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Journal of the Korean Physical Society

Resonance fluorescence of ladder- and triangular-type three-level systems: Continuous coherent photon generation

Kwang Jun Ahn

Published Sep 15, 2017• 2 citations
Publisher

Abstract

We theoretically investigate resonance fluorescence of a ladder- and a triangular-type three-level atomic system in the full quantization regime. By solving Heisenberg’s quantum kinetic equations of motion of an electron interacting with photons and two coherent laser fields, we obtain the firstorder electric field correlation function, which corresponds to photoluminescence spectrum. When the single electrons in both systems are resonantly excited by two strong cw-laser fields, in contrast to the ladder-type atomic systems emitting mainly incoherent photons, the triangular-type system shows that continuous coherent photons can be selectively generated from three optical transitions by trapping electronic population inversions and manipulated by changing the transition rates.

DOI
10.3938/jkps.71.657

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We theoretically investigate resonance fluorescence of a ladder- and a triangular-type three-level atomic system in the full quantization regime. By solving Heisenberg’s quantum kinetic equations of motion of an electron interacting with photons and two coherent laser fields, we obtain the firstorder electric field correlation function, which corresponds to photoluminescence spectrum. When the single electrons in both systems are resonantly excited by two strong cw-laser fields, in contrast to the ladder-type atomic systems emitting mainly incoherent photons, the triangular-type system shows that continuous coherent photons can be selectively generated from three optical transitions by trapping electronic population inversions and manipulated by changing the transition rates.
A theoretical study is made of the steady-state intensity and squeezing properties of the fluorescent light from a three-level-atom system in a ladder configuration, which is subject to spontaneous-emission decay to the electromagnetic-field vacuum. Two cases are examined: in the equispaced (ES) level case, the two atomic transition frequencies are nearly equal and two photon absorption processes occur from a single coherent laser field that couples both transitions and has a small detuning from each; in the non- equispaced (NES) level case, the atomic transition frequencies are rather different and two photon absorption processes occur from two coherent laser fields, each coupled to a single transition and in near resonance with it. In both cases, a situation of small two-photon detuning occurs. Optical Bloch equations for the atomic density matrix in rotating frames are given and matrix expressions for determining the steady-state populations and coherences are obtained. Analytic expressions are also given for special cases. The fluorescent intensity is obtained from the populations of the intermediate and upper states, with the normally ordered variance (NOV) for quadrature components of the fluorescent field involving, in addition, the atomic coherences. The fluorescent intensities are shown graphically as a function of two-photon detuning for a variety of one-photon detunings and Rabi frequencies for the ES and NES cases.In both cases, the fluorescent intensities show the well known resonances from the upper state at zero two-photon detuning and from the intermediate state at zero one-photon detuning for the lower transition. However, further resonances are also found. The intermediate-state intensity displays a resonance at zero two-photon detuning. Also, the upper-state intensity shows a resonance at zero one-photon detuning for the upper transition, but only for the NES case; evidently, the transfer rate from upper to lower transition coherences destroys this resonance for the ES case. The time-averaged NOV is also shown graphically as a function of two-photon detuning for a variety of one-photon detunings and Rabi frequencies for the ES and NES cases. For the ES case, the quadrature frequency is chosen as the single laser frequency and for the NES case, it is chosen as either the average of the two laser frequencies or the lower transition laser frequency. Squeezing occurs near zero two-photon detuning for both ES and NES cases, though only for the quadrature frequency equal to the average laser frequency in the latter case. It also occurs near zero detuning for the lower transition for both cases, though only for the quadrature frequency equal to the lower transition laser frequency in the NES case. The squeezing minima show a splitting effect for large Rabi frequencies corresponding to two-photon or one-photon Rabi splitting of the dressed atom levels for the situation near two-photon or one-photon resonance, respectively. The large squeezing near two-photon resonance for moderate Rabi frequencies and large one-photon detuning corresponds to essentially pure three-level squeezing, while that near one-photon resonance for weak Rabi frequencies involves two-level squeezing.
We consider a three-level atomic system interacting with two coherent fields in the ladder configuration. Namely, the pumping field couples the ground and first excited state while the driving field interacts with the two excited states. The intensity spectrum of resonant optical fluorescence at the two-photon transition is studied. It is shown that coherent driving in this scheme allows for efficient control of fluorescence distribution between the one-photon (elastic with respect to pumping field) and two-photon (anti-Stoke Raman with respect to the driving field) channels.
Resonance fluorescence of two-level quantum systems has emerged as a powerful tool in quantum information processing. Extension of this approach to higher-level systems provides new opportunities for quantum optics applications. Here we introduce an all-optical tuning functionality into a well-established resonance fluorescence coherent driving scheme. We accomplish this by resonant excitation of a three-level ladder system with two laser fields utilizing Autler-Townes and ac Stark effects. We propose theoretically and demonstrate experimentally the feasibility of this approach toward all-optical spectral tuning of quantum-dot-based single-photon sources and investigate photon indistinguishability and purity levels. Our tuning technique allows for fast optical control of the quantum emitter spectrum which paves the way toward temporal and spectral shaping of the single photons, formation of topological Floquet states, or generation of high-dimensional frequency-encoded quantum states of light.
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.
We consider the possible physical processes that may arise in a three-level atom when only two of its levels interact with a strong electromagnetic field and when the atomic transition frequency is nearly equal to once and twice the frequency of the laser field, respectively. There have been found pronounced cooperative effects in the spectrum of the two-level system, which is in resonance with the laser field, arising from the presence of the third level. The excitation spectra describing the transitions from the first excited state into the second excited state and from that to the ground state consist, apart from the two central peaks, of two pairs of sidebands which are induced by the laser field of the neighbouring system. Detailed expressions of the spectral functions for the physical processes of one- and two-photon resonance fluorescence have been derived and discussed in the limit of high photon densities. The excitation spectrum of the low frequency modes has been considered and discussed in detail. It is found that quantum beats in spontaneous emission may appear in the spectra of the one- and two-photon resonance fluorescence arising from the interference between the two atomic transition frequencies and the frequency of the laser field. The importance of the low frequency modes that occur in the processes in question has been pointed out.