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ACS Photonics

Cavity QED in the Ultrastrong Coupling Regime: Photon Bunching from the Emission of Individual Dressed Qubits

Luigi Garziano, A. Ridolfo, Simone De Liberato, Salvatore Savasta

Published Aug 24, 2017• 39 citations
Publisher

Abstract

Photon antibunching in the light scattered by single quantum emitters is one of the hallmarks of quantum optics, providing an unequivocal demonstration of the quantized nature of the electromagnetic field. Antibunching can be intuitively understood by the need for a two-level system lying in its lower state after emitting a photon to be re-excited into the upper one before a second emission can take place. Here we show that such a picture breaks down in the ultrastrong light–matter coupling regime, when the coupling strength becomes comparable to the bare emitter frequency. Specializing to the cases of both a natural and an artificial atom, we thus show that a single emitter coupled to a photonic resonator can emit bunched light. The result presented herein is clear evidence of how the ultrastrong coupling regime is able to change the nature of individual atoms.

DOI
10.1021/acsphotonics.7b00635

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Photon antibunching in the light scattered by single quantum emitters is one of the hallmarks of quantum optics, providing an unequivocal demonstration of the quantized nature of the electromagnetic field. Antibunching can be intuitively understood by the need for a two-level system lying in its lower state after emitting a photon to be re-excited into the upper one before a second emission can take place. Here we show that such a picture breaks down in the ultrastrong light–matter coupling regime, when the coupling strength becomes comparable to the bare emitter frequency. Specializing to the cases of both a natural and an artificial atom, we thus show that a single emitter coupled to a photonic resonator can emit bunched light. The result presented herein is clear evidence of how the ultrastrong coupling regime is able to change the nature of individual atoms.
Photon antibunching in the light scattered by single quantum emitters is one of the hallmarks of quantum optics, providing an unequivocal demonstration of the quantized nature of the electromagnetic field. Antibunching can be intuitively understood by the need for a two-level system lying in its lower state after emitting a photon to be re-excited into the upper one before a second emission can take place. Here we show that such a picture breaks down in the ultrastrong light-matter coupling regime, when the coupling strength becomes comparable to the bare emitter frequency. Specialising to the cases of both a natural and a superconducting artificial atom, we thus show that a single emitter coupled to a photonic resonator can emit bunched light. The result presented herein is a clear evidence of how the ultrastrong coupling regime is able to change the nature of individual atoms.
Being bosons, photons like to group together, with the behavior of photon bunching described as an attribute of classical light. At the other extreme, photons emitted by a single emitter are expected to antibunch, trickling out of the emitter one at a time. Although bunching and antibunching are well established behaviors of classical and nonclassical light, respectively, the transition between the two has not been observed. It is expected that as the number of emitters is increased, a smooth transition should occur. Using a high-quality cavity into which they can place a variable number of atoms, Hennrich et al. show that they can probe the transition systematically as the number of emitters (atoms in the cavity) is gradually increased. They observe that the antibunching behavior disappears when the average number of atoms in the cavity is one, and they are able to explain the experimental data well if the emitters are assumed to form an independent ensemble. — ISO
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.
In quantum field theory, bare particles are dressed by a cloud of virtual particles to form physical particles. The virtual particles affect properties such as the mass and charge of the physical particles, and it is only these modified properties that can be measured in experiments, not the properties of the bare particles. The influence of virtual particles is prominent in the ultrastrong-coupling regime of cavity quantum electrodynamics (QED), which has recently been realised in several condensed-matter systems. In some of these systems, the effective interaction between atom-like transitions and the cavity photons can be switched on or off by external control pulses. This offers unprecedented possibilities for exploring quantum vacuum fluctuations and the relation between physical and bare particles. We consider a single three-level quantum system coupled to an optical resonator. Here we show that, by applying external electromagnetic pulses of suitable amplitude and frequency, each virtual photon dressing a physical excitation in cavity-QED systems can be converted into a physical observable photon, and back again. In this way, the hidden relationship between the bare and the physical excitations can be unravelled and becomes experimentally testable. The conversion between virtual and physical photons can be clearly pictured using Feynman diagrams with cut loops.
The interaction between quantized electromagnetic fields in cavities and natural or artificial atoms has played a crucial role in developing our understanding of light-matter interactions and quantum technologies.Recently, new regimes beyond the weak and strong light-matter coupling of cavity-QED have been explored in several settings, wherein the light-matter coupling rate becomes comparable to (ultrastrong coupling) or even exceeds (deep-strong coupling) the photon frequency.These ultrastrong coupling regimes can give rise to new physical effects and applications, and they challenge our understanding of cavity QED; fundamental issues like the proper definition of subsystems, their quantum measurements, the structure of light-matter ground states, and the analysis of time-dependent interactions are subject to gauge ambiguities that lead to even qualitatively distinct predictions.The resolution of these ambiguities is important for understanding and designing next-generation quantum devices that can operate in extreme coupling regimes.Here we discuss and provide solutions to these ambiguities by adopting an approach based on operational procedures involving measurements on the individual light and matter components of the interacting system.
We present a systematic study of the properties of systems composed of NNN 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 $(N\ensuremath{\rightarrow}\ensuremath{\infty})$. 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 NNN. Our analysis also clarifies the evolution of the system as the number of emitters increases, ultimately converging toward an equivalent system composed of two interacting single-mode bosonic fields.