Quantum state engineering in strongly correlated ultracold atomic gases
Exciting new prospects for atomic physics to help gaining insight into very complicated condensed matter systems and the physical effects which lead to important and intriguing phenomena like high Tc superconductivity and superfluidity have arisen recently. A cloud of very cold Rubidium atoms which all behave in exactly the same way due to their low temperatures (a so called atomic BoseEinstein condensate) is loaded into an optical lattice. This lattice is created by three pairs of counter propagating laser beams which produce a periodic potential that traps atoms at each of its minima. An example of such a system is schown in the figure. When the depth of the lattice is increased the atoms get pushed closer together and the barrier height between the minima increases. It thus gets harder for the particles to hop from one site to the next and at the same time the repulsion between two atoms sitting in the same lattice site gets larger. In this situation the atoms become strongly correlated with each other and behave very similarly to condensed matter systems. However, the system of atoms is in many ways much easier to work with since the underlying physics is precisely known. Loss processes and impurities are much rarer than in genuine condensed matter systems and the control over the atoms by the external laser parameters is unprecedented. One can therefore experimentally realize Hamiltonian quantum dynamics with varying controllable parameters. Based on these properties we study the dynamics of atoms which can be trapped in two different internal hyperfine states (i.e. states which correspond to different stable configurations of the electron shell and the nucleus) in this research project. This will give significant insight into the transfer of entanglement and superposition states when the depth of the lattice is varied and we will suggest possible applications of the resulting quantum states for quantum computing, entanglement assisted metrology and condensed matter studies.
Then we will use a recent observation that an atom which is trapped in an excited motional state of a lattice can emit a phonon (which is a special kind of excitation) into a surrounding cloud of atoms to be deexcited back to its ground state just like it emits photons to go from excited electronic states to its ground state. This mechanism will be combined with blocking due to the repulsion between the atoms to yield an experimentally feasible scheme for creating arbitrary atomic patterns in optical lattices with very high accuracy. Since the emission of phonons is irreversible, loading can be repeated for improving the quality of the patterns. Variations of the loading methods will furthermore enable us to cool atomic patterns to their ground state and thus repair holes in patterns that emerged from loss processes where particles escape the lattice. The generation of virtually defect free atomic patterns is of paramount importance in quantum computing and for quantum simulators which always assume a perfect quantum register for performing calculations.
We will use analytical as well as numerical methods in our work. Strongly correlated systems are very difficult to describe on a classical computer due to their large number of degrees of freedom. However, we will utilize a new simulation method which emerged from theoretical entanglement studies in one dimensional strongly correlated systems with nearest neighbour interactions. They showed that for such arrangements the amount of entanglement is limited and using methods from quantum information theory one can thus efficiently simulate these setups on a classical computer. We will extend those algorithms to multi component systems, finite temperatures, and loss processes to be applicable to the setups explored in this project. Furthermore we will work on the difficult task of performing numerical simulations for two dimensional strongly correlated systems. There the amount of entanglement is not limited and thus new approaches will be necessary.
Investigators:  M. Rodriguez, S.R. Clark and D. Jaksch

 
Funded by:  EPSRC First Grant scheme; Grant No EP/C519833/1(P)

 
Start date:  20050101

End date:  20070228

 
Related Publications

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

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

M. Rodriguez, S.R. Clark and D. Jaksch,
Generation of twin Fock states via transition from a twocomponent Mott insulator to a superfluid,
Phys. Rev. A 75, 011601(R) (2007).
We propose the dynamical creation of twin Fock states, which exhibit Heisenberglimited interferometric
phase sensitivities, in an optical lattice. In our scheme a twocomponent 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.
created: 15072006, last modified: 24072007

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

S.R. Clark and D. Jaksch,
Signatures of the superfluid to Mottinsulator transition in the excitation spectrum of ultracold atoms,
New J. Phys. 8, 160 (2006).
We present a detailed analysis of the dynamical response of
ultracold bosonic atoms in a onedimensional optical lattice
subjected to a periodic modulation of the lattice depth. Following
the experimental realization by Stoferle et al [Phys.
Rev. Lett. 92, 130403 (2004)] we study the excitation
spectrum of the system as revealed by the response of the total
energy as a function of the modulation frequency Omega. By
using the Time Evolving Block Decimation algorithm, we are able to
simulate onedimensional systems comparable in size to those in
the experiment, with harmonic trapping and across many lattice
depths ranging from the Mottinsulator to the superfluid regime.
Our results produce many of the features seen in the experiment,
namely a broad response in the superfluid regime, and narrow
discrete resonances in the Mottinsulator regime. We identify
several signatures of the superfluidMott insulator transition
that are manifested in the spectrum as it evolves from one limit
to the other.
created: 27042006, last modified: 30082006

T. Kramer and M. Rodriguez,
Quantum theory of an atom laser originating from a BoseEinstein condensate or a Fermi gas in the presence of gravity,
Phys. Rev. A 74, 013611 (2006).
We present a 3D quantum mechanical theory of radiofrequency outcoupled atom lasers from trapped atomic gases in the presence of the gravitational force. Predictions for the total outcoupling rate as a function of the radiofrequency and for the beam wave function are given. We establish a sum rule for the energy integrated outcoupling, which leads to a separate determination of the coupling strength between the atoms and the radiation field. For a noninteracting BoseEinstein condensate analytic solutions are derived which are subsequently extended to include the effects of atomic interactions. The interactions enhance interference effects in the beam profile and modify the outcoupling rate of the atom laser. We provide a complete quantum mechanical solution which is in line with experimental findings and allows to determine the validity of commonly used approximative methods. We also extend the formalism to a fermionic atom laser and analyze the effect of superfluidity on the outcoupling of atoms.
created: 17052006, last modified: 11082006

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, 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

A. Griessner, A.J. Daley, D. Jaksch and P. Zoller,
FaultTolerant Dissipative Preparation of Atomic Quantum Registers with Fermions,
Phys. Rev. A 72, 032332 (2005).
We propose a fault tolerant loading scheme to produce an array of fermions in an optical lattice of the high fidelity required for applications in quantum information processing and the modelling of strongly correlated systems. A cold reservoir of Fermions plays a dual role as a source of atoms to be loaded into the lattice via a Raman process and as a heat bath for sympathetic cooling of lattice atoms. Atoms are initially transferred into an excited motional state in each lattice site, and then decay to the motional ground state, creating particlehole pairs in the reservoir. Atoms transferred into the ground motional level are no longer coupled back to the reservoir, and doubly occupied sites in the motional ground state are prevented by Pauli blocking. This scheme has strong conceptual connections with optical pumping, and can be extended to load highfidelity patterns of atoms.
created: 08082005, last modified: 10102005

A. Griessner, A.J. Daley, D. Jaksch and P. Zoller,
FaultTolerant Dissipative Preparation of Atomic Quantum Registers with Fermions,
Phys. Rev. A 72, 032332 (2005).
We propose a fault tolerant loading scheme to produce an array of fermions in an optical lattice of the high fidelity required for applications in quantum information processing and the modelling of strongly correlated systems. A cold reservoir of Fermions plays a dual role as a source of atoms to be loaded into the lattice via a Raman process and as a heat bath for sympathetic cooling of lattice atoms. Atoms are initially transferred into an excited motional state in each lattice site, and then decay to the motional ground state, creating particlehole pairs in the reservoir. Atoms transferred into the ground motional level are no longer coupled back to the reservoir, and doubly occupied sites in the motional ground state are prevented by Pauli blocking. This scheme has strong conceptual connections with optical pumping, and can be extended to load highfidelity patterns of atoms.
created: 08082005, last modified: 10102005

S.R. Clark, C. Moura Alves and D. Jaksch,
Efficient generation of graph states for quantum computation,
New J. Phys. 7, 124 (2005).
We present an entanglement generation scheme which allows arbitrary graph states to be efficiently created in a linear quantum register via an auxiliary entangling bus (EB). The dynamical evolution of the EB is described by an effective noninteracting fermionic system undergoing mirrorinversion in which qubits, encoded as local fermionic modes, become entangled purely by Fermi statistics. We discuss a possible implementation using two species of neutral atoms stored in an optical lattice and find that the scheme is realistic in its requirements even in the presence of noise.
created: 08082005, last modified: 26082005