for vortex nucleation. At these lattice depths the system formed an array of Josephsoncoupled condensates. The effective magnetic field produced by rotation introduced characteristic relative phases between neighboring condensates, such that vortices were observed upon ramping down the lattice depth and recombining the condensates.
created: 23022010

S.W. Lee, H. Jeong and D. Jaksch,
Witnessing entanglement in phase space using inefficient detectors,
Phys. Rev. A 81, 012302 (2010).
We propose a scheme for witnessing entanglement in phase space by significantly inefficient detectors. The implementation of this scheme does not require any additional process for correcting errors, in contrast to previous proposals. Moreover, it allows us to detect entanglement without full a priori knowledge of the detection efficiency. It is shown that entanglement in singlephoton entangled and twomode squeezed states can be witnessed with detection efficiency as low as 40 percent. Our approach enhances the possibility of witnessing entanglement in various physical systems using current detection technologies.
created: 08042009, last modified: 07012010

S. Broadfoot, U. Dorner and D. Jaksch,
Entanglement Percolation with Bipartite Mixed States,
EuroPhys. Lett. 88, 50002 (2009).
We develop a concept of entanglement percolation for longdistance singlet generation in quantum networks with neighboring nodes connected by partially entangled bipartite mixed states. We give a necessary and sufficient condition on the class of mixed network states for the generation of singlets. States beyond this class are insufficient for entanglement percolation. We find that neighboring nodes are required to be connected by multiple partially entangled states and devise a rich variety of distillation protocols for the conversion of these states into singlets. These distillation protocols are suitable for a variety of network geometries and have a sufficiently high success probability even for significantly impure states. In addition to this, we discuss possible further improvements achievable by using quantum strategies including generalized forms of entanglement swapping.
created: 11122009, last modified: 29012010

S.W. Lee, H. Jeong and D. Jaksch,
Testing quantum nonlocality by generalized quasiprobability functions,
Phys. Rev. A 80, 022104 (2009).
We derive a Bell inequality based on a generalized quasiprobability
function which is parameterized by one nonpositive real value. Two
types of known Bell inequalities formulated in terms of the Wigner
and Qfunctions are included as limiting cases. We investigate
violations of our Bell inequalities for single photon entangled
states and twomode squeezed vacuum states when varying the detector
efficiency. We show that the Bell inequality for the Qfunction
allows the lowest detection efficiency for violations of local
realism.
created: 04082009

M. J. Hartmann, J. Prior, S.R. Clark and M.B. Plenio,
Density Matrix Renormalization Group in the Heisenberg Picture,
Phys. Rev. Lett. 102, 057202 (2009).
In some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density matrix renormalization group, which makes use of redundancies in the description of the state. Here we show that the achievable efficiency can be much better when performing density matrix renormalization group calculations in the Heisenberg picture, as only the observable of interest but not the entire state is considered. In some nontrivial cases, this approach can even be exact for finite bond dimensions.
created: 07012009, last modified: 02022009

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
 R. A. Williams, J. D. Pillet, S. AlAssam, B. Fletcher, M. Shotter, and C. J. Foot,
Dynamic optical lattices: twodimensional rotating and accordion lattices for ultracold atoms,
Optics Express, 16, 16977 (2008).
We demonstrate a novel experimental arrangement which can rotate a 2D optical lattice at frequencies up to several kilohertz. Ultracold atoms in such a rotating lattice can be used for the direct quantum simulation of strongly correlated systems under large effective magnetic fields, allowing investigation of phenomena such as the fractional quantum Hall effect. Our arrangement also allows the periodicity of a 2D optical lattice to be varied dynamically, producing a 2D accordion lattice.
created: 23022010

R.N. Palmer, A. Klein and D. Jaksch,
Optical lattice quantum Hall effect,
Phys. Rev. A 78, 013609 (2008).
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 ReadRezayi 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 twospecies 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.
created: 08072008, last modified: 15072008

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

M. Rodriguez, S.R. Clark and D. Jaksch,
Adiabatic evolution of onsite superposition states in a completelyconnected optical lattice,
J. Phys.: Conf. Ser. 99, 012017 (2008).
We analyze the dynamical melting of twocomponent atomic MottInsulator states in a completelyconnected optical lattice within the adiabatic approximation. We examine in detail the effect of the dynamical phase acquired by the state during the adiabatic melting of the lattice potential. We show how for certain limits an onsite superposition state with two particles per site melts into a macroscopic superposition state, while an onsite superposition state with only one particle per site melts into a coherent state.
created: 06122007, last modified: 06032008

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

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