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arXiv:2009.13388 · Optics Communications

Second-order coherence of fluorescence in multi-photon blockade

Th. K. Mavrogordatos, Cristóbal Lledó

Published Jan 13, 2021• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1016/j.optcom.2021.126791

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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.
We explore the role of quantum fluctuations in the strong-coupling limit of the dissipative Jaynes–Cummings oscillator driven on resonance. For weak excitation, we derive analytical expressions for the spectrum and the intensity correlation function for the photons scattered by the two-state atom coupled to the coherently driven cavity mode. We do so by writing down a birth–death process adding the higher orders in the excitation strength needed to go beyond the pure-state factorization, following the method introduced in Carmichael (2008). Our results for the first and second-order correlation functions are complemented by the numerical investigation of the waiting-time distribution for the photon emissions directed sideways, and the comparison with ordinary resonance fluorescence. To close out our discussion, we increase the driving field amplitude and approach the critical point organizing a second-order dissipative quantum phase transition by depicting the excitation pathways in the intracavity field distribution for a finite system size.
We study multiphoton blockade and photon-induced tunneling effects in the two-photon Jaynes-Cummings model, where a single-mode cavity field and a two-level atom are coupled via a two-photon interaction. We consider both the cavity-field-driving and the atom-driving cases and find that single-photon blockade and photon-induced tunneling effects can be observed when the cavity mode is driven, while the two-photon blockade effect appears when the atom is driven. For the atom-driving case (the two-photon transition process), we present a criterion of the correlation functions for the multiphoton blockade effect. Specifically, we show that quantum interference can enhance the photon blockade effect in the single-photon cavity-field-driving case. Our results are confirmed by analytically and numerically calculating the correlation function of the cavity-field mode. Our work has potential applications in quantum information processing and paves the way for the study of multiphoton quantum coherent devices.
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 propose a reliable scheme to recover the conventional photon blockade effect in the dispersive Jaynes-Cummings model, which describes a two-level atom coupled to a single-mode cavity field in the large-detuning regime. This is achieved by introducing a transversal driving to the atom and then photonic nonlinearity is obtained. The eigenenergy spectrum of the system is derived analytically and the photon blockade effect is confirmed by numerically calculating the photon-number distributions and equal-time second-order correlation function of the cavity field in the presence of system dissipations. We find that the conventional photon blockade effect can be recovered at proper atomic and cavity-field drivings. This work will provide a method to generate the conventional photon blockade effect in the dispersively coupled quantum optical systems.
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 explore a method for achieving photon blockade (PB) through a two-photon Jaynes-Cummings (JC) model that includes both cavity and atom drivings. Analytical expressions for the steady state are derived to calculate photon-number distribution and correlation functions. Based on this analysis, we establish the theoretical conditions required for generating PB by controlling both drivings and propose a scheme to identify conventional photon blockade (CPB) and unconventional photon blockade (UPB) by analyzing the second- and third-order correlation functions. We validate our findings through numerical simulations conducted in an artificial atom system. We discuss two cases, one in which the transition frequency of the two-level atom is in two-photon resonance with the cavity frequency and the other in which it is off-resonance. We observe a significant interplay between CPB and UPB effects in the resonant case. In the off-resonance case, we demonstrate that UPB can be achieved by manipulating the strengths of atom driving and cavity driving to satisfy a specific relationship while meeting the requirements for optimal detuning relations. This work provides essential insights into controlling the PB effect using the two-photon JC model with both the atom and cavity drivings.