Comment on "Absence versus Presence of Dissipative Quantum Phase Transition in Josephson Junctions''

In a recent Letter [Phys. Rev. Lett. 129, 087001, (2022)], Masuki, Sudo, Oshikawa, and Ashida studied a Josephson junction, with Josephson energy $E_{\rm J}$ and charging energy $E_{\rm C}$, shunted by an ohmic transmission line with conductance $\alpha (2e)^2/h$. Their model includes a realistic high frequency cutoff of order $\alpha E_c$, that is typically smaller than the plasma frequency $W$. The authors present a phase diagram showing surprising features, not anticipated in the established literature [eg. Sch\"on and Zaikin, Phys. Reports 198, 237, (1990)]. For $E_{\rm J}/E_{\rm C}$ above a certain value, they find that the junction remains superconducting for all $\alpha$, while below this value, they find that the insulating phase leads to re-entrant superconductivity at small $\alpha$. In this Comment, we show that their Numerical Renormalization Group (NRG) implementation is uncontrolled, and that there is no evidence for the re-entrant superconductivity in the phase diagram presented in Fig. 1a of PRL 129, 087001.Comment: 3 pages. Text of the version accepted for publication, plus an appendix with additional informatio

Revealing the finite-frequency response of a bosonic quantum impurity

Quantum impurities are ubiquitous in condensed matter physics and constitute the most stripped-down realization of many-body problems. While measuring their finite-frequency response could give access to key characteristics such as excitations spectra or dynamical properties, this goal has remained elusive despite over two decades of studies in nanoelectronic quantum dots. Conflicting experimental constraints of very strong coupling and large measurement bandwidths must be met simultaneously. We get around this problem using cQED tools, and build a precisely characterized quantum simulator of the boundary sine-Gordon model, a non-trivial bosonic impurity problem. We succeeded to fully map out the finite frequency linear response of this system. Its reactive part evidences a strong renormalisation of the nonlinearity at the boundary in agreement with non-perturbative calculations. Its dissipative part reveals a dramatic many-body broadening caused by multi-photon conversion. The experimental results are matched quantitatively to a resummed diagrammatic calculation based on a microscopically calibrated model. Furthermore, we push the device into a regime where diagrammatic calculations break down, which calls for more advanced theoretical tools to model many-body quantum circuits. We also critically examine the technological limitations of cQED platforms to reach universal scaling laws. This work opens exciting perspectives for the future such as quantifying quantum entanglement in the vicinity of a quantum critical point or accessing the dynamical properties of non-trivial many-body problems.Comment: 39 pages, 14 figure

Universal control of a bosonic mode via drive-activated native cubic interactions

Linear bosonic modes offer a hardware-efficient alternative for quantum information processing but require access to some nonlinearity for universal control. The lack of nonlinearity in photonics has led to encoded measurement-based quantum computing, which rely on linear operations but requires access to resourceful ('nonlinear') quantum states, such as cubic phase states. In contrast, superconducting microwave circuits offer engineerable nonlinearities but suffer from static Kerr nonlinearity. Here, we demonstrate universal control of a bosonic mode composed of a superconducting nonlinear asymmetric inductive element (SNAIL) resonator, enabled by native nonlinearities in the SNAIL element. We suppress static nonlinearities by operating the SNAIL in the vicinity of its Kerr-free point and dynamically activate nonlinearities up to third order by fast flux pulses. We experimentally realize a universal set of generalized squeezing operations, as well as the cubic phase gate, and exploit them to deterministically prepare a cubic phase state in 60 ns. Our results initiate the experimental field of universal continuous-variables quantum computing.Comment: 11 pages, 6 figures and supplementary material

Simulateurs supraconducteurs de modèles d'impuretés quantiques

Condensed matter physics is the branch of quantum mechanics which studies large assemblies of interacting particles. It sprouted from solid state physics: the study of the electron sea hosted by a metallic material was the earliest representative of the theoretical hardships encountered when predicting the behavior of such a myriad of quantum particles. The field was soon enriched by many other models describing other types of quantum matter, from magnetism to superconductivity, Dirac materials or quantum fluids of light. All these seemingly different applications are united by one ubiquitous aspect of many-body problems: the interplay of many elementary particles, electrons, photons, magnetic moments, leads to emergent collective behaviors, such as quasi-particles and phase transitions. As Anderson famously wrote, "more is different''.In the recent years, important technological advances in the nanofabrication of superconducting circuits allowed to recreate all the ingredients of a condensed matter system in a finely controlled experimental setup. The quantum particles are emulated by excitations of the circuit, while quantum coherence is ensured by the absence of dissipation of the superconducting state as well as the low temperatures in the milliKelvin range. Finally, interactions are created textit{via} the Josephson effect, a by-product of superconducting phase rigidity across a tunnel barrier, which introduces non-linearity in the circuit. Such a device is called a quantum simulator.This thesis has been motivated by the urge to review well known impurity models, the spin boson and boundary sine-Gordon models, in the light of their recent implementation by superconducting circuits. Starting from an exhaustive modelisation of a generic microscopic circuit, we formulated a novel model taking into account the multi-level structure of charge qBits, that we called the ``charge boson Hamiltonian''. Only in some regions of its parameter space this model indeed reduces to the sought-after spin boson or boundary sine-Gordon Hamiltonian. We then established its phase diagram by numerical renormalisation group, and explored the experimentally relevant regions by newly devised theoretical tools.A striking aspect of the charge boson model is that the number of Cooper pairs on the impurity's superconducting island is discrete, or equivalently that its superconducting phase is compact. We introduced a variational ansatz --- nicknamed the compact ansatz --- to study the relevance of this charge granularity. It allowed us to reach quantitative prediction on ground state observables in the experimentally pertinent region, and to describe compactness fading in the overdamped, strong coupling regime.One can shunt the impurity's capacitive coupling to its environment to reach this highly interacting regime shielded from charge noise by decompactification. The circuit then reduces to the celebrated boundary sine-Gordon model. Recent experiments allowed to probe the dissipative response of such a system, which displays spectacularly high inelastic cross-sections. Armed with a microscopic model of the system, we showed analytically and numerically how the plasma frequency introduces an ultraviolet cutoff which spoils the anomalous power laws of dissipative response that are known from the study of the Tomonaga-Luttinger liquid. Finally, a diagrammatic self-consistent technique performed at finite temperature allowed us to demonstrate how a smooth dissipative response emerges from a system in the mesoscopic size range, formed by a few thousand narrow Fabry-Perot modes, by overcrowding of thermally assisted multi-photons resonances.La physique de la matière condensée est une banche de la mécanique quantique qui étudie les grandes assemblées de particules quantiques en interaction. Elle a germée à partir de la physique de l'état solide : l'étude de la mer d'électrons contenue dans un métal fut le premier exemple des difficultés rencontrées par le théoricien voulant prédire le comportement d'une telle myriade de particules quantiques. Le domaine fut rapidement enrichi par de nombreux autres modèles, décrivant d'autres types de matière quantique, depuis le magnétisme jusqu'à la supraconductivité, les matériaux de Dirac et les fluides de lumière quantique. Toutes ces applications apparemment différentes se retrouvent unies par l'aspect essentiel du problème à N-corps quantique : l'interaction d'un grand nombre de particules élémentaires, électrons, photons, moments magnétiques, conduit à l'émergence de phénomènes collectifs, comme les quasi-particules ou les transitions de phase. Comme l'écrivait Anderson, "more is different".Ces dernières années, d'importantes avancées technologiques dans la nanofabrication de circuits supraconducteurs ont permis de recréer tous les ingrédients d'un système de matière condensée dans un dispositif expérimental finement contrôlé. Les particules quantiques sont émulées par les excitations du circuit, tandis que la cohérence quantique est maintenue par l'absence de dissipation de l'état supraconducteur autant que par les basses températures employées, aux environs de la dizaine de milliKelvins. Enfin, les interactions sont suscitées par effet Josephson, une conséquence de la rigidité de la phase supraconductrice à travers une barrière tunnel, qui introduit des non-linéarités dans le circuit. Une telle plateforme expérimentale est appelée un simulateur quantique.Cette thèse a été motivée par la nécessité de revoir certains modèles d'impuretés bien connus, modèle spin boson et modèle sine-Gordon à bord, à l'aune de leur implémentation récente sous forme de circuits supraconducteurs. Commençant par une modélisation complète d'un circuit microscopique générique, nous formulons un nouvel Hamiltonien prenant en compte la structure multi-niveaux des qBits de charge, et que nous baptisons l'Hamiltonien charge boson. Celui-ci ne se réduit aux modèles standards de la littérature que dans certaines limites que nous précisons. Nous traçons son diagramme de phase complet à l'aide du groupe de renormalisation numérique, et explorons ses régions expérimentalement pertinentes par des outils théoriques nouvellement créés.Un aspect frappant du modèle charge boson est que le nombre de paires de Cooper occupant l'îlot supraconducteur de l'impureté est un entier, ou bien de façon équivalente que sa phase supraconductrice est compacte. Nous présentons un ansatz variationnel, que nous appelons l'ansatz compact, pour étudier la pertinence de cet aspect granulaire de la charge. Cela nous a permis de décrire la disparition des effets compacts dans le régime suramorti à fort couplage.Il est possible de court-circuiter le couplage capacitif de l'impureté à son environnement, pour atteindre ce régime d'interaction forte, que la décompactification protège du bruit de charge. Le circuit se réduit alors à simuler le fameux modèle sine-Gordon à bord. Des expériences récentes on sondé la réponse dissipative d'un tel circuit, qui présente une section efficace inélastique spectaculairement élevée. Armé d'un modèle microscopique détaillé du système, nous montrons que la fréquence plasma introduit une coupure ultraviolette qui supprime les lois de puissance anormales de la réponse dissipative, bien connues par l'étude des liquides de Luttinger. Enfin, une technique diagrammatique auto-cohérente, entreprise à température finie, a permis de démontrer comment une réponse dissipative lisse en fréquence peut émerger d'un système de taille mésoscopique, par surpopulation de résonances multi-photons assistée par excitations thermiques

Simulateurs supraconducteurs de modèles d'impuretés quantiques

Condensed matter physics is the branch of quantum mechanics which studies large assemblies of interacting particles. It sprouted from solid state physics: the study of the electron sea hosted by a metallic material was the earliest representative of the theoretical hardships encountered when predicting the behavior of such a myriad of quantum particles. The field was soon enriched by many other models describing other types of quantum matter, from magnetism to superconductivity, Dirac materials or quantum fluids of light. All these seemingly different applications are united by one ubiquitous aspect of many-body problems: the interplay of many elementary particles, electrons, photons, magnetic moments, leads to emergent collective behaviors, such as quasi-particles and phase transitions. As Anderson famously wrote, "more is different''.In the recent years, important technological advances in the nanofabrication of superconducting circuits allowed to recreate all the ingredients of a condensed matter system in a finely controlled experimental setup. The quantum particles are emulated by excitations of the circuit, while quantum coherence is ensured by the absence of dissipation of the superconducting state as well as the low temperatures in the milliKelvin range. Finally, interactions are created textit{via} the Josephson effect, a by-product of superconducting phase rigidity across a tunnel barrier, which introduces non-linearity in the circuit. Such a device is called a quantum simulator.This thesis has been motivated by the urge to review well known impurity models, the spin boson and boundary sine-Gordon models, in the light of their recent implementation by superconducting circuits. Starting from an exhaustive modelisation of a generic microscopic circuit, we formulated a novel model taking into account the multi-level structure of charge qBits, that we called the ``charge boson Hamiltonian''. Only in some regions of its parameter space this model indeed reduces to the sought-after spin boson or boundary sine-Gordon Hamiltonian. We then established its phase diagram by numerical renormalisation group, and explored the experimentally relevant regions by newly devised theoretical tools.A striking aspect of the charge boson model is that the number of Cooper pairs on the impurity's superconducting island is discrete, or equivalently that its superconducting phase is compact. We introduced a variational ansatz --- nicknamed the compact ansatz --- to study the relevance of this charge granularity. It allowed us to reach quantitative prediction on ground state observables in the experimentally pertinent region, and to describe compactness fading in the overdamped, strong coupling regime.One can shunt the impurity's capacitive coupling to its environment to reach this highly interacting regime shielded from charge noise by decompactification. The circuit then reduces to the celebrated boundary sine-Gordon model. Recent experiments allowed to probe the dissipative response of such a system, which displays spectacularly high inelastic cross-sections. Armed with a microscopic model of the system, we showed analytically and numerically how the plasma frequency introduces an ultraviolet cutoff which spoils the anomalous power laws of dissipative response that are known from the study of the Tomonaga-Luttinger liquid. Finally, a diagrammatic self-consistent technique performed at finite temperature allowed us to demonstrate how a smooth dissipative response emerges from a system in the mesoscopic size range, formed by a few thousand narrow Fabry-Perot modes, by overcrowding of thermally assisted multi-photons resonances.La physique de la matière condensée est une banche de la mécanique quantique qui étudie les grandes assemblées de particules quantiques en interaction. Elle a germée à partir de la physique de l'état solide : l'étude de la mer d'électrons contenue dans un métal fut le premier exemple des difficultés rencontrées par le théoricien voulant prédire le comportement d'une telle myriade de particules quantiques. Le domaine fut rapidement enrichi par de nombreux autres modèles, décrivant d'autres types de matière quantique, depuis le magnétisme jusqu'à la supraconductivité, les matériaux de Dirac et les fluides de lumière quantique. Toutes ces applications apparemment différentes se retrouvent unies par l'aspect essentiel du problème à N-corps quantique : l'interaction d'un grand nombre de particules élémentaires, électrons, photons, moments magnétiques, conduit à l'émergence de phénomènes collectifs, comme les quasi-particules ou les transitions de phase. Comme l'écrivait Anderson, "more is different".Ces dernières années, d'importantes avancées technologiques dans la nanofabrication de circuits supraconducteurs ont permis de recréer tous les ingrédients d'un système de matière condensée dans un dispositif expérimental finement contrôlé. Les particules quantiques sont émulées par les excitations du circuit, tandis que la cohérence quantique est maintenue par l'absence de dissipation de l'état supraconducteur autant que par les basses températures employées, aux environs de la dizaine de milliKelvins. Enfin, les interactions sont suscitées par effet Josephson, une conséquence de la rigidité de la phase supraconductrice à travers une barrière tunnel, qui introduit des non-linéarités dans le circuit. Une telle plateforme expérimentale est appelée un simulateur quantique.Cette thèse a été motivée par la nécessité de revoir certains modèles d'impuretés bien connus, modèle spin boson et modèle sine-Gordon à bord, à l'aune de leur implémentation récente sous forme de circuits supraconducteurs. Commençant par une modélisation complète d'un circuit microscopique générique, nous formulons un nouvel Hamiltonien prenant en compte la structure multi-niveaux des qBits de charge, et que nous baptisons l'Hamiltonien charge boson. Celui-ci ne se réduit aux modèles standards de la littérature que dans certaines limites que nous précisons. Nous traçons son diagramme de phase complet à l'aide du groupe de renormalisation numérique, et explorons ses régions expérimentalement pertinentes par des outils théoriques nouvellement créés.Un aspect frappant du modèle charge boson est que le nombre de paires de Cooper occupant l'îlot supraconducteur de l'impureté est un entier, ou bien de façon équivalente que sa phase supraconductrice est compacte. Nous présentons un ansatz variationnel, que nous appelons l'ansatz compact, pour étudier la pertinence de cet aspect granulaire de la charge. Cela nous a permis de décrire la disparition des effets compacts dans le régime suramorti à fort couplage.Il est possible de court-circuiter le couplage capacitif de l'impureté à son environnement, pour atteindre ce régime d'interaction forte, que la décompactification protège du bruit de charge. Le circuit se réduit alors à simuler le fameux modèle sine-Gordon à bord. Des expériences récentes on sondé la réponse dissipative d'un tel circuit, qui présente une section efficace inélastique spectaculairement élevée. Armé d'un modèle microscopique détaillé du système, nous montrons que la fréquence plasma introduit une coupure ultraviolette qui supprime les lois de puissance anormales de la réponse dissipative, bien connues par l'étude des liquides de Luttinger. Enfin, une technique diagrammatique auto-cohérente, entreprise à température finie, a permis de démontrer comment une réponse dissipative lisse en fréquence peut émerger d'un système de taille mésoscopique, par surpopulation de résonances multi-photons assistée par excitations thermiques

Spin-Boson Quantum Phase Transition in Multilevel Superconducting Qubits

5 pages, 4 figures and Supplementary MaterialInternational audienceSuperconducting circuits are currently developed as a versatile platform for the exploration of many-body physics, by building on nonlinear elements that are often idealized as two-level qubits. A classic example is given by a charge qubit that is capacitively coupled to a transmission line, which leads to the celebrated spin-boson description of quantum dissipation. We show that the intrinsic multilevel structure of superconducting qubits drastically restricts the validity of the spin-boson paradigm due to phase localization, which spreads the wave function over many charge states. Numerical renormalization group simulations also show that the quantum critical point moves out of the physically accessible range in the multilevel regime. Imposing charge discreteness in a simple variational state accounts for these multilevel effects, which are relevant for a large class of devices

Particle production in ultrastrong-coupling waveguide QED

International audienc

Revealing the finite-frequency response of a bosonic quantum impurity

Quantum impurities are ubiquitous in condensed matter physics and constitute the most stripped-down realization of many-body problems. While measuring their finite-frequency response could give access to key characteristics such as excitations spectra or dynamical properties, this goal has remained elusive despite over two decades of studies in nanoelectronic quantum dots. Conflicting experimental constraints of very strong coupling and large measurement bandwidths must be met simultaneously. We get around this problem using cQED tools, and build a precisely characterized quantum simulator of the boundary sine-Gordon model, a non-trivial bosonic impurity problem. We succeeded to fully map out the finite frequency linear response of this system. Its reactive part evidences a strong renormalisation of the nonlinearity at the boundary in agreement with non-perturbative calculations. Its dissipative part reveals a dramatic many-body broadening caused by multi-photon conversion. The experimental results are matched quantitatively to a resummed diagrammatic calculation based on a microscopically calibrated model. Furthermore, we push the device into a regime where diagrammatic calculations break down, which calls for more advanced theoretical tools to model many-body quantum circuits. We also critically examine the technological limitations of cQED platforms to reach universal scaling laws. This work opens exciting perspectives for the future such as quantifying quantum entanglement in the vicinity of a quantum critical point or accessing the dynamical properties of non-trivial many-body problems

Revealing the finite-frequency response of a bosonic quantum impurity

Quantum impurities are ubiquitous in condensed matter physics and constitute the most stripped-down realization of many-body problems. While measuring their finite-frequency response could give access to key characteristics such as excitations spectra or dynamical properties, this goal has remained elusive despite over two decades of studies in nanoelectronic quantum dots. Conflicting experimental constraints of very strong coupling and large measurement bandwidths must be met simultaneously. We get around this problem using cQED tools, and build a precisely characterized quantum simulator of the boundary sine-Gordon model, a non-trivial bosonic impurity problem. We succeeded to fully map out the finite frequency linear response of this system. Its reactive part evidences a strong renormalisation of the nonlinearity at the boundary in agreement with non-perturbative calculations. Its dissipative part reveals a striking many-body broadening caused by multi-photon conversion. The experimental results are matched quantitatively to a perturbative calculation based on a microscopically calibrated model. Furthermore, we push the device into a regime where perturbative calculations break down, which calls for more advanced theoretical tools to model many-body quantum circuits. We also critically examine the technological limitations of cQED platforms to reach universal scaling laws. This work opens exciting perspectives for the future such as quantifying quantum entanglement in the vicinity of a quantum critical point or accessing the dynamical properties of non-trivial many-body problems