Effective theory for matter in non-perturbative cavity QED

Starting from a general material system of N particles coupled to a cavity, we use a coherent-state path integral formulation to produce a effective theory for the material degrees of freedom. We tackle the effects of image charges, the A^2 term and a multimode arbitrary-geometry cavity. The resulting (non-local) action has the photonic degrees of freedom replaced by an effective position-dependent interaction between the particles. In the large-NN limit, we discuss how the theory can be cast into an effective Hamiltonian where the cavity induced interactions are made explicit. The theory is applicable, beyond cavity QED, to any system where bulk material is linearly coupled to a diagonalizable bosonic bath. We highlight the differences of the theory with other well-known methods and numerically study its finite-size scaling on the Dicke model. Finally, we showcase its descriptive power with three examples: photon condensation, the 2D free electron gas in a cavity and the modification of magnetic interactions between molecular spins; recovering, condensing and extending some recent results in the literature

Exact solution for quantum strong long-range models via a generalized Hubbard-Stratonovich transformation

We present an exact analytical solution for quantum strong long-range models in the canonical ensemble by extending the classical solution proposed in Campa et al. [J. Phys. A: Math. Gen. 36, 6897 (2003)]. Specifically, we utilize the equivalence between generalized Dicke models and interacting quantum models as a generalization of the Hubbard-Stratonovich transformation. To demonstrate our method, we apply it to the Ising chain in transverse field and discuss its potential application to other models, such as the Fermi-Hubbard model, combined short- and long-range models, and models with antiferromagnetic interactions. Our findings indicate that the critical behavior of a model is independent of the range of interactions, within the strong long-range regime, and the dimensionality of the model. Moreover, we show that the order-parameter expression is equivalent to that provided by mean-field theory, thus confirming the exactness of the latter. Finally, we examine the algebraic decay of correlations and characterize its dependence on the range of interactions in the full phase diagram

Distant emitters in ultrastrong waveguide QED: Ground-state properties and non-Markovian dynamics

Starting from the paradigmatic spin-boson model (SBM), we investigate the static and dynamical properties of a system of two distant two-level emitters coupled to a one-dimensional Ohmic waveguide beyond the rotating wave approximation. Employing static and dynamical polaron Ansätze we study the effects of finite separation distance on the behavior of the photon-mediated Ising-like interaction, qubit frequency renormalization, ground-state magnetization, and entanglement entropy of the two-qubit system. Based on previous works we derive an effective approximate Hamiltonian for the two-impurity SBM that preserves the excitation-number and thus facilitates the analytical treatment. In particular, it allows us to introduce non-Markovianity arising from delay-feedback effects in two distant emitters in the so-called ultrastrong coupling (USC) regime. We test our results with numerical simulations performed over a discretized circuit-QED model, finding perfect agreement with previous results, and showing interesting dynamical effects arising in ultrastrong waveguide QED with distant emitters. In particular, we revisit the Fermi two-atom problem showing that, in the USC regime, initial correlations yield two different evolutions for symmetric and antisymmetric states even before the emitters become causally connected. Finally, we demonstrate that the collective dynamics, e.g., superradiance or subradiance, are affected not only by the distance between emitters, but also by the coupling, due to significant frequency renormalization. This constitutes another dynamical consequence of the USC regime

Circuit Complexity through phase transitions: consequences in quantum state preparation

In this paper, we analyze the circuit complexity for preparing ground states of quantum many-body systems. In particular, how this complexity grows as the ground state approaches a quantum phase transition. We discuss different definitions of complexity, namely the one following the Fubini-Study metric or the Nielsen complexity. We also explore different models: Ising, ZZXZ or Dicke. In addition, different forms of state preparation are investigated: analytic or exact diagonalization techniques, adiabatic algorithms (with and without shortcuts), and Quantum Variational Eigensolvers. We find that the divergence (or lack thereof) of the complexity near a phase transition depends on the non-local character of the operations used to reach the ground state. For Fubini-Study based complexity, we extract the universal properties and their critical exponents. In practical algorithms, we find that the complexity depends crucially on whether or not the system passes close to a quantum critical point when preparing the state. For both VQE and Adiabatic algorithms, we provide explicit expressions and bound the growth of complexity with respect to the system size and the execution time, respectively.Comment: 25 pages, 12 figure

Modelos cuánticos de muy largo alcance: solución general y su aplicación a cadenas de Ising

En este Trabajo de Fin de Grado se presenta una nueva técnica analítica que permite resolver en el formalismo canónico modelos cuánticos con interacciones de muy largo alcance (quantum strong long-range models).Para mostrar su aplicabilidad se estudiará el modelo de Ising cuántico con interacciones de muy largo alcance, tanto ferromagnéticas como antiferromagnéticas.<br /

Modelos de reservorios magnónicos basados en "Waveguide QED"

Este trabajo estudia la posibilidad de implementar modelos ferromagnéticos de reservorios de energía en tecnologías cuánticas. Los modelos aportados son originales, se basan en la interacción espín-magnón y están inspirados en las guías de onda en electrodinámica cuántica. A lo largo del escrito, se describen las características teóricas de los modelos construidos y se muestra su aplicación al cálculo de la dinámica de los autoestados del hamiltoniano del sistema completo.<br /

Treatment with tocilizumab or corticosteroids for COVID-19 patients with hyperinflammatory state: a multicentre cohort study (SAM-COVID-19)

Objectives: The objective of this study was to estimate the association between tocilizumab or corticosteroids and the risk of intubation or death in patients with coronavirus disease 19 (COVID-19) with a hyperinflammatory state according to clinical and laboratory parameters. Methods: A cohort study was performed in 60 Spanish hospitals including 778 patients with COVID-19 and clinical and laboratory data indicative of a hyperinflammatory state. Treatment was mainly with tocilizumab, an intermediate-high dose of corticosteroids (IHDC), a pulse dose of corticosteroids (PDC), combination therapy, or no treatment. Primary outcome was intubation or death; follow-up was 21 days. Propensity score-adjusted estimations using Cox regression (logistic regression if needed) were calculated. Propensity scores were used as confounders, matching variables and for the inverse probability of treatment weights (IPTWs). Results: In all, 88, 117, 78 and 151 patients treated with tocilizumab, IHDC, PDC, and combination therapy, respectively, were compared with 344 untreated patients. The primary endpoint occurred in 10 (11.4%), 27 (23.1%), 12 (15.4%), 40 (25.6%) and 69 (21.1%), respectively. The IPTW-based hazard ratios (odds ratio for combination therapy) for the primary endpoint were 0.32 (95%CI 0.22-0.47; p < 0.001) for tocilizumab, 0.82 (0.71-1.30; p 0.82) for IHDC, 0.61 (0.43-0.86; p 0.006) for PDC, and 1.17 (0.86-1.58; p 0.30) for combination therapy. Other applications of the propensity score provided similar results, but were not significant for PDC. Tocilizumab was also associated with lower hazard of death alone in IPTW analysis (0.07; 0.02-0.17; p < 0.001). Conclusions: Tocilizumab might be useful in COVID-19 patients with a hyperinflammatory state and should be prioritized for randomized trials in this situatio

Effective theory for matter in non-perturbative cavity QED

Starting from a general material system of N particles coupled to a cavity, we use a coherent-state path integral formulation to produce a effective theory for the material degrees of freedom. We tackle the effects of image charges, the A^2 term and a multimode arbitrary-geometry cavity. The resulting (non-local) action has the photonic degrees of freedom replaced by an effective position-dependent interaction between the particles. In the large-NN limit, we discuss how the theory can be cast into an effective Hamiltonian where the cavity induced interactions are made explicit. The theory is applicable, beyond cavity QED, to any system where bulk material is linearly coupled to a diagonalizable bosonic bath. We highlight the differences of the theory with other well-known methods and numerically study its finite-size scaling on the Dicke model. Finally, we showcase its descriptive power with three examples: photon condensation, the 2D free electron gas in a cavity and the modification of magnetic interactions between molecular spins; recovering, condensing and extending some recent results in the literature

Teorías efectivas para el acoplo ultrafuerte entre luz y materia

This End-of-Degree Thesis is structured as follows: In Section 1, we briefly show how the linear cavity array with coupled qubits naturally leads to the spin-boson model, we also analyse the motivation behind the introduction of the Polaron Transform for the study of said model. In Section 2 we apply the PT to a single-qubit system in order to assert its superiority over the RWA in the USC regime. We benchmark it using exact diagonalisation in small-sized systems and characterise both the GS and spontaneous emission. In Section 3 we present a generalisation of the PT for the two-qubit model and apply it successfully, proving that it converges to the single qubit scenario for sufficiently distant qubits. We show that the two-qubit system presents a ferromagnetic Ising ground state, as well as bound excited states that can be described using a simple tight-binding model, and serve as the basis for a proposed lossless state-transfer protocol. Finally, we draw some conclusions from our results and outline possible continuations. Technical details are left for the Appendix, including a link to a public repository where all the code, originally developed for this project, can be found.<br /

Condensación fotónica en magnetic cavity QED

More than 47 years ago Hepp and Lieb showed that photon condensation was theoretically possible in Dicke’s model. In this model, symmetry breaking was induced by the coupling of an electromagnetic cavity to the electric dipoles of N free atoms in the thermodynamic limit. The experimental realization of this model has been pursued for the last 47 years. However, the transition has never been measured. During this time, the community has enjoyed a tortuous succession of proposals on how to achieve photon condensation, each shortly matched with a corresponding no-go theorem.In this Master’s Thesis we present a no-go theorem that unifies all these no-go theorems (including some recent ones) and we propose a rather straightforward way to avoid them: harnessing magnetic coupling. Therefore, we solve this long-standing theoretical controversy and provide a realistic experimental layout to measure the transition, using magnetic molecules (instead of electric-dipole-coupled ones).This Master’s Thesis is divided in two blocks. The first block discusses the problem of photon condensation as presented in the literature, with electric-dipole coupling. Section 1 starts with a brief presentation of Pauli’s equation and how it leads to the Hamiltonian of the model under study, we then proceed to give a thorough overview of the historical contributions to the topic, from Hepp and Lieb’s original contribution to the present day. Then, in Sec. 2, we present a unified no-go theorem that settles the debate, proving that photon condensation does not occur when the coupling between light and matter is through the electric dipole. The second block explores magnetic cavity QED. In Sec. 3 we introduce Zeeman coupling in our Hamiltonian of the model while considering molecules without electric dipole, we show that this leads to the Dicke model, in which superradiance occurs. After finding that magnetic cavity QED permits photon condensation we test the robustness of the model against some generalizations. Following the success in Sec. 3, in Sec. 4 we discuss a transmission experiment designed to measure the phase transition. Finally, we draw some conclusions from our results and outline possible continuations. Technical details are left for the appendices.<br /