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arXiv:2306.11348 · ACS Nano

Nonlinear Quantum Light Generation in Collective Spontaneous Emission

Offek Tziperman, Gefen Baranes, Alexey A. Gorlach, Ron Ruimy, Chen Mechel, Michael Faran, Nir Gutman, Andrea Pizzi, Ido E. Kaminer

Published May 29, 2025• 2 citations
arXivHTMLPDF

Abstract

Collective spontaneous emission occurs when multiple quantum emitters decay into common radiation modes, resulting in enhanced or suppressed emission. Here, we find the quantum state of light collectively emitted from emitters exhibiting quantum correlations. We unveil under what conditions the quantum correlations are not lost during the emission but are instead transferred to the output light. Under these conditions, the inherent nonlinearity of the emitters can be tailored to create desired photonic states in the form of traveling single-mode pulses, such as Gottesman-Kitaev-Preskill and Schrödinger-cat states, that are useful for error correction in quantum computation. To facilitate such predictions, our work reveals the multimode nature of collective spontaneous emission, capturing the role of the emitters' positions, losses, interactions, and beyond-Markov dynamics on the emitted quantum state of light. We present manifestations of these effects in different physical systems, with examples of cavity QED, waveguide QED, and atomic arrays with up to a few dozen emitters. Our findings suggest paths for creating and manipulating multiphoton quantum light for bosonic codes in continuous-variable-based quantum computation, communications, and sensing.

DOI
10.1021/acsnano.4c15257

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Collective spontaneous emission occurs when multiple quantum emitters decay into common radiation modes, resulting in enhanced or suppressed emission. Here, we find the quantum state of light collectively emitted from emitters exhibiting quantum correlations. We unveil under what conditions the quantum correlations are not lost during the emission but are instead transferred to the output light. Under these conditions, the inherent nonlinearity of the emitters can be tailored to create desired photonic states in the form of traveling single-mode pulses, such as Gottesman-Kitaev-Preskill and Schrödinger-cat states, that are useful for error correction in quantum computation. To facilitate such predictions, our work reveals the multimode nature of collective spontaneous emission, capturing the role of the emitters' positions, losses, interactions, and beyond-Markov dynamics on the emitted quantum state of light. We present manifestations of these effects in different physical systems, with examples of cavity QED, waveguide QED, and atomic arrays with up to a few dozen emitters. Our findings suggest paths for creating and manipulating multiphoton quantum light for bosonic codes in continuous-variable-based quantum computation, communications, and sensing.
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Abstract This work introduces a theoretical framework to model the collective dynamics of quantum emitters in highly non-Markovian environments, interacting through the exchange of photons with significant retardations. The formalism consists on a set of coupled delay differential equations for the emitter’s raising/lowering operators σ i ± , supplemented by input–output relations that describe the field mediating the interactions. These equations capture the dynamics of both linear (bosonic) and nonlinear (two-level) emitter arrays. It is exact in some limits—e.g. bosonic emitters or generic systems with up to one collective excitation—and can be integrated to provide accurate results for larger numbers of photons. These equations support a study of collective spontaneous emission of emitter arrays in open waveguide-QED environments. This study uncovers an effect we term cascaded super- and sub-radiance, characterized by light-cone-limited propagation and increasingly correlated photon emission across distant emitters. The collective nature of this dynamics for two-level systems is evident both in the enhancement of collective emission rates, as well as in a superradiant burst with a faster than linear growth. While these effects should be observable in existing circuit QED devices or slight generalizations thereof, the formalism put forward in this work can be extended to model other systems such as network of quantum emitters or the generation of correlated photon states.
Modification of spontaneous decay in space and time is a central topic of quantum physics. It has been predominantly investigated in the context of cavity quantum electrodynamics (QED), gaining new interest recently in the domain of nano-optics. Beyond cavity-QED, spontaneous emission may be modified also in free space due to correlations among the photon emitters, a phenomenon known as super- and sub-radiance. Correlations may stem either from direct interactions between the particles, from long-range exchange of photons, or by measuring single photons in a common mode. Yet, the genuine spatial spontaneous emission pattern of an atomic ensemble in an entangled quantum state has not been observed so far, due to the lack of ultra-fast cameras with high spatial resolution suited for recording single photons from single atoms. Preparing two trapped ions in free space in entangled Dicke states via photon detection, we study the resulting collective spontaneous emission patterns. Depending on the symmetry of the Dicke states, associated with the direction of detection of the first state-determining photon, we observe fundamentally different emission patterns for the subsequently scattered photon, including super- and sub-radiance. Our results demonstrate that the detection of a single photon can profoundly modify the collective emission of an atomic array, here represented by its most elementary building block of two atoms in free space.
In recent years, the study of quantum electrodynamics (QED) in light-matter interactions has discovered various interesting phenomenons that orient many applications. However, due to the ambient entanglement among photons and atoms, few-particle dynamics remains challenging to analyze precisely and limits the progress in several fields. In few-particle systems, different number of atoms interacting with the light field generates drastically different results, even when there is only a single photon involved in the system. The interference between individual atom’s spontaneous emission wavefunctions can cooperatively alter the effective atom-light coupling strength. Depending on the spatial distance between individual of atoms and the involved cavities in the interaction progresses, the collective spontaneous emission rate can alter drastically from superradiance, where the emission rate is enhanced to a high value proportional to the atom number, to subradiance, where the excited atom ensemble stays in a dark state with the light trapped forever. Superradiance provides a promising mechanism to create an ultra-strong light-matter coupling environment, which is an important ingredient for the design of ultra-fast optical devices, frequency comb generation and quantum mirrors. The dark state of subradiance, on the other hand, is essential for the quantum memory implementation. Also, nontrivial phenomenons also occur when multiple photons interacting with a single atom simultaneously. When a finite number of photons incidents on an atom, their scattering through an atom is highly nonlinear, and one special eigenstate component of such nonlinear process, namely photonic bound states, exhibits many interesting properties in nonlinear quantum optical systems. The photons in such state are strongly bunched with each other, as if a virtual attractive force is in effect. Also, the frequency of photons are anti-correlated so that their total frequency remains a constant value, no matter how arbitrary the frequency of any individual is. Thesefeatures benefit certain nonlinear quantum processes for quantum computing and quantum imaging. Specially for two-photon excitation imaging, the same-parity two-level fluorophore molecules suffers from extremely low excitation efficiencies due to the far off-resonant intermediate states. However, by replacing the current commonly used ultrashort laser pulse illuminations with two photon bound state photon pairs, namely photonic dimers, the efficiency can be enhanced to orders of magnitude higher. Such exceptionally high excitation efficiency can potentially bring the current in vivo deep brain imaging depth from millimeter level to several centimeters. To obtain a stable source of such photonic dimers, it is found that a laser structure with gain medium of two-photon emission materials is capable of generating the coherent state of photonic dimer and can serve as a promising light source for nonlinear quantum optical devices.
We study the collective emission of a few emitters (up to three) in a cavity. In addition to the radiation coupling responsible for sub- and superradiance, we investigate emitters additionally coupled through a joint carrier reservoir. For such emitters, typically embedded in a solid state environment, the carrier reservoir provides a continuous pumping mechanism for the steady state emission. We show that the statistical properties of the emitted light depend strongly on the interaction between the emitters and the reservoir. Unexpectedly, the presence of the reservoir enhances the coherence of the emitted light already for a few emitters. This results from the fact that the carrier reservoir introduces new many-body correlations to the electronic transition and in this way suppresses multiphoton processes.