Spontaneous Conversion from Virtual to Real Photons in the Ultrastrong-Coupling Regime

Abstract

We show that a spontaneous release of virtual photon pairs can occur in a quantum optical system in the ultrastrong coupling regime. In this regime, which is attracting interest both in semiconductor and superconducting systems, the light-matter coupling rate ΩR becomes comparable to the bare resonance frequency of photons ω0. In contrast to the dynamical Casimir effect and other pair creation mechanisms, this phenomenon does not require external forces or time dependent parameters in the Hamiltonian.PACS numbers: 42.50. Pq, 03.70.+k, 03.65.Yz One of the most surprising predictions of modern quantum theory is that the vacuum of space is not empty but filled with a sea of virtual particles. These short-lived fluctuations are the origin of some of the most important physical processes in the universe. A quite direct evidence of the existence of such virtual particles is provided by the dynamical Casimir effect (DCE). It predicts that rapid modulations of the boundary conditions of a quantum field induce vacuum amplification effects that result in the creation of real particles out of vacuum fluctuations. The DCE [1] has been recently experimentally realized in superconducting circuits [2,3]. Other proposed vacuum amplification mechanisms [4], as the Schwinger process [5] and the Hawking radiation [6], require the presence of huge external fields or, as the Unruh effect, the presence of a rapidly nonuniformly accelerating observer [7], and still await observation. In this Letter we consider a three level emitter where the transition between the two upper levels couples ultrastrongly to a cavity mode and show that the spontaneous relaxation of the emitter from its intermediate to its ground state is accompanied by the creation of photons in the cavity mode (see Fig. 1).The Hamiltonian of a realistic atom-cavity system contains so-called counter-rotating terms allowing the simultaneous creation or annihilation of an excitation in both atom and cavity mode. These terms can be safely neglected for small coupling rates Ω R in the so called rotating-wave approximation (RWA). However, when Ω R becomes comparable to the cavity resonance frequency of the emitter or the resonance frequency of the cavity mode, the counter-rotating terms are expected to manifest, giving rise to exciting effects in cavity-QED [8][9][10][11]. This ultrastrong-coupling (USC) regime is difficult to reach in quantum-optical cavity-QED, but was recently realized in a variety of solid-state quantum systems [10,[12][13][14][15]. Such regime is challenging from a theoretical point of view as the total number of excitations in the cavity-emitter system is not preserved, even though its parity is [9]. It has been shown that, in the USC regime, the quantum optical master equation fails to provide the correct description of the system's interaction with reservoirs [16]. Moreover quantum optical normal order correlation functions fail to describe photodetection experiments for such systems [17,18]. Specifically, for a single mode resonator, the photon r...

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“…(11). We should note that the Lamb-Dicke parameter η can become very large in circuit QED systems in the ultrastrong [71][72][73] and deep-strong [74][75][76][77] coupling regime. Our discussion below is in the ultrastrong coupling, but can be straightforwardly extended to the deep-strong coupling regime.…”

Photon correlations from ultrastrong optical nonlinearities

“…This solution relies on w [11][01] and w [11][10], which can be expressed in terms of four lower-order correlators:…”

“…The characterization of the physics of optically ultranonlinear devices is therefore a very timely question of high interest [8][9][10][11]. Here we investigate the output photon statistics of optical nonlinearities for the regime where the anharmonicity of their frequency spectrum becomes comparable to the frequency of single photons.…”

On-chip photonic transistor based on the spike synchronization in circuit QED

“…Input-output relations in the ultrastrong coupling regime makes the multiphoton transitions possible in three-level cascaded atomic system. Conversion of the virtual photons into real photons is succeeded by suitable designs of the Hamiltonians of the cascaded three-level atoms supporting the dark states [40][41][42][43]. In the presence of atomic transitions, Waveguide-QED systems reveal the importance of the correlation functions in describing the output cavity fields by relating the scattering theory and input output formalism of single and few photon transportation [44][45][46].…”

“…Interactions between the cavities is described by the hoping term corresponding to the atomic transitions in the lowest lying states of the artificial atom [39]. Input/output formalism is employed to describe the extracavity emission in terms of the quadrature operators in the absence of the input field [40][41][42][43]. Two frequency JT hamiltonian is described as the interaction of the bright and dark polaritons and diagonalized in terms of the upper and lower polariton components.…”