arXiv subjects

Ulf Leonhardt

Publications and source records attributed to Ulf Leonhardt.

At least 19 recordsLinked to original sources

arXiv2026

Backreaction of stimulated Hawking radiation in an optical analogue

Hawking radiation - the emission of quantum particles at the event horizon of a black hole - connects gravity with quantum mechanics and thermodynamics; the Bekenstein-Hawking entropy has been the benchmark for potential quantum theories of gravity. But Hawking radiation has never been observed in astronomy, only in laboratory analogues and the chances of ever observing it in space are astronomically small. The energy of Hawking radiation must come from the gravitational field around the black hole, but how field quanta generate Hawking quanta has been unknown. Here we report on experimental and theoretical evidence for the process that generates Hawking radiation in a fibre-optical analogue of the event horizon. There, as in gravity, it has been believed that Hawking radiation comes from a complicated, cascaded process; here we have found a simple, direct process and measured its backreaction on the field. Our findings suggest an equally direct process for other laboratory analogues and perhaps also for gravitational fields, shedding light on how black holes might radiate.

gr-qc↗

arXiv2025

Dispersion in Analogue Gravity

Analogue models of gravity, from Newton to Unruh, have evolved from simple fluid--mechanical models to sophisticated modern experiments. They have shown the robustness of Hawking radiation and highlighted the role of dispersion for quantum fields in curved space. We speculate whether some underlying dispersion may also play a role in explaining the cosmological constant and in resolving the cosmological tensions.

gr-qc↗

arXiv2025

Einstein's Equations in Electromagnetic Media

In this paper, we extend Plebanski's mapping to encode the Einstein equations in ADM form within a bianisotropic electromagnetic medium. We realise this by translating the ADM constraints and evolution equations into dynamical conditions on the medium's constitutive parameters. These transformed equations are then linearised in vacuum to derive gravitational-wave analogues as perturbations of the optical medium.

gr-qc↗

arXiv2025

Quantum noise in time-dependent media and cosmic expansion

In spatially uniform, but time-dependent dielectric media with equal electric and magnetic response, classical electromagnetic waves propagate exactly like in empty, flat space with transformed time, called conformal time, and so do quantum fluctuations. In empty, flat space the renormalized vacuum energy is exactly zero, but not in time-dependent media, as we show in this paper. This is because renormalization is local and causal, and so cannot compensate fully for the transformation to conformal time. The expanding universe appears as such a medium to the electromagnetic field. We show that the vacuum energy during cosmic expansion effectively reduces the weights of radiation and matter by characteristic factors. This quantum buoyancy naturally resolves the Hubble tension, the discrepancy between the measured and the inferred Hubble constant, and it might resolve other cosmological tensions as well.

quant-ph↗

arXiv2024

Wigner function method for the Gibbons-Hawking and the Unruh effect

An observer at rest with the expanding universe experiences some extra noise in the quantum vacuum, and so does an accelerated observer in a vacuum at rest (in Minkowski space). The literature mainly focuses on the ideal cases of exponential expansion (de-Sitter space) or uniform acceleration (Rindler trajectories) or both, but the real cosmic expansion is non-exponential and real accelerations are non-uniform. Here we use the frequency-time Wigner function of vacuum correlations to define time-dependent spectra. We found excellent Planck spectra for a class of realistic cosmological models, but also strongly non-Planckian, negative Wigner functions for a standard scenario testable with laboratory analogues.

gr-qc↗

arXiv2024

How to find optimal quantum states for optical micromanipulation and metrology in complex scattering problems: tutorial

The interaction of quantum light with matter is of great importance to a wide range of scientific disciplines, ranging from optomechanics to high precision measurements. A central issue we discuss here, is how to make optimal use of both the spatial and the quantum degrees of freedom of light for characterizing and manipulating arbitrary observable parameters in a linear scattering system into which suitably engineered light fields are injected. Here, we discuss a comprehensive framework based on a quantum operator that can be assembled solely from the scattering matrix of a system and its dependence on the corresponding local parameter, making this operator experimentally measurable from the far-field using only classical light. From this, the effect of quantum light in the near-field, i.e., in the vicinity of the target object, can be inferred. Based on this framework, it is straightforward to formulate optimal protocols on how to jointly design both the spatial shape and the quantum characteristics of light for micromanipulation as well as for parameter estimation in arbitrarily complex media. Also the forces of the quantum vacuum naturally emerge from this formalism. The aim of our tutorial is to bring different perspectives into alignment and thereby build a bridge between the different communities of wave control, quantum optics, micromanipulation, quantum metrology and vacuum physics.

quant-ph↗

arXiv2023

Wave correlations and quantum noise in cosmology

Wave noise is correlated. While it may look random in space, correlations appear in space-time, because the noise is carried by wave propagation. These correlations of wave noise give rise to fluctuation forces such as the Casimir force, they are responsible for the particle creation in the dynamical Casimir effect and in the expanding universe. This paper considers the noise correlations for light waves in non-exponentially expanding flat space. The paper determines the high-frequency asymptotics of the correlation spectrum in the conformal vacuum. These noise correlations give rise to a nontrivial vacuum energy that may appear as the cosmological constant.

gr-qc↗

arXiv2022

Transforming space with non-Hermitian dielectrics

Coordinate transformations are a versatile tool to mould the flow of light, enabling a host of astonishing phenomena such as optical cloaking with metamaterials. Moving away from the usual restriction that links isotropic materials with conformal transformations, we show how non-conformal distortions of optical space are intimately connected to the complex refractive index distribution of an isotropic non-Hermitian medium. Remarkably, this insight can be used to circumvent the material requirement of working with refractive indices below unity, which limits the applications of transformation optics. We apply our approach to design a broadband unidirectional dielectric cloak, which relies on non-conformal coordinate transformations to tailor the nonHermitian refractive index profile around a cloaked object. Our insights bridge the fields of two-dimensional transformation optics and non-Hermitian photonics.

physics.optics↗

arXiv2022

Casimir cosmology

In 1998 astronomers discovered that the expansion of the universe is accelerating. Somehow, something must have made gravity repulsive on cosmological scales. This something was called dark energy; it is described by Einstein's cosmological constant; and it amounts to about 70% of the total mass of the universe. It has been conjectured that the cosmological constant is a form of vacuum energy, but its prediction from quantum field theory has failed by many orders of magnitude, until recently. Informed by empirical evidence on Casimir forces, Lifshitz theory has not only produced the correct order of magnitude, but is quantitatively consistent with the astronomical data. Moreover, the theory appears to resolve the tension between the measured and the predicted Hubble constant. There is therefore a good chance that Casimir physics explains dark energy. This article introduces cosmology for practitioners of vacuum forces as part of "The State of the Quantum Vacuum: Casimir Physics in the 2020s" edited by K. A. Milton. It may also be interesting for other physicists and engineers who wish to have a concise introduction to cosmology.

gr-qc↗

arXiv2021

Van der Waals Anomaly

In inhomogeneous dielectric media the divergence of the electromagnetic stress is related to the gradients of \varepsilon and μ, which is a consequence of Maxwell's equations. Investigating spherically symmetric media we show that this seemingly universal relationship is violated for electromagnetic vacuum forces such as the generalized van der Waals and Casimir forces. The stress needs to acquire an additional anomalous pressure. The anomaly is a result of renormalization, the need to subtract infinities in the stress for getting a finite, physical force. The anomalous pressure appears in the stress in media like dark energy appears in the energy-momentum tensor in general relativity. We propose and analyse an experiment to probe the van der Waals anomaly with ultracold atoms. The experiment may not only test an unusual phenomenon of quantum forces, but also an analogue of dark energy, shedding light where nothing is known empirically.

quant-ph↗

arXiv2021

Lifshitz cosmology: quantum vacuum and Hubble tension

Dark energy is one of the greatest scientific mysteries of today. The idea that dark energy originates from quantum vacuum fluctuations has circulated since the late '60s, but theoretical estimations of vacuum energy have disagreed with the measured value by many orders of magnitude, until recently. Lifshitz theory applied to cosmology has produced the correct order of magnitude for dark energy. Furthermore, the theory is based on well-established and experimentally well-tested grounds in atomic, molecular and optical physics. In this paper, we confront Lifshitz cosmology with astronomical data. We find that the dark-energy dynamics predicted by the theory is able to resolve the Hubble tension, the discrepancy between the observed and predicted Hubble constant within the standard cosmological model. The theory is consistent with supernovae data, Baryon Acoustic Oscillations and the Cosmic Microwave Background. Our findings indicate that Lifshitz cosmology is a serious candidate for explaining dark energy.

gr-qc↗

arXiv2020

Cosmological horizons radiate

Gibbons and Hawking [Phys. Rev. D 15, 2738 (1977)] have shown that the horizon of de Sitter space emits radiation in the same way as the event horizon of the black hole. But actual cosmological horizons are not event horizons, except in de Sitter space. Nevertheless, this paper proves Gibbons' and Hawking's radiation formula as an exact result for any flat space expanding with strictly positive Hubble parameter. The paper gives visual and intuitive insight into why this is the case. The paper also indicates how cosmological horizons are related to the dynamical Casimir effect, which makes experimental tests with laboratory analogues possible.

gr-qc↗

arXiv2020

Cherenkov Radiation of Light Bullets

Electrically charged particles, moving faster than the speed of light in a medium, emit Cherenkov radiation. Theory predicts electric and magnetic dipoles to radiate as well, with a puzzling behavior for magnetic dipoles pointing in transversal direction [I. M. Frank, Izv. Akad. Nauk SSSR, Ser. Fiz. 6, 3 (1942)]. A discontinuous Cherenkov spectrum should appear at threshold, where the particle velocity matches the phase velocity of light. Here we deduce theoretically that light bullets [Y. Silberberg, Opt. Lett. 15, 1282 (1990)] emit an analogous radiation with exactly the same spectral discontinuity for point-like sources. For extended sources the discontinuity turns into a spectral peak at threshold. We argue that this Cherenkov radiation has been experimentally observed in the first attempt to measure Hawking radiation in optics [F. Belgiorno et al., Phys. Rev. Lett. 105, 203901 (2010)] thus giving experimental evidence for a puzzle in Cherenkov radiation instead.

gr-qc↗

arXiv2020

The case for a Casimir cosmology

The cosmological constant, also known as dark energy, was believed to be caused by vacuum fluctuations, but naive calculations give results in stark disagreement with fact. In the Casimir effect, vacuum fluctuations cause forces in dielectric media, which is very well described by Lifshitz theory. Recently, using the analogy between geometries and media, a cosmological constant of the correct order of magnitude was calculated with Lifshitz theory [U. Leonhardt, Ann. Phys. (New York) 411, 167973 (2019)]. This paper discusses the empirical evidence and the ideas behind the Lifshitz theory of the cosmological constant without requiring prior knowledge of cosmology and quantum field theory.

gr-qc↗

arXiv2019

Comment on Self-Stress on a Dielectric Ball and Casimir-Polder Forces

In our paper [Ann. Phys. (NY) 395, 326 (2018)] we calculate the Casimir stress on a sphere immersed in a homogeneous background, assuming dispersionless dielectrics. Our results appear to challenge the conventional picture of Casimir forces. The paper [arXiv:1909.05721] criticises our approach without offering an alternative. In particular, the paper [arXiv:1909.05721] claims that we have made an unjustified mathematical step. This brief comment clarifies the matter.

hep-th↗

arXiv2019

Lifshitz theory of the cosmological constant

Astrophysics has given empirical evidence for the cosmological constant that accelerates the expansion of the universe. Atomic, Molecular, and Optical Physics has proven experimentally that the quantum vacuum exerts forces - the van der Waals and Casimir forces - on neutral matter. It has long been conjectured [Ya. B. Zel'dovich, Usp. Fiz. Nauk 95, 209 (1968)] that the two empirical facts, the cosmological constant and the Casimir force, have a common theoretical explanation, but all attempts of deriving both from a unified theory in quantitative detail have not been successful so far. In AMO Physics, Lifshitz theory has been the standard theoretical tool for describing the measured forces of the quantum vacuum. This paper develops a version of Lifshitz theory that also accounts for the electromagnetic contribution to the cosmological constant. Assuming that the other fields of the Standard Model behave similarly, gives a possible quantum-optical explanation for what has been called dark energy.

gr-qc↗

arXiv2019

Observation of Stimulated Hawking Radiation in Optics

The theory of Hawking radiation can be tested in laboratory analogues of black holes. We use light pulses in nonlinear fiber optics to establish artificial event horizons. Each pulse generates a moving perturbation of the refractive index via the Kerr effect. Probe light perceives this as an event horizon when its group velocity, slowed down by the perturbation, matches the speed of the pulse. We have observed in our experiment that the probe stimulates Hawking radiation, which occurs in a regime of extreme nonlinear fiber optics where positive and negative frequencies mix.

gr-qc↗

arXiv2018

Resonant Hawking radiation as an instability

We consider a simple model for a black-hole laser: a Bose-Einstein condensate with uniform speed of sound and partially uniform flow, establishing two horizons, a black-hole and a white-hole horizon. Waves confined between the horizons are amplified similar to radiation in a laser cavity. Black-hole lasing appears as an instability with discrete sets of modes given approximately by a round-trip condition. We found that, in addition to the regular Hawking radiation, trans-Planckian radiation does tunnel out of the black-hole laser.

gr-qc↗