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arXiv:1607.05062 · Physical Review A

Fate of photon blockade in the deep strong-coupling regime

Alexandre Le Boité, Myung-Joong Hwang, Hyunchul Nha, Martin Bodo Plenio

Published Sep 15, 2016• 75 citations
arXivHTMLPDF

Abstract

We investigate the photon emission properties of the driven-dissipative Rabi model in the so-called ultrastrong- and deep strong-coupling regimes where the atom-cavity coupling rate $g$ becomes comparable or larger than the cavity frequency ${\ensuremath{\omega}}_{c}$. By solving numerically the master equation in the dressed-state basis, we compute the output field correlation functions in the steady-state for a wide range of coupling rates. We find that, as the atom-cavity coupling strength increases, the system undergoes multiple transitions in the photon statistics. In particular, a first sharp antibunching-to-bunching transition, occurring at $g\ensuremath{\sim}0.45{\ensuremath{\omega}}_{c}$, leading to the breakdown of the photon blockade due to the counter-rotating terms, is shown to be the consequence of a parity shift in the energy spectrum. A subsequent revival of the photon blockade and the emergence of the quasicoherent statistics for even larger coupling rates are attributed to an interplay between the nonlinearity in the energy spectrum and the transition rates between the dressed states.

DOI
10.1103/physreva.94.033827

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We explore photon coincidence counting statistics in the ultrastrong coupling regime, where the atom-cavity coupling rate becomes comparable to the cavity resonance frequency. In this regime, usual normal order correlation functions fail to describe the output photon statistics. By expressing the electric-field operator in the cavity-emitter dressed basis, we are able to propose correlation functions that are valid for arbitrary degrees of light-matter interaction. Our results show that the standard photon blockade scenario is significantly modified for ultrastrong coupling. We observe parametric processes even for two-level emitters and temporal oscillations of intensity correlation functions at a frequency given by the ultrastrong photon emitter coupling. These effects can be traced back to the presence of two-photon cascade decays induced by counterrotating interaction terms.
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.
We explore the photon statistics of light emitted from a system comprising a single four-level atom strongly coupled to a high-finesse optical cavity mode that is driven by a coherent laser field. In the weak driving regime this system is found to exhibit a photon blockade effect. For intermediate driving strengths we find a sudden change in the photon statistics of the light emitted from the cavity. Photon antibunching switches to photon bunching over a very narrow range of intracavity photon number. It is proven that this sudden change in photon statistics occurs due to the existence of robust quantum interference of transitions between the dressed states of the atom-cavity system. Furthermore, it is shown that the strong photon bunching is a nonclassical effect for certain values of driving field strength, violating classical inequalities for field correlations.
We explore the photon statistics of light emitted from a system comprising a single four--level atom strongly coupled to a high-finesse optical cavity mode which is driven by a coherent laser field. In the weak driving regime this system is found to exhibit a photon blockade effect. For intermediate driving strengths we find a sudden change in the photon statistics of the light emitted from the cavity. Photon antibunching switches to photon bunching over a very narrow range of intracavity photon number. It is proven that this sudden change in photon statistics occurs due to the existence of robust quantum interference of transitions between the dressed states of the atom-cavity system. Furthermore, it is shown that the strong photon bunching is a nonclassical effect for certain values of driving field strength, violating classical inequalities for field correlations.
We consider a generalized version of the Rabi model that includes a nonlinear, dispersive-type atom-field interaction in addition to the usual linear dipole coupling, as well as cavity dissipation. An effective system of this sort arises, for example, in a quantum simulation of the Rabi model based upon Raman transitions in an optical cavity QED setting [A. L. Grimsmo and S. Parkins, Phys. Rev. A 87, 033814 (2013)]. For a range of the nonlinear interaction strength about a special value, degeneracies or near degeneracies of the states in the cavity-mode vacuum and single-photon subspaces, in combination with cavity loss, gives rise to an essentially closed cycle of excitations and photon emissions within these subspaces. Consequently, the cavity output field is strongly antibunched, while over this range of nonlinear strengths the atomic population undergoes an abrupt inversion. We develop a quantum-trajectory-based description of the system that models its key properties very well, and use a simple dressed-state picture to explain the novel structure of the cavity fluorescence spectrum. We also present numerical results for a potential realization of the system using a rubidium atom coupled strongly to a high-finesse optical cavity mode.
Frequency-resolved photon emission is central to applications from quantum information encoding to high-resolution spectroscopy, and then studying their correlations is therefore essential for revealing the underlying emission pathways and multiphoton statistics. Here, we investigate frequency-resolved N-photon correlations in an ultrastrongly coupled cavity QED system where a qubit interacts with a single-mode cavity. Owing to counter-rotating interactions, the eigenstates and energy spectrum are strongly modified, giving rise to rich spectral and statistical properties in the emitted frequency-resolved photons. Through frequency-selective detection, we reveal pronounced multiphoton antibunching, as well as multiphoton bunching originating from cascade transitions among dressed eigenstates. In particular, we show that parity symmetry plays a decisive role in shaping these correlations. The symmetry-breaking opens additional transition channels and dramatically enhances the generation of correlated photon pairs and even photon triplets of different frequencies. Our work extends frequency-resolved correlations to the ultra-strong coupling regime and demonstrates their potential as a sensitive probe of symmetry in light-matter interaction systems.