arXiv subjects

Ulf Leonhardt

Publications and source records attributed to Ulf Leonhardt.

At least 37 records · Page 2Linked to original sources

arXiv2018

Electronic zero-point fluctuation forces inside circuit components

One of the most intriguing manifestations of quantum zero-point fluctuations are the van der Waals and Casimir forces, often associated with vacuum fluctuations of the electromagnetic field. Here we study generalized fluctuation potentials acting on internal degrees of freedom of components in electrical circuits. These electronic Casimir-like potentials are induced by the zero-point current fluctuations of any general conductive circuit. For realistic examples of an electromechanical capacitor and a superconducting qubit, our results reveal the possibility of tunable forces between the capacitor plates, or the level shifts of the qubit, respectively. Our analysis suggests an alternative route towards the exploration of Casimir-like fluctuation potentials, namely, by characterizing and measuring them as a function of parameters of the environment. Such tunable potentials may be useful for future nanoelectromechanical and quantum technologies.

quant-ph↗

arXiv2018

Questioning the recent observation of quantum Hawking radiation

A recent article [J. Steinhauer, Nat. Phys. 12, 959 (2016)] has reported the observation of quantum Hawking radiation and its entanglement in an analogue black hole. This paper analyses the published evidence, its consistency with theoretical bounds and the statistical significance of the results. The analysis raises severe doubts on the observation of Hawking radiation.

gr-qc↗

arXiv2018

Casimir self-stress in a dielectric sphere

The dielectric sphere has been an important test case for understanding and calculating the vacuum force of a dielectric body onto itself. Here we develop a method for computing this force in homogeneous spheres of arbitrary dielectric properties embedded in arbitrary homogeneous backgrounds, assuming only that both materials are isotropic and dispersionless. Our results agree with known special cases; most notably we reproduce the prediction of Boyer and Schwinger et al. of a repulsive Casimir force of a perfectly reflecting shell. Our results disagree with the literature in the dilute limit. We argue that Casimir forces can not be regarded as due to pair-wise Casimir-Polder interactions, but rather due to reflections of virtual electromagnetic waves.

quant-ph↗

arXiv2017

Classical analogue of the Unruh effect

In the Unruh effect an observer with constant acceleration perceives the quantum vacuum as thermal radiation. The Unruh effect has been believed to be a pure quantum phenomenon, but here we show theoretically how the effect arises from the classical correlation of noise. We demonstrate this idea with a simple experiment on water waves where we see the first indications of a Planck spectrum in the correlation energy.

gr-qc↗

arXiv2017

Casimir stress inside planar materials

Current theory is able to predict the Casimir force between macroscopic bodies with an accuracy only limited by the knowledge of the material parameters. Yet surprisingly after almost 70 years of research, while theory describes the Casimir force between bodies, the force inside macroscopic bodies is poorly understood. In this paper, we develop from a physically intuitive picture the macroscopic theory of the Casimir stress inside inhomogeneous planar media. Our result agrees with a previous ad hoc procedure [T. G. Philbin et al., Ann. Phys. (New York) 325, 579 (2010)], giving both mathematical and physical justification to a conjecture that was only tested numerically so far. Our theory is likely to be extendable; it may open the gate to the computation of Casimir forces inside arbitrary materials.

quant-ph↗

arXiv2017

Casimir stress in materials: hard divergency at soft walls

The Casimir force between macroscopic bodies is well understood, but not the Casimir stress inside bodies. Suppose empty space or a uniform medium meets a soft wall where the refractive index is continuous but its derivative jumps. For this situation we predict a characteristic power law for the stress inside the soft wall and close to its edges. Our result shows that such edges are not tolerated in the aggregation of liquids at surfaces, regardless whether the liquid is attracted or repelled.

quant-ph↗

arXiv2017

Dialogues about geometry and light

Throughout human history, people have used sight to learn about the world, but only in relatively recent times the science of light has been developed. Egyptians and Mesopotamians made the first known lenses out of quartz, giving birth to what was later known as optics. On the other hand, geometry is a branch of mathematics that was born from practical studies concerning lengths, areas and volumes in the early cultures, although it was not put into axiomatic form until the 3rd century BC. In this work, we will discuss the connection between these two timeless topics and show some "new things in old things". There has been several works in this direction, but taking into account the didactic approach of the Enrico Fermi Summer School, we would like to address the subject and our audience in a new light.

physics.optics↗

arXiv2016

Hawking spectrum for a fiber-optical analog of the event horizon

Hawking radiation has been regarded as a more general phenomenon than in gravitational physics, in particular in laboratory analogs of the event horizon. Here we consider the fiber-optical analog of the event horizon, where intense light pulses in fibers establish horizons for probe light. Then, we calculate the Hawking spectrum in an experimentally realizable system. We found that the Hawking radiation is peaked around group-velocity horizons in which the speed of the pulse matches the group velocity of the probe light. The radiation nearly vanishes at the phase horizon where the speed of the pulse matches the phase velocity of light.

gr-qc↗

arXiv2014

Integral method for the calculation of Hawking radiation in dispersive media I. Symmetric asymptotics

Hawking radiation has become experimentally testable thanks to the many analogue systems which mimic the effects of the event horizon on wave propagation. These systems are typically dominated by dispersion, and give rise to a numerically soluble and stable ODE only if the rest-frame dispersion relation $Ω^{2}(k)$ is a polynomial of relatively low degree. Here we present a new method for the calculation of wave scattering in a one-dimensional medium of arbitrary dispersion. It views the wave equation as an integral equation in Fourier space, which can be solved using standard and efficient numerical techniques.

gr-qc↗

arXiv2012

Optical black hole lasers

Using numerical simulations we show how to realise an optical black hole laser, i.e. an amplifier formed by travelling refractive index perturbations arranged so as to trap light between a white and a black hole horizon. The simulations highlight the main features of these lasers: the growth inside the cavity of positive and negative frequency modes accompanied by a weaker emission of modes that occurs in periodic bursts corresponding to the cavity round trips of the trapped modes. We then highlight a new regime in which the trapped mode spectra broaden until the zero-frequency points on the dispersion curve are reached. Amplification at the horizon is highest for zero-frequencies, therefore leading to a strong modification of the structure of the trapped light. For sufficiently long propagation times, lasing ensues only at the zero-frequency modes.

physics.optics↗

arXiv2012

Perfect imaging in the optical domain using dielectric materials

The promise of perfect imaging in the optical domain, where light can be imaged without aberrations and with ultra-high resolution, could revolutionize technology and nanofabrication [1, 2, 3, 4, 5, 6]. Recently it has been shown theoretically that perfect imaging can be achieved in a dielectric medium with spatially varying refractive index [7, 8]. The lens geometry is defined using transformation optics [9, 10, 11, 12, 13, 14, 15] for projecting a spherical space onto a real plane space, forming Maxwells fish eye [16, 17, 18, 19]. Most transformation optics demonstrations have been achieved for Euclidean spaces and in the microwave regime, due to ease of fabrication. Here we demonstrate a transformation to a non-Euclidean space [20] in the optical regime using silicon nanophotonic structures.

physics.optics↗

arXiv2011

An exact solution for the Casimir force in a spherically symmetric medium

We calculated the force of the quantum vacuum, the Casimir force, in a spherically symmetric medium, Maxwell's fish eye, surrounded by a perfect mirror and derived an exact analytic solution. Our solution questions the idea that the Casimir force of a spherical mirror is repulsive - we found an attractive force that diverges at the mirror.

quant-ph↗

arXiv2011

Invisibility cloaking without superluminal propagation

Conventional cloaking based on Euclidean transformation optics requires that the speed of light should tend to infinity on the inner surface of the cloak. Non-Euclidean cloaking still needed media with superluminal propagation. Here we show by giving an example that this is no longer necessary.

physics.optics↗

arXiv2011

Partial Transmutation of Singularities in Optical Instruments

Some interesting optical instruments such as the Eaton lens and the Invisible Sphere require singularities of the refractive index for their implementation. We show how to transmute those singularities into harmless topological defects in anisotropic media without the need for anomalous material properties.

physics.optics↗

arXiv2011

Conformal cloak for waves

Conformal invisibility devices are only supposed to work within the validity range of geometrical optics. Here we show by numerical simulations and analytical arguments that for certain quantized frequencies they are nearly perfect even in a regime that clearly violates geometrical optics. The quantization condition follows from the analogy between the Helmholtz equation and the stationary Schrodinger equation.

physics.optics↗

arXiv2011

Luneburg lens in silicon photonics

The Luneburg lens is an aberration-free lens that focuses light from all directions equally well. We fabricated and tested a Luneburg lens in silicon photonics. Our technique is sufficiently versatile for making perfect imaging devices on silicon platforms.

physics.optics↗

arXiv2010

Reply to Comment on Reply to Comment on `Perfect imaging without negative refraction'

Kinsler and Favaro point out correctly that Blaikie's numerical solution of Maxwell's equations in Maxwell's fish eye is causal and hence valid, a solution where no perfect image is formed. It is wrong to conclude from the existence of a causal solution with perfect imaging that one without perfect resolution is not causal; both are allowed by causality. However, Maxwell's fish eye can still perfectly image, as the Reply shows.

physics.optics↗

arXiv2010

Horizon effects with surface waves on moving water

Surface waves on a stationary flow of water are considered, in a linear model that includes the surface tension of the fluid. The resulting gravity-capillary waves experience a rich array of horizon effects when propagating against the flow. In some cases three horizons (points where the group velocity of the wave reverses) exist for waves with a single laboratory frequency. Some of these effects are familiar in fluid mechanics under the name of wave blocking, but other aspects, in particular waves with negative co-moving frequency and the Hawking effect, were overlooked until surface waves were investigated as examples of analogue gravity [Schützhold R and Unruh W G 2002 Phys. Rev. D 66 044019]. A comprehensive presentation of the various horizon effects for gravity-capillary waves is given, with emphasis on the deep water/short wavelength case kh>>1 where many analytical results can be derived. A similarity of the state space of the waves to that of a thermodynamic system is pointed out.

gr-qc↗