arXiv subjects

Omar Di Stefano

Publications and source records attributed to Omar Di Stefano.

At least 19 recordsLinked to original sources

arXiv2025

From Few to Many Emitters Cavity QED: Energy Levels and Emission Spectra From Weak to Deep-Strong Coupling

We present a systematic study of the properties of systems composed of $N$ two-level quantum emitters coupled to a single cavity mode, for light-matter interaction strengths ranging from the weak to the ultrastrong and deep-strong coupling regimes. Beginning with an analysis of the energy spectrum as a function of the light-matter coupling strength, we examine systems with varying numbers of emitters, from a pair to large collections, approaching the thermodynamic limit ($N \to \infty$). Additionally, we explore the emission properties of these systems under incoherent excitation of the emitters, employing a general theoretical framework for open cavity-QED systems, which is valid across all light-matter interaction regimes and preserves gauge invariance within truncated Hilbert spaces. Furthermore, we study the influence of the emitter-environment interaction on the spectral properties of the system. Specifically, when each emitter interacts independently with its own reservoir, we observe the emergence of an emission peak at the cavity's resonant frequency for even values of $N$. Our analysis also clarify the evolution of the system as the number of emitters increases, ultimately converging towards an equivalent system composed of two interacting single-mode bosonic fields.

quant-ph↗

arXiv2025

Renormalization and Low-Energy Effective Models in Cavity and Circuit QED

The quantum Rabi model (QRM) is a cornerstone in the study of light-matter interactions within cavity and circuit quantum electrodynamics (QED). It effectively captures the dynamics of a two-level system coupled to a single-mode resonator, serving as a foundation for understanding quantum optical phenomena in a great variety of systems. However, this model may produce inaccurate results for large coupling strengths, even in systems with high anharmonicity. Moreover, issues of gauge invariance further undermine its reliability. In this work, we introduce a renormalized QRM that incorporates the effective influence of higher atomic energy levels, providing a significantly more accurate representation of the system while still maintaining a two-level description. To demonstrate the versatility of this approach, we present two different examples: an atom in a double-well potential and a superconducting artificial atom (fluxonium qubit). This procedure opens new possibilities for precisely engineering and understanding cavity and circuit QED systems, which are highly sought-after, especially for quantum information processing.

quant-ph↗

arXiv2024

Circuit QED Spectra in the Ultrastrong Coupling Regime: How They Differ from Cavity QED

Cavity quantum electrodynamics (QED) studies the interaction between resonator-confined radiation and natural atoms or other formally equivalent quantum excitations, under conditions where the quantum nature of photons is relevant. Phenomena studied in cavity QED can also be explored using superconducting artificial atoms and microwave photons in superconducting resonators. These circuit QED systems offer the possibility to reach the ultrastrong coupling regime with individual artificial atoms, unlike their natural counterparts. In this regime, the light-matter coupling strength reaches a considerable fraction of the bare resonance frequencies in the system. Here, we provide a careful analysis of both incoherent and coherent spectra in circuit QED systems consisting of a flux qubit interacting with an LC resonator. Despite these systems can be effectively described by the quantum Rabi model, as the corresponding cavity QED ones, we find distinctive features, depending on how the system is coupled to the output port, which become evident in the ultrastrong coupling regime.

quant-ph↗

arXiv2024

Quantum Phase Transitions in Many-Dipole Light-Matter Systems

A potential phase transition between a normal ground state and a photon-condensed ground state in many-dipole light-matter systems is a topic of considerable controversy, exasperated by conflicting no-go and counter no-go theorems and often ill-defined models. We clarify this long-lasting debate by analyzing two specific arrangements of atoms, including a 3D cubic lattice and a cavity-embedded square lattice layer, which provides a physical model for single-mode cavity QED with coupled dipoles in the thermodynamic limit. These models are shown to significantly differ from the standard Dicke model and, in the thermodynamic limit, give rise to renormalized Hopfield models. We show that a ferroelectric phase transition can (in principle) still occur and the description of the abnormal phase beyond the critical point requires the inclusion of nonlinear terms in the Holstein-Primakoff mapping. We also show how our model agrees with recent experiments.

quant-ph↗

arXiv2024

Photon condensation, Van Vleck paramagnetism, and chiral cavities

We introduce a gauge-invariant model of planar, square molecules coupled to a quantized spatially-varying cavity electromagnetic vector potential A(r). Specifically, we choose a temporally chiral cavity hosting a uniform magnetic field B, as this is the simplest instance in which a transverse spatially-varying A(r) is at play. We show that when the molecules are in the Van Vleck paramagnetic regime, an equilibrium quantum phase transition to a photon condensate state occurs.

cond-mat.mes-hall↗

arXiv2023

Ultrastrong Magnon-Photon Coupling Achieved by Magnetic Films in Contact with Superconducting Resonators

Coherent coupling between spin wave excitations (magnons) and microwave photons in a cavity may disclose new paths to unconventional phenomena as well as for novel applications. Here, we present a systematic investigation on YIG (Yttrium Iron Garnet) films on top of coplanar waveguide resonators made of superconducting YBCO. We first show that spin wave excitations with frequency higher than the Kittel mode can be excited by putting in direct contact a 5~$μ$m thick YIG film with the YBCO coplanar resonator (cavity frequency $ω_c/2 π= 8.65$~GHz). With this configuration, we obtain very large values of the collective coupling strength $λ/2 π\approx 2$~GHz and cooperativity $C=5 \times 10^4$. Transmission spectra are analyzed by a modified Hopfield model for which we provide an exact solution that allows us to well reproduce spectra by introducing a limited number of free parameters. It turns out that the coupling of the dominant magnon mode with photons exceeds 0.2 times the cavity frequency, thus demonstrating the achievement of the ultrastrong coupling regime with this architecture. Our analysis also shows a vanishing contribution of the diamagnetic term which is a peculiarity of pure spin systems.

cond-mat.mes-hall↗

arXiv2022

Gauge-Independent Emission Spectra and Quantum Correlations in the Ultrastrong Coupling Regime of Open System Cavity-QED

A quantum dipole interacting with an optical cavity is one of the key models in cavity quantum electrodynamics (cavity-QED). To treat this system theoretically, the typical approach is to truncate the dipole to two levels. However, it has been shown that in the ultrastrong-coupling regime, this truncation naively destroys gauge invariance. By truncating in a manner consistent with the gauge principle, we introduce master equations {for open systems} to compute gauge-invariant emission spectra, photon flux rates, and quantum correlation functions which show significant disagreement with previous results obtained using the standard quantum Rabi model. Explicit examples are shown using both the dipole gauge and the Coulomb gauge.

quant-ph↗

arXiv2022

Ultrastrong Coupling of a Qubit with a Nonlinear Optical Resonator

We study the interaction of a two-level atom with a single-mode nonlinear electromagnetic resonator, considering coupling strengths ranging from zero to the so-called deep strong coupling regime. When the qubit-resonator coupling is very strong, the standard Kerr model for the resonator becomes questionable. Moreover, recently, it has been shown that extra care is needed when constructing gauge-independent theories in the presence of approximations as the truncation of the Hilbert space of the matter system. Such a truncation can ruin gauge invariance leading to non-physical results, especially when the light-matter interactions strength is very high. Here we face and solve this issues to provide a consistent nonlinear-resonator quantum Rabi model satisfying the gauge principle.

quant-ph↗

arXiv2022

Pure Dephasing of Light-Matter Systems in the Ultrastrong and Deep-Strong Coupling Regimes

Pure dephasing originates from the non-dissipative information exchange between quantum systems and environments, and plays a key-role in both spectroscopy and quantum information technology. Often pure dephasing constitutes the main mechanism of decay of quantum correlations. Here we investigate how pure dephasing of one of the components of a hybrid quantum system affects the dephasing rate of the system transitions. We find that, in turn, the interaction, in the case of a light-matter system, can significantly affect the form of the stochastic perturbation describing the dephasing of a subsystem, depending on the adopted gauge. Neglecting this issue can lead to wrong and unphysical results when the interaction becomes comparable to the bare resonance frequencies of subsystems, which correspond to the ultrastrong and deep-strong coupling regimes. We present results for two prototypical models of cavity quantun electrodynamics: the quantum Rabi and the Hopfield model.

quant-ph↗

arXiv2020

TRK Sum Rule for Interacting Photons

The Thomas-Reiche-Kuhn sum rule is a fundamental consequence of the position-momentum commutation relation for an atomic electron and it provides an important constraint on the transition matrix elements for an atom. Here we propose a TRK sum rule for electromagnetic fields which is valid even in the presence of very strong light-matter interactions and/or optical nonlinearities. While the standard TRK sum rule involves dipole matrix moments calculated between atomic energy levels (in the absence of interaction with the field), the sum rule here proposed involves expectation values of field operators calculated between general eigenstates of the interacting light-matter system. This sum rule provides constraints and guidance for the analysis of strongly interacting light-matter systems and can be used to test the validity of approximate effective Hamiltonians often used in quantum optics.

quant-ph↗

arXiv2020

Gauge Principle and Gauge Invariance in Quantum Two-Level Systems

The quantum Rabi model is a widespread description for the coupling between a two-level system and a quantized single mode of an electromagnetic resonator. Issues about this model's gauge invariance have been raised. These issues become evident when the light-matter interaction reaches the so-called ultrastrong coupling regime. Recently, a modified quantum Rabi model able to provide gauge-invariant physical results in any interaction regime was introduced [Nature Physics 15, 803 (2019)]. Here we provide an alternative derivation of this result, based on the implementation in two-state systems of the gauge principle, which is the principle from which all the fundamental interactions in quantum field theory are derived. The adopted procedure can be regarded as the two-site version of the general method used to implement the gauge principle in lattice gauge theories. Applying this method, we also obtain the gauge-invariant quantum Rabi model for asymmetric two-state systems, and the multi-mode gauge-invariant quantum Rabi model beyond the dipole approximation.

quant-ph↗

arXiv2020

Gauge invariance of the Dicke and Hopfield models

The Dicke model, which describes the dipolar coupling between N two-level atoms and a quantized electromagnetic field, seemingly violates gauge invariance in the presence of ultrastrong light-matter coupling, a regime that is now experimentally accessible in many physical systems. Specifically, it has been shown that, while the two-level approximation can work well in the dipole gauge, the Coulomb gauge fails to provide the correct spectra in the ultrastrong coupling regime. Here we show that, taking into account the nonlocality of the atomic potential induced by the two-level approximation, gauge invariance is fully restored for arbitrary interaction strengths, even in the limit of N going to infinity. Finally, we express the Hopfield model, a general description based on the quantization of a linear dielectric medium, in a manifestly gauge invariant form, and show that the Dicke model in the dilute regime can be regarded as a particular case of the more general Hopfield model.

quant-ph↗

arXiv2020

Gauge freedom, quantum measurements, and time-dependent interactions in cavity and circuit QED

The interaction between the electromagnetic field inside a cavity and natural or artificial atoms has played a crucial role in developing our understanding of light-matter interaction, and is central to various quantum technologies. Recently, new regimes beyond the weak and strong light-matter coupling have been explored in several settings. These regimes, where the interaction strength is comparable (ultrastrong) or even higher (deep-strong) than the transition frequencies in the system, can give rise to new physical effects and applications. At the same time, they challenge our understanding of cavity QED. When the interaction strength is so high, fundamental issues like the proper definition of subsystems and of their quantum measurements, the structure of light-matter ground states, or the analysis of time-dependent interactions are subject to ambiguities leading to even qualitatively distinct predictions. The resolution of these ambiguities is also important for understanding and designing next-generation quantum devices that will exploit the ultrastrong coupling regime. Here we discuss and provide solutions to these issues.

quant-ph↗

arXiv2019

Scully-Lamb quantum laser model for parity-time-symmetric whispering-gallery microcavities: Gain saturation effects and non-reciprocity

We use a non-Lindbladian master equation of the Scully-Lamb laser model for the analysis of light propagation in a parity-time symmetric photonic system composed of coupled active and passive whispering-gallery microresonators. Performing the semiclassical approximation, we obtain a set of two nonlinear coupled differential equations describing the time evolution of intracavity fields. These coupled equations are able to explain the experimentally-observed light non-reciprocity [Peng {\em et al.}, Nature Physics {\bf 10}, 394 (2014), Chang {\em et al.}, Nature Photonics {\bf 8}, 524 (2014)]. We show that this effect arises from the interplay between gain saturation in the active microcavity, intercavity coupling, and losses in the cavities. Additionally, using this approach, we study the effect of the gain saturation on exceptional points, i.e., exotic degeneracies in non-Hermitian systems. Namely, we demonstrate that the inclusion of gain saturation leads to a modification of the exceptional points in the presence of intense intracavity fields. The Scully-Lamb master equation for systems of coupled optical structures, as proposed and applied here, constitutes a promising tool for the study of quantum optical effects in coupled systems with losses, gain, and gain saturation.

quant-ph↗

arXiv2019

Conversion of Mechanical Noise into Correlated Photon Pairs: Dynamical Casimir effect from an incoherent mechanical drive

We show that the dynamical Casimir effect in an optomechanical system can be achieved under incoherent mechanical pumping. We adopt a fully quantum-mechanical approach for both the cavity field and the oscillating mirror. The dynamics is then evaluated using a recently-developed master equation approach in the dressed picture, including both zero and finite temperature photonic reservoirs. This analysis shows that the dynamical Casimir effect can be observed even when the mean value of the mechanical displacement is zero. This opens up new possibilities for the experimental observation of this effect. We also calculate cavity emission spectra both in the resonant and the dispersive regimes, providing useful information on the emission process.

quant-ph↗

arXiv2018

Dissipation and Thermal Noise in Hybrid Quantum Systems in the Ultrastrong Coupling Regime

The interaction among the components of a hybrid quantum system is often neglected when considering the coupling of these components to an environment. However, if the interaction strength is large, this approximation leads to unphysical predictions, as has been shown for cavity-QED and optomechanical systems in the ultrastrong-coupling regime. To deal with these cases, master equations with dissipators retaining the interaction between these components have been derived for the quantum Rabi model and for the standard optomechanical Hamiltonian. In this article, we go beyond these previous derivations and present a general master equation approach for arbitrary hybrid quantum systems interacting with thermal reservoirs. Specifically, our approach can be applied to describe the dynamics of open hybrid systems with harmonic, quasi-harmonic, and anharmonic transitions. We apply our approach to study the influence of temperature on multiphoton vacuum Rabi oscillations in circuit QED. We also analyze the influence of temperature on the conversion of mechanical energy into photon pairs in an optomechanical system, which has been recently described at zero temperature. We compare our results with previous approaches, finding that these sometimes overestimate decoherence rates and understimate excited-state populations.

quant-ph↗

arXiv2018

Interaction of Mechanical Oscillators Mediated by the Exchange of Virtual Photon Pairs

Two close parallel mirrors attract due to a small force (Casimir effect) originating from the electromagnetic quantum vacuum uctuations of the electromagnetic field. These vacuum uctuations can also induce motional forces exerted upon one mirror when the other one moves. Here we consider an optomechanical system consisting of two vibrating mirrors coupled to an optical resonator. We find that motional forces can determine noticeable coupling rates between the two spatially separated vibrating mirrors. We show that, by tuning the two mechanical oscillators into resonance, energy is exchanged between them at the quantum level. This coherent motional coupling is enabled by the exchange of virtual photon pairs, originating from the dynamical Casimir effect. The process proposed here shows that the electromagnetic quantum vacuum is able to transfer mechanical energy somewhat like an ordinary uid. We show that this system can also operate as a mechanical parametric down-converter even at very weak excitations. These results demonstrate that vacuuminduced motional forces open up new possibilities for the development of optomechanical quantum technologies.

quant-ph↗

arXiv2017

Photodetection probability in quantum systems with arbitrarily strong light-matter interaction

Cavity-QED systems have recently reached a regime where the light-matter interaction strength amounts to a non-negligible fraction of the resonance frequencies of the bare subsystems. In this regime, it is known that the usual normal-order correlation functions for the cavity-photon operators fail to describe both the rate and the statistics of emitted photons. Following Glauber's original approach, we derive a simple and general quantum theory of photodetection, valid for arbitrary light-matter interaction strengths. Our derivation uses Fermi's golden rule, together with an expansion of system operators in the eigenbasis of the interacting light-matter system, to arrive at the correct photodetection probabilities. We consider both narrow- and wide-band photodetectors. Our description is also valid for point-like detectors placed inside the optical cavity. As an application, we propose a gedanken experiment confirming the virtual nature of the bare excitations that enrich the ground state of the quantum Rabi model.

quant-ph↗