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arXiv:2405.13597 · Journal of the Optical Society of America B

Quantum-fluctuation asymmetry in multiphoton Jaynes–Cummings resonances

Th. K. Mavrogordatos

Published May 28, 2024• 2 citations
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Abstract

We explore the statistical behavior of the light emanating from a coherently driven Jaynes–Cummings (JC) oscillator operating in the regime of multiphoton blockade with two monitored output channels causing the loss of coherence at equal rates. We do so by adopting an operational approach that draws the particle and wave aspects of the forward-scattered radiation together, building upon the relationship between quantum optical correlation functions and conditional measurements. We first derive an analytical expression of the intensity cross-correlation function at the peak of the two-photon JC resonance to demonstrate the breakdown of detailed balance. The application of the quantum trajectory theory in parallel with the quantum regression formula subsequently uncovers various aspects of temporal asymmetry in the quantum fluctuations characterizing the cascaded process through which a multiphoton resonance is established and read out. We find that monitoring different quadratures of the cavity field in conditional homodyne detection affects the times waited between successive photon counter “clicks,” which in turn trigger the sampling of the homodyne current. Despite the fact that the steady-state cavity occupation is of the order of a photon, monitoring of the developing bimodality also impacts the ratio between the emissions directed along the two decoherence channels.

DOI
10.1364/josab.523720

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We explore the statistical behavior of the light emanating from a coherently driven Jaynes–Cummings (JC) oscillator operating in the regime of multiphoton blockade with two monitored output channels causing the loss of coherence at equal rates. We do so by adopting an operational approach that draws the particle and wave aspects of the forward-scattered radiation together, building upon the relationship between quantum optical correlation functions and conditional measurements. We first derive an analytical expression of the intensity cross-correlation function at the peak of the two-photon JC resonance to demonstrate the breakdown of detailed balance. The application of the quantum trajectory theory in parallel with the quantum regression formula subsequently uncovers various aspects of temporal asymmetry in the quantum fluctuations characterizing the cascaded process through which a multiphoton resonance is established and read out. We find that monitoring different quadratures of the cavity field in conditional homodyne detection affects the times waited between successive photon counter “clicks,” which in turn trigger the sampling of the homodyne current. Despite the fact that the steady-state cavity occupation is of the order of a photon, monitoring of the developing bimodality also impacts the ratio between the emissions directed along the two decoherence channels.
We discuss the conditional measurement of field amplitudes by a nonclassical photon sequence in the Jaynes-Cummings (JC) model under multiphoton operation. We do so by employing a correlator of immediate experimental relevance to reveal a distinct nonclassical evolution in the spirit of Foster []. The correlator relies on the complementary nature of the pictures obtained from different unravelings of a JC source master equation. We demonstrate that direct photodetection entails a conditioned separation of timescales, a quantum beat, and a semiclassical oscillation, produced by the coherent light-matter interaction in its strong-coupling limit. We single out the quantum beat in the analytical expression for the waiting-time distribution, pertaining to the particle nature of the scattered light, and find a negative spectrum of quadrature amplitude squeezing, characteristic of its wave nature for certain operation settings. Finally, we jointly detect the dual aspects through the wave-particle correlator, showing an asymmetric regression of fluctuations to the steady state which depends on the quadrature amplitude being measured. Published by the American Physical Society 2024
Abstract We operationally uncover aspects of wave/particle duality for the open driven Jaynes–Cummings (JC) model in its strong-coupling limit. We lay special emphasis on the vacuum Rabi resonance, and determine the corresponding normalized intensity-field correlation function via mapping to ordinary resonance fluorescence. We demonstrate that temporal wave–particle fluctuations of light emanating from an established vacuum Rabi resonance are explicitly non-classical, while the limit of vanishing spontaneous emission restores detailed balance. When photon blockade sets in, individual realizations show a rapidly increasing frequency of fluctuations towards the two-photon resonance, arising as a direct consequence of a resolved JC spectrum. About the two-photon resonance peak, spontaneous emissions are more likely to revive a high-frequency quantum beat in the conditioned electromagnetic field amplitude than photons escaping out of the cavity mode. The beat originates from a coherent superposition of the first excited JC couplet states, and sets the background against which nonclassical phase shifts are observed in the conditioned quadrature amplitudes. We also find that the onset of steady-state bimodality reduces the variation of the normalized intensity-field correlation, at the expense of its temporal symmetry.
We show that the saturation of a multiphoton transition is accompanied by a gradual collapse of quantum multimodality in the strong-coupling limit of the weakly driven Jaynes-Cummings (JC) model. By means of a perturbative method, we illustrate the prominent role of quantum fluctuations by focusing on the two- and three-photon resonance operation in a regime where the steady-state average photon number is below or marginally above unity. We also reveal two coexistent quantum beats in the intensity correlation function of the forwards scattered photons. These beats, originating from the states mediating the cascaded decay, arise as a direct consequence of the distinct JC spectrum. Their interference coordinates with the alternation of positive and negative values of the Wigner function around the phase-space origin in the transient conditioned on a photodetection.
We address the consequences of back action 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 forward 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.
We calculate the cavity-field distribution in the Wigner representation for the two-photon resonance of the weakly driven Jaynes-Cummings (JC) oscillator in its strong-coupling limit. Using an effective four-level system, we analytically demonstrate the presence of steady-state and transient bimodality which breaks azimuthal symmetry in phase space. The two steady-state peaks are located at opposite positions and do not correspond to the two-photon amplitude of the driven transition. The developing bimodality is portrayed in parallel with the evolution of the intensity correlation function for the forward-scattered photons, before being finally contrasted to the few-photon steady-state and transient phase-space profiles for the cavity mode in the JC model driven on resonance.
We calculate the second-order correlation function for the atomic fluorescence in the two-photon resonance operation of a driven dissipative Jaynes–Cummings oscillator. We employ a minimal four-level model comprising the driven two-photon transition alongside two intermediate states visited in the dissipative cascaded process, in the spirit of Shamailov et al. (2010). We point to the difference between the output of a JC oscillator exhibiting two-photon blockade and the scattered field of ordinary resonance fluorescence, and discuss the quantum interference effect involving the intermediate states, which is also captured in the axially transmitted light. The spectrum and intensity correlation of atomic emission explicitly reflect the particulars of the cascaded model.