arXiv subjects

U. Leonhardt

Publications and source records attributed to U. Leonhardt.

At least 19 recordsLinked to original sources

arXiv2026

Optical time travel: proposal for testing Hawking's Chronology Protection Conjecture in an optical analogue

Classical general relativity allows time travel, but Hawking [Phys. Rev. D 46, 603 (1992)] conjectured that quantum mechanics ultimately prevents it. Here we propose a feasible experiment to test Hawking's Chronology Protection Conjecture in optics. In this scheme, time travel is inherently related to lasing, and the amplified vacuum fluctuations above laser threshold establish the quantum limits of time travel

quant-ph↗

arXiv2023

Van der Waals chain: a simple model for Casimir forces in dielectrics

The Casimir force between dielectric bodies is well-understood, but not the Casimir force inside a dielectric, in particular its renormalization. We develop and analyse a simple model for the Casimir forces inside a medium that is completely free of renormalization and show then how renormalization emerges. We consider a one-dimensional chain of point particles interacting with each other by scattering the zero-point fluctuations of the electromagnetic field confined to one dimension. We develop a fast, efficient algorithm for calculating the forces on each particle and apply it to study the macroscopic limit of infinitely many, infinitely weak scatterers. The force density converges for piece-wise homogeneous media, but diverges in inhomogeneous media, which would cause instant collapse in theory. We argue that short-range counter forces in the medium prevent this collapse in reality. Their effect appears as the renormalization of the Casimir stress in dielectrics. Our simple model also allows us to derive an elementary analogue of the trace anomaly of quantum fields in curved space.

quant-ph↗

arXiv2012

Soliton-induced relativistic-scattering and amplification

Solitons are of fundamental importance in photonics due to applications in optical data transmission and also as a tool for investigating novel phenomena ranging from light generation at new frequencies and wave-trapping to rogue waves. Solitons are also relativistic scatterers: they generate refractive-index perturbations moving at the speed of light. Here we found that such perturbations scatter light in an unusual way: they amplify light by the mixing of positive and negative frequencies, as we describe using a first Born approximation and numerical simulations. The simplest scenario in which these effects may be observed is within the initial stages of optical soliton propagation: a steep shock front develops that may efficiently scatter a second, weaker probe pulse into relatively intense positive and negative frequency modes with amplification at the expense of the soliton. Our results show a novel all-optical amplification scheme that relies on relativistic scattering.

physics.optics↗

arXiv2012

Negative frequency resonant radiation

Optical solitons or soliton-like states shed light to blue-shifted frequencies through a resonant emission process. We predict a mechanism by which a second propagating mode is generated. This mode, called negative resonant radiation originates from the coupling of the soliton mode to the negative frequency branch of the dispersion relation. Measurements in both bulk media and photonic crystal fibres confirm our predictions.

physics.optics↗

arXiv2009

Casimir stress in an inhomogeneous medium

The Casimir effect in an inhomogeneous dielectric is investigated using Lifshitz's theory of electromagnetic vacuum energy. A permittivity function that depends continuously on one Cartesian coordinate is chosen, bounded on each side by homogeneous dielectrics. The result for the Casimir stress is infinite everywhere inside the inhomogeneous region, a divergence that does not occur for piece-wise homogeneous dielectrics with planar boundaries. A Casimir force per unit volume can be extracted from the infinite stress but it diverges on the boundaries between the inhomogeneous medium and the homogeneous dielectrics. An alternative regularization of the vacuum stress is considered that removes the contribution of the inhomogeneity over small distances, where macroscopic electromagnetism is invalid. The alternative regularization yields a finite Casimir stress inside the inhomogeneous region, but the stress and force per unit volume diverge on the boundaries with the homogeneous dielectrics. The case of inhomogeneous dielectrics with planar boundaries thus falls outside the current understanding of the Casimir effect.

quant-ph↗

arXiv2009

Evolution of light trapped by a soliton in a microstructured fiber

We observe the dynamics of pulse trapping in a microstructured fiber. Few-cycle pulses create a system of two pulses: a Raman shifting soliton traps a pulse in the normal dispersion regime. When the soliton approaches a wavelength of zero group velocity dispersion the Raman shifting abruptly terminates and the trapped pulse is released. In particular, the trap is less than 4ps long and contains a 1ps pulse. After being released, this pulse asymmetrically expands to more than 10ps. Additionally, there is no disturbance of the trapping dynamics at high input pulse energies as the supercontinuum develops further.

physics.optics↗

arXiv2009

Casimir-Lifshitz force between moving plates at different temperatures

The zero-temperature Casimir-Lifshitz force between two plates moving parallel to each other at arbitrary constant speed was found in [New J. Phys. 11, 033035 (2009)]. The solution is here generalized to the case where the plates are at different temperatures. The Casimir-Lifshitz force is obtained by calculating the electromagnetic stress tensor, using the method employed by Antezza et al. [Phys. Rev. A 77, 022901 (2008)] for non-moving plates at different temperatures. The perpendicular force on the plates has contributions from the quantum vacuum and from the thermal radiation; both of these contributions are influenced by the motion. In addition to the perpendicular force, thermal radiation from the moving plates gives rise to a lateral component of the Casimir-Lifshitz force, an effect with no quantum-vacuum contribution. The zero-temperature results are reproduced, in particular the non-existence of a quantum-vacuum friction between the plates.

quant-ph↗

arXiv2009

No quantum friction between uniformly moving plates

The Casimir forces between two plates moving parallel to each other are found by calculating the vacuum electromagnetic stress tensor. The perpendicular force between the plates is modified by the motion but there is no lateral force on the plates. Electromagnetic vacuum fluctuations do not therefore give rise to "quantum friction" in this case, contrary to previous assertions. The result shows that the Casimir-Polder force on a particle moving at constant speed parallel to a plate also has no lateral component.

quant-ph↗

arXiv2008

An alternative calculation of the Casimir forces between birefringent plates

Barash has calculated the Casimir forces between parallel birefringent plates with optical axes parallel to the plate boundaries [Izv. Vyssh. Uchebn.\ Zaved., Radiofiz., {\bf 12}, 1637 (1978)]. The interesting new feature of the solution compared to the case of isotropic plates is the existence of a Casimir torque which acts to line up the optical axes if they are not parallel or perpendicular. The forces were found from a calculation of the Helmholtz free energy of the electromagnetic field. Given the length of the calculations in this problem and hopes of an experimental measurement of the torque, it is important to check the results for the Casimir forces by a different method. We provide this check by calculating the electromagnetic stress tensor between the plates and showing that the resulting forces are in agreement with those found by Barash.

quant-ph↗

arXiv2008

A Novel Design of Dielectric Perfect Invisibility Devices

The aim of an invisibility device is to guide light around any object put inside, being able to hide objects from sight. In this work, we propose a novel design of dielectric invisibility media based on negative refraction and optical conformal mapping that seems to create perfect invisibility. This design has some advantages and more relaxed constraints compared with already proposed schemes. In particular, it represents an example where the time delay in a dielectric invisibility device is zero. Furthermore, due to impedance matching of negatively refracting materials, the reflection should be close to zero. These findings strongly indicate that perfect invisibility with optically isotropic materials is possible. Finally, the area of the invisible space is also discussed.

physics.optics↗

arXiv2007

Quantum levitation by left-handed metamaterials

Left-handed metamaterials make perfect lenses that image classical electromagnetic fields with significantly higher resolution than the diffraction limit. Here we consider the quantum physics of such devices. We show that the Casimir force of two conducting plates may turn from attraction to repulsion if a perfect lens is sandwiched between them. For optical left-handed metamaterials this repulsive force of the quantum vacuum may levitate ultra-thin mirrors.

quant-ph↗

arXiv2005

Slow light, superadiabaticity and shape-preserving pulses

We analyze the nonlinear dynamics of atomic dark states in Lambda configuration that interact with light at exact resonance. We found a generalization of shape-preserving pulses [R. Grobe, F. T. Hioe, and J. H. Eberly, Phys. Rev. Lett. 73, 3183 (1994)] and show that the condition for adiabaticity of the atomic dynamics is never violated, as long as spontaneous emission is negligible.

quant-ph↗

arXiv2004

Conditions for one-dimensional supersonic flow of quantum gases

One can use transsonic Bose-Einstein condensates of alkali atoms to establish the laboratory analog of the event horizon and to measure the acoustic version of Hawking radiation. We determine the conditions for supersonic flow and the Hawking temperature for realistic condensates on waveguides where an external potential plays the role of a supersonic nozzle. The transition to supersonic speed occurs at the potential maximum and the Hawking temperature is entirely determined by the curvature of the potential.

cond-mat.soft↗

arXiv2004

The Perfectly Matched Layer for nonlinear and matter waves

We discuss how the Perfectly Matched Layer (PML) can be adapted to numerical simulations of nonlinear and matter wave systems, such as Bose-Einstein condensates. We also present some examples which illustrate the benefits of using the PML in the simulation of nonlinear and matter waves.

cond-mat.soft↗

arXiv2003

Explicit effective Hamiltonians for general linear quantum-optical networks

Linear optical networks are devices that turn classical incident modes by a linear transformation into outgoing ones. In general, the quantum version of such transformations may mix annihilation and creation operators. We derive a simple formula for the effective Hamiltonian of a general linear quantum network, if such a Hamiltonian exists. Otherwise we show how the scattering matrix of the network is decomposed into a product of three matrices that can be generated by Hamiltonians.

quant-ph↗

arXiv2003

Optical Analog of the Iordanskii Force in a Bose-Einstein Condensate

A vortex in a Bose-Einstein condensate generates the optical analog of the Aharonov-Bohm effect when illuminated with slow light. In contrast to the original Aharonov-Bohm effect the vortex will exchange forces with the light that lead to a measurable motion of the vortex.

cond-mat.soft↗

arXiv2002

Theory of elementary excitations in unstable Bose-Einstein condensates

Like classical fluids, quantum gases may suffer from hydrodynamic instabilities. Our paper develops a quantum version of the classical stability analysis in fluids, the Bogoliubov theory of elementary excitations in unstable Bose-Einstein condensates. In unstable condensates the excitation modes have complex frequencies. We derive the normalization conditions for unstable modes such that they can serve in a mode decomposition of the non-condensed component. Furthermore, we develop approximative techniques to determine the spectrum and the mode functions. Finally, we apply our theory to a sonic white hole and find that the spectrum of unstable modes is intrinsically discrete.

cond-mat.soft↗

arXiv2002

Bogoliubov theory of the Hawking effect in Bose-Einstein condensates

Artificial black holes may demonstrate some of the elusive quantum properties of the event horizon, in particular Hawking radiation. One promising candidate is a sonic hole in a Bose-Einstein condensate. We clarify why Hawking radiation emerges from the condensate and how this condensed-matter analog reflects some of the intriguing aspects of quantum black holes.

cond-mat.soft↗