⚛️ quantum physics

The quantum state of light in collective spontaneous emission

This paper investigates the quantum state of light emitted through collective spontaneous decay, revealing how quantum correlations can be preserved and transferred to output pulses to engineer specific non-classical photonic states like GKP and Schrödinger-cat states across various physical systems for applications in continuous-variable quantum technologies.

Original authors: Offek Tziperman, Gefen Baranes, Alexey Gorlach, Ron Ruimy, Chen Mechel, Michael Faran, Nir Gutman, Andrea Pizzi, Ido Kaminer

Published 2026-01-30

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CC BY 4.0

Original authors: Offek Tziperman, Gefen Baranes, Alexey Gorlach, Ron Ruimy, Chen Mechel, Michael Faran, Nir Gutman, Andrea Pizzi, Ido Kaminer

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a choir of singers (the "emitters") and you want them to sing a specific, complex song that creates a beautiful, unique sound (the "quantum state of light"). Usually, when singers sing together, they might just make a loud noise or a simple harmony. But this paper discovers a way to make them sing a very specific, high-tech song that could be used for future quantum computers, all by carefully arranging how they stand and interact.

Here is the breakdown of their discovery using simple analogies:

1. The Problem: Making "Quantum" Light is Hard

In the world of quantum physics, light isn't just a beam; it can be in strange, "correlated" states (like a Schrödinger's cat, which is both alive and dead at the same time). Creating these states is like trying to bake a perfect, delicate soufflé.

The Old Way: Scientists tried to use special crystals (nonlinear materials) to bend light into these shapes. But it's like trying to sculpt a statue out of wet sand; the materials are too weak and inefficient to get the job done, especially for traveling light pulses.
The New Idea: Instead of using weak materials, use the singers themselves! Atoms and quantum dots are naturally "nonlinear" (they have a built-in complexity). The paper asks: Can we make a group of these singers work together to spit out a perfect quantum light pulse?

2. The Solution: The "Choir" Effect (Collective Emission)

The paper studies collective spontaneous emission. Imagine the singers are all excited and ready to sing.

Superradiance (The Loud Chorus): If the singers are perfectly synchronized, they don't just sing louder; they sing in a burst of intense, coordinated energy.
Subradiance (The Whisper): If they are arranged just right, they can cancel each other out, making them sing very slowly or quietly.

The researchers found that when these singers are correlated (their states are linked mathematically), the light they emit isn't just a random burst. It carries the "memory" of their complex internal state.

3. The Magic Trick: Transferring the "Recipe" to the Light

The most surprising finding is that under the right conditions, the complex quantum information inside the atoms is transferred to the light pulse without getting lost.

The Analogy: Think of the atoms as a master chef holding a secret recipe (a complex quantum state like a "GKP state" or a "Cat state"). The light is the dish being served. Usually, when you cook, the flavor gets diluted or changed. But this paper shows that if you arrange the kitchen (the atoms) correctly, the dish comes out tasting exactly like the recipe, even if the cooking process is chaotic.
The Result: They successfully created traveling pulses of light that look like "Schrödinger's cats" (superpositions) and "GKP states" (error-correcting codes) just by letting the atoms decay.

4. The Importance of Positioning (The Stage Setup)

The paper emphasizes that where the singers stand matters immensely.

The Perfect Spacing: If the singers stand at specific distances (multiples of the light's wavelength), they act as one giant super-singer. The light comes out as a pure, single beam.
The "Wrong" Spacing: If they stand at the wrong distance, the sound gets messy, or they get stuck in a "dark state" where they can't sing at all.
The Surprise: Even if the singers start out uncorrelated (just a normal choir), placing them at a specific distance (half a wavelength apart) forces them to emit a "Cat state" light pulse. It's like arranging a group of strangers in a room so that they accidentally start singing a complex opera together just by standing in the right spots.

5. The "Nonlinear" Secret Sauce

Why does this work so well? Because the atoms are nonlinear.

The Analogy: Imagine a swing. If you push it gently, it moves in a simple, predictable arc (linear). But if you push it hard, the physics gets weird and complex (nonlinear).
The Paper's Claim: Most previous research only looked at the "gentle push" (linear regime). This paper dives into the "hard push" (nonlinear regime). They found that this natural complexity of the atoms is actually a feature, not a bug. It allows them to create these fancy quantum states using a small number of atoms, rather than needing thousands.

6. Keeping the Light Pure (Robustness)

The researchers tested if this would break if the environment was noisy (like a drafty room).

The Finding: The system is surprisingly tough. Even if some light leaks out the wrong way or the singers get a bit out of tune (decoherence), the main beam of light often keeps its special quantum shape.
The Catch: The more "singers" (atoms) you have, the more robust the system becomes. If you have a large choir, the "good" sound (superradiance) gets louder and faster, overpowering the "bad" noise.

Summary

This paper provides a new "recipe" for creating high-tech quantum light. Instead of trying to force light to behave using weak materials, it suggests using a group of quantum atoms arranged in a specific pattern. When these atoms "sing" together, they naturally produce traveling pulses of light that carry complex quantum information (like error-correcting codes or cat states). This works best when the atoms are arranged precisely and when they are allowed to interact strongly, turning their natural complexity into a powerful tool for generating quantum light.

Technical Summary: The Quantum State of Light in Collective Spontaneous Emission

Problem Statement
The generation of high-quality, multi-photon quantum states of light (such as Schrödinger cat and Gottesman-Kitaev-Preskill (GKP) states) in the optical regime remains a significant challenge. Existing methods relying on weak nonlinearities in bulk materials are inefficient at the single-photon level, while approaches using single emitters in the optical range often lack the strong coupling and long lifetimes found in microwave circuit QED. Furthermore, while collective spontaneous emission (superradiance and subradiance) is well-studied, previous theoretical works have largely focused on emitter dynamics or the "linear" regime (where excitations are few compared to emitters). A comprehensive quantum optical description of collective spontaneous emission in the nonlinear regime (high excitation), including the full quantum state of the emitted light and its dependence on emitter correlations, positions, and losses, has been absent.

Methodology
The authors develop a theoretical framework to determine the quantum state of light emitted from a system of $N$ correlated quantum emitters. The approach utilizes Wigner quasi-probability functions to characterize the states of the emitters, cavity/waveguide fields, and the emitted radiation. The methodology proceeds in three distinct steps:

Internal Dynamics: The system (emitters + cavity/waveguide field) is modeled using a master equation (Lindblad equation) that traces out the continuum of external modes. This captures non-Markovian effects, such as Rabi-type oscillations where energy flows back and forth between emitters and the cavity before leaking out.
Mode Identification: The first-order correlation function of the output radiation is computed and diagonalized to identify the principal temporal modes. The authors focus on the dominant mode (highest photon occupancy) to reconstruct the emitted pulse, treating other modes as loss channels.
Quantum State Reconstruction: An adapted input-output formalism for quantum pulses is applied. The system is re-solved by explicitly including the dominant emitted mode in the Hamiltonian and dissipator. This reduces the Hilbert space to a finite size, allowing for the numerical integration of the master equation to obtain the Wigner function of the emitted pulse.

The theory is generalized across three physical platforms: Cavity QED, Waveguide QED (1D arrays), and Atomic Arrays (2D free space or cavity-coupled).

Key Contributions and Results

Nonlinear State Transfer: The paper demonstrates that intrinsic nonlinearities in quantum-correlated systems allow for the transfer of complex quantum states from matter to light, even in the nonlinear regime where the number of excitations is comparable to the number of emitters.
- Superradiance: For fully inverted emitters, the system emits a pulse resembling a Fock state (83% fidelity). When emitters are prepared in collective Schrödinger cat or GKP states, these states are transferred to the emitted light with high fidelities (97% and 99%, respectively).
- Subradiance: By controlling emitter positions (specifically at half-wavelength spacing, $\lambda/2$ ), the system can emit Schrödinger cat states even from initially uncorrelated (coherent) states. This occurs due to destructive interference suppressing decay into unwanted modes while preserving quantum correlations in the dominant mode.
Role of Reabsorption Efficiency ( $\xi$ ): The authors identify a dimensionless parameter, reabsorption efficiency $\xi = 2g^2N/\kappa^2$ , which governs the system's nonlinearity. High $\xi$ leads to strong energy exchange between emitters and the cavity, enhancing multimode entanglement. However, the system can still produce nearly pure single-mode states under specific conditions.
Spatial Engineering: The quantum state of the emitted light is highly sensitive to emitter spacing.
- Spacings that are integer multiples of the wavelength ( $\lambda$ ) retrieve the Dicke limit, enabling efficient state transfer.
- Spacings far from integer multiples lead to multimode entangled emission or subradiant "dark states," reducing the purity of the dominant mode.
- The $\lambda/2$ spacing is identified as a unique regime where subradiant emission yields pure, non-Gaussian quantum states.
Robustness to Decoherence: The study quantifies the impact of decoherence channels (collective decay to unwanted spatial modes, independent decay, and dephasing).
- Collective decay into unwanted modes is the most detrimental to fidelity.
- The system is surprisingly robust to independent decoherence (e.g., dephasing or independent decay), provided the collective decay rate into the desired mode is sufficiently high.
- Increasing the number of emitters while keeping the total number of excitations constant improves fidelity, as the superradiant decay rate scales with $N$ , outpacing independent decay rates.

Significance
The paper establishes collective spontaneous emission as a viable mechanism for controllably translating correlated states of matter into quantum states of light, specifically within the nonlinear regime. By leveraging the intrinsic nonlinearity of quantum emitters and their collective states, this approach offers a path to generate desirable non-Gaussian photonic states (such as GKP and cat states) using a modest number of emitters. This relaxes the stringent requirement of having a vast number of emitters relative to excitations, which was a limitation in previous linear-regime theories.

The findings contribute to the emerging field of many-body quantum optics by providing the first multi-mode description of superradiant and subradiant emission for arbitrary initial conditions and emitter positions. The work suggests new pathways for creating and manipulating multi-photon quantum light, which are essential resources for continuous-variable quantum computation, communication, and sensing, particularly for bosonic codes that require non-Gaussian states.