1,721,071 research outputs found
Nonlinear dynamics and quantum chaos: an introduction
No full textThe field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field
Dynamik ultrakalter Quantengase
No full textModern quantum and atom-optical experiments allow for an unprecedented control
of microscopic degrees of freedom, not just in the initialization but also
in the dynamical evolution of quantum states. This talk focuses on the dynamics
of ultracold bosons in optical lattice structures. As a paradigm, we report on
experimental as well as theoretical results on the interband transport in a
tilted lattice, i.e., a realization of the famous Wannier-Stark problem. An
extended Bose-Hubbard model is presented for two coupled energy bands. For
reasonable lattice sizes, this model gives access to the full quantum
spectrum, which allows us a good characterization of ``horizontal''
(spatially) and ``vertical'' (energetic) quantum transport. For specific
parameters, resonant tunnelling between the bands can be exploited to map the
original model onto a much simpler effective spin Hamiltonian. We conclude with general perspectives on future directions of our study of strongly correlated bosons in lattice structures
Die wunderbare Welt der ultrakalten Atome
No full textChaos und Unordnung bedeuten in unserem Alltagsleben üblicherweise nichts Gutes. Schon die antike griechische Mythologie belegte den Begriff „Chaos“ mit negativen Assoziationen, ein ungeordneter Zustand, eine unklare „Ursuppe“, die erst durch Regeln und das Einführen einer göttlichen Ordnung zum „Kosmos“, also zu unserem Universum, wurde
Applications of fidelity measures to complex quantum systems
No full textWe revisit fidelity as a measure for the stability and the complexity of the quantum motion of singleand many-body systems. Within the context of cold atoms, we present an overview of applications of two fidelities, which we call static and dynamical fidelity, respectively. The static fidelity applies to quantum problems which can be diagonalized since it is defined via the eigenfunctions. In particular, we show that the static fidelity is a highly effective practical detector of avoided crossings characterizing the complexity of the systems and their evolutions. The dynamical fidelity is defined via the time-dependent wave functions. Focusing on the quantum kicked rotor system, we highlight a few practical applications of fidelity measurements in order to better understand the large variety of dynamical regimes of this paradigm of a low-dimensional system with mixed regular-chaotic phase space
Hybrid quantum systems - New perspectives on quantum state control
No full textWe give a brief sketch of the emerging field of quantum mechanical hybrid systems through a cross section of research papers on topics of current interest contained in this Topical Issue
Kalt, kälter, am kältesten
No full textFundamentale Quanteneigenschaften für neue technische Anwendunge
The role of quasi-momentum in the resonant dynamics of the atom-optics kicked rotor
No full textWe examine the effect of the initial atomic momentum distribution on the dynamics of the atom-optical realization of the quantum kicked rotor. The atoms are kicked by a pulsed optical lattice, the periodicity of which implies that quasi-momentum is conserved in the transport problem. We study and compare experimentally and theoretically two resonant limits of the kicked rotor: in the vicinity of the quantum resonances and in the semiclassical limit of the vanishing kicking period. It is found that for the same experimental distribution of quasi-momenta, significant deviations from the kicked rotor model are induced close to quantum resonance, while close to the classical resonance (i.e. for a small kicking period) the effect of the quasi-momentum vanishes
Quantum random walk of a Bose-Einstein condensate in momentum space
No full textEach step in a quantum random walk is typically understood to have two basic components: a “coin toss” which produces a random superposition of two states, and a displacement which moves each component of the superposition by different amounts. Here we suggest the realization of a walk in momentum space with a spinor Bose-Einstein condensate subject to a quantum ratchet realized with a pulsed, off-resonant optical lattice. By an appropriate choice of the lattice detuning, we show how the atomic momentum can be entangled with the internal spin states of the atoms. For the coin toss, we propose to use a microwave pulse to mix these internal states. We present experimental results showing an optimized quantum ratchet, and through a series of simulations, demonstrate how our proposal gives extraordinary control of the quantum walk. This should allow for the investigation of possible biases, and classical-to-quantum dynamics in the presence of natural and engineered noise
Induced delocalization by correlation and interaction in the one-dimensional Anderson model
No full textWe consider long-range correlated disorder and mutual interacting particles according to a dipole-dipole coupling as modifications to the one-dimensional Anderson model. Technically, we rely on the numerical exact diagonalization of the system's Hamilitonian. From the perspective of different localizationmeasures, we confirm and extend the picture of the emergence of delocalized states with increasing correlations. Besides these studies, a definition for multiparticle localization is proposed. In the case of two interacting bosons, we observe a sensitivity of localization with respect to the range of the particle-particle interaction and insensitivity to the coupling's sign, which should stimulate new theoretical approaches and experimental investigations with, e. g., dipolar cold quantum gases
Pseudo-classical theory for directed transport at quantum resonance
No full textRecent studies have demonstrated that a directed current arises in kicked atom systems at quantum resonance (so-called 'resonance ratchets'). Here, we demonstrate that this effect can be explained using a pseudo-classical model by taking classical initial conditions analogous to the initial quantum state. A corollary of our result is that a current is also expected to arise in the actual standard classical limit of the kicked atoms, demonstrating that the phenomenon can arise even in the absence of quantum interference. We show that in the standard classical limit, the momentum current undergoes far less saturation due to quasi-momentum spread than for the quantum resonance case. Additionally, we demonstrate that a phase-independent analytical scaling law exists for the mean momentum as a function of a single combined parameter and show that it predicts an unexpected current inversion regime
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