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Ole Steuernagel

Publications and source records attributed to Ole Steuernagel.

At least 37 records · Page 2Linked to original sources

Dynamic shear suppression in quantum phase space

Classical phase space flow is inviscid. Here we show that in quantum phase space Wigner's probability current J can be effectively viscous. This results in shear suppression in quantum phase space dynamics which enforces Zurek's limit for the minimum size scale of spotty structures that develop dynamically. Quantum shear suppression is given by gradients of the quantum terms of J's vorticity. Used as a new measure of quantum dynamics applied to several evolving closed conservative 1D bound state systems, we find that shear suppression explains the saturation at Zurek's scale limit and additionally singles out special quantum states.

quant-ph↗

Anharmonic quantum mechanical systems do not feature phase space trajectories

Phase space dynamics in classical mechanics is described by transport along trajectories. Anharmonic quantum mechanical systems do not allow for a trajectory-based description of their phase space dynamics. This invalidates some approaches to quantum phase space studies. We first demonstrate the absenceof trajectories in general terms. We then give an explicit proof for all quantum phase space distributions with negative values: we show that the generation of coherences in anharmonic quantum mechanical systems is responsible for the occurrence of singularities in their phase space velocity fields, and vice versa. This explains numerical problems repeatedly reported in the literature, and provides deeper insight into the nature of quantum phase space dynamics.

quant-ph↗

Wigner`s quantum phase-space current in weakly-anharmonic weakly-excited two-state systems

There are no phase-space trajectories for anharmonic quantum systems, but Wigner's phase-space representation of quantum mechanics features Wigner current~$\bf J$. This current reveals fine details of quantum dynamics -- finer than is ordinarily thought accessible according to quantum folklore invoking Heisenberg's uncertainty principle. Here, we focus on the simplest, most intuitive, and analytically accessible aspects of~$\bf J$. We investigate features of~$\bf J$ for bound states of time-reversible, weakly-anharmonic one-dimensional quantum-mechanical systems which are weakly-excited. We establish that weakly-anharmonic potentials can be grouped into three distinct classes: hard, soft, and odd potentials. We stress connections between each other and the harmonic case. We show that their Wigner current fieldline patterns can be characterised by~$\bf J$'s discrete stagnation points, how these arise and how a quantum system's dynamics is constrained by the stagnation points' topological charge conservation. We additionally show that quantum dynamics in phase space, in the case of vanishing Planck constant $\hbar$ or vanishing anharmonicity, does not pointwise converge to classical dynamics.

quant-ph↗

Structures far below sub-Planck scale in quantum phase-space through superoscillations

In 2001, Zurek derived the generic minimum scale $a_{Z}$ for the area of structures of Wigner's quantum phase distribution. Here we show by construction, using superoscillatory functions, that the Wigner distribution can locally show regular spotty structures on scales much below Zurek's scale $a_{Z}$. The price to pay for the presence of such structures is their exponential smallness. For the case we construct there is no increased interferometric sensitivity from the presence of patches with superoscillatory structure in phase-space.

quant-ph↗

Wigner's representation of quantum mechanics in integral form and its applications

We consider quantum phase-space dynamics using Wigner's representation of quantum mechanics. We stress the usefulness of the integral form for the description of Wigner's phase-space current~$\bm J$ as an alternative to the popular Moyal bracket. The integral form brings out the symmetries between momentum and position representations of quantum mechanics, is numerically stable, and allows us to perform some calculations using elementary integrals instead of Groenewold star products. Our central result is an explicit, elementary proof which shows that only systems up to quadratic in their potential fulfill Liouville's theorem of volume preservation in quantum mechanics. Contrary to a recent suggestion, our proof shows that the non-Liouvillian character of quantum phase-space dynamics cannot be transformed away.

quant-ph↗

The Quantum Liouville Equation is non-Liouvillian

The Hamiltonian flow of a classical, time-independent, conservative system is incompressible, it is Liouvillian. The analog of Hamilton's equations of motion for a quantum-mechanical system is the quantum-Liouville equation. It is shown that its associated quantum flow in phase space, Wigner flow, is not incompressible. It gives rise to a quantum analog of classical Hamiltonian vector fields: the Wigner phase space velocity field~$\bm w$, the divergence of which can be unbounded. The loci of such unbounded divergence form lines in phase space which coincide with the lines of zero of the Wigner function. Along these lines exist characteristic pinch points which coincide with stagnation points of the Wigner flow.

quant-ph↗

Equivalence between free quantum particles and those in harmonic potentials and its application to instantaneous changes

In quantum physics the free particle and the harmonically trapped particle are arguably the most important systems a physicist needs to know about. It is little known that, mathematically, they are one and the same. This knowledge helps us to understand either from the viewpoint of the other. Here we show that all general time-dependent solutions of the free-particle Schroedinger equation can be mapped to solutions of the Schroedinger equation for harmonic potentials, both the trapping oscillator and the inverted 'oscillator'. This map is fully invertible and therefore induces an isomorphism between both types of system, they are equivalent. A composition of the map and its inverse allows us to map from one harmonic oscillator to another with a different spring constant and different center position. The map is independent of the state of the system, consisting only of a coordinate transformation and multiplication by a form factor, and can be chosen such that the state is identical in both systems at one point in time. This transition point in time can be chosen freely, the wave function of the particle evolving in time in one system before the transition point can therefore be linked up smoothly with the wave function for the other system and its future evolution after the transition point. Such a cut-and-paste procedure allows us to describe the instantaneous changes of the environment a particle finds itself in. Transitions from free to trapped systems, between harmonic traps of different spring constants or center positions, or, from harmonic binding to repulsive harmonic potentials are straightforwardly modelled. This includes some time-dependent harmonic potentials. The mappings introduced here are computationally more efficient than either state-projection or harmonic oscillator propagator techniques conventionally employed when describing instantaneous (non-a 1,920 characters

quant-ph↗

Wigner flow reveals topological order in quantum phase space dynamics

The behaviour of classical mechanical systems is characterised by their phase portraits, the collections of their trajectories. Heisenberg's uncertainty principle precludes the existence of sharply defined trajectories, which is why traditionally only the time evolution of wave functions is studied in quantum dynamics. These studies are quite insensitive to the underlying structure of quantum phase space dynamics. We identify the flow that is the quantum analog of classical particle flow along phase portrait lines. It reveals hidden features of quantum dynamics and extra complexity. Being constrained by conserved flow winding numbers, it also reveals fundamental topological order in quantum dynamics that has so far gone unnoticed.

quant-ph↗

Bright and Dark Helices of Light

Laser beams can be made to form bright and dark intensity helices of light. Such helices have a pitch length on the order of a wavelength and may have applications in lithography and the manipulation of particles through optical forces. The formation of bright helices is more strongly constrained by optical resolution limits than that of dark helices, corresponding scaling laws are derived and their relevance for photo-lithography pointed out. It is shown how to arrange dark helices on a grid in massively parallel fashion in order to create handed materials using photo-lithographic techniques.

quant-ph↗

Imprinting interference fringes in massive optomechanical systems

An interferometric scheme for the creation of momentum superposition states of mechanical oscillators, using a quantum mirror kicked by free photons is analyzed. The scheme features ultra-fast preparation with immediate detection and should allow for the observation of signatures of momentum superpositions in a massive macroscopic system at non-zero temperatures. It is robust against thermalized initial states, displacement and movement, mirror imperfections, and the measurements' back-actions.

quant-ph↗

Time Evolution of Harmonic Oscillator Thermal Momentum Superposition States

The time evolution of thermal states of a mirror released from a tight harmonic trap is studied. After the release no dissipation is assumed to be present and the mirror is, after a time delay, kicked into a momentum superposition state. The thermal character of the initial state washes out the telltale interference patterns of the superposition but no loss of coherence is found. This investigation resolves a controversy about decoherence--without--dissipation and shows that entrained measurements can be surprisingly insensitive to temperature effects.

quant-ph↗

Double-Well Quantum Tunneling Visualized via Wigner's Function

We investigate quantum tunneling in smooth symmetric and asymmetric double-well potentials. Exact solutions for the ground and first excited states are used to study the dynamics. We introduce Wigner's quasi-probability distribution function to highlight and visualize the non-classical nature of spatial correlations arising in tunneling.

quant-ph↗

Equivalence between free and harmonically trapped quantum particles

It is shown that general solutions of the free-particle Schroedinger equation can be mapped onto solutions of the Schroedinger equation for the harmonic oscillator. This is done in such a way that the time evolution of a free particle subjected to a sudden transition to a harmonic potential can be described by a simple coordinate transformation applied at the transition time. This procedure is computationally more efficient than either state-projection or propagator techniques. A concatenation of the map and its inverse allows us to map from one harmonic oscillator to another with a different spring constant.

quant-ph↗

Optimal strategies for fighting persistent bugs

Some microbial organisms are known to randomly slip into and out of hibernation, irrespective of environmental conditions [1]. In a (genetically) uniform population a typically very small subpopulation becomes metabolically inactive whereas the majority subpopulation remains active and grows. Bacteria such as E. coli, Staphylococcus aureus (MRSA-superbug), Mycobacterium tuberculosis, and Pseudomonas aeruginosa [1-3] show persistence. It can render bacteria less vulnerable in adverse environments [1, 4, 5] and their effective eradication through medication more difficult [2, 3, 6]. Here we show that medication treatment regimes may have to be modified when persistence is taken into account and characterize optimal approaches assuming that the total medication dose is constrained. The determining factors are cumulative toxicity, eradication power of the medication and bacterial response timescales. Persistent organisms have to be fought using tailored eradication strategies which display two fundamental characteristics. Ideally, the treatment time should be significantly longer than in the case of persistence with the medication uniformly spread out over time; however, if treatment time has to be limited, then the application of medication has to be concentrated towards the beginning and end of the treatment. These findings deviate from current clinical practice, and may therefore help to optimize and simplify treatments. Our use of multi-objective optimization [7] to map out the optimal strategies can be generalized to other related problems.

q-bio.OT↗

Unequal intensity splitting can reduce back action in interferometers

Typical two-path interferometers are intensity-balanced because this maximizes the visibility of their interference patterns. Unbalancing the interferometer can be advised when back action on the object whose position is monitored is to be reduced. Variations of the intensity splitting ratios in two-path interferometers are analyzed in order to determine optimal interferometric performance while minimizing back action: it turns out that homodyning-like schemes perform best.

quant-ph↗

Wide cylindrical or spherical optical potentials from laser beam superpositions

Superpositions of paraxial Laguerre-Gauss laser beam modes to generate optical potentials based on the optical dipole force are investigated theoretically. Parabolic and other monomial potentials with even powers, in cylindrical and spherical symmetry, with large diameters, can be synthesized. This superposition approach promises to help with high quality atom cloud manipulation and imaging.

physics.optics↗

Optical Lenses for Atomic Beams

Superpositions of paraxial laser beam modes to generate atom-optical lenses based on the optical dipole force are investigated theoretically. Thin, wide, parabolic, cylindrical and circular atom lenses with numerical apertures much greater than those reported in the literature to date can be synthesized. This superposition approach promises to make high quality atom beam imaging and nano-deposition feasible.

quant-ph↗