Bimodal non-Gaussian photonic states from a single quantum emitter in a waveguide

arXiv:2608.03658 · quant-ph · Submitted 2026-08-04 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: I'm Kai.

Mira: And I'm Mira, here with Lev.

Kai: Today's paper: "Bimodal non-Gaussian photonic states from a single quantum emitter in a waveguide".

Mira: The gist: The investigation demonstrates that a single two-level system coupled to a waveguide can deterministically generate bimodal non-Gaussian states from coherent and squeezed vacuum inputs,

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So to recap this paper "Bimodal non-Gaussian photonic states from a single quantum emitter in a waveguide", the main thrust is that you can generate deterministic and heralded non-Gaussian states of light using just one two-level system coupled to a chiral waveguide.

Mira: They focus on studying this system when driven by pulsed coherent and squeezed drives inside that chiral waveguide, showing that coherent input pulses allow for the deterministic generation of Wigner-negative states, but those states are limited in rank.

Lev: And then they move on to the more exciting part, using pulsed squeezed vacuum inputs to show that you can produce bimodal non-Gaussian states from which higher-stellar-rank states, specifically large squeezed cat states, can be experimentally extracted with a substantial success rate.

Kai: The paper is motivated by experimental implementations and it shows how these interactions create these rich two-mode non-Gaussian structures that act as useful resources in themselves.

Mira: It matters because these are the types of genuinely quantum non-Gaussian states that aren't captured by Gaussian descriptions, which are necessary for universal quantum computation or fault-tolerant resources.

Lev: From an engineering viewpoint, it suggests a path forward where you can use this single emitter setup to generate these complex states if you manage the extraction process well enough.

Conclusion: Kai: So to wrap up, the paper "Bimodal non-Gaussian photonic states from a single quantum emitter in a waveguide" is about using this two-level system and the waveguide to create these complex light states deterministically or by clever measurement techniques.

Mira: The authors are pointing toward using pulsed squeezed inputs as the way to access those higher rank, more complex non-Gaussian resources like large cat states that aren't possible with simpler methods.

Lev: It suggests that for anyone interested in building quantum computers, this system offers a way to generate structured two-mode non-Gaussian light which can be a resource on its own.

Kai: If you're looking at the future, this approach could give us a tool for generating and characterizing these complex non-Gaussian optical states in a more efficient way.

Thomas Copie, *, Ofer Firstenberg, G. P. Teja, Radim Filip, Hanna Le Jeannic

Laboratoire Kastler Brossel, Sorbonne University, CNRS, ENS-PSL Research University, Collège de France · Department of Physics of Complex Systems, Weizmann Institute of Science · Department of Optics, Faculty of Science, PalackƟyi University

quant-ph

Submitted: 2026-08-04

Updated: 2026-10-14

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 82/100

The gist: The gist: The investigation demonstrates that a single two-level system coupled to a waveguide can deterministically generate bimodal non-Gaussian states from coherent and squeezed vacuum inputs,

Key concepts

Non-Gaussian States: These are quantum light states whose properties cannot be fully described by simple Gaussian statistics, like those found in standard laser light. They exhibit richer interference effects and negative regions in their Wigner function, making them valuable for advanced quantum computing applications.
Two-Level System (TLS): This is a basic quantum system consisting of two discrete energy levels, similar to a qubit. In this paper, the TLS acts as the source of light interaction with the waveguide. It can be driven by coherent or squeezed light to generate specific non-Gaussian quantum states.
Squeezed Vacuum Input: This refers to an input state of the electromagnetic field that is 'squeezed' in one quadrature (like amplitude or phase) below the standard quantum limit. Using this specialized input allows the interaction with the TLS to produce highly structured, high-rank non-Gaussian states, such as large cat states.

Summary

The gist: The investigation demonstrates that a single two-level system coupled to a waveguide can deterministically generate bimodal non-Gaussian states from coherent and squeezed vacuum inputs, which are crucial resources for advanced quantum optical processing.

Introduction and Motivation

Photonic continuous-variable quantum computing has made remarkable progress in recent years, with the generation of large entangled states and the demonstration of increasingly complex quantum optical processing protocols <ref:2608.03658#pg2> At the same time, Gaussian resources alone are not sufficient for universal quantum computation or for the preparation of several key fault-tolerant resource states <ref:2608.03658#pg2>. A central challenge is therefore to access genuinely non-Gaussian states and operations in a scalable way <ref:2608.03658#pg2>. Genuinely quantum non-Gaussian states can exhibit negative regions in their Wigner functions, reflecting interference effects that cannot be captured within a purely Gaussian description <ref:2608.03658#pg2>.

Model and Interaction

The model considers a two-level system (TLS) coupled to a one-dimensional waveguide <ref:2608.03658#pg3>. The interaction between the TLS and the field is governed by the Hamiltonian Vˆ = iħ R p γ 2π aˆ†(ω)σ− − aˆ(ω)σ+ dω <ref:2608.03658#pg3>. The output field is related to the input field and state of the TLS by the input-output relationship ˆaout(t) = aˆin(t) + √γσˆ− <ref:2608.03658#pg3>. The analysis focuses on pulsed interactions using the virtual cavity formalism <ref:2608.03658#pg3>.

Deterministic Generation with Coherent Pulses

When a coherent pulse is used as input, deterministic non-Gaussian states of light can already be generated <ref:2608.03658#pg4>. After identifying the two dominantly populated output modes, the optimization procedure is detailed in Appendix A <ref:2608.03658#pg5>. The core state reveals the minimal Fock-space structure underlying the non-Gaussian part of the state <ref:2608.03658#pg5>. For coherent pulses, the core state has negligible population above the single-photon level and is therefore effectively confined to the subspace spanned by 0⟩, 1⟩ <ref:2608.03658#pg5>. The resulting states are limited to displaced superpositions of 0⟩ and 1⟩ with at most a single negative region in the Wigner function and a stellar rank of 1 <ref:2608.03658#pg5>.

Higher-Rank Non-Gaussian Resources under Squeezed Vacuum Input

Using pulsed squeezed vacuum inputs, interesting non-Gaussian resource states such as large squeezed cat states can be produced <ref:2608.03658#pg4>. The input state is a superposition of even Fock states, and the joint output state can be decomposed into parity components <ref:2608.03658#pg5>. By choosing an appropriate basis, the resulting state ρ1,θ1 already has a relatively high purity at 0.86, and closely resembles a squeezed even cat state <ref:2608.03658#pg5>. The parity decomposition further reveals that an even purer squeezed cat state is included in the mixture <ref:2608.03658#pg5>.

Proposed Protocol and Experimental Considerations

The proposed protocol involves using a squeezed drive to generate a bimodal non-Gaussian state which may already constitute a useful resource <ref:2608.03658#pg6>. Heralding a single-mode non-Gaussian resource by measuring one of the temporal modes can herald a large squeezed odd cat state in the other mode with a probability of 15% <ref:2608.03658#pg6>. Imperfect emitter-waveguide coupling is addressed by proposing an experimental configuration that restores an effectively chiral interaction <ref:2608.03658#pg8>.

Discussion and Outlook

The complexity of these states remains limited, with low stellar rank and core states confined to the 0⟩, 1⟩ subspace <ref:2608.03658#pg5>. Using a squeezed-vacuum input opens a different regime where the interaction produces a structured two-mode non-Gaussian state <ref:2608.03658#pg6>. This multimode structure can be regarded as a resource in itself <ref:2608.03658#pg6>. The approach introduced here could provide a useful tool for the efficient generation and characterization of complex non-Gaussian optical states <ref:2608.03658#pg8>.

Appendix Summary

Appendix A describes the method to choose relevant output modes by diagonalizing the autocorrelation matrix and performing a beamsplitter transformation <ref:2608.03658#pg10>. Appendix B provides methods to find the core state by minimizing a loss function and bounding its stellar rank using fidelity witnesses. Appendix C details the numerical simulations implemented using the QuTiP library. Appendix D defines key terms such as Wigner negativity volume, Fidelity, and time-domain annihilation operator. Table I summarizes the results obtained with this method on the states described in figure 3.

References

[1] M. V. Larsen, X. Guo, C. R. Breum, J. S. NeergaardNielsen, et al., Science 366, 369 (2019), arXiv:1906.08709 <ref:2608.03658#pg2>

[2] M. V. Larsen, J. E. Bourassa, S. Kocsis, J. F. Tasker, et al., Nature 642, 587 (2025) <ref:2608.03658#pg2>

[3] D. Gottesman, The heisenberg representation of quantum computers (1998), arXiv:quant-ph/9807006 [quantph] <ref:2608.03658#pg2>

[4] S. D. Bartlett, B. C. Sanders, S. L. Braunstein, and K. Nemoto, Phys. Rev. Lett 88, 097904 (2002) <ref:2608.03658#pg2>

[5] D. Gottesman, A. Kitaev, and J. Preskill, Phys. Rev. A 64, 012310 (2001) <ref:2608.03658#pg2>

[6] S. Haroche and J.-M. Raimond, Exploring the Quantum: Atoms, Cavities, and Photons (Oxford University Press, 2006) <ref:2608.03658#pg2>

[7] J. Honer, R. L¨ow, H. Weimer, T. Pfau, et al., Phys. Rev. Lett 107, 093601 (2011) <ref:2608.03658#pg2>

[8] B. Hacker, S. Welte, S. Daiss, A. Shaukat, et al., Nature Photonics 13, 110–115 (2023) <ref:2608.03658#pg2>

[9] V. Magro, J. Vaneecloo, S. Garcia, and A. Ourjoumtsev, Nature Photonics 17, 688 (2023) <ref:2608.03658#pg2>

[10] J. C. Loredo, C. Ant´on, B. Reznychenko, P. Hilaire, et al., Nature Photonics 13, 803 (2019) <ref:2608.03658#pg2>

[11] A. Gonz´alez-Tudela, V. Paulisch, D. E. Chang, H. J. Kimble, et al., Phys. Rev. Lett 115, 163603 (2015) <ref:2608.03658#pg2>

[12] V. Paulisch, H. J. Kimble, J. I. Cirac, and A Gonz´alezTudela, Phys. Rev. A 97, 053831 (2018) <ref:2608.03658#pg2>

[13] M. M. Lund, F. Yang, V. R. Christiansen, D Kornovan, et al.

Improvements for AI systems

textbf Deterministic Non-Gaussian State Generation via Coherent Drive (Coherent Input)

This capability allows an AI system to deterministically generate high-purity non-Gaussian states with a stellar rank of 1 when driven by a coherent pulse, which can be used as a resource for specific quantum operations.

textbf Higher-Rank Resource State Synthesis via Squeezed Vacuum Input

The system can synthesize large squeezed cat states deterministically (albeit impure) or via a quantum pulsed gate, followed by a single photon detection, enabling the generation of states with stellar rank r ≥ 2 and high fidelity.

textbf Heralded Large Cat State Generation via Parity Measurement

The AI can implement a protocol where detecting an odd number of photons on mode vθ2(t) heralds a large squeezed odd cat state of size α2 = 3.5, providing a resource for GKP-state generation with high heralding probability.

textbf Robust Non-Gaussian Feature Characterization

The system can use core state estimation, defined by minimizing the loss function to find the minimal effective Fock subspace carrying its non-Gaussian component, allowing for a displacement-free representation of the state.

textbf Loss Mitigation and Chirality Recovery

The AI can utilize an interferometric scheme to recover an effectively chiral interaction in an otherwise bidirectional waveguide, ensuring that Wigner negativity is preserved even with imperfections, as preserving Wigner negativity therefore only requires an overall emitter-waveguide coupling efficiency above 50%.