Abstract
We address the consequences of backaction in the unidirectional coupling of two cascaded open quantum subsystems connected to the same reservoir at different spatial locations. In the spirit of [H. J. Carmichael, Phys. Rev. Lett. 70, 2273 (1993)], the second subsystem is a two-level atom, while the first transforms from a driven empty cavity to a perturbative QED configuration and ultimately to a driven Jaynes-Cummings (JC) oscillator through a varying light-matter coupling strength. For our purpose, we appeal at first to the properties of resonance fluorescence in the statistical description of radiation emitted along two channels -- those of forwards and sideways scattering -- comprising the monitored output. In the simplest case of an empty cavity coupled to an external atom, we derive analytical results for the nonclassical fluctuations in the fields occupying the two channels, pursuing a mapping to the bad-cavity limit of the JC model to serve as a guide for the description of the more involved dynamics. Finally, we exemplify a conditional evolution for the composite system of a critical JC oscillator on resonance coupled to an external monitored two-level target, showing that coherent atomic oscillations of the target probe the onset of a second-order dissipative quantum phase transition in the source.
Highlights
The late 1980s and early 1990s witnessed the development of the formalism for describing the statistical properties of light emitted from a quantum system, driven by another nonclassical source [1,2,3,4,5]
We have derived analytical results for the statistics of the forward and sideways emission channel by means of a mapping to an atom inside the coherently driven cavity coupled to the supported resonant mode with a strength determined by the dissipation rates of the initial cascadedsystem configuration
We at first set to zero the coupling strength between the cavity and the two-level atom comprising the JC oscillator, developing a treatment which relied on several well-known results from ordinary resonance fluorescence and the bad-cavity limit of quantum electrodynamics (QED)
Summary
The late 1980s and early 1990s witnessed the development of the formalism for describing the statistical properties of light emitted from a quantum system, driven by another nonclassical source [1,2,3,4,5]. The breakdown of photon blockade in zero dimensions [14], which was experimentally demonstrated in [15], is associated with a distinct presence of quantum nonlinearity leading to a definition of a strong-coupling “thermodynamic limit,” where fluctuations persist, while the mean-field and quantum predictions manifestly disagree Such an√out-ofequilibrium phase transition probes the paradigmatic n nonlinearity of the Jaynes-Cummings (JC) oscillator [16], which has been revealed in a series of experiments in cavity and circuit QED (see, e.g., [17] and [18]). Some brief comments on our results and extension to future work close out the paper
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