arXiv subjects

Gert-Ludwig Ingold

Publications and source records attributed to Gert-Ludwig Ingold.

At least 19 recordsLinked to original sources

arXiv2026

Over forty years of research towards the understanding of Quantum Brownian Motion -- the contributions of A. O. Caldeira

This article presents a brief account of Amir O. Caldeira's contributions to the theory of quantum Brownian motion. Motivated by its importance, we outline the description of Brownian motion in the quantum regime following Caldeira's first works. In this context, we particularly highlight the effect of dissipation on the tunneling rate out of a metastable state. We then journey along the alternative ways to approach quantum Brownian motion developed by Caldeira during his career, which go beyond the so-called Caldeira-Leggett model. We conclude by summarizing some of Caldeira's contributions to contemporary fields such as the theory of quantum decoherence and quantum thermodynamics, that were strongly inspired by his eponymous approach to quantum Brownian motion.

quant-ph↗

arXiv2025

Classifying destructive quantum interference in molecular junctions: Towards molecular quantum rulers

Destructive quantum interference in molecular junctions might be used to build molecular quantum rulers, allowing to quantify changes in external control parameters electrically. For this reason, it is important to understand which patterns of destructive quantum interference can occur inside the electronic excitation gap of a molecule, coupled to conducting electrodes. By considering a four-level model, we show that much more complex destructive quantum interference behavior can arise than expected for just two levels. We classify the destructive quantum interferences analytically and show that they may even occur in regions forbidden by the standard orbital rule for electron transport. Our results suggest that appropriate molecular design may indeed allow to construct highly sensitive molecular quantum rulers.

cond-mat.mes-hall↗

arXiv2024

Probing the chirality of a single microsphere trapped by a focused vortex beam through their orbital period

When microspheres are illuminated by tightly focused vortex beams, they can be trapped in a non-equilibrium steady state where they orbit around the optical axis. By using the Mie-Debye theory for optical tweezers, we demonstrate that the orbital period strongly depends on the particle's chirality index. Taking advantage of such sensitivity, we put forth a method to experimentally characterize with high precision the chiroptical response of individual optically trapped particles. The method allows for an enhanced precision at least one order of magnitude larger than that of similar existing enantioselective approaches. It is particularly suited to probe the chiroptical response of individual particles, for which light-chiral matter interactions are typically weak.

physics.optics↗

arXiv2024

Switching the sign of the Casimir force between two PEMC spheres

For non-reciprocal objects in vacuum, the Casimir interaction can become repulsive. Here, we present a comprehensive study for idealized non-reciprocal materials known as perfect electromagnetic conductors (PEMC). The system consists of two spheres made of different PEMC materials, including the plane-sphere geometry as a particular case. The sign of the Casimir force does not only depend on the distance between the spheres and their geometric parameters but can be controlled by adjusting the temperature. A repulsive Casimir interaction at small distances allows for stable equilibrium configurations of the spheres. A sum rule previously derived for the plane-plane geometry at zero temperature is violated in general, if at least one plane is replaced by a sphere.

quant-ph↗

arXiv2023

Precise in situ radius measurement of individual optically trapped microspheres using negative optical torque exerted by focused vortex beams

We demonstrate a new method for determining the radius of micron-sized particles trapped by a vortex laser beam. The technique is based on measuring the rotation experienced by the center of mass of a microsphere that is laterally displaced by a Stokes drag force to an off-axis equilibrium position. The rotation results from an optical torque pointing along the direction opposite to the vortex beam angular momentum. We fit the rotation angle data for different Laguerre-Gaussian modes taking the radius as a fitting parameter in the Mie-Debye theory of optical tweezers. We also discuss how micron-sized beads can be used as probes for optical aberrations introduced by the experimental setup.

physics.optics↗

arXiv2022

Universal Casimir interactions in the sphere-sphere geometry

We study universal Casimir interactions in two configurations which appear as dual to each other. The first involves spheres described by the Drude model and separated by vacuum while the second involves dielectric spheres immersed in a salted solution at distances larger than the Debye screening length. In both cases, the long-distance limit, equivalently the high-temperature limit, is dominated by the effect of low-frequency transverse magnetic thermal fluctuations. They are independent of the details of dielectric functions of materials, due to the finite conductivity of metals in the former case and of salted water in the latter one. They also show universality properties in their dependence on geometric dimensions, in relation to an approximate conformal invariance of the reduced free energy.

quant-ph↗

arXiv2022

Casimir effect between spherical objects: proximity-force approximation and beyond using plane waves

For the Casimir interaction between two nearby objects, the plane-wave basis proves convenient for numerical calculations as well as for analytical considerations leading to an optical interpretation of the relevant scattering processes of electromagnetic waves. We review work on the proximity-force approximation and corrections to it within the plane-wave basis for systems involving spherical objects. Previous work is extended by allowing for polarization mixing during the reflection at a sphere. In particular, explicit results are presented for perfect electromagnetic conductors. Furthermore, for perfect electric conductors at zero temperature, it is demonstrated that beyond the leading-order correction to the proximity-force approximation, terms of half-integer order in the distance between the sphere surfaces appear.

quant-ph↗

arXiv2021

Universal Casimir interaction between two dielectric spheres in salted water

We study the Casimir interaction between two dielectric spheres immersed in a salted solution at distances larger than the Debye screening length. The long distance behavior is dominated by the non-screened interaction due to low-frequency transverse magnetic thermal fluctuations. It shows universality properties in its dependence on geometric dimensions and independence of dielectric functions of the particles, with these properties related to approximate conformal invariance.

quant-ph↗

arXiv2021

Measurement of the Casimir Force between 0.2 and 8 mum: Experimental Procedures and Comparison with Theory

We present results on the determination of the differential Casimir force between an Au-coated sapphire sphere and the top and bottom of Au-coated deep silicon trenches performed by means of the micromechanical torsional oscillator in the range of separations from 0.2 to 8 $\upmu$m. The random and systematic errors in the measured force signal are determined at the 95\% confidence level and combined into the total experimental error. The role of surface roughness and edge effects is investigated and shown to be negligibly small. The distribution of patch potentials is characterized by Kelvin probe microscopy, yielding an estimate of the typical size of patches, the respective r.m.s. voltage and their impact on the measured force. A comparison between the experimental results and theory is performed with no fitting parameters. For this purpose, the Casimir force in the sphere-plate geometry is computed independently on the basis of first principles of quantum electrodynamics using the scattering theory and the gradient expansion. In doing so, the frequency-dependent dielectric permittivity of Au is found from the optical data extrapolated to zero frequency by means of the plasma and Drude models. It is shown that the measurement results exclude the Drude model extrapolation over the region of separations from 0.2 to 4.8~$\upmu$m, whereas the alternative extrapolation by means of the plasma model is experimentally consistent over the entire measurement range. A discussion of the obtained results is provided.

quant-ph↗

arXiv2021

Casimir Interaction Between a Plane and a Sphere: Correction to the Proximity-Force Approximation at Intermediate Temperatures

We consider the Casimir interaction energy between a plane and a sphere of radius $R$ at finite temperature $T$ as a function of the distance of closest approach $L$. Typical experimental conditions are such that the thermal wavelength $λ_T=\hbar c/k_\mathrm{B}T$ satisfies the condition $L\ll λ_T\ll R$. We derive the leading correction to the proximity-force approximation valid for such intermediate temperatures by developing the scattering formula in the plane-wave basis. Our analytical result captures the joint effect of the spherical geometry and temperature and is written as a sum of temperature-dependent logarithmic terms. Surprisingly, two of the logarithmic terms arise from the Matsubara zero-frequency contribution.

quant-ph↗

arXiv2021

Classical Casimir free energy for two Drude spheres of arbitrary radii: A plane-wave approach

We derive an exact analytic expression for the high-temperature limit of the Casimir interaction between two Drude spheres of arbitrary radii. Specifically, we determine the Casimir free energy by using the scattering approach in the plane-wave basis. Within a round-trip expansion, we are led to consider the combinatorics of certain partitions of the round trips. The relation between the Casimir free energy and the capacitance matrix of two spheres is discussed. Previously known results for the special cases of a sphere-plane geometry as well as two spheres of equal radii are recovered. An asymptotic expansion for small distances between the two spheres is determined and analytical expressions for the coefficients are given.

quant-ph↗

arXiv2020

The quantum canonical ensemble in phase space

The density operator for a quantum system in thermal equilibrium with its environment depends on Planck's constant, as well as the temperature. At high temperatures, the Weyl representation, that is, the thermal Wigner function, becomes indistinguishable from the corresponding classical distribution in phase space, whereas the low temperature limit singles out the quantum ground state of the system's Hamiltonian. In all regimes, thermal averages of arbitrary observables are evaluated by integrals, as if the thermal Wigner function were a classical distribution. The extension of the semiclassical approximation for quantum propagators to an imaginary thermal time, bridges the complex intervening region between the high and the low temperature limit. This leads to a simple quantum correction to the classical high temperature regime, irrespective of whether the motion is regular or chaotic. A variant of the full semiclassical approximation with a real thermal time, though in a doubled phase space, avoids any search for particular trajectories in the evaluation of thermal averages. The double Hamiltonian substitutes the stable minimum of the original system's Hamiltonian by a saddle, which eliminates local periodic orbits from the stationary phase evaluation of the integrals for the partition function and thermal averages.

quant-ph↗

arXiv2020

Plane-wave approach to the exact van der Waals interaction between colloid particles

The numerically exact evaluation of the van der Waals interaction, also known as Casimir interaction when including retardation effects, constitutes a challenging task. We present a new approach based on the plane-wave basis and demonstrate that it possesses advantages over the more commonly used multipole basis. The rotational symmetry of the plane-sphere and sphere-sphere geometries can be exploited by means of a discrete Fourier transform. The new technique is applied to a study of the interaction between a colloid particle made of polystyrene or mercury and another polystyrene sphere or a polystyrene wall in an aqueous solution. Special attention is paid to the influence of screening caused by a variable salt concentration in the medium. It is found that in particular for low salt concentrations the error implied by the proximity force approximation is larger than usually assumed. For a mercury droplet, a repulsive interaction is found for sufficiently large distances provided screening is negligible. We emphasize that the effective Hamaker parameter depends significantly on the scattering geometry on which it is based.

cond-mat.soft↗

arXiv2019

Quantum revival patterns from classical phase-space trajectories

A general semiclassical method in phase space based on the final value representation of the Wigner function is considered that bypasses caustics and the need to root-search for classical trajectories. We demonstrate its potential by applying the method to the Kerr Hamiltonian, for which the exact quantum evolution is punctuated by a sequence of intricate revival patterns. The structure of such revival patterns, lying far beyond the Ehrenfest time, is semiclassically reproduced and revealed as a consequence of constructive and destructive interferences of classical trajectories.

quant-ph↗

arXiv2018

The role of diffraction in the Casimir effect beyond the proximity force approximation

We derive the leading-order correction to the proximity force approximation (PFA) result for the electromagnetic Casimir interaction in the plane-sphere geometry by developing the scattering approach in the plane-wave basis. Expressing the Casimir energy as a sum over round trips between plane and sphere, we find two distinct contributions to the correction. The first one results from the variation of the Mie reflection operator, calculated within the geometric optical WKB approximation, over the narrow Fourier interval associated to specular reflection at the vicinity of the point of closest approach on the spherical surface. The second contribution, accounting for roughly 90% of the total correction, results from the modification of the geometric optical WKB Mie scattering amplitude due to diffraction. Our derivation provides a clear physical understanding of the nature of the PFA correction for spherical surfaces.

quant-ph↗

arXiv2018

Advancing numerics for the Casimir effect to experimentally relevant aspect ratios

Within the scattering theoretical approach, the Casimir force is obtained numerically by an evaluation of the round trip of an electromagnetic wave between the objects involved. Recently [Hartmann M et al. 2017, Phys. Rev. Lett. 119 043901] it was shown that a symmetrization of the scattering operator provides significant advantages for the numerical evaluation of the Casimir force in the experimentally relevant sphere-plane geometry. Here, we discuss in more detail how the symmetrization modifies the scattering matrix in the multipole basis and how computational time is reduced. As an application, we discuss how the Casimir force in the sphere-plane geometry deviates from the proximity force approximation as a function of the geometric parameters.

quant-ph↗

arXiv2018

Proximity force approximation and specular reflection: Application of the WKB limit of Mie scattering to the Casimir effect

The electromagnetic Casimir interaction between two spheres is studied within the scattering approach using the plane-wave basis. It is demonstrated that the proximity force approximation (PFA) corresponds to the specular-reflection limit of Mie scattering. Using the leading-order semiclassical WKB approximation for the direct reflection term in the Debye expansion for the scattering amplitudes, we prove that PFA provides the correct leading-order divergence for arbitrary materials and temperatures in the sphere-sphere and the plane-sphere geometry. Our derivation implies that only a small section around the points of closest approach between the interacting spherical surfaces contributes in the PFA regime. The corresponding characteristic length scale is estimated from the width of the Gaussian integrand obtained within the saddle-point approximation. At low temperatures, the area relevant for the thermal corrections is much larger than the area contributing to the zero-temperature result.

quant-ph↗

arXiv2017

Plasma vs Drude modelling of the Casimir force: beyond the proximity force approximation

We calculate the Casimir force and its gradient between a spherical and a planar gold surface. Significant numerical improvements allow us to extend the range of accessible parameters into the experimental regime. We compare our numerically exact results with those obtained within the proximity force approximation (PFA) employed in the analysis of all Casimir force experiments reported in the literature so far. Special attention is paid to the difference between the Drude model and the dissipationless plasma model at zero frequency. It is found that the correction to PFA is too small to explain the discrepancy between the experimental data and the PFA result based on the Drude model. However, it turns out that for the plasma model, the corrections to PFA lie well outside the experimental bound obtained by probing the variation of the force gradient with the sphere radius [D. E. Krause et al., Phys. Rev. Lett. 98, 050403 (2007)]. The corresponding corrections based on the Drude model are significantly smaller but still in violation of the experimental bound for small distances between plane and sphere.

quant-ph↗