The ultrastrong and deep strong coupling regimes exhibit a variety of intriguing physical phenomena. In this work, we utilize the Hopfield model of a two-mode bosonic system, with each mode interacting with a heat reservoir, to research the behavior of quantum coherence. Our results indicate that a coupled oscillator system can exhibit significant quantum coherence in the ultrastrong and deep strong coupling regimes. In the ground state, the photon mode and the matter mode coherences are equal. The larger coherences that encompass the photon mode, the matter mode, and the overall system are achieved at lower optical frequencies and with increased coupling strengths. Notably, the beam splitter and phase rotation terms alone do not generate coherences for either total coherence or subsystem coherences; instead, the generation of quantum coherences originates from the one-mode and two-mode squeezing terms. When hot environments are present, the total coherence can be enhanced by the beam splitter and phase rotation terms, while it has no effect on subsystem coherences. Moreover, when the one-mode and two-mode squeezing terms and the beam splitter and phase rotation terms are considered together, the total coherence increases with stronger coupling. We also observe that lower frequencies maximize total coherence in the deep strong coupling regime. These results demonstrate that the ultrastrong coupling and deep strong coupling regimes give rise to characteristics of quantum coherences. This work provides valuable insights into the quantum coherence properties, particularly in the ultrastrong and deep strong coupling regimes between light and matter, and may have potential applications in quantum information processing.
The ultrastrong and deep strong coupling regimes exhibit a variety of intriguing physical phenomena. In this work, we utilize the Hopfield model of a two-mode bosonic system, with each mode interacting with a heat reservoir, to research the behavior of quantum coherence. Our results indicate that a coupled oscillator system can exhibit significant quantum coherence in the ultrastrong and deep strong coupling regimes. In the ground state, the photon mode and the matter mode coherences are equal. The larger coherences that encompass the photon mode, the matter mode, and the overall system are achieved at lower optical frequencies and with increased coupling strengths. Notably, the beam splitter and phase rotation terms alone do not generate coherences for either total coherence or subsystem coherences; instead, the generation of quantum coherences originates from the one-mode and two-mode squeezing terms. When hot environments are present, the total coherence can be enhanced by the beam splitter and phase rotation terms, while it has no effect on subsystem coherences. Moreover, when the one-mode and two-mode squeezing terms and the beam splitter and phase rotation terms are considered together, the total coherence increases with stronger coupling. We also observe that lower frequencies maximize total coherence in the deep strong coupling regime. These results demonstrate that the ultrastrong coupling and deep strong coupling regimes give rise to characteristics of quantum coherences. This work provides valuable insights into the quantum coherence properties, particularly in the ultrastrong and deep strong coupling regimes between light and matter, and may have potential applications in quantum information processing.
The prototypical system constituted by a two-level atom interacting with a quantized single-mode electromagnetic field is described by the quantum Rabi model (QRM). The QRM is potentially valid at any light-matter interaction regime, ranging from the weak (where the decay rates exceeds the coupling rate) to the deep strong coupling (where the interaction rate exceeds the bare transition frequencies of the subsystems). However, when reaching the ultrastrong coupling regime, several theoretical issues may prevent the correct description of the observable dynamics of such a system: (i) the standard quantum optics master equation fails to correctly describe the interaction of this system with the reservoirs; (ii) the correct output photon rate is no longer proportional to the intracavity photon number; and (iii) they appear to violate gauge invariance. Here, we study the photon flux emission rate of this system under the incoherent excitation of the two-level atom for any light-matter interaction strength and consider different effective temperatures. The dependence of the emission spectra on the coupling strength is the result of the interplay between energy levels, matrix elements of the observables, and the density of states of the reservoirs. Within this approach, we also study the occurrence of light-matter decoupling in the deep strong-coupling regime and show how all of the obtained results are gauge invariant.
This work presents a scheme for engineering quantum entanglement and Einstein-Podolsky-Rosen (EPR) steering with Gaussian measurements based on the quantum Hopfield model that incorporates a common thermal reservoir. We begin by examining quantum correlations, specifically quantum entanglement and EPR steering, in the ground state. These quantum correlations primarily stem from squeezing interactions in weak-coupling and normal strong-coupling regimes. As the coupling strength increases, especially upon entering the ultrastrong-coupling regime, the correlations emerge from the combined effect of squeezing and mix-mode interactions. Importantly, this scenario enables the realization of two-way EPR steering. Moreover, lower optical frequencies enhance both quantum entanglement and EPR steering. Further, when considering thermal effects, the ultrastrong-coupling and deep strong-coupling regimes, paired with lower optical frequencies, lead to improved entanglement. The one-way EPR steering for the resonant case can be effectively controlled in the ultrastrong-coupling and deep strong-coupling regimes which originate from the asymmetry of the subsystem and reservoir coupling induced by the diamagnetic term. Additionally, one-way EPR steering can also be produced for the nonresonant case. In this case, the asymmetry of the subsystem and reservoir originates from the combined effect of nonresonant frequencies and the diamagnetic term. Our findings have the potential to inspire further research into quantum information processing that leverages light-matter entanglement and EPR steering.
Pure dephasing originates from the nondissipative 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.
In the last decades, the experimental and theoretical study of light-matter interactions in confined quantum systems has allowed to considerably widen and deepen our understanding of the quantum world.The simplest fully-quantized light-matter interaction is the quantum Rabi model (QRM), where a two-level system is coupled to a single bosonic mode.The implementation of quantum-optical systems in which the interaction strength overcomes losses brought a revolution to this research area.Under this condition, dubbed strong coupling (SC) regime, quantum processes can be observed at the single-photon level, and even exploited to perform Quantum Information tasks.Recent developments in solid-state Quantum Technologies have made possible to push the line further, achieving the ultrastrong coupling (USC) regime of the QRM, in which the interaction strength is comparable with the bare frequencies of the interacting systems.In the USC regime of the QRM, light and matter degrees of freedom merge into collective bound states called polaritons, the system ground state is not the vacuum and excitations are not conserved.The growing interest in USC-related phenomena is mainly motivated by the fundamental counterintuitive modifications to light-matter interactions entailed by this regime.At the same time, the USC regime is also expected to provide computational benefits in terms of operational speed, coherence time, and noise protection.In this Thesis, we theoretically analyze novel quantum phenomena emerging in the USC regime, which can be observed using nowadays technology and can motivate foreseeable improvements.The results here presented have been derived using two conceptually different approaches.On one side, we have analyzed interesting models that can be implemented in superconducting circuits, a quantum platform where the USC regime can be naturally achieved.In particular, we focused on excitation transfer across USC impurities, entanglement generation via modulation of electrical boundary conditions and quantum state engineering in ultrastrongly-coupled systems.On the other hand, we have developed methods to reproduce the physics of light-matter interactions in the USC regime, by tailoring the Hamiltonian of atomic systems, like trapped ions and cold atoms.These proposals take profit of the specific features of such quantum platforms, in order to implement regimes and measurements that are not directly accessible.We believe that this Thesis will contribute to develop a thorough understanding of quantum phenomena related to the USC regime of light-matter interaction, and that it will foster the dialog between experimental and theoretical research in this area.I would like to thank first my PhD supervisor Prof. Enrique Solano, for his constant support and invaluable guidance.Countless thought-provoking discussions held with him during my PhD studies have contributed to develop my critical skills, and his advice has covered all facets of nowadays top-level research.
Ultrastrong coupling between light and matter has, in the past decade, transitioned from a theoretical idea to an experimental reality. It is a new regime of quantum light–matter interaction, which goes beyond weak and strong coupling to make the coupling strength comparable to the transition frequencies in the system. The achievement of weak and strong coupling has led to increased control of quantum systems and to applications such as lasers, quantum sensing, and quantum information processing. Here we review the theory of quantum systems with ultrastrong coupling, discussing entangled ground states with virtual excitations, new avenues for nonlinear optics, and connections to several important physical models. We also overview the multitude of experimental setups, including superconducting circuits, organic molecules, semiconductor polaritons, and optomechanical systems, that have now achieved ultrastrong coupling. We conclude by discussing the many potential applications that these achievements enable in physics and chemistry.
We propose a reliable scheme to simulate tunable and ultrastrong mixed (first-order and quadratic optomechanical couplings coexisting) optomechanical interactions in a coupled two-mode bosonic system, in which the two modes are coupled by a cross-Kerr interaction and one of the two modes is driven through both the single- and two-excitation processes. We show that the mixed-optomechanical interactions can enter the single-photon strong-coupling and even ultrastrong-coupling regimes. The strengths of both the first-order and quadratic optomechanical couplings can be controlled on demand, and hence first-order, quadratic, and mixed optomechanical models can be realized. In particular, the thermal noise of the driven mode can be suppressed totally by introducing a proper squeezed vacuum bath. We also study how to generate the superposition of coherent squeezed state and vacuum state based on the simulated interactions. The quantum coherence effect in the generated states is characterized by calculating the Wigner function in both the closed- and open-system cases. This work will pave the way to the observation and application of ultrastrong optomechanical effects in quantum simulators.