Rotating optical lattices and quantum Hall effects
Since their discovery, the integer and fractional quantum Hall effects have attracted much attention on the theoretical as well as on the experimental side. Despite the work which has been put into this field, the mechanisms which lead to these phenomena are not completely understood.
Theoretical investigations are especially hampered by the complexity of the system: A many-body quantum description is necessary to capture the relevant effects such as the strong correlation of the electrons, which means that the calculational effort scales exponentially with the number of particles to be described. To gain insight into the quantum Hall effects it is therefore worthwhile to investigate whether these phenomena occur in different, easier to handle, systems as well.
Ultracold atoms in optical lattices are a versatile setup in order to study phenomena in condensed matter physics, and theoretical investigations have shown that a whole wealth of models can be simulated. In this project we investigate whether it is possible to observe the Hall effects and related phenomena in rotating optical lattices. On the theory side, we concentrate on finding suitable characteristics, which enable the identification of the expected states. We are especially interested in the identification of non-abelian excitations, as they allow for the implementation of topological quantum computation.
The experimental realisation of the system is conducted in the group of Christopher Foot, where a BEC is loaded into a rotating optical lattice potential and appropriate probing techniques are under development.| Investigators: | S. Al-Assam, A. Klein and D. Jaksch |
| Collaborators: | C.J. Foot (Co-ordinator) |
| Start date: | 2008-01-01 |
| End date: | 2008-12-31 |
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 many-body systems to model important strongly-correlated systems from Condensed Matter Physics (CMP). Optical-lattice 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 strongly-correlated systems. The intense current interest in this powerful interdisciplinary approach to fundamental quantum many-body 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 ground-breaking work on disorder will be continued by Dr Fort, using both bosons and fermions, and including time-dependent 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 high-field 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 state-of-the-art techniques to model the experimental systems, e.g. studying time-dependent transport phenomena and methods for preparing specialised many-body states via controlled addition of noise.| Investigators: | D. Jaksch |
| Collaborators: | C.J. Foot (Co-ordinator) , I. Bloch, A.J. Daley and C. Fort |
| Home page: | http://gow.epsrc.ac.uk/ViewGrant.aspx?GrantRef=EP/E041612/1 |
| Funded by: | EPSRC grant EP/E041612/1; ESF EuroQUAM call; value: £837,524 |
| Start date: | 2007-06-01 |
| End date: | 2010-05-31 |
Fidelity measures for quantum memories
Recent progress in transferring quantum information from flying to stationary qubits will soon allow the realization of reliable quantum memories. The experimental characterization of their quality is an important task. Determining the quality of a quantum memory will require new experimentally accessible figures of merit. The main aim of this project is to propose and implement fidelity measures which can be used to determine the suitability of a given quantum memory for different types of applications and can be measured with reasonable experimental effort in atomic and quantum dot memories. First, we will consider existing general measures, like e.g. the entanglement fidelity, which are well known in quantum information theory. We will study how they can best be experimentally determined and which kind of useful information on the quantum memory is provided by them. For instance, we will investigate how useful they are when trying to violate Bell inequalities with qubits stored in two quantum memories. Based on these results we will develop measures which are more easily accessible in the experiments and better suited for characterizing a quantum memory. The work carried out in this theoretical part of the project will be analytical in nature. The resulting fidelity measures will be directly applicable for analyzing experimental data and numerical results from modeling quantum memories. A second component of the project will be to develop such methods in the laboratory. These will be based around an atomic-vapour prototype quantum memory that is configured to read-in and read-out single photons using an off-resonant Raman scheme suitable for use with ultrafast photonic wavepackets. A source of photon pairs will be developed that will enable the memory fidelity to be tested by comparing a stored and retrieved photon with its twin, using various accessible detection schemes, such as Franson or Hon-Ou-Mandel interferometry and Bell-state detection or two-photon Bell-type correlation measurements. This project will be jointly supervised by Prof. I. Walmsley (experiment) and Dr. D. Jaksch (theory) and carried out in close collaboration between the two research groups. The development of novel fidelity measures will be guided by what is currently available in the laboratory and the combination of theoretical and experimental work will guarantee tools of practical significance. The main scientific aim of the QIP IRC is to study the conversion of different physical types of qubits. This project will contribute to this aim by providing and implementing practical tools for measuring how well this conversion works in the case of quantum memories.| Investigators: | D. Jaksch, I.A. Walmsley and K. Surmacz |
| Funded by: | QIP IRC |
| Start date: | 2006-10-01 |
| End date: | 2009-09-30 |
Multipartite entanglement enhanced quantum clocks
It is well known today that the use of certain types of quantum states can in principle improve the precision of frequency measurements. Using maximally entangled states one can overcome the shot-noise limit and reach the so called Heisenberg limit which bears an improvement on the order of the square root of the number of states used. Unfortunately, even simple noise models destroy this enhancement. On the other hand, it is known that special types of multipartite entangled states, namely cluster, or more general, graph states, are very robust against different kinds of noise. The aim of this project is to combine these two findings and to study the usefulness of graph states as a resource for precision frequency measurements. We will take into account different noise models to investigate on the robustnes of this measurement under realistic experimental conditions.| Investigators: | M. Rosenkranz and D. Jaksch |
| Funded by: | QIPEST |
| Start date: | 2006-10-01 |
| End date: | 2009-09-30 |
Bell inequalities in phase space
One may doubt whether Bell inequalities originally proposed for discrete variables can be also applied for continuous variables. Indeed the first argument of entanglement and nonlocality by EPR was based on the continuous variable state associated with position and momentum. Bell argued that the Wigner function of original EPR state is positive everywhere and hence serves as a classical probability distribution. In this sense any violation for the EPR state does not occur. On the other hand Banaszek et al. showed the nonlocality of the EPR state exploiting the Wigner function as a dichotomic observable. Though intensive investigations have been done, we still do not have a clear understanding of the relation between the phase space distribution and the nonlocality of quantum mechanics. Moreover we still do not have an efficient Bell inequality in phase space violated by the EPR state strongly. In this project we generalize Bell inequalities in phase space and derive several new types aiming to obtain strong violations by the EPR state. We also expect to obtain clear pictures of the quantum nonlocality in phase space.| Investigators: | S.-W. Lee and D. Jaksch |
| Funded by: | OLAQUI |
| Start date: | 2006-10-01 |
| End date: | 2008-07-31 |
Entanglement purification for high dimensional multipartite systems
Due to the effect of decoherence pure entangled states in noise channel become mixed and lose their entanglement. Therefore it is essential for quantum communication to stabilize entanglement. Entanglement purification protocols have been proposed to recover entanglement from the decohered ensemble. In this project, we investigate entanglement purification protocols in order to stabilize the GHZ state in multipartite high dimensional systems. We aim to design an entanglement purification protocol from the correlation properties of the GHZ state. We investigate the required minimum fidelity of an initial state for successful purifications. We also study its efficiency as comparing to that of the generalized protocol for the Bell state.| Investigators: | S.-W. Lee and D. Jaksch |
| Funded by: | OLAQUI |
| Start date: | 2006-10-01 |
| End date: | 2007-09-30 |
A generalized structure of Bell inequalities in arbitrary dimensions
Local-realistic theories impose constraints on any correlations obtained from local measurements. It was shown that these constraints, known as Bell inequalities, are incompatible with the quantitative predictions by quantum mechanics in case of entangled states. Therefore Bell inequalities are great importance for understanding the conceptual features of entanglement. In this project we study Bell inequalities for high dimensional systems. In order to obtain an efficient Bell inequality we design a generalized structure of Bell inequalities for arbitrary dimensional systems. Based on this generalized structure we investigate the violation and tightness of Bell inequalities. We also study the extension of its formalism to more complex systems.| Investigators: | S.-W. Lee and D. Jaksch |
| Funded by: | OLAQUI |
| Start date: | 2006-10-01 |
| End date: | 2007-09-30 |
Simulation of quantum networks
In experimental implementations of quantum networks unwanted errors will occur, which decrease the fidelity of the respective quantum network or make the results in the worst case unusable. Several methods have been proposed to circumvent this problem, such as active error correction or avoiding errors by using decoherence-free subspaces (DFSs). In this project we investigate the influence of errors on quantum networks. We derive error models for quantum gates and simulate the whole network stochastically. For this purpose we develop a programme package with a flexible, modular structure which allows the simulation of complex quantum networks in a simple (i.e. user-friendly) way. As an example, we want to compare the fidelities of a quantum repeater scheme using DFSs with one that does not use DFSs, but instead stores a qubit in a single atom.| Investigators: | U. Dorner, A. Klein and D. Jaksch |
| Start date: | 2006-09-01 |
| End date: | 2007-06-01 |
Quantum Information Processing Early Stage Training Network
Quantum information processing (QIP) algorithms and the basic theory for quantum computers are already well established. The important next step which will make a huge impact on the whole field of information technology is to develop quantum information processing devices which contain small quantum processors. A single physical system will probably not be able to fulfil all requirements for its realization. Hybrid architectures which combine the best properties of several physical systems are thus very likely to be among the first to realize such quantum information processing devices. Scientific and industrial research on such hybrid technologies as well as their industrial development require scientists with very broad background knowledge in different theoretical and experimental areas of physics and material sciences who are able to work successfully in an interdisciplinary team. Advanced theoretical concepts and quantum algorithms need to be adapted to concrete physical realizations which might contain components developed in different areas of physics and material science. The unique combination of research training opportunities in an interdisciplinary environment of highest level research will train students in all important areas of quantum information processing. Their training will end in 2009/2010 when according to current projections (ARDA roadmap, ERA-Pilot QIST) the transfer of basic QIP knowledge to the industry is likely to be of increasing importance. There will be a high demand for researchers with the expertise provided in this research training project in the academic as well as in the industrial sectors.| Investigators: | D. Jaksch |
| Collaborators: | D. Jaksch (Co-ordinator) , I.A. Walmsley and G.A.D. Briggs |
| Home page: | http://www.physics.ox.ac.uk/qubit/QIPEST/ |
| Acronym: | QIPEST |
| Funded by: | EU Early stage training network; MEST-CT-2005-020505 |
| Start date: | 2006-04-22 |
| End date: | 2010-04-21 |
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 so-called Mott-Insulator 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 qu-bits 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 quantum-level 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 Bose-Einstein 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; two-bit gates and compatible stable qubits; generation and characterisation of multi-particle 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 long-term commitment to emerging applications.| Investigators: | D. Jaksch |
| Collaborators: | E. Arimondo (Co-ordinator) , 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: FP6-2002-IST-C, Fet Open; Contract No 013501 |
| Start date: | 2005-02-01 |
| End date: | 2008-07-31 |
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 Bose-Einstein 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 de-excited 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: | 2005-01-01 |
| End date: | 2007-02-28 |
Quantum simulators and simulated magnetic fields in optical lattices
The simulation of many-body systems, such as a superconducting electron gas, is computationally a very difficult task that is in general not possible to solve without resorting to approximations such as mean-field theories. Feynman pointed out that simulating a quantum system (for example, a superconductor) using another quantum system would prove more efficient than using a classical computer. In this project we investigate how the properties of a superconducting material can be simulated by using ultracold atoms in optical lattices. Using analogies drawn between both systems we investigate whether simulation of the superconducting system is possible, and how one might realize this experimentally. Atoms in optical lattices are the ideal candidates for this task due to the wide range of possible system parameters available. Furthermore, the possibility of simulating effective magnetic fields using optical lattices enables investigation of phenomena similar to the Meissner-Ochsenfeld effect.| Investigators: | A. Klein and D. Jaksch |
| Funded by: | QIP IRC |
| Start date: | 2005-01-01 |
| End date: | 2007-12-31 |
Optical lattices immersed in degenerate quantum gases
Cold atoms trapped in optical lattices have attracted considerable theoretical and experimental interest in recent years since they give a clean realization of condensed matter toy-models, such as the Bose-Hubbard model, and have direct applications in quantum computing. In the framework of this project we extend the scope of the optical lattice paradigm by adding a reservoir consisting of a degenerate quantum gas. More precisely, we consider atoms of species A trapped in an optical lattice, which is immersed in a degenerate quantum gas of species B. We assume that the atoms of species B do not 'see' the optical lattice and that the two species undergo collisional interactions. We intend to develop an effective model for the atoms in the optical lattice where the effects caused by the reservoir only enter as external parameters. This effective model is likely to exhibit interesting physical phenomena since it includes dephasing, dissipation and phonon-mediated forces. In addition, we mean to evaluate the consequences of these effects for quantum computing with cold atoms.| Investigators: | M. Bruderer, A. Klein and D. Jaksch |
| Start date: | 2005-01-01 |
| End date: | 2007-09-30 |
Robust atomic quantum information processing networks in periodic lattice structures
The main scientific objective of this project is the development of schemes for scalable and robust quantum computing in periodic lattice structures which are feasible with current or short-term experimental technology. We plan to achieve this by using decoherence free subspaces in ensembles of atoms stored in periodic traps and examine methods for performing robust single and two qubit gates in these subspaces. We study implementations based on strong atomic interactions (e.g. controllable molecular interactions) and on flexible interactions mediated by a cavity field. These schemes are extended to quantum networks and checked for their suitability for implementation in concrete experimental setups. Such proposals have become realistic due to recent experimental breakthroughs in manipulating and controlling atoms in optical lattices and the networks we investigate should allow to build special purpose quantum computers which can be used e.g. for small specific tasks in quantum cryptography or for simulations of more complicated quantum systems.| Investigators: | U. Dorner and D. Jaksch |
| Acronym: | RAQUIN |
| Funded by: | EU Marie Curie Intra European Fellowship; Call: FP6-2002-Mobility-5; Contract No. MEIF-CT-2004-010796 |
| Start date: | 2004-12-01 |
| End date: | 2006-11-30 |
Robust implementation of quantum repeaters
One of the major obstacles in the realization of quantum information processing is decoherence, caused by the unwanted interaction of the system with its environment leading to irreversible loss of quantum information. A number of concepts have been developed to increase the reliability of quantum information processing including active error correction and fault tolerant quantum computing. Aside from this, it was shown that under certain conditions there are subspaces of the system's Hilbert space which are immune to decoherence. These decoherence free subspaces are therefore also known as a method of ``passive'' error correction or error prevention and can significantly increase the lifetime of quantum information and reliability of quantum computing. A particularly interesting application of decoherence free subspaces are quantum repeaters which are used to distribute maximally entangled pairs of qubits over a long distance since in this case long storage times of quantum information are required. Such entangled pairs have important applications, e.g. for quantum cryptography and teleportation and since the effort, e.g. in terms of the number of required gate operations, is relatively low it is seen as one of the most promising near future applications of quantum information processing. The basic idea of a quantum repeater is to divide the transmission line into smaller segments with a length which is of the order of the attenuation length of the channel. On each segment entangled particle pairs are created and by applying entanglement swapping and purification protocols they are used to create entangled pairs of bigger distance. The latter are then used to purify pairs of even larger distance and so on until a final pair with high entanglement fidelity is obtained. In this project we combine ideas of decoherence free subspaces and quantum repeaters and examine its implementation with cold, neutral atoms stored in dipole traps, a field where extraordinary progress has been made over the past few years both on the theoretical and experimental side. Atomic arrays have been realized by atoms in a Mott-Insulator state in optical lattices and in arrays of microlenses, single and many atoms have been manipulated coherently and atoms stored in standing waves have been transported over macroscopic distances. A very promising and versatile technology is also given by holographic traps which can be controlled by liquid crystal Spatial Light Modulators allowing for essentially arbitrary designs of optical potentials. We consider the implementation of decoherence free qubits with a small number of neutral atoms in an array of dipole traps and develop methods for robust gate operations on encoded qubits by using the collisional interaction between the atoms. Interactions between different decoherence free qubits are mediated by ancilla atoms which can be transported through the decoherence free register by means of ``conveyor-belt'' techniques or optical tweezers. We analyze the performance and stability of all required gate operations and emphasize that all techniques we use are feasible with current experimental technology.| Investigators: | A. Klein, U. Dorner, C. Moura Alves and D. Jaksch |
| Funded by: | Marie Curie Intra European Fellowship (RAQUIN) |
| Start date: | 2004-12-01 |
| End date: | 2006-11-30 |
Interdisciplinary Research Collaboration in Quantum Information Processing
The IRC brings together a multidisciplinary team of researchers in the UK to address key challenges in quantum information processing. The theoretical studies range from the most fundamental concepts of QIP to theoretical analysis of how QIP can be implemented in practice, together with modelling of specific experimental configurations. The experimental research focuses on the interaction between static and flying qubits, something that will be crucial for successful exploitation of QIP. Ways are sought to enhance the inherently weak interaction between photons and static qubits in microcavities and arrays, and to implement photon-photon entanglement via conditional detection. Information transfer in ionic and atomic systems is studied. Electrons in solids are investigated as candidate short range flying qubits.| Investigators: | A. Klein, K. Surmacz and D. Jaksch |
| Collaborators: | G.A.D. Briggs (Co-ordinator) and I.A. Walmsley |
| Home page: | http://www.qipirc.org/ |
| Acronym: | QIPIRC |
| Funded by: | EPSRC Grant Reference: GR/S82176/01 |
| Start date: | 2004-04-01 |
| End date: | 2009-10-31 |
Efficient simulation of quantum lattice systems
Computing the quasi-exact properties of a quantum lattice system on a classical computer is a fundamentally difficult task due to the exponential growth in the size of a quantum systems Hilbert space with its size. Crucial progress was made over a decade ago now with the introduction of the Density Matrix Renormalization Group (DMRG) method by Steve White. This has allowed the properties of the groundstate and low-lying excitations for non-critical one-dimensional (1D) systems to be compute efficiently and accurately. More recently the reasons for the tremendous success of DMRG has been clarified with the use of concepts and methods from Quantum Information theory. Specifically, the sucess can be attributed to the bounded amount of "entanglement" between contiguous blocks of the system with the size of the system for the groundstate and low-lying excitations. This in turn permits these states to be described by a Matrix Product Decomposition (MPD) accurately which is the underlying description used in DMRG. Using this approach Guifre Vidal devised a new algorithm called Time-Evolving Block Decimation (TEBD) which allows the low-energy dynamical time-evolution to be computed directly on the MPD of the state for systems with nearest neighbour Hamiltonians. There are a wide variety of interesting 1D systems which this method can be applied to; most notably spin- and (Bose) Hubbard-like models.
So far our research has focussed on implementing and applying this method to the dynamics of the Bose-Hubbard for one or two species of atoms to obtain results relevant to possible experiments with ultra-cold bosons in optical lattices. We have also implemented an extention of TEBD to the simulation of dissipative / finite temperature dynamics and are now using this to examine how the interplay between coherent and incoherent evolution can be used to engineer novel atomic states in optical lattices.
Since Vidal's original proposal there has been several significant developments in the simulation of quantum lattice systems. For example, Vidal has recently devised an extention to TEBD allowing translationally invariant infinite systems to be simulated. We will implement this method in the near-future. In addition to this Frank Verstraete and Vidal have both recently proposed new simulation methods, based on projected entangled pairs and entanglement renormalization respectively, which have the potential to work in higher-dimensional quantum lattices (where blockwise entanglement is not bounded as it is in 1D). Our future work will consist of investigating these algorithms suitablity to optical lattice problems, and eventually fully implementing one of them.| Investigators: | S.R. Clark and D. Jaksch |
| Funded by: | EPSRC and QIP IRC |
| Start date: | 2004-01-01 |
| End date: | 2007-01-01 |
Quantum Networks
Quantum repeaters are an important tool for the long-distance distribution of entangled states, e.g. via optical fibres, and thus for long-distance, secure quantum communication. Quantum repeaters typically operate in a 1D setup of network nodes and are a very promising tool for the generation of long-distance entanglement. However, like classical communication networks which are in use today, future quantum networks will be two (or higher) dimensional culminating in the predicted 'quantum internet' which provides a very high connectivity between all participating network nodes. It is therefore desirable to study whether one can make use of this fact to improve the efficiency of entanglement distribution. Based on the idea of 'entanglement percolation' we therefore develop schemes for entanglement generation in 2D and 3D quantum networks which generate a maximally entangled state shared between two nodes in the network no matter how far apart the nodes are. In the case of a realistic, i.e. noisy network, we proved that entanglement percolation is only possible if a certain class of noise, caused e.g. by photon loss in a transmission line, is present in the system. Maximally entangled states can then be created over arbitrary distances by using significantly less physical resources and time than a 1D quantum repeater.| Investigators: | U. Dorner, S. Broadfoot and D. Jaksch |
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