Ultrastrong light-matter interaction in quantum technologies

120 p.En esta Tesis, hemos analizado teóricamente fenómenos cuánticos novedosos emergentes en el régimenultrafuerte (USC) de interacción entre luz y materia. Nos hemos enfocado en procesos que pueden serobservados usando tecnologías cuánticas actuales o que puedan motivar desarrollos tecnológicospróximos. Los resultados presentados en esta Tesis pueden ser agrupados en dos categorías. Por un lado,hemos estudiado modelos que pueden ser implementados usando circuitos superconductores, unaplataforma cuántica donde el régimen USC puede ser alcanzado de forma natural. En especifico, hemosestudiado la transferencia de excitaciones en cadenas de resonadores cuánticos, generación deentrelazamiento cuántico vía efecto Casimir dinámico y ingeniería de estados cuánticos en el régimenUSC. Por otro lado, hemos desarrollado métodos para reproducir la física de la interacción ultrafuerte ensistemas de iones atrapados y de átomos fríos en retículos ópticos. Esas propuestas aprovechan lasventajas de cada plataforma cuántica para alcanzar regímenes de parámetros e implementar medidas queno son accesibles en implementaciones naturales de los procesos considerados.Los resultados presentado en esta Tesis profundizan nuestra comprensión de fenómenos cuánticosrelativos al régimen ultrafuerte de interacción entre luz y materia. Además, nuestras propuestas aspiran apromover el desarrollo conjunto de herramientas teóricas y técnicas experimentales en esta área deinvestigació

Universal spectral features of ultrastrongly coupled systems

We identify universal properties of the low-energy subspace of a wide class of quantum optical models in the ultrastrong coupling limit, where the coupling strength dominates over all other energy scales in the system. We show that the symmetry of the light-matter interaction is at the origin of a twofold degeneracy in the spectrum. We prove analytically this result for bounded Hamiltonians and extend it to a class of models with unbounded operators. As a consequence, we show that the emergence of superradiant phases previously investigated in the context of critical phenomena, is a general property of the ultrastrong coupling limit. The set of models we consider encompasses different scenarios of possible interplay between critical behavior and superradianceS. F. acknowledges support from the European Research Council (ERC-2016-STG-714870

Classification of Dark States in Multi-level Dissipative Systems

Dark states are eigenstates or steady-states of a system that are decoupled from the radiation. Their use, along with associated techniques such as Stimulated Raman Adiabatic Passage, has extended from atomic physics where it is an essential cooling mechanism, to more recent versions in condensed phase where it can increase the coherence times of qubits. These states are often discussed in the context of unitary evolution and found with elegant methods exploiting symmetries, or via the Bruce-Shore transformation. However, the link with dissipative systems is not always transparent, and distinctions between classes of CPT are not always clear. We present a detailed overview of the arguments to find stationary dark states in dissipative systems, and examine their dependence on the Hamiltonian parameters, their multiplicity and purity. We find a class of dark states that depends not only on the detunings of the lasers but also on their relative intensities. We illustrate the criteria with the more complex physical system of the hyperfine transitions of $^{87}$Rb and show how a knowledge of the dark state manifold can inform the preparation of pure states.Comment: additional example

Two-photon interaction effects in the bad-cavity limit

Various experimental platforms have proven to be valid testbeds for the implementation of non-dipolar light-matter interactions, where atomic systems and confined modes interact via two-photon couplings. Here, we study a damped quantum harmonic oscillator interacting with $N$ qubits via a two-photon coupling in the so-called bad-cavity limit, in the presence of finite-temperature baths and coherent and incoherent drivings. We have succeeded in applying a recently developed adiabatic elimination technique to derive an effective master equation for the qubits, presenting two fundamental differences compared to the case of a dipolar interaction: an enhancement of the qubits spontaneous-like emission rate, including a thermal contribution and a quadratic term in the coherent driving, and an increment of the effective temperature perceived by the qubits. These differences give rise to striking effects in the qubits dynamics, including a faster generation of steady-state coherence and a richer dependence on temperature of the collective effects, which can be made stronger at higher temperature.Comment: 11 pages, 4 figures. Comments welcom

Exponential precision by reaching a quantum critical point

Quantum metrology shows that by exploiting nonclassical resources it is possible to overcome the fundamental limit of precision found for classical parameter-estimation protocols. The scaling of the quantum Fisher information -- which provides an upper bound to the achievable precision -- with respect to the protocol duration is then of primarily importance to assess its performances. In classical protocols the quantum Fisher information scales linearly with time, while typical quantum-enhanced strategies achieve a quadratic (Heisenberg) or even higher-order polynomial scalings. Here we report a protocol that is capable of surpassing the polynomial scaling, and yields an exponential advantage. Such exponential advantage is achieved by approaching, but without crossing, the critical point of a quantum phase transition of a fully-connected model in the thermodynamic limit. The exponential advantage stems from the breakdown of the adiabatic condition close to a critical point. As we demonstrate, this exponential scaling is well captured by the new bound derived in arXiv:2110.04144, which in turn allows us to obtain approximate analytical expressions for the quantum Fisher information that agree with exact numerical simulations. In addition, we discuss the limitations to the exponential scaling when considering a finite-size system as well as its robustness against decoherence effects. Hence, our findings unveil a novel quantum metrological protocol whose precision scaling goes beyond the paradigmatic Heisenberg limit with respect to the protocol duration.Comment: 12 pages, 4 figures; comments welcome

Ultrastrong coupling regime of non-dipolar light-matter interactions

We present a circuit-QED scheme which allows to reach the ultrastrong coupling regime of a nondipolar interaction between a single qubit and a quantum resonator. We show that the system Hamiltonian is well approximated by a two-photon quantum Rabi model and propose a simple scattering experiment to probe its fundamental properties. In particular, we identify a driving scheme that reveals the change in selection rules characterizing the breakdown of the rotating-wave approximation and the transition from strong to ultrastrong two-photon interactions. Finally, we show that a frequency crowding in a narrow spectral region is observable in the output fluoresce spectrum as the coupling strength approaches the collapse point, paving the way to the direct observation of the onset of the spectral collapse in a solid-state device.Comment: 5+6 pages, 2 figure

Critical Quantum Metrology in the Non-Linear Quantum Rabi Model

The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a non-linear coupling term exhibits much higher measurement precisions due to its first order like phase transition at \emph{finite} frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magnetometer if implemented in circuit QED platforms.Comment: 7 pages, 5 figure

Metrological advantage at finite temperature for Gaussian phase estimation

In the context of phase estimation with Gaussian states, we introduce a quantifiable definition of metrological advantage that takes into account thermal noise in the preparation procedure. For a broad set of states, \textit{isotropic non-pure Gaussian states}, we show that squeezing is not only necessary, but sufficient, to achieve metrological advantage. We interpret our results in the framework of resource theory, and discuss possible sources of advantage other than squeezing. Our work is a step towards using phase estimation with pure and mixed state to define and quantify nonclassicality. This work is complementary with studies that defines nonclassicality using quadrature displacement estimation.Comment: Changes to wording, figures replace