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arXiv:2610.09776

Stimulated emission for a three-level artificial atom in waveguide quantum electrodynamics

O. A. Chuikin, Ya. S. Greenberg, V. V. Taravkova, O. V. Kibis

quant-phSubmitted Oct 7, 2026• Announced Oct 8, 2026• 0 citations
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Abstract

This work is devoted to a theoretical study of the interaction of a quantum three-level ladder system with a continuous electromagnetic field in a one-dimensional open waveguide. We consider a situation closely resembling stimulated emission - the scattering of a single-photon exponential pulse by an excited three-level emitter. Using the real-space formalism, we obtain an analytical expression for the wavefunction of our system. We show that, for the low anharmonicity of a three-level system inherent to a transmon (the most common type of artificial atom), the influence of the third level can have a significant effect on the system's behavior. Namely, the presence of the third level largely suppresses the stimulated emission effect if the relative anharmonicity is lower than $| α_r | < 4\%$. However, for a three-level system, it is possible to obtain correlation effects such as photon bunching in the reflected field, which can also be 'switched off' by tuning the incident photon parameters.

Comments
10 pages, 8 figures

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This work is devoted to a theoretical study of the interaction of a quantum three-level ladder system with a continuous electromagnetic field in a one-dimensional open waveguide. We consider a situation closely resembling stimulated emission - the scattering of a single-photon exponential pulse by an excited three-level emitter. Using the real-space formalism, we obtain an analytical expression for the wavefunction of our system. We show that, for the low anharmonicity of a three-level system inherent to a transmon (the most common type of artificial atom), the influence of the third level can have a significant effect on the system's behavior. Namely, the presence of the third level largely suppresses the stimulated emission effect if the relative anharmonicity is lower than ∣αr∣<4%| α_r | < 4\%∣αr​∣<4%. However, for a three-level system, it is possible to obtain correlation effects such as photon bunching in the reflected field, which can also be 'switched off' by tuning the incident photon parameters.
We study the dynamical and spectral characteristics of a quantum three-level ladder system, interacting with a continuous electromagnetic field in one-dimensional open waveguide. Common realization of such systems is a waveguide QED setup - a superconducting artificial atom (transmon), coupled to an open microwave transmission line. We derive an analytical solution for spontaneous emission of initially excited atom, and use it to study the probability of state detection and spectral density of output photon states. We find that for strong coupling of transmon to a waveguide emitted photons show correlation in frequency and can have the same energies, even if the three-level system is anharmonic.
Usually it is assumed that the stimulated emission appears as a consequence of the Bose—Einstein statistics of photons and that to observe this effect at least two excitations have to be initially present in the atom—field system. That is, both the atom and the electromagnetic field have to be excited. In this paper we show that stimulated emission can appear exclusively as a consequence of quantum interference in a system with just a single excitation. Specifically, we consider a single two-level atom which is initially in its lower energy state and it interacts with a single-photon multi-mode wave packet. We show that for a proper choice of the photon-wave packet the atom can exhibit stimulated emission.
We theoretically investigate signatures of stimulated emission at the single-photon level for a two-level atom interacting with a one-dimensional light field. We consider the transient regime where the atom is initially excited, and the steady-state regime where the atom is continuously driven with an external pump. The influence of pure dephasing is studied, clearly showing that these effects can be evidenced with state-of-the-art solid-state devices. We finally propose a scheme to demonstrate the stimulation of one optical transition by monitoring another one, in three-level one-dimensional atoms.
Stimulated emission can be defined as the process when an incoming photon stimulates an additional quantum of energy from an atom into the same electromagnetic mode as the impinging photon. Hence, the two outgoing photons are identical. In a waveguide or free space, this intuition is typically found through Fermi's Golden rule, however, this does not properly account for the wave-like nature of the photons. Here, I present an exact solution to stimulated emission from a quantum two-level atom that properly accounts for the incoming and outgoing electromagnetic modes. This result is valid over a huge range of incident photon numbers. For a single incident photon, it shows how the photon must properly mode match the two-level system to cause stimulated emission. For a Fock state drive with large photon number, the exact solution shows how a two-level system Rabi oscillates with the traveling Fock mode as it passes by. I additionally use the same formalism to show that stimulated emission by a coherent pulse cannot be understood as an additional photon being emitted into the incident coherent state because the two-level system's state factorizes with the electromagnetic field's coherent state. Recent advances in superconducting circuits make them an ideal platform to test these predictions.
The interaction between photons and a single two-level atom constitutes a fundamental paradigm in quantum physics. The nonlinearity provided by the atom leads to a strong dependence of the light-matter interface on the number of photons interacting with the two-level system within its emission lifetime. This nonlinearity unveils strongly correlated quasiparticles known as photon bound states, giving rise to key physical processes such as stimulated emission and soliton propagation. Although signatures consistent with the existence of photon bound states have been measured in strongly interacting Rydberg gases, their hallmark excitation-number-dependent dispersion and propagation velocity have not yet been observed. Here we report the direct observation of a photon-number-dependent time delay in the scattering off a single artificial atom-a semiconductor quantum dot coupled to an optical cavity. By scattering a weak coherent pulse off the cavity-quantum electrodynamics system and measuring the time-dependent output power and correlation functions, we show that single photons and two- and three-photon bound states incur different time delays, becoming shorter for higher photon numbers. This reduced time delay is a fingerprint of stimulated emission, where the arrival of two photons within the lifetime of an emitter causes one photon to stimulate the emission of another.