Collapse and Revival of the Matter Wave Field of a Bose-Einstein Condensate

At the heart of a Bose-Einstein condensate lies its description as a single giant matter wave. Such a Bose-Einstein condensate represents the most "classical" form of a matter wave, just as an optical laser emits the most classical form of an electromagnetic wave. Beneath this giant matter wave, however, the discrete atoms represent a crucial granularity, i.e. a quantization of this matter wave field. Here we show experimentally that this quantization together with the cold collisions between atoms lead to a series of collapses and revivals of the coherent matter wave field of a Bose-Einstein condensate. We observe such collapses and revivals directly in the dynamical evolution of a multiple matter wave interference pattern, and thereby demonstrate a striking new behaviour of macroscopic quantum matter

Interference pattern and visibility of a Mott insulator

We analyze theoretically the experiment reported in [F. Gerbier et al, cond-mat/0503452], where the interference pattern produced by an expanding atomic cloud in the Mott insulator regime was observed. This interference pattern, indicative of short-range coherence in the system, could be traced back to the presence of a small amount of particle/hole pairs in the insulating phase for finite lattice depths. In this paper, we analyze the influence of these pairs on the interference pattern using a random phase approximation, and derive the corresponding visibility. We also account for the inhomogeneity inherent to atom traps in a local density approximation. The calculations reproduce the experimental observations, except for very large lattice depths. The deviation from the measurement in this range is attributed to the increasing importance of non-adiabatic effects.Comment: 6 pages, 4 figure

Entanglement with quantum gates in an optical lattice

The concept of a "quantum computer" has attracted much attention in recent years. Many research groups around the world are studying the extraordinary potential of quantum computers and attempting their realisation. Current fundamental experiments are directed towards the individual building blocks of such a computer. The concept of using quantum mechanical systems to calculate complex problems was created in 1982 with Feynmans proposal of the quantum simulator. This concept represents a well controlled framework of interacting quantum systems. The intention is to map a different system of interest not mastered in the lab onto the quantum simulator. From the behaviour of the quantum simulator the behaviour of the system of interest can be deduced. A quantum mechanical measurement on the quantum simulator is thus comparable to one run of a numerical simulation of the system of interest. The difference is that a numerical simulation can often only be run under severe simplifications that then challenge the practical relevance of the result. Only very small quantum systems can be calculated on today's computers without simplifications. In this work a system of ground state atoms stored in a 3D optical lattice is presented. Each of the up to 100,000 atoms is stored in its own potential minimum, isolated from the other atoms. This state is a formidable starting point for the realisation of a quantum simulator: every atom is considered the information carrier of a spin-1/2 system. Only very few of the other concepts currently under investigation have as many information carriers as a Mott-Insulator state in an optical lattice. We have already shown in preparatory experiments a long storage time and good coherence times. Here this system is extended by a major prerequisite for a quantum simulator: controllable interactions between individual atoms are essential in order to model the interaction terms of the system of interest. These interactions are realised by a state-selective in the optical lattice by state-selective trapping potentials. If the states of an atom are called |0> and |1>, then there are two distinct potentials V0 and V1 that each act on only one of the states. The two potentials are shifted with respect to each other and thus allow bringing neighbouring atoms into contact. Since the shifting is always performed along one of the three lattice axes, the interaction is not confined to a single pair of atoms, but all pairs of neighbouring atoms along a lattice axis interact. This inherent parallelism has allowed us to create entanglement in large systems in just a single operation. The entanglement has then been measured in a Ramsey interferometer. A sequence of one nearest-neighbour interaction produces the cluster state, a maximally entangled state. More recent proposals suggest to use a cluster state as the basis for a new kind of quantum computer. As opposed to today's computers, this quantum computer would not be a Touring machine whose working algorithm is only controlled by programming. Instead the wiring of the quantum gates would have to be changed in order to solve a new problem. This is loosely comparable to today's FPGA (Field Programmable Gate Arrays - programmable logic chips). Until these quantum computers are built, quite some improvements on the experimental techniques will be necessary. But the first quantum simulators are now practically within reach.Das Konzept eines "Quantencomputers" hat in den letzten Jahren viel Aufmerksamkeit errungen. Viele Forschungsgruppen weltweit befassen sich mit den außergewöhnlichen Möglichkeiten von Quantencomputern und mit ihrer Realisierung. Aktuelle Grundlagenexperimente arbeiten an den einzelnen Bausteinen eines solchen Rechners. Den Anfang nahm das Konzept, quantenmechanische Systeme zur Berechnung komplexer Probleme zu verwenden, 1982 mit Feynmans Vorschlag des Quantensimulators. Dieser stellt ein gut kontrollierbares System aus miteinander wechselwirkenden Quantensystemen dar. Das Ziel ist es, ein im Labor nicht beherrschbares Ziel-System auf den Quantensimulator abzubilden. Aus dem Verhalten des Quantensimulators läßt sich dann auf das Verhalten des Ziel-Systems schließen. Eine quantenmechanische Messung am Quantensimulator ist somit vergleichbar zu dem Durchlauf einer numerischen Simulation des Ziel-Systems. Der entscheidende Unterschied besteht darin, dass eine numerische Simulation häufig nur unter sehr starken Vereinfachungen durchführbar ist, die dann die praktische Bedeutung des Ergebnisses in Frage stellen. Nur sehr kleine Quantensysteme können ohne Vereinfachungen auf heutigen Computern berechnet werden. In dieser Arbeit wird ein System bestehend aus einzelnen Grundzustands-Atomen vorgestellt, das in einem drei-dimensionalen optischen Gitter gespeichert ist. Dabei ist jedes der bis zu 100.000 Atome in einem eigenen Potentialminimum gefangen, isoliert von den anderen Atomen. Dieser Zustand bildet einen hervorragenden Ausgangspunkt für die Realisierung eines Quantensimulators: jedes Atom wird als Informationsträger für ein Spin-1/2 System betrachtet. Kaum ein anderes der momentan untersuchten Konzepte hat so viele Informationsträger wie ein Mott-Isolator Zustand in einem optischen Gitter. Wir haben in Vorexperimenten bereits hohe Speicherzeiten und gute Kohärenzzeiten nachgewiesen. Hier wird dieses System nun um eine wesentliche Grundvoraussetzung für einen Quantensimulator erweitert: man benötigt genau kontrollierbare Wechselwirkungen zwischen den einzelnen Atomen, um die Wechselwirkungs-Terme des Ziel-Systems modellieren zu können. Diese Wechselwirkungen werden im optischen Gitter durch zustandsselektive Fallen-Potentiale realisiert. Wenn die Zustände eines Atoms als |0> und |1> bezeichnet werden, dann gibt es zwei unterschiedliche Potentiale V0 und V1, die jeweils nur auf einen der Zustände wirken. Diese beiden Potentiale werden gegeneinander verschoben und erlauben es so, benachbarte Atome miteinander in Wechselwirkung zu bringen. Da das Verschieben immer entlang einer der drei Gitterachsen stattfindet, ist auch die Wechselwirkung nicht auf ein Atom-Paar beschränkt, sondern alle in einer Gitterachse benachbarten Atom-Paare treten miteinander in Wechselwirkung. Diese inhärente Parallelität hat es uns erlaubt, in nur einer Operation Verschränkung in großen Systemen zu erzeugen. Die Verschränkung wurde mit einem Ramsey-Interferometer gemessen. Eine Sequenz aus einer Wechselwirkung zwischen nächsten Nachbarn erzeugt den Cluster-Zustand, einen maximal verschränktern Zustand. Neuere Veröffentlichungen schlagen vor, den Cluster-Zustand als Basis für eine neue Art Quantencomputer zu nutzen. Im Gegensatz zu unseren heutigen Computern wäre dieser Quantencomputer keine Touring-Maschine, bei der ausschliesslich die Programmierung die Arbeitsweise bestimmt. Stattdessen müsste die Verschaltung der Quanten-Gates geändert werden, um ein neues Problem zu lösen. Dies ist entfernt vergleichbar zu heutigen FPGAs (Field Programmable Gate Arrays - Frei programmierbare Logikbausteine). Bis diese Quantencomputer gebaut werden dürften zwar noch einige weitere Verbesserungen an der Experiment-Technik notwendig sein, aber die ersten Quantensimulatoren sind jetzt in greifbare Nähe gerückt

Phase coherence of an atomic Mott insulator

We investigate the phase coherence properties of ultracold Bose gases in optical lattices, with special emphasis on the Mott insulating phase. We show that phase coherence on short length scales persists even deep in the insulating phase, preserving a finite visibility of the interference pattern observed after free expansion. This behavior can be attributed to a coherent admixture of particle/hole pairs to the perfect Mott state for small but finite tunneling. In addition, small but reproducible ``kinks'' are seen in the visibility, in a broad range of atom numbers. We interpret them as signatures for density redistribution in the shell structure of the trapped Mott insulator

Resonant control of spin dynamics in ultracold quantum gases by microwave dressing

We study experimentally interaction-driven spin oscillations in optical lattices in the presence of an off-resonant microwave field. We show that the energy shift induced by this microwave field can be used to control the spin oscillations by tuning the system either into resonance to achieve near-unity contrast or far away from resonance to suppress the oscillations. Finally, we propose a scheme based on this technique to create a flat sample with either singly- or doubly-occupied sites, starting from an inhomogeneous Mott insulator, where singly- and doubly-occupied sites coexist.Comment: 4 pages, 5 figure

Entanglement interferometry for precision measurement of atomic scattering properties

We report on a two-particle matter wave interferometer realized with pairs of trapped 87Rb atoms. Each pair of atoms is confined at a single site of an optical lattice potential. The interferometer is realized by first creating a coherent spin-mixture of the two atoms and then tuning the inter-state scattering length via a Feshbach resonance. The selective change of the inter-state scattering length leads to an entanglement dynamics of the two-particle state that can be detected in a Ramsey interference experiment. This entanglement dynamics is employed for a precision measurement of atomic interaction parameters. Furthermore, the interferometer allows to separate lattice sites with one or two atoms in a non-destructive way.Comment: 4 pages, 5 figure

Coherent transport of neutral atoms in spin-dependent optical lattice potentials

We demonstrate the controlled coherent transport and splitting of atomic wave packets in spin-dependent optical lattice potentials. Such experiments open intriguing possibilities for quantum state engineering of many body states. After first preparing localized atomic wave functions in an optical lattice through a Mott insulating phase, we place each atom in a superposition of two internal spin states. Then state selective optical potentials are used to split the wave function of a single atom and transport the corresponding wave packets in two opposite directions. Coherence between the wave packets of an atom delocalized over up to 7 lattice sites is demonstrated.Comment: 4 pages, 6 figure

Coherent collisional spin dynamics in optical lattices

We report on the observation of coherent, purely collisionally driven spin dynamics of neutral atoms in an optical lattice. For high lattice depths, atom pairs confined to the same lattice site show weakly damped Rabi-type oscillations between two-particle Zeeman states of equal magnetization, induced by spin changing collisions. This paves the way towards the efficient creation of robust entangled atom pairs in an optical lattice. Moreover, measurement of the oscillation frequency allows for precise determination of the spin-changing collisional coupling strengths, which are directly related to fundamental scattering lengths describing interatomic collisions at ultracold temperatures.Comment: revised version; 4 pages, 5 figure

Sympathetic Cooling of Mixed Species Two-Ion Crystals for Precision Spectroscopy

Sympathetic cooling of trapped ions has become an indispensable tool for quantum information processing and precision spectroscopy. In the simplest situation a single Doppler-cooled ion sympathetically cools another ion which typically has a different mass. We analytically investigate the effect of the mass ratio of such an ion crystal on the achievable temperature limit in the presence of external heating. As an example, we show that cooling of a single Al+ with Be+, Mg+ and Ca+ ions provides similar results for heating rates typically observed in ion traps, whereas cooling ions with a larger mass perform worse. Furthermore, we present numerical simulation results of the rethermalisation dynamics after a background gas collision for the Al+/Ca+ crystal for different cooling laser configurations.Comment: Made Graphics black & white print compatible, clarified abstract and summar