title: Thesis supplement: texts, images, data, codes, consent letters, etc.
title: Stationary optomechanical entanglement detection (PhD thesis)
titleType: Other
Creators: name: Gut, Corentin
Publisher: name: Zenodo
Year: 2024

description: Supplementary information to my Ph.D. thesis "Stationary optomechanical entanglement detection" accepted in october 2024 by the University of Vienna, Austria.

The intention of this supplement is two-fold: making the content and appearance of the thesis transparent, and making the developed knowledge (re-)usable.

Version details

The 1s version (cf. DOI: 10.5281/zenodo.11176106) is the official document submitted, evaluated, and accepted by the University of Vienna. Subsequent versions -- named "errata" -- incorporate minimal modifications to fix typos, mistakes (e.g. in sentences and formulas), and imporve clarity or readability. 

The zip contains the modified '/chapter_structure' folder including:



the raw Latex code to produce the PDF file of this 2nd updated version of the thesis ("errata1"),

the images appearing in this version including the updated ones with the raw data and the codes to produce them.


The zip of the 1st version contains:



the submitted version of the thesis as a PDF file,

the raw Latex code to produce that PDF file,

a version of the thesis prior improving it with AI tools,

the original images appearing in the thesis with the raw data and the codes to produce them,

all the relevant codes I produced and used in the thesis (all with a plain text version),

codes from other creators with clearly signalised authorship at the beginning of the files,

written consent from the authors and creators whose code or data are used and/or presented in the thesis.
description: Measurement apparatuses mark the boundary between the probabilistic quantum description of nature, and the intrinsic definiteness of observations; this is the Heisenberg--von Neumann cut between unitary and projective dynamics, in the related models of measurement devices. The closer the cut is to the observer, the larger their knowledge and control of the apparatus' quantum state -- possibly enabling quantum enhancement of the measurement. We propose a protocol to demonstrate that the motion of an object is entangled with the light probing its position in optomechanical devices; thus shifting the cut towards the photodetection.

Our scheme applies in a broad range of parameters and for comparatively little experimental efforts (e.g., datasets generated for another purpose can be used). In particular, it applies to the stationary regime where optomechanical entanglement has not yet been experimentally verified. Theoretical analyses of five currently existing implementations (membranes, photonic crystal, and levitated nano-particles with and without cavity) indicate that they are limited by the presence of additional mechanical modes. We find that reducing the temperature of the mechanical bath(s) is the most efficient way to overcome the limitations. Additionally, high temperatures set stringent constraints on the stability of the mechanical frequency during the measurement.

We perform extensive, systematic, and creative analyses of experimental datasets from four of these devices. The gathered experience highlighted several pitfalls in certifying Gaussian entanglement from measurement records and we propose solutions to mitigate them. Unfortunately, we could not demonstrate entanglement convincingly.

Our protocol entails, first, a general verification theorem to infer light--mechanics entanglement form entanglement between measurable modes of light only. Second, we propose an explicit procedure based on successive and non-overlapping temporal modes of light; it is designed for high-$Q$ mechanical devices, in the high-temperature limit, and in the unresolved sideband regime or without an optical cavity. Third, the exact symbolic expression of the measured state can be computed, enabling fast parameter sweeps. Fourth, we provide an explicit approximate expression for the Einstein-Podolsky-Rosen (EPR) variance test of entanglement. It allows to understand and interpret physically how our protocol detects entanglement in terms of the devices' parameters.