Workshop 2012, DFG-Forschergruppe 635
Quantum Walks, Quantum Simulators, and Quantum Networks

Begin: Monday, 30/07, 08:50
End: Tuesday, 31/07, 20:00

Conference center Gustav-Stresemann-Institut (GSI)
Langer Grabenweg 68, D-53175 Bonn – Bad Godesberg.
Reception tel: +49 (0) 228 / 8107-0
Sun. July 29
Mon. July 30
Tue. July 31
Wed. August 1
(lab tour)
Opening remarks (FOR)  
A. Alberti, Bonn University (FOR)
Andrea Alberti
Institut für Angewandte Physik, Universität Bonn
Quantum walks for discrete-time quantum simulations

Quantum walks represent the quantum motion of a particle on a lattice with a strictly local dynamics, meaning that in a finite time the quantum walker propagates only over a finite distance. The dynamics of these systems is determined by periodically reiterating a certain set of discrete quantum operations.

The same set of operations – e.g., spin-dependent displacements, spin rotations, and collisional phase shifts – can be employed to simulate complex physical systems, by stroboscopically decomposing their evolution into a sequence of discrete steps.

Individual atoms trapped in spin-dependent optical lattices are ideal candidates to implement a discrete-time digital simulator. We will report on the experimental creation of mesoscopically delocalized wave packets through tens of quantum walk steps. In order to explore coherent properties of delocalized matter waves we developed an interferometer which coherently splits single atoms by more than 10 µm [1].

In addition, we will present our latest experimental results, where we employ quantum walks to simulate charged particles in an electric field. We are able to reproduce the mechanism of Bloch oscillations. Along the same line, we will also present ideas to simulate magnetic fields with 2D spin-dependent optical lattices, and the possibility to reach the strong-field regime by all-optical means.

[1]: A. Steffen et al., "A digital atom interferometer with single particle control on a discretized spacetime geometry", PNAS 109, 9770 (2012).

M. Aidelsburger, MPQ (FOR)
Monika Aidelsburger
Max-Planck Institute of Quantum Optics
Realization of strong effective magnetic fields with ultracold atoms in optical superlattices

Ultracold atoms in optical lattices are promising candidates to study quantum many-body phenomena, such as the integer or fractional quantum Hall effect. Here we report about the experimental realization of strong effective magnetic fields, on the order of one flux quantum per plaquette, with ultracold atoms using Raman assisted tunneling in an optical superlattice. When hopping in the lattice, the accumulated phase shift by an atom is equivalent to the Aharonov-Bohm phase of a charged particle exposed to a large staggered magnetic field. We studied the nature of the ground state from its momentum distribution and observed that the frustration induced by the magnetic field can lead to a degenerate ground state for noninteracting particles. A local measurement performed in a lattice of isolated plaquettes directly revealed the quantum cyclotron orbit of a single atom exposed to the magnetic field.

M. Atala, MPQ (FOR)
Marcos Atala
Max-Planck Institute of Quantum Optics
First Experimental measurement of the Zak-Berry phase in optical lattices

Topological properties of Bloch bands in one dimensional solids are characterized by the Zak phase, which is the integral of the Berry's connection over the Brillouin zone. In this talk I will present very recent results on the Zak phase measurement for a dimmerized 1-D system (SSH model) using Ramsey interferometry together with Bloch oscillations.

A. Werner, Hannover Uni. (FOR)
Albert Werner
Leibniz Universität Hannover
Propagation properties of quantum walks

Quantum walks describe the time discrete evolution of a single particle with an internal degree of freedom on a lattice with an additional locality condition. We study the propagation behaviour of such quantum walks in the translation invariant case as well as for different regimes of decoherence and disorder. We show that the possible propagation behaviour of the particle ranges from ballistic transport over diffusive spreading to dynamical localization. In the translation invariant case it is known that the asymptotic position distribution is governed by the group velocity that is the gradient of the dispersion relation. We prove that this convergence obeys a large deviation estimate.

In the case of a two particle quantum walk with on site interactions we show the existence of a bound state of these two particles that itself undergoes a quantum walk dynamics.

P. Windpassinger, Hamburg Uni.
Patrick Windpassinger
Institut für Laserphysik, Universität Hamburg
Simulating classical magnetism and creating artificial gauge fields in optical lattices

Ultracold bosons in optical lattices have during the past years been applied to emulate various solid state systems. The presentation will discuss the experimentally realized simulation of a frustrated classical spin system in a triangular optical lattice and the verification of the corresponding spin-phase diagram. Particular focus will be put on the frustrated regions of the phase diagram and the associated phase transitions.

The second part will be concerned with the recent realization of an artificial vector gauge field in a one dimensional optical lattice and the extensions to two dimensional systems. In the latter case, the gauge field will be used to control the frustration on the classical spin system described in the first part.

As the findings rely on the application of an external periodic force, the main underlying technical method will also be discussed in detail.

Coffee break
J. O'Brien, Bristol University
Jeremy O'Brien
University of Bristol
Integrated quantum photonics for multi-particle quantum walks

Integrated quantum photonics (IQP) has opened an entirely new level of complexity achievable in quantum experiments [1,2,3]. One particular area where this is having significant impact is with the realisation of multi-photon quantum walks [4]. I will review our recent developments in IQP and its application to multi-particle quantum walks including recent results on realising two-dimensional quantum walks using 3D laser written photonics and simulation of fermion and fractional statistics with entangled photons in integrated optics [5].

[1] A. Politi, J. C. F. Matthews, J. L. O'Brien, Science, 325, 1221 (2009).

[2] J. C. F. Matthews, A. Politi, A. Stefanov, J. L. O'Brien, Nature Photonics, 3, 346-350 (2009).

[3] P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, J. L. O'Brien, Nature Photonics, 6, 45-49 (2012).

[4] A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, et. al., Science 329, 1500-1503 (2010).

[5] J. C. F. Matthews, et. al., arXiv:1106.1166v1 [quant-ph]

Anne Nielsen, MPQ (FOR)
Anne Nielsen
Max-Planck Institute of Quantum Optics
Laughlin-like states on finite lattices

Laughlin's wavefunctions have played a key role in explaining the fractional quantum Hall effect, and lattice versions of the states are expected to be important for understanding topological phases of spin models. Guided by conformal field theory, we propose a set of wavefunctions, which can be seen as a slight modification of Laughlin's states on lattices. The modification builds convenient mathematical properties into the states, which allow us to obtain various analytical results, while important physical characteristics of the states remain practically unchanged. In particular, we derive a parent Hamiltonian for the state with Landau level filling factor 1/2 and show that the resulting model unifies the Haldane-Shastry model and the Kalmeyer-Laughlin state into the same model. The Hamiltonian contains long-range two- and three-body interactions, but we find numerically that the ground state has a large overlap with the ground state of a Hamiltonian containing only short-range interactions, which makes the model simpler to simulate experimentally.

A. Kuhn, Oxford Uni.
Axel Kuhn
University of Oxford
Photonic Qubits, Qutrits and Ququads in Linear Optical Quantum Circuits

The ability of encoding arbitrary information in elementary quantum systems is the key to a novel approach to computing based on quantum mechanics. Particular attention has been paid toward the field of linear optics quantum computing (LOQC) which in principle is a scalable, albeit often restricted by the spontaneous nature of parametric down-conversion sources. Here, I will show that single photons emitted on demand from a single atom into an optical cavity can be used to get past those limits. With a coherence time greater than 500 ns, a subdivision of photons into d time bins of arbitrary amplitudes and phases has been achieved, which we use for encoding arbitrary qu-d-its in one single photon. The fidelity of the quantum state preparation is verified in time-resolved quantum-homodyne measurements, and the photons are used to operate elementary quantum gates in integrated photonic circuits.

J. Simon, Harvard Uni.
Jonathan Simon
Harvard/MIT Center for Ultracold Atoms
Building Synthetic Materials from Ultracold Atoms: Quantum Magnetism in an Optical Lattice

Ultracold atoms in optical lattices form a unique testbed for quantum many-body physics. Using such systems it has recently become possible to engineer strongly-correlated materials from the ground up and probe them with single-atom resolution. I will describe experiments in which we have synthesized the first magnetic material composed of ultracold atoms, and watched it undergo a quantum phase transition from a paramagnet to an antiferromagnet. I will then introduce a new algorithmic cooling scheme that we have demonstrated, which points the way to even more exotic quantum phases that exist at lower temperatures. In addition, I will describe recent experiments studying bilayer quantum gases, with promising applications in generation and detection of even more varied strongly correlated materials.

(lab tour)
G. Rempe, MPQ (FOR)
Gerhard Rempe
Max-Planck Institute of Quantum Optics
An Elementary Quantum Network With Individual Atoms And Photons

Quantum physics allows a new approach to information processing. A grand challenge is the realization of a quantum network for long-distance quantum communication and large-scale quantum simulation [1]. The talk will highlight a first implementation of an elementary quantum network with two fiber-linked high-finesse optical resonators, each containing a single quasi-permanently trapped atom as a stationary quantum node [2]. Reversible quantum state transfer between the two atoms and entanglement of the two atoms are achieved by the controlled exchange of a time-symmetric single photon. This approach to quantum networking is efficient and offers a clear perspective for scalability. It allows for arbitrary topologies and features controlled connectivity as well as, in principle, infinite-range interactions. Our system constitutes the largest man-made material quantum system to date and is an ideal test bed for fundamental investigations, e.g. quantum nonlocality.

[1] J.I. Cirac et al., "Quantum state transfer and entanglement distribution among distant nodes in a quantum network", Phys. Rev. Lett. 78, 3221 (1997).

[2] S. Ritter et al., "An Elementary Quantum Network of Single Atoms in Optical Cavities", Nature 484, 195 (2012).

A. Browaeys, Institut d'Optique
Antoine Browaeys
CNRS – Institut d'Optique
Experimental investigation of the dipole-dipole interaction between cold atoms

This talk will present our ongoing effort to understand and use the dipole-dipole interaction between ultra-cold atoms. This dipole interaction can result from the interaction of the atoms with near-resonant light. In this case the scattering of light by an ensemble of atoms is modified if the inter-atomic distance is on the order of the wavelength of the light. The atoms then behave collectively, leading to super or sub-radiant phenomena. The dipoles can also be prepared by exciting the atoms to a Rydberg state leading to interaction strength large enough to make the atoms interact even at long distance. This Rydberg interaction is at the basis of the preparation of entangled states.

Y. Lahini, Weizmann Inst.
Yoav Lahini
The Weizmann Institute of Science
Correlated quantum walks and topological phases in photonic lattices
I will describe the study of quantum walks in photonic lattices, including the emergence of Hanbury-Brown Twiss correlations between multiple particles and the effects of interactions, disorder and quasi-periodicity on the dynamics. In addition, I will describe the emergence of non-trivial topological effects in quasi-periodic potentials.
A. Widera, TU Kaiserslautern
Artur Widera
TU Kaiserslautern
Immersing Single Atomic Impurities into a Quantum Gas

I will present our approach to merge the two worlds of single individually controlled atoms and large-scale many-body systems for realizing a paradigm of experimental quantum physics: a single well controlled impurity immersed in a quantum gas. Such systems are promising candidates for studies of condensed matter problems such as Fröhlich-type polarons, or for non-destructive, local probing of quantum many-body systems.

We have immersed single Cs atoms into an ultracold Rb gas and observed cooling of the single atom down to the temperature of the many-body system through s-wave collisions. Our results not only suggest a method for the preparation of ultracold mesoscopic samples, they also allow to probe non-equilibrium dynamics of quantum systems, where the full energy distribution is accessible at all times. Furthermore, inelastic collisions can be studied event-by-event with single atom sensitivity, allowing to distinguish various channels of molecule formation and to extract a precise number for the three-body recombination coefficient.

Coffee break
S. Kuhr, Strathclyde Uni.
Stefan Kuhr
University of Strathclyde & Max-Planck-Institut für Quantenoptik
Quantum dynamics of a mobile single-spin impurity in a 1D optical lattice

The Heisenberg model is fundamental to quantum magnetism, as it describes properties of many materials such as transition metal oxides and cuprate superconductors. Mobile spin impurities are unique probes of its physics but are usually difficult to track in a space-time resolved way. Ultracold atoms in optical lattices offer an ideal testbed for these phenomena, in particular the novel techniques for single-atom imaging [1] and single-spin addressing [2] with a high-resolution optical microscope. Using this technique we have prepared a single spin impurity in a one-dimensional Mott insulator and have directly observed its coherent quantum dynamics. We measured its propagation velocity as the system undergoes the transition from a Mott insulator to a superfluid and found excellent agreement with analytical and numerical predictions. We also used the high-resolution imaging technique for in-situ detection of individual Rydberg excitations in a 2D atomic Mott insulator, and we could directly observe Rydberg blockade and spatially ordered crystalline structures.

[1] J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, S. Kuhr, Single-atom-resolved fluorescence imaging of an atomic Mott insulator, Nature 467, 68 (2010).

[2] C. Weitenberg, M. Endres, J. F. Sherson, M. Cheneau, P. Schauß, T. Fukuhara, I.Bloch, S. Kuhr, Single-spin addressing in an atomic Mott insulator, Nature 471, 319 (2011).

T. Lompe, Heidelberg Uni.
Thomas Lompe
Physikalisches Institut, Universität Heidelberg
Observation of Ferromagnetic Spin Correlations in a 1D Fermi System

One of the simplest models used to explain ferromagnetism of delocalized spin 1/2 fermions is the Stoner model, which predicts a transition to a ferromagnetic state when the strength of the repulsive interaction exceeds the Pauli repulsion between identical fermions. Whether this Stoner mechanism can create Ferromagnetic order is still an open question in both theory and experiment. Here we report on our studies of a quasi one-dimensional system of ultracold fermionic 6Li atoms in two different hyperfine states. For such a 1D system it has been shown that the Stoner transition to ferromagnetism does not occur for a finite strength of the repulsive interaction. We start from ground-state systems of three to five particles and tune the interaction strength across ±∞ using a Feshbach resonance. This allows us to create long-lived metastable states in which the energy of the interacting spin |↑↓> system is larger than energy of the corresponding spin-polarized system. We probe the spin-spin correlations in the system by spilling a fraction of the particles from the trap and measuring the total spin of the remaining ensemble. For weak repulsive interactions we observe no significant fraction of spin polarized samples, which corresponds to an anticorrelation between the spins of the remaining particles. When the interaction strength diverges the system becomes fermionized and the spin correlations in the system vanish. For the metastable branch across the resonance we find a strong enhancement in the number of spin polarized systems created by the spilling process, which signals the appearance of ferromagnetic correlations.

Poster session
(FOR): partner of the Forschergruppe 635.
(lab tour): we are glad to offer guide tours through our laboratories. If you would like to visit them on the arrival day, July 29th, please let us know beforehand.
(in blue color): full board free of charges, covered by the Forschergruppe 635.