# Publications by Stephen Clark

## Dephasing enhanced transport in nonequilibrium strongly correlated quantum systems

ArXiv (0)

A key insight from recent studies is that noise, such as dephasing, can improve the efficiency of quantum transport by suppressing coherent single-particle interference effects. However, it is not yet clear whether dephasing can enhance transport in an interacting many-body system. Here, we address this question by analyzing the transport properties of a boundary driven spinless fermion chain with nearest-neighbor interactions subject to bulk dephasing. The many-body nonequilibrium stationary state is determined using large-scale matrix product simulations of the corresponding quantum master equation. We find dephasing enhanced transport only in the strongly interacting regime, where it is shown to induce incoherent transitions bridging the gap between bound dark states and bands of mobile eigenstates. The generic nature of the transport enhancement is illustrated by a simple toy model, which contains the basic elements required for its emergence. Surprisingly, the effect is significant even in the linear response regime of the full system, and it is predicted to exist for any large and finite chain. The response of the system to dephasing also establishes a signature of an underlying nonequilibrium phase transition between regimes of transport degradation and enhancement. The existence of this transition is shown not to depend on the integrability of the model considered. As a result, dephasing enhanced transport is expected to persist in more realistic nonequilibrium strongly correlated systems.

## Breathing oscillations of a trapped impurity in a Bose gas

ArXiv (0)

Motivated by a recent experiment [J. Catani et al., arXiv:1106.0828v1 preprint, 2011], we study breathing oscillations in the width of a harmonically trapped impurity interacting with a separately trapped Bose gas. We provide an intuitive physical picture of such dynamics at zero temperature, using a time-dependent variational approach. In the Gross-Pitaevskii regime we obtain breathing oscillations whose amplitudes are suppressed by self trapping, due to interactions with the Bose gas. Introducing phonons in the Bose gas leads to the damping of breathing oscillations and non-Markovian dynamics of the width of the impurity, the degree of which can be engineered through controllable parameters. Our results reproduce the main features of the impurity dynamics observed by Catani et al. despite experimental thermal effects, and are supported by simulations of the system in the Gross-Pitaevskii regime. Moreover, we predict novel effects at lower temperatures due to self-trapping and the inhomogeneity of the trapped Bose gas.

## Decoherence of a quantum memory coupled to a collective spin bath

International Journal of Quantum Information **8** (2010) 271-294

We study the quantum dynamics of a single qubit coupled to a bath of interacting spins as a model for decoherence in solid state quantum memories. The spin bath is described by the Lipkin-Meshkov-Glick model and the bath spins are subjected to a transverse magnetic field. We investigate the qubit interacting via either an Ising- or an XY-type coupling term to subsets of bath spins of differing size. The large degree of symmetry of the bath allows us to find parameter regimes where the initial qubit state is revived at well-defined times after the qubit preparation. These times may become independent of the bath size for large baths and thus enable faithful qubit storage even in the presence of strong coupling to a bath. We analyze a large range of parameters and identify those which are best suited for quantum memories. In general we find that a small number of links between qubit and bath spins leads to less decoherence and that systems with Ising coupling between qubit and bath spins are preferable. © 2010 World Scientific Publishing Company. © 2010 World Scientific Publishing Company.

## Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain

ArXiv (0)

In recent work Hartmann et al [Phys. Rev. Lett. 102, 057202 (2009)] demonstrated that the classical simulation of the dynamics of open 1D quantum systems with matrix product algorithms can often be dramatically improved by performing time evolution in the Heisenberg picture. For a closed system this was exemplified by an exact matrix product operator solution of the time-evolved creation operator of a quadratic fermi chain with a matrix dimension of just two. In this work we show that this exact solution can be significantly generalized to include the case of an open quadratic fermi chain subjected to master equation evolution with Lindblad operators that are linear in the fermionic operators. Remarkably even in this open system the time-evolution of operators continues to be described by matrix product operators with the same fixed dimension as that required by the solution of a coherent quadratic fermi chain for all times. Through the use of matrix product algorithms the dynamical behaviour of operators in this non-equilibrium open quantum system can be computed with a cost that is linear in the system size. We present some simple numerical examples which highlight how useful this might be for the more detailed study of open system dynamics. Given that Heisenberg picture simulations have been demonstrated to offer significant accuracy improvements for other open systems that are not exactly solvable our work also provides further insight into how and why this advantage arises.

## Density matrix renormalization group in the Heisenberg picture

Physical Review Letters **102** (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. © 2009 The American Physical Society.

## Adiabatic evolution of on-site superposition states in a completely-connected optical lattice

Journal of Physics: Conference Series **99** (2008)

We analyze the dynamical melting of two-component atomic Mott-Insulator states in a completely-connected 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 on-site superposition state with two particles per site melts into a macroscopic superposition state, while an on-site superposition state with only one particle per site melts into a coherent state. © 2008 IOP Publishing Ltd.

## Adiabatic melting of two-component Mott-insulator states

Physical Review A - Atomic, Molecular, and Optical Physics **77** (2008)

We analyze the outcome of a Mott insulator to superfluid transition for a two-component 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, and that, in general, the obtained superfluid states are highly depleted even for initial ground Mott-insulator states. © 2008 The American Physical Society.

## Transport of strong-coupling polarons in optical lattices

New Journal of Physics **10** (2008)

We study the transport of ultracold impurity atoms immersed in a Bose-Einstein condensate (BEC) and trapped in a tight optical lattice. Within the strong-coupling 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 Esaki-Tsu-type relation with the effective relaxation time of the impurities as a temperature-dependent parameter. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

## Generation of twin Fock states via transition from a two-component Mott insulator to a superfluid

Physical Review A - Atomic, Molecular, and Optical Physics **75** (2007)

We propose the dynamical creation of twin Fock states, which exhibit Heisenberg-limited interferometric phase sensitivities, in an optical lattice. In our scheme a two-component Mott insulator with two bosonic atoms per lattice site is melted into a superfluid. This process transforms local correlations between hyperfine states of atom pairs into multiparticle correlations extending over the whole system. The melting time does not scale with the system size which makes our scheme experimentally feasible. © 2007 The American Physical Society.

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

New Journal of Physics **9** (2007)

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 (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 super-decoherence 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. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

## Fast initialization of a high-fidelity quantum register using optical superlattices

New Journal of Physics **9** (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. We develop a Bose-Hubbard-like model for describing the dynamics of cold atoms in a lattice when doubling the lattice periodicity via the addition of a superlattice potential. The dynamics of the transition from a half filled to a commensurately filled lattice is analysed numerically with the help of the time evolving block decimation algorithm and analytically using the Kibble-Zurek theory. We show that the timescale 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 timescale. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

## Dissipative dynamics of atomic Hubbard models coupled to a phonon bath: Dark state cooling of atoms within a Bloch band of an optical lattice

New Journal of Physics **9** (2007)

We analyse a laser assisted sympathetic cooling scheme for atoms within the lowest Bloch band of an optical lattice. This scheme borrows ideas from sub-recoil laser cooling, implementing them in a new context in which the atoms in the lattice are coupled to a Bose-Einstein condensate (BEC) reservoir. In this scheme, excitation of atoms between Bloch bands replaces the internal structure of atoms in normal laser cooling, and spontaneous emission of photons is replaced by creation of excitations in the BEC reservoir. We analyse the cooling process for many bosons and fermions, and obtain possible temperatures corresponding to a small fraction of the Bloch band width within our model. This system can be seen as a novel realisation of a many-body open quantum system. © IOP Publishing Ltd and Deutsche Physlkallsche Gesellschaft.

## Polaron physics in optical lattices

Physical Review A - Atomic, Molecular, and Optical Physics **76** (2007)

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. © 2007 The American Physical Society.

## Graph state generation with noisy mirror-inverting spin chains

New Journal of Physics **9** (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 multi-partite entanglement. The noise 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 single-qubit channel and as a mediator of a two-qubit entangling gate, since these are basic operations necessary for graph state generation using the EB. In particular, for the single-qubit 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 power-law 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. The concatenation of these noisy gates for the construction of a five-qubit linear cluster state and a Greenberger-Horne-Zeilinger state indicates that the level of noise that can be tolerated for graph state generation is tightly constrained. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

## Signatures of the superfluid to Mott-insulator transition in the excitation spectrum of ultracold atoms

New Journal of Physics **8** (2006)

We present a detailed analysis of the dynamical response of ultracold bosonic atoms in a one-dimensional optical lattice subjected to a periodic modulation of the lattice depth. Following the experimental realization by Stöferle et al (2004 Phys. Rev. Lett. 92 130403), we study the excitation spectrum of the system as revealed by the response of the total energy as a function of the modulation frequency ω. By using the Time Evolving Block Decimation algorithm, we are able to simulate one-dimensional systems comparable in size to those in the experiment, with harmonic trapping and across many lattice depths ranging from the Mott-insulator (MI) to the superfluid (SF) regime. Our results produce many of the features seen in the experiment, namely a broad response in the SF regime, and narrow discrete resonances in the MI regime. We identify several signatures of the SF-MI transition that are manifested in the spectrum as it evolves from one limit to the other. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

## Dark-state cooling of atoms by superfluid immersion.

Phys Rev Lett **97** (2006) 220403-

We propose and analyze 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 Bose-Einstein condensate, in which the lattice is immersed. In our model, achievable temperatures correspond to a small fraction of the Bloch bandwidth and are much lower than the reservoir temperature. This is also a novel realization of an open quantum optical system, where known tools are combined with new ideas involving cooling via a reservoir.

## Efficient dynamical simulation of strongly correlated one-dimensional quantum systems

LECT NOTES COMPUT SC **3743** (2006) 555-563

Studying the unitary time evolution of strongly correlated quantum systems is one of the most challenging theoretical and experimental problems in physics. For an important class of one-dimensional (11)) systems dynamical simulations have become possible since the advent of the time-evolving block decimation (TEBD) algorithm. We study the computational properties of TEBD using the Bose-Hubbard model (BHM) as a test-bed. We demonstrate its efficiency and verify its accuracy through comparisons with an exactly solvable small system and via the convergence of one- and two-particle observables in a larger system.

## Efficient generation of graph states for quantum computation

New Journal of Physics (2005)

## Numerical analysis of coherent many-body currents in a single atom transistor

Physical Review A - Atomic, Molecular, and Optical Physics **72** (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 localized spin-12 impurity is used to switch the transport of atoms in a one-dimensional optical lattice: in one state the impurity is transparent to probe atoms, but in the other acts as a single-atom mirror. We calculate time-dependent 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 time scales. © 2005 The American Physical Society.

## Dynamics of the superfluid to Mott-insulator transition in one dimension

Physical Review A - Atomic, Molecular, and Optical Physics **70** (2004) 043612-1-043612-13