arXiv subjects

Alexandre Delattre

Publications and source records attributed to Alexandre Delattre.

3 recordsLinked to original sources

arXiv2026

Canonical Quantization of Cylindrical Waveguides: A Gauge-Based Approach

We present a canonical quantization of electromagnetic modes in cylindrical waveguides, extending a gauge-based formalism previously developed for Cartesian geometries [1]. By introducing the two field quadratures $X,Y$ of TEM (transverse electric-magnetic), but also of TM (transverse magnetic) and TE (transverse electric) traveling modes, we identify for each a characteristic one-dimensional scalar field (a generalized flux $\varphi$) governed by a Klein-Gordon type equation. The associated Hamiltonian is derived explicitly from Maxwell's equations, allowing the construction of bosonic ladder operators. The generalized flux is directly deduced from the electromagnetic potentials $A,V$ by a proper gauge choice, generalizing Devoret's approach [2]. Our analysis unifies the treatment of cylindrical and Cartesian guided modes under a consistent and generic framework, ensuring both theoretical insight and experimental relevance. Especially, we find out that TE$_{n=0}$ modes break a fundamental gauge symmetry that is observed by all other families. We derive mode-specific capacitance and inductance from the field profiles and express voltage and current in terms of the canonical field variables. Measurable quantities are therefore properly defined from the mode quantum operators, especially for the non-trivial TM and TE ones. The formalism shall extend in future works to any other type of waveguides, especially on-chip coplanar geometries particularly relevant to quantum technologies.

quant-ph↗

arXiv2025

Waveguides in a quantum perspective

Solid state quantum devices, operated at dilution cryostat temperatures, are relying on microwave signals to both drive and read-out their quantum states. These signals are transmitted into the cryogenic environment, out of it towards detection devices, or even between quantum systems by well-designed waveguides, almost lossless when made of superconducting materials. Here we report on the quantum theory that describes the simplest Cartesian-type geometries: parallel plates, and rectangular tubes. The aim of the article is twofold: first on a technical and pragmatic level, we provide a full and compact quantum description of the different traveling wave families supported by these guides. Second, on an ontological level, we interpret the results and discuss the nature of the light fields corresponding to each mode family. The concept of potential difference is extended from transverse electric-magnetic (TEM) waves to all configurations, by means of a specific gauge fixing. The generalized flux $\phi$ introduced in the context of quantum electronics becomes here essential: it is the scalar field, conjugate of a charge $Q$, that confines light within the electrodes, let them be real or virtual. The gap in the dispersion relations of non-TEM waves turns out to be linked either to a potential energy necessary for the photon confinement, or to a kinetic energy arising from a photon mass. We finally compute the field zero-point fluctuations in every configuration. The theory is predictive: the lowest transverse magnetic (TM) modes should have smaller quantum noise than the higher ones, which at large wavevectors recover a conventional value similar to TEM and transverse electric (TE) ones. Such low-noise modes might be particularly useful for the routing of quantum information.

quant-ph↗

arXiv2025

Quantitative calibration of a TWPA applied to an optomechanical platform

In the last decade, the microwave quantum electronics toolbox has been enriched with quantum-limited detection devices such as Traveling Wave Parametric Amplifiers (TWPAs). The extreme sensitivity they provide is not only mandatory for some physics applications within quantum information processing, but is also the key element that will determine the detection limit of quantum sensing setups. In the framework of microwave optomechanical systems, an unprecedented range of small motions and forces is accessible, for which a specific quantitative calibration becomes necessary. We report on near quantum-limited measurements performed with an aluminum drumhead mechanical device within the temperature range 4 mK - 400 mK. The whole setup is carefully calibrated, especially taking into account the power-dependence of microwave absorption in the superconducting optomechanical cavity. This effect is commonly attributed to Two-Level-Systems (TLSs) present in the metal oxide. We demonstrate that a similar feature exists in the TWPA, and can be phenomenologically fit with adapted expressions. If not taken into account, the error on the signal strength can be as large as a factor of about 2, which is unacceptable for quantitative experiments. The power and temperature dependence is studied over the full parameter range, leading to an absolute definition of phonon population (i.e. Brownian motion amplitude), with an uncertainty +- 20 % limited by sources of noise internal to the optomechanical element.

quant-ph↗