Photon exchange and entanglement formation during the transmission through a rectangular quantum barrier

When a quantum particle traverses a rectangular potential created by a quantum field both photon exchange and entanglement between particle and field take place. We present analytic results for the transition amplitudes of any possible photon exchange processes for an incoming plane wave and initial Fock, thermal and coherent field states. We show that for coherent field states the entanglement correlates the particle's position to the photon number in the field instead of the particle's energy as usual. Besides entanglement formation, remarkable differences to the classical field treatment also appear with respect to the symmetry between photon emission and absorption, resonance effects and if the field initially occupies the vacuum state.Comment: 6 pages (double column), 6 figure

Experimental demonstration of a universally valid error-disturbance uncertainty relation in spin-measurements

The uncertainty principle generally prohibits determination of certain pairs of quantum mechanical observables with arbitrary precision and forms the basis of indeterminacy in quantum mechanics. It was Heisenberg who used the famous gamma-ray microscope thought experiment to illustrate this indeterminacy. A lower bound was set for the product of the measurement error of an observable and the disturbance caused by the measurement. Later on, the uncertainty relation was reformulated in terms of standard deviations, which focuses solely on indeterminacy of predictions and neglects unavoidable recoil in measuring devices. A correct formulation of the error-disturbance relation, taking recoil into account, is essential for a deeper understanding of the uncertainty principle. However, the validity of Heisenberg's original error-disturbance uncertainty relation is justifed only under limited circumstances. Another error-disturbance relation, derived by rigorous and general theoretical treatments of quantum measurements, is supposed to be universally valid. Here, we report a neutron optical experiment that records the error of a spin-component measurement as well as the disturbance caused on another spin-component measurement. The results confirm that both error and disturbance completely obey the new, more general relation but violate the old one in a wide range of an experimental parameter.Comment: 11 pages, 5 figures, Nature Physics (in press

Photon exchange and decoherence in neutron interferometry

Zsfassung in dt. SpracheÜbergeordneter Gegenstand der vorliegenden Arbeit ist die Wirkung zeitabhängiger, räumlich beschränkter Magnetfelder auf die Wellenfunktion eines Neutrons mit spezieller Berücksichtigung ihrer Anwendung in der Neutronen-Interferometrie. Für beliebig zeitperiodische Felder wird die entsprechende Schrödingergleichung analytisch gelöst. Es wird gezeigt, wie der dabei auftretende Austausch von Energiequanten zwischen dem Neutron und den Moden des Magnetfeldes anhand der zeitlichen Modulation des Interferenzbildes von ungestörter und vom Magnetfeld veränderter Wellenfunktion bestimmt werden kann. Durch Fourieranalyse des zeitaufgelösten Interferenzmusters lassen sich die Übergangswahrscheinlichkeiten für alle möglichen Energietransfers bestimmen. Messergebnisse für Felder, die bis zu fünf Moden beinhalten, werden präsentiert. Ein erweiterter theoretischer Ansatz, in dem auch das Feld quantisiert wird, gewährt zusätzliche Einblicke in die zugrunde liegenden physikalischen Vorgänge und führt für den kohärenten Feldzustand mit hoher mittlerer Photonenzahl wieder auf die Resultate der Rechnung mit klassischen Feldern.Wird die Anzahl der im Magnetfeld vorkommenden Frequenzen, deren relative Phasenlage völlig zufällig zueinander ist, weiter erhöht, bewegt man sich in Richtung Rauschfelder. Mit ihnen kann man Dekohärenz im Neutroneninterferometer modellieren. Theoretisch und experimentell wird gezeigt, auf welche Weise diese Modellierung zu verstehen ist, welche Möglichkeiten sie bietet und wo ihre Grenzen liegen. Die Untersuchungen beziehen sich dabei auf Rauschquellen in einem oder beiden Interferometerpfaden, auf die Stärke und den Frequenzbereich der Rauschfelder, ihre Lage zueinander und auf den Einfluss der räumlichen Trennung der Neutronen-Wellenpakete. Letzteres führt auf die sogenannten Schrödingerschen Katzenzustände, die aufgrund ihrer makroskopischen Abmessungen in der Dekohärenztheorie eine besondere Rolle spielen.The general subject of the present work concerns the action of time-dependent, spatially restricted magnetic fields on the wave function of a neutron. Special focus lies on their application in neutron interferometry.For arbitrary time-periodic fields, the corresponding Schrödinger equation is solved analytically. It is then shown, how the occurring exchange of energy quanta between the neutron and the modes of the magnetic field appears in the temporal modulation of the interference pattern between the original wavefunction and the wavefunction altered by the magnetic field. By Fourier analysis of the time-resolved interference pattern, the transition probabilities for all possible energy transfers are deducible. Experimental results for fields consisting of up to five modes are presented. Extending the theoretical approach by quantizing the magnetic field allows deeper insights on the underlying physical processes. For a coherent field state with a high mean photon number, the results of the calculation with classical fields is reproduced. By increasing the number of field modes whose relative phases are randomly distributed, one approaches the noise regime which offers the possibility of modelling decoherence in the neutron interferometer.Options and limitations of this modelling procedure are investigated in detail both theoretically and experimentally. Noise sources are applied in one or both interferometer path, and their strength, frequency bandwidth and position to each other is varied. In addition, the influence of increasing spatial separation of the neutron wave packet is examined, since the resulting Schrödinger cat-like states play an important role in decoherence theory.12

Quantum Dynamics and Non-Local Effects Behind Ion Transition States during Permeation in Membrane Channel Proteins

We present a comparison of a classical and a quantum mechanical calculation of the motion of K+ ions in the highly conserved KcsA selectivity filter motive of voltage gated ion channels. We first show that the de Broglie wavelength of thermal ions is not much smaller than the periodic structure of Coulomb potentials in the nano-pore model of the selectivity filter. This implies that an ion may no longer be viewed to be at one exact position at a given time but can better be described by a quantum mechanical wave function. Based on first principle methods, we demonstrate solutions of a non-linear Schrödinger model that provide insight into the role of short-lived (~1 ps) coherent ion transition states and attribute an important role to subsequent decoherence and the associated quantum to classical transition for permeating ions. It is found that short coherences are not just beneficial but also necessary to explain the fast-directed permeation of ions through the potential barriers of the filter. Certain aspects of quantum dynamics and non-local effects appear to be indispensable to resolve the discrepancy between potential barrier height, as reported from classical thermodynamics, and experimentally observed transition rates of ions through channel proteins

Quantum Mechanical Coherence of K+ Ion Wave Packets Increases Conduction in the KcsA Ion Channel

We simulate the transmission of K+ ions through the KcsA potassium ion channel filter region at physiological temperatures, employing classical molecular dynamics (MD) at the atomic scale together with a quantum mechanical version of MD simulation (QMD), treating single ions as quantum wave packets. We provide a direct comparison between both concepts, embedding the simulations into identical force fields and thermal fluctuations. The quantum simulations permit the estimation of coherence times and wave packet dispersions of a K+ ion over a range of 0.5 nm (a range that covers almost 50% of the filter domains longitudinal extension). We find that this observed extension of particle delocalization changes the mean orientation of the coordinating carbonyl oxygen atoms significantly, transiently suppressing their ‘caging action’ responsible for selective ion coordination. Compared to classical MD simulations, this particular quantum effect allows the K+ ions to ‘escape’ more easily from temporary binding sites provided by the surrounding filter atoms. To further elucidate the role of this observation for ion conduction rates, we compare the temporal pattern of single conduction events between classical MD and quantum QMD simulations at a femto-sec time scale. A finding from both approaches is that ion permeation follows a very irregular time pattern, involving flushes of permeation interrupted by non-conductive time intervals. However, as compared with classical behavior, the QMD simulation shortens non-conductive time by more than a half. As a consequence, and given the same force-fields, the QMD-simulated ion current appears to be considerably stronger as compared with the classical current. To bring this result in line with experimentally observed ion currents and the predictions based on Nernst–Planck theories, the conclusion is that a transient short time quantum behavior of permeating ions can successfully compromise high conduction rates with ion selectivity in the filter of channel proteins