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Journal de physique

Correlation signals in resonance fluorescence : interpretation via photon scattering amplitudes

Jean Dalibard, Serge Reynaud

Published Jan 1, 1983• 85 citations
Publisher

Abstract

Resonance fluorescence is treated as a collision process where incident laser photons are scattered by an atom. Correlation signals are extracted from an expansion to the second order of the post collision field state. Photon antibunching effect appears as a quantum interference between all the possible scattering amplitudes. When Rayleigh photons are rejected, some amplitudes vanish, leading to a bunching behaviour.

DOI
10.1051/jphys:0198300440120133700

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Resonance fluorescence is treated as a collision process where incident laser photons are scattered by an atom. Correlation signals are extracted from an expansion to the second order of the post collision field state. Photon antibunching effect appears as a quantum interference between all the possible scattering amplitudes. When Rayleigh photons are rejected, some amplitudes vanish, leading to a bunching behaviour.
Resonance fluorescence arises from the coherent interaction of laser light with a two-level system and constitutes a quantum light source exhibiting single-photon emission and antibunching, making it a fundamental building block for future quantum networks. Our recent work [Nat. Commun.16, 6453 (2025)10.1038/s41467-025-61884-x] demonstrates that under continuous-wave excitation and in the absence of pure dephasing, the single-time joint state of resonance fluorescence and the two-level system can be described by a pure entangled state. Here, we analyze the cross-correlation and auto-correlation properties of the quantum optical field generated by the interference of resonance fluorescence with laser light at the resonance excitation frequency. Simulation results indicate that by varying the intensity or phase of the interfering laser light, the higher-order coherence of the post-interference quantum optical field transitions from anti-bunching to super-bunching behavior, consistent with recent theoretical and experimental advances by mean-field engineering. This approach offers a complementary framework to characterize and manipulate the multiphoton quantum optical fields.
The cooperative resonance fluorescence radiation from two atoms separated by an arbitrary distance and driven by a coherent laser field is studied, taking into account the dipole-dipole near-field interaction. The steady-state total scattering intensity, as a function of laser frequency and field strength, differs considerably from the single-atom one for sufficiently small distances. Photon bunching and antibunching occur in the scattered radiation depending on the laser frequency. Practically a full antibunching effect is found, especially if the laser is tuned to resonance with a transition frequency of the two-atom system. This is in contrast to a recent result of Agarwal et al., who studied the two-atom system but neglected the frequency splitting due to the dipole-dipole near-field interaction.
The authors give a theoretical description of the spectrally resolved intensity correlations of an electromagnetic field, in analogy with the definition of the physical time-dependent spectrum. The results are applied to evaluate the time correlations between the three lines in the spectrum of resonance fluorescence of a two-level atom. The authors include the possibility of a finite bandwidth of the incident radiation, and they allow for collisions with perturber atoms. Photons in the central Rayleigh line are emitted in a fully random fashion, without any correlation with previous or subsequent emissions. Two photons from the same sideband display antibunching in time, whereas two photons from opposite sidebands tend to bunch with a strong asymmetry in time. The effect of collisions and of a finite bandwidth is to diminish this asymmetry.
We suggest that the statistical properties of the scattered radiation in resonance-fluorescence experiments may be affected significantly by the existence of atomic correlations. The scattered light spectrum from two- and three-atom collective systems has been calculated and compared with the one-atom spectrum. The differences are quite significant for weak fields, but become less pronounced as the intensity of the driving field is increased. In addition, we have calculated the scattered intensity correlation function for collectively interacting systems, and found that its behavior is very different from that of the single-atom intensity correlation function, both for weak and strong incident fields. The implications of our findings for the observation of photon antibunching are also discussed.
Resonance fluorescence has played a major role in quantum optics with predictions and later experimental confirmation of nonclassical features of its emitted light such as antibunching or squeezing. In the Rayleigh regime where most of the light originates from the scattering of photons with subnatural linewidth, antibunching would appear to coexist with sharp spectral lines. Here, we demonstrate that this simultaneous observation of subnatural linewidth and antibunching is not possible with simple resonant excitation. Using an epitaxial quantum dot for the two-level system, we independently confirm the single-photon character and subnatural linewidth by demonstrating antibunching in a Hanbury Brown and Twiss type setup and using high-resolution spectroscopy, respectively. However, when filtering the coherently scattered photons with filter bandwidths on the order of the homogeneous linewidth of the excited state of the two-level system, the antibunching dip vanishes in the correlation measurement. Our observation is explained by antibunching originating from photon-interferences between the coherent scattering and a weak incoherent signal in a skewed squeezed state. This prefigures schemes to achieve simultaneous subnatural linewidth and antibunched emission.
Resonance fluorescence of a two-level emitter displays persistently anti-bunching irrespective of the excitation intensity, but inherits the driving laser’s linewidth under weak monochromatic excitation. These properties are commonly explained in terms of two disjoined pictures, i.e., the emitter’s single photon saturation or passively scattering light. Here, we propose a unified model that treats all fluorescence photons as spontaneous emission, one at a time, and can explain simultaneously both the spectral and correlation properties of the emission. We theoretically derive the excitation power dependencies, measurable at the single-photon incidence level, of the first-order coherence of the whole resonance fluorescence and super-bunching of the spectrally filtered, followed by experimental confirmation on a semiconductor quantum dot micro-pillar device. Furthermore, our model explains peculiar coincidence bunching observed in phase-dependent two-photon interference experiments. Our work provides an intuitive understanding of coherent light-matter interaction and may stimulate new applications. Standard descriptions of resonance fluorescence consider either absorption and re-emission in a single-photon picture or passive scattering. This study shows that resonance fluorescence can be described by a pure quantum state of the emitter and photon, revealing a coherent superposition that challenges the conventional view of spontaneous emission as an incoherent process.