Wolfgang P. Schleich

Bose-Einstein Condensation in Microgravity

Going Down the Tube Two pillars of modern physics are quantum mechanics and general relativity. So far, both have remained apart with no quantum mechanical description of gravity available. Van Zoest et al. (p. 1540; see the Perspective by Nussenzveig and Barata) present work with a macroscopic quantum mechanical system—a Bose-Einstein condensate (BEC) of rubidium atoms in which the cloud of atoms is cooled into a collective quantum state—in microgravity. By dropping the BEC down a 146-meter-long drop chamber and monitoring the expansion of the quantum gas under these microgravity conditions, the authors provide a proof-of-principle demonstration of a technique that can probe the boundary of quantum mechanics and general relativity and perhaps offer the opportunity to reconcile the two experimentally. Studies of atomic quantum states in free-fall conditions may provide ways to test predictions of general relativity. Albert Einstein’s insight that it is impossible to distinguish a local experiment in a “freely falling elevator” from one in free space led to the development of the theory of general relativity. The wave nature of matter manifests itself in a striking way in Bose-Einstein condensates, where millions of atoms lose their identity and can be described by a single macroscopic wave function. We combine these two topics and report the preparation and observation of a Bose-Einstein condensate during free fall in a 146-meter-tall evacuated drop tower. During the expansion over 1 second, the atoms form a giant coherent matter wave that is delocalized on a millimeter scale, which represents a promising source for matter-wave interferometry to test the universality of free fall with quantum matter.

Quantum Test of the Universality of Free Fall

The universality of free fall (UFF) emerges [1] from theequality of the inertial and the gravitational mass, whichHeinrich Hertz [2] already in 1884 called a ”wonderfulmystery”. In 1915 Albert Einstein made this postulateinto one of the cornerstones of general relativity. Al-though UFF has been verified in numerous tests [3, 4] to-day different scenarios reconciling general relativity andquantum mechanics allow a violation of the UFF. Forthis reason more precise tests are presently pursued [5–7] and new measurement techniques are developed. Oneintriguing approach consists of comparing the accelera-tions of different quantum objects to a high precision. Inthis Letter, we report the first quantum test of the UFFwith matter waves of two different atomic species.We simultaneously compare the free-fall accelerationsg

NMR Experiment Factors Numbers with Gauss Sums

We factor the number 157573 using an NMR implementation of Gauss sums. Although the current implementation is classical and scales exponentially, we believe that an extension to the quantum regime using entangled states is possible.

FERMI ACCELERATOR IN ATOM OPTICS

We study the classical and quantum dynamics of a Fermi accelerator realized by an atom bouncing off a modulated atomic mirror. We find that in a window of the modulation amplitude, dynamical localization occurs in both position and momentum. A recent experiment [A. Steane, P. Szriftgiser, P. Desbiolles, and J. Dalibard, Phys. Rev. Lett. 74, 4972 (1995)] shows that this system can be implemented experimentally.

Autler-Townes microscopy on a single atom

Abstract The detection of a spontaneously emitted photon from a threelevel atom, in which the two upper levels are driven by a classical standing light field, yields information about the centre-of-mass position of the atom relative to the nodes of the driving field. We present a pure state treatment of the system and show that the measurement leads to a reduction of the systems wavefunction, which manifests itself in a localization of the atom.

Gauss Sum Factorization with Cold Atoms

We report the first implementation of a Gauss sum factorization algorithm by an internal state Ramsey interferometer using cold atoms. A sequence of appropriately designed light pulses interacts with an ensemble of cold rubidium atoms. The final population in the involved atomic levels determines a Gauss sum. With this technique we factor the number N=263193.

Factorization of Numbers with the temporal Talbot effect: Optical implementation by a sequence of shaped ultrashort pulses

We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed, the frequency component of the electric field corresponding to a sequence of appropriately shaped femtosecond pulses is determined by a Gauss sum which allows us to find the factors of a number.

Studying vibrational wavepacket dynamics by measuring fluorescence interference fluctuations

The principle of coherence observation by interference noise [COIN, Kinrot et al., Phys. Rev. Lett. 75, 3822 (1995)] has been applied as a new approach to measuring wavepacket motion. In the COIN experiment pairs of phase-randomized femtosecond pulses with relative delay time τ prepare interference fluctuations in the excited state population, so the correlated noise of fluorescence intensity—the variance varF(τ)—directly mimics the dynamics of the propagating wavepacket. The scheme is demonstrated by measuring the vibrational coherence of wavepacket motion in the B-state of gaseous iodine. The COIN interferograms obtained recover propagation, recurrences and spreading as the typical signature of wavepackets. The COIN measurements were performed with precisely tuned excitation pulses which cover the bound part of the B-state surface up to the dissociative limit. In combination with preliminary numerical calculations, comparison has been made with results from previous phase-locked wavepacket interferometr...

From photon counts to quantum phase

Abstract We derive an exact expression for the joint count probability in an eight-port homodyne detector, when the signal field is in an arbitrary state, the local oscillator is in a coherent state and the other two input states are the vacuum. In the limit of a strong local oscillator this photon count statistics is the scaled Q-function of the signal state. The phase distribution corresponding to this measurement scheme is then the Q-function of the signal field integrated over radius. The physical reason for the Q-function lies in the simultaneous measurement of two two-mode operators. We discuss the dependence of the photon count statistics on the local oscillator intensity using the example of a one-photon Fock state.

Mathematical analysis of evolution, information, and complexity

Weyls Law Wolfgang Arendt, Robin Nittka, Wolfgang Peter, Frank Steiner Solutions of Systems of Linear Ordinary Differential equations Werner Balser, Claudia Roescheisen, Frank Steiner, Eric Straeng A Scalar-Tensor Theory of Gravity with a Higgs Potential Nils Manuel Bezares-Roder, Frank Steiner Relating Simulation and Modelling of Neural Networks Stefano Cardanobile, Heiner Markert, Delio Mugnolo, Guenther Palm, Friedhelm Schwenker Boolean Networks for Modelling Gene Regulation Christian Wawra, Michael Kuehl, Hans A. Kestler Symmetries in Quantum Graphs Jens Bolte, Stefano Cardanobile, Delio Mugnolo, Robin Nittka Distributed Architecture for Speech Controlled Systems Based on Associative Memories Zoehre Kara Kayikci, Dmitry Zaykovskiy, Heiner Markert, Wolfgang Minker, Guenther Palm Machine Learning for Categorisation of Speech Utterances Amparo Albalate, David Suendermann, Roberto Pieraccini, Wolfgang Minker Semi-supervised Clustering in Functional Genomics Johann M. Kraus, Guenther Palm, Friedhelm Schwenker, Hans A. Kestler Image Processing and Feature Extraction from a Perspective of Computer Vision and Physical Cosmology Holger Stefan Janzer, Florian Raudies, Heiko Neumann, Frank Steiner Boosting Ensembles of Weak Classifiers in High Dimensional Input Spaces Ludwig Lausser, Friedhelm Schwenker, Hans A. Kestler The Sampling Theorem in Theory and Practice Wolfgang Arendt, Michal Chovanec, Jurgen Lindner, Robin Nittka Coding and Decoding of Algebraic-Geometric Codes Martin Bossert, Werner Luetkebohmert, Joerg Marhenke Investigation of input-output gain in dynamical systems for neural information processing Stefano Cardanobile, Michael Cohen, Silvia Corchs, Delio Mugnolo, Heiko Neumann Wave Packet Dynamics and Factorization Ruediger Mack, Wolfgang P. Schleich, Daniel Haase, Helmut Maier Isomorphism and factorization - classical and quantum algorithms Sebastian Doern, Daniel Haase, Jacobo Toran, Fabian Wagner QuickSort from an Information Theoretic View Beatrice List, Markus Maucher, Uwe Schoning, Rainer Schuler