Thèse Entropie Fractionnaire dans des Nano-Circuits Quantiques H/F

Doctorat.Gouv.Fr

Établissement : Université Paris-Saclay GS Physique
École doctorale : Physique en Ile de France
Laboratoire de recherche : Centre de Nanosciences et de Nanotechnologies
Direction de la thèse : Frédéric PIERRE ORCID 0000000312436808
Début de la thèse : 2026-10-01
Date limite de candidature : 2026-06-30T23:59:59

Les systèmes quantiques hébergeant des états électroniques corrélés présentent un intérêt majeur aussi bien fondamental que technologique. Des quasi-particules « exotiques » peuvent y émerger, telles que les fermions de Majorana, dont la robustesse topologique intrinsèque constitue le fondement d'une approche prometteuse pour le calcul quantique. Cependant, la complexité des matériaux massifs et le contrôle limité que l'on peut exercer entravent leur étude. Une approche alternative consiste à concevoir artificiellement des corrélations électroniques, par l'ingénierie de circuits quantiques. Ces circuits, ajustables in-situ et complètement caractérisés, peuvent être sondés non seulement par des mesures de transport, mais aussi par des sondes thermodynamiques particulièrement bien adaptées à la mise en évidence de nouveaux états de la matière.

L'objectif général de ce projet est de concevoir des circuits quantiques pour créer et explorer de nouveaux états quantiques corrélés, et pour les caractériser de manière non ambiguë par la mesure de quantités thermodynamiques. L'objectif spécifique de ce travail de thèse expérimental sera de réaliser l'observation univoque d'états très exotiques, notamment des fermions de Majorana et des anyons de Fibonacci, à partir de leur entropie résiduelle fractionnaire (une fraction de kB ln(2)). Ces états émergeront de l'ingénierie de corrélations induites par l'interaction de Coulomb, en développant une approche pionnière de l'équipe du C2N (voir par exemple Science 360, 1315 (2018), Nature Communications 14, 7263 (2023)). L'entropie de l'état fondamental sera mesurée en adaptant une stratégie démontrée pour un spin 1/2 (Nature Physics 14, 1083 (2018)), basée sur la relation thermodynamique de Maxwell : dS/dN=d/dT.

Le doctorant ou la doctorante se familiarisera avec une grande variété de techniques de mesure ultra-sensibles (conductance électrique et fluctuations, sondes thermodynamiques incluant l'entropie), les techniques cryogéniques à température millikelvin, la nanofabrication par lithographie électronique au sein de la centrale de technologie du C2N, ainsi qu'avec la mécanique quantique avancée. Le travail de l'étudiant englobera tous les aspects du projet, y compris l'analyse théorique et la modélisation.

Strongly correlated materials, from topological matter to heavy fermions, are currently the focus of extensive research. They attract interest from a fundamental point of view because they display unconventional phenomena, such as the emergence of exotic excitations. They also bring the promise of future applications, including for quantum technologies. Relevant to this PhD project are non-Abelian anyons - quasiparticles with unusual and yet unobserved braiding statistics as well as fractional quantum dimensions - which form the basis of much sought after schemes for topologically protected quantum computation. Improving our understanding of the microscopic mechanisms at play in such correlated materials is a step toward engineering quantum materials with novel properties.

However, bulk correlated materials often prove challenging to investigate because of the complexity and disorder inherent to macroscopic samples, as well as the difficulty to tune independently the relevant microscopic parameters. Additionally, ascertaining the presence of exotic states is notoriously difficult. For example, establishing the (abelian) anyonic statistics in the Fractional Quantum Hall Effect took almost three decades, and the controversy regarding the existence of Majorana Zero Modes remains unresolved due to the lack of a robust observable able to unambiguously discern these non-abelian states from trivial ones.

The PhD projects aims at investigating highly correlated electronic states emerging at the vicinity of different classes of quantum critical points and predicted to host a variety of non-abelian anyons. To circumvent the difficulties of bulk materials, our approach is to study engineered nanocircuits which are fully characterizable. Careful circuit design leads to the quantum simulation of many-body Hamiltonians with tunable interactions and frustrations of different symmetry classes. The resulting correlated, quantum critical states will be characterized through several complementary observables: most importantly, a recently developed strategy to measure the entropy is predicted to be particularly effective at demonstrating the non-Abelian character of quasi-particles.

Specific objectives:
1. Clear observation of non-Abelian quasiparticles, at the heart of topologically protected quantum computation. Specifically addressed quasiparticles are Majorana zero modes, Fibonacci anyons and Z3 parafermions. Although in the present context such quasiparticles would be localized (see Methods), there exist measurement-based proposals to use them for topologically protected quantum manipulations.

2. Exploring the interplay between dissipation and strong correlations. We plan to perform a comprehensive study of the Bose-Fermi Kondo model, a model inspired by the physics of heavy fermions where the bosonic bath acts as a dissipative environment, and which has never been implemented experimentally. Other aspects of this objective include a thermodynamic investigation of the Luttinger liquid physics of interacting 1D conductors, where the strength of interactions is controlled in the hybrid-circuit implementation by the amount of dissipation.

The engineered circuits. Our QPC team at C2N has developed a novel type of quantum circuit --metal-semiconductor hybrids-- and demonstrated its potential to explore and quantum simulate strongly correlated electron systems. These circuits are particularly relevant to implement generalized Kondo models (using charge states to play the role of the Kondo impurity, it is referred to as the charge Kondo' implementation) where a variety of quantum critical states involving exotic non-Abelian quasiparticles are expected.

More specifically, micron-size metallic islands are connected to a GaAlAs 2D electron gas. These islands can be assembled together and with other well-characterized building blocks (quantum point contacts, quantum dots and linear resistances) to form complex circuits (see electron-beam micrograph of such a device in attached PDF). Such circuits have repeatedly proven effective to quantitatively probe new physics. The progressive destruction of charge quantization in a metallic island by controlled charge fluctuations was a seminal example [Jezouin16]. Another remarkable use case is the quantum simulation of Luttinger liquids with an impurity [Anthore18]. Important starting points for this PhD project are the realization of the standard 1-channel' Kondo (1CK) and the quantum critical 2-channel Kondo (2CK) and 3-channel Kondo (3CK) models with the charge Kondo implementation illustrated in the attached figure [Iftikhar18].

In charge-Kondo circuits, the metallic island is gated to have two degenerate charge states [Matveev91]. At low enough temperature compared to the characteristic charging energy (experiments are performed at 10-50 mK), this realizes a charge pseudo-spin in which the original magnetic Kondo impurity is replaced by a charge degree of freedom much easier to control and measure. Independent electron baths can be individually connected to the island through tunable quantum tunnel point contacts. The tunneling of electrons in or out of the central metallic island realizes the analogue of the Kondo spin exchange coupling. Such circuits are adaptable: multiple baths (Kondo channels) can be controllably coupled to the charge Kondo impurity, a dissipative resistor can be capacitively coupled or put in series with a quantum point contact, several islands can be coupled together, hence providing a versatile platform.

Revealing non-Abelian quasiparticles with entropy. A major goal of this PhD project is to reveal unambiguously the most exotic features of these strongly correlated states, including non-Abelian quasiparticles. For this purpose, we plan to make use of revealing thermodynamic observables, such as thermoelectricity, heat and entropy. In particular, the residual entropy connected with the presence of an impurity informs on the ground state degeneracy, which is itself directly connected with the peculiar degeneracy of non-Abelian anyons. Indeed, the non-Abelian character translates in a non-trivial increase of the ground-stage degeneracy as d^N, with d the quantum dimension of the considered quasiparticles and N their number. This comes from a defining property with direct implication for quantum computation: braiding two non-Abelian anyons can result in a different ground state, which constitutes a mean to encode topologically protected qubits. This property directly implies an increase of the ground state entropy by kB ln(d) per additional non-Abelian anyon. Remarkably, d is not restricted to integer values, which constitutes a very discerning character: d=2^1/2 for Majorana (expected at 2CK), (1+5^1/2)/2 for Fibonacci (expected at 3CK) and 3^1/2 for Z3 parafermions (expected at 4CK). In practice, the impurity entropy will be obtained using a thermodynamic Maxwell relation, involving the measurement, with a built-in field effect sensor, of the charge of a metallic island or of a small quantum dot as a function of a plunger gate voltage and at different temperatures [Hartman18].

Interplay of strong electronic correlations and dissipation. We plan to investigate the destruction of Kondo screening by dissipation by engineering a competition between bosonic and fermionic channels coupled to the same Kondo impurity. This will realize the so-called Bose-Fermi Kondo model originally discussed in the context of heavy fermions, and providing a tractable setting for exploring the impact of dissipation on strongly correlated systems. Thanks to the charge character of the Kondo impurity in our circuits, we can capacitively couple a bosonic bath made of an on-chip linear resistance [LeHur04].