Prof Dieter Jaksch

Abstract:

We adapt the time-evolving block decimation (TEBD) algorithm, originally devised to simulate the dynamics of one-dimensional quantum systems, to simulate the time evolution of nonequilibrium stochastic systems. We describe this method in detail; a system’s probability distribution is represented by a matrix product state (MPS) of finite dimension and then its time evolution is efficiently simulated by repeatedly updating and approximately refactorizing this representation. We examine the use of MPS as an approximation method, looking at parallels between the interpretations of applying it to quantum state vectors and probability distributions. In the context of stochastic systems we consider two types of factorization for use in the TEBD algorithm: non-negative matrix factorization (NMF), which ensures that the approximate probability distribution is manifestly non-negative, and the singular value decomposition (SVD). Comparing these factorizations, we find the accuracy of the SVD to be substantially greater than current NMF algorithms. We then apply TEBD to simulate the totally asymmetric simple exclusion process (TASEP) for systems of up to hundreds of lattice sites in size. Using exact analytic results for the TASEP steady state, we find that TEBD reproduces this state such that the error in calculating expectation values can be made negligible even when severely compressing the description of the system by restricting the dimension of the MPS to be very small. Out of the steady state we show for specific observables that expectation values converge as the dimension of the MPS is increased to a moderate size.

Abstract:

Arrays of atoms trapped in optical lattices are appealing as storage media for photons, since motional dephasing of the atoms is eliminated. The regular lattice is also associated with band structure in the dispersion experienced by incident photons. Here we study the influence of this band structure on the efficiency of quantum memories based on electromagnetically induced transparency (EIT) and on Raman absorption. We observe a number of interesting effects, such as both reduced and superluminal group velocities, enhanced atom-photon coupling, and anomalous transmission. These effects are ultimately deleterious to the memory efficiency, but they are easily avoided by tuning the optical fields away from the band edges. © 2010 The American Physical Society.

Abstract:

Relativistic causality has dramatic consequences on the measurability of nonlocal variables and poses the fundamental question of whether it is physically meaningful to speak about the value of nonlocal variables at a particular time. Recent work has shown that by weakening the role of the measurement in preparing eigenstates of the variable, it is in fact possible to measure all nonlocal observables instantaneously by exploiting entanglement. However, for these measurement schemes to succeed with certainty, an infinite amount of entanglement must be distributed initially and all this entanglement is necessarily consumed. In this work, we sharpen the characterization of instantaneous nonlocal measurements by explicitly devising schemes in which only a finite amount of the initially distributed entanglement is ever utilized. This enables us to determine an upper bound to the average consumption for the most general cases of nonlocal measurements. This includes the tasks of state verification, where the measurement verifies if the system is in a given state, and verification measurements of a general set of eigenstates of an observable. Despite its finiteness, the growth of entanglement consumption is found to display an extremely unfavourable exponential of an exponential scaling with either the number of qubits needed to contain the Schmidt rank of the target state or the total number of qubits in the system for an operator measurement. This scaling is seen to be a consequence of the combination of the generic exponential scaling of unitary decompositions combined with the highly recursive structure of our scheme required to overcome the no-signalling constraint of relativistic causality. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

Abstract:

We study the generation of singlets in quantum networks with nodes initially sharing a finite number of partially entangled bipartite mixed states. We prove that singlets between arbitrary nodes in such networks can be created if and only if the initial states connecting the nodes have a particular form. We then generalize the method of entanglement percolation, previously developed for pure states, to mixed states of this form. As part of this, we find and compare different distillation protocols necessary to convert groups of mixed states shared between neighboring nodes of the network into singlets. In addition, we discuss protocols that only rely on local rules for the efficient connection of two remote nodes in the network via entanglement swapping. Further improvements of the success probability of singlet generation are developed by using particular forms of "quantum preprocessing" on the network. This includes generalized forms of entanglement swapping and we show how such strategies can be embedded in regular and hierarchical quantum networks. © 2010 The American Physical Society.

Abstract:

Quantum memories, capable of controllably storing and releasing a photon, are a crucial component for quantum computers1 and quantum communications2. To date, quantum memories3-6 have operated with bandwidths that limit data rates to megahertz. Here we report the coherent storage and retrieval of sub-nanosecond low-intensity light pulses with spectral bandwidths exceeding 1GHz in caesium vapour. The novel memory interaction takes place through a far off-resonant two-photon transition in which the memory bandwidth is dynamically generated by a strong control field7,8. This should allow data rates more than 100 times greater than those of existing quantum memories. The memory works with a total efficiency of 15%, and its coherence is demonstrated through direct interference of the stored and retrieved pulses. Coherence times in hot atomic vapours are on the order of microseconds, the expected storage time limit for this memory. © 2010 Macmillan Publishers Limited. All rights reserved.