Strong and ultra-strong light-matter coupling are remarkable phenomena of quantum electrodynamics arising when a matter excitation interacts so strongly with the electromagnetic field that the two systems cannot be distinguished as in usual perturbation theory. This is generally achieved by coupling an excitation with large oscillator strength to the confined electromagnetic mode of an optical microcavity. In this work we report on a phenomenon of non-perturbative spontaneous emission taking place in the absence of optical confinement, when a collective electronic excitation superradiantly decays into free space radiation. By using a quantum model based on the input-output formalism, we calculate the linear optical properties of a dense electron gas displaying superradiant excitations. We show that the commonly used rotating-wave and Markov approximations yield unphysical results when the radiative broadening is comparable to the matter excitation energy, i.e. in the ultra-strong coupling regime. Our formalism also allows computing the electron gas thermal emission, showing that Kirchhoff's law applies in all the regimes of light-matter interaction.
Strong and ultra-strong light-matter coupling are remarkable phenomena of quantum electrodynamics arising when a matter excitation interacts so strongly with the electromagnetic field that the two systems cannot be distinguished as in usual perturbation theory. This is generally achieved by coupling an excitation with large oscillator strength to the confined electromagnetic mode of an optical microcavity. In this work we report on a phenomenon of non-perturbative spontaneous emission taking place in the absence of optical confinement, when a collective electronic excitation superradiantly decays into free space radiation. By using a quantum model based on the input-output formalism, we calculate the linear optical properties of a dense electron gas displaying superradiant excitations. We show that the commonly used rotating-wave and Markov approximations yield unphysical results when the radiative broadening is comparable to the matter excitation energy, i.e. in the ultra-strong coupling regime. Our formalism also allows computing the electron gas thermal emission, showing that Kirchhoff's law applies in all the regimes of light-matter interaction.
The interaction of confined atoms with a single mode radiation field is the main subject in the theory of cavity quantum electrodynamics . The constraints imposed by the cavity on matter and radiation fields give rise to collective phenomena. One possible outcome is the enhanced and coherent spontaneous emission of photons by the atoms: the superradiance. As predicted by Dicke, conservation laws are essential in superradiance and are derived from the matter-interaction Hamiltonian . Here, we consider N two-level ultracold atoms interacting with a single mode bosonic field, in the Dicke Hamiltonian, and trapped inside a non-dissipative optical cavity . Numerical and analytical results derived from finite size regime indicate the matter–radiation coupling strength, λ , is insufficient to draw the complete picture of the system. Instead, they support the relevance of U ( 1 ) symmetry, which prompts the study of (i) particle and angular momentum conservation, (ii) the constraints imposed to correlation functions and (iii) the influence of symmetries in the system dynamics . Further exploring the U ( 1 ) and rotational symmetries permits a simple interpretation of antirotating contributions as spin–orbit operators. As application, we show two species of ultracold clouds develop interactions due to antirotating operators.
Recent technological developments have made it increasingly easy to access the non-perturbative regimes of cavity quantum electrodynamics known as ultrastrong or deep strong coupling, where the light-matter coupling becomes comparable to the bare modal frequencies. In this work, we address the adequacy of the broadly used single-mode cavity approximation to describe such regimes. We demonstrate that, in the non-perturbative light-matter coupling regimes, the single-mode models become unphysical, allowing for superluminal signalling. Moreover, considering the specific example of the quantum Rabi model, we show that the multi-mode description of the electromagnetic field, necessary to account for light propagation at finite speed, yields physical observables that differ radically from their single-mode counterparts already for moderate values of the coupling. Our multi-mode analysis also reveals phenomena of fundamental interest on the dynamics of the intracavity electric field, where a free photonic wavefront and a bound state of virtual photons are shown to coexist.
Abstract Recent technological developments have made it increasingly easy to access the non-perturbative regimes of cavity quantum electrodynamics known as ultrastrong or deep strong coupling, where the light–matter coupling becomes comparable to the bare modal frequencies. In this work, we address the adequacy of the broadly used single-mode cavity approximation to describe such regimes. We demonstrate that, in the non-perturbative light–matter coupling regimes, the single-mode models become unphysical, allowing for superluminal signalling. Moreover, considering the specific example of the quantum Rabi model, we show that the multi-mode description of the electromagnetic field, necessary to account for light propagation at finite speed, yields physical observables that differ radically from their single-mode counterparts already for moderate values of the coupling. Our multi-mode analysis also reveals phenomena of fundamental interest on the dynamics of the intracavity electric field, where a free photonic wavefront and a bound state of virtual photons are shown to coexist.
Improvements in both the photonic confinement and the emitter design have led to a steady increase in the strength of the light-matter coupling in cavity quantum electrodynamics experiments. This has allowed us to access interaction-dominated regimes in which the state of the system can only be described in terms of mixed light-matter excitations. Here we show that, when the coupling between light and matter becomes strong enough, this picture breaks down, and light and matter degrees of freedom totally decouple. A striking consequence of such a counterintuitive phenomenon is that the Purcell effect is reversed and the spontaneous emission rate, usually thought to increase with the light-matter coupling strength, plummets instead for large enough couplings.
In nanostructures where confinement of a light wave is manifested, the conditions of strong light–matter interaction become feasible. In this case, the approach based on the environment-sensitive probability of quantum transitions is no longer applicable. Instead, joint states of light and matter should be considered and their time evolution explored. The content of the previous Chapters 13 and 14 can then be treated as a perturbative description of light–matter interactions with a limited range of applicability. In this chapter a few representative examples are given where joint light–matter states bring an unprecedented flavor of nanophotonic engineering to frozen excited states for quantum memory devices and single photon sources for quantum computing. Cavity quantum electrodynamics in the strong coupling regime The regime of strong coupling of a quantum system with an electromagnetic field can be performed in a cavity with very high Q-factor, where light can survive for a reasonable time until it either leaves the cavity or dies through being absorbed by cavity imperfections. In a simplified picture, a photon once emitted stays within the cavity so long that it is absorbed again by the emitter (an imaginary two-level system, an atom or a quantum dot). Thus spontaneous emission appears to become reversible. In a more accurate presentation, an “atom+field” state develops which evolves via oscillations between the state | E , 0〉 (“excited atom, depleted cavity”) to the state | G , 1〉 (“de-excited atom, a photon in the cavity”).
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.