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arXiv:1603.04984 · New Journal of Physics

Feynman-diagrams approach to the quantum Rabi model for ultrastrong cavity QED: stimulated emission and reabsorption of virtual particles dressing a physical excitation

Omar Di Stefano, Roberto Stassi, Luigi Garziano, Anton Frisk Kockum, Salvatore Savasta, Franco Nori

Published Apr 12, 2017• 60 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/aa6cd7

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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.
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.
We present an interaction scheme that exhibits a dynamical effect of virtual photons carried by a vacuum-field dressed two-level atom in the ultrastrong-coupling regime. We show that, with the aid of an external driving field, virtual photons provide a transition matrix element that enables the atom to evolve coherently and reversibly to an auxiliary level accompanied by the emission of a real photon. The process corresponds to a type of vacuum Rabi oscillation, and we show that the effective vacuum Rabi frequency is proportional to the amplitude of a single virtual photon in the ground state. Therefore, the interaction scheme could serve as a probe of ground-state structures in the ultrastrong-coupling regime.
The ultrastrong coupling regime has emerged as a fascinating and distinctive phenomenon in cavity-QED and light-matter interactions, where the occupation of virtual excitations (e.g., photons) is possible in vacuum, which is a consequence of counter-rotating wave effects and breaking U(1) symmetry. However, an ongoing challenge is how to convert these virtual photons into real photons. We will first discuss how to “Floquet engineer” the quantum Rabi model for a two-level system coupled to a quantized cavity mode, under periodic modulation of the cavity-dipole coupling rate, leading to rich Floquet states. Exploiting the quantum vacuum, in the ultrastrong coupling regime, we show how purely mechanical driving can produce real photons. These periodic driving schemes are promising for the coherent manipulation of hybrid quantum systems and quantum vacuum effects, with applications for quantum state engineering and the study of nonequilibrium quantum phenomena.
Specific properties of quantum field theory are described by considering the combination of the system under investigation and the cloud of virtual or real particles associated with the field. Such a structure is called a “dressed system”, in contrast with the bare one in the absence of the interaction with the field. The description of the properties of such clouds in various physical situations is, today, an active research area. Here, we present the main features associated with virtual and real dressings, focusing on photon dressing. In analogy to virtual photon clouds dressing electrons in vacuum, virtual phonon clouds appear in solid-state physics. The interaction between real photons and the schematized two-level structure of an atom paves the way to flexible quantum control. Here, a unifying Floquet engineering approach is applied to describe single- and multiple-dressed atom configurations. Connections with the past and present atomic physics experiments are presented.
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.
We study the extracavity quantum vacuum radiation generated by a sudden switch on and off of the vacuum Rabi frequency of a single two-level system coupled to a single cavity mode in the strong and ultrastrong coupling regime. Dissipation is described by including the qubit-resonator coupling in the derivation of the master equation. The output stream of photons and their second-order correlation functions are calculated by exploiting a recently developed input-output formulation of resonators valid for arbitrary light-matter couplings. The obtained output photon correlations provide direct information on the quantum correlations among the virtual excitations of the dressed vacuum.