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arXiv:2401.02738 · Nature Communications

Strong coupling between a single-photon and a two-photon Fock state

Shuai-Peng Wang, Alberto Mercurio, A. Ridolfo, Yuqing Wang, Mo Chen, Wenyan Wang, Yulong Liu, Huanying Sun, Tiefu Li, Franco Nori, Salvatore Savasta, J. Q. You

Published Sep 30, 2025• 7 citations

Abstract

The realization of strong nonlinear coupling between single photons has been a long-standing goal in quantum optics and quantum information science, promising wide impact applications, such as all-optical deterministic quantum logic and single-photon frequency conversion. Here, we report an experimental observation of the strong coupling between a single-photon and a two-photon Fock state in an ultrastrongly-coupled circuit-QED system. This strong nonlinear interaction is realized by introducing a detuned flux qubit working as an effective coupler between two modes of a superconducting coplanar waveguide resonator. The ultrastrong light–matter interaction breaks the excitation number conservation, and an external flux bias breaks the parity conservation. The combined effect of the two enables the strong one–two-photon coupling. Quantum Rabi-like avoided crossing is resolved when tuning the two-photon resonance frequency of the first mode across the single-photon resonance frequency of the second mode. Within this new photonic regime, we observe the thresholdless second harmonic generation for a mean photon number below one. Our results represent a key step towards a new regime of quantum nonlinear optics, where individual photons can deterministically and coherently interact with each other in the absence of any stimulating fields. Systems with strong photon-photon interactions enable advanced quantum optical applications as well as the study of highly correlated light-matter states. Here the authors report strong coupling between single- and two-photon states in a superconducting circuit, enabling a new regime of nonlinear quantum optics.

DOI: 10.1038/s41467-025-63783-7

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The realization of strong nonlinear coupling between single photons has been a long-standing goal in quantum optics and quantum information science, promising wide impact applications, such as all-optical deterministic quantum logic and single-photon frequency conversion. Here, we report an experimental observation of the strong coupling between a single-photon and a two-photon Fock state in an ultrastrongly-coupled circuit-QED system. This strong nonlinear interaction is realized by introducing a detuned flux qubit working as an effective coupler between two modes of a superconducting coplanar waveguide resonator. The ultrastrong light–matter interaction breaks the excitation number conservation, and an external flux bias breaks the parity conservation. The combined effect of the two enables the strong one–two-photon coupling. Quantum Rabi-like avoided crossing is resolved when tuning the two-photon resonance frequency of the first mode across the single-photon resonance frequency of the second mode. Within this new photonic regime, we observe the thresholdless second harmonic generation for a mean photon number below one. Our results represent a key step towards a new regime of quantum nonlinear optics, where individual photons can deterministically and coherently interact with each other in the absence of any stimulating fields. Systems with strong photon-photon interactions enable advanced quantum optical applications as well as the study of highly correlated light-matter states. Here the authors report strong coupling between single- and two-photon states in a superconducting circuit, enabling a new regime of nonlinear quantum optics.

Quantum nonlinear optics seeks to harness strong photon-photon interactions for scalable quantum technologies, although dissipative losses still pose a major barrier to near-unity conversion efficiency. Here, we bridge non-Hermitian physics with the quantum nonlinear domain by exploiting perfect absorption to identify and optimize few-photon nonlinear processes. We theoretically investigate two circuit QED systems, operating in the light-matter ultrastrong coupling regime. The first (i) enables simultaneous two-atom excitations by single photons, while the second (ii) realizes the strong coupling between a single-photon and a two-photon Fock states. We demonstrate that, since the strong optical nonlinearities cause quantum spectral features to emerge already at the level of linear response theory, the perfect absorption condition in

|S_{11}|

enables near-deterministic single-photon down-conversion into (i) a qubit-qubit-correlated pair and (ii) a two-photon pair. We show that the conversion efficiency can be systematically optimized through experimentally accessible parameters, both linked to the emergence of Hermitian subspaces within the effective non-Hermitian Hamiltonians. These findings position non-Hermitian engineering as a broadly applicable route to optimizing quantum devices at the single-photon level, even beyond circuit-QED platforms.

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A cavity quantum electrodynamical (QED) system beyond the strong-coupling regime is expected to exhibit intriguing quantum phenomena. Here we report a direct measurement of the photon-dressed qubit transition frequencies up to four photons by harnessing the same type of state transitions in an ultrastrongly coupled circuit QED system realized by inductively coupling a superconducting flux qubit to a coplanar-waveguide resonator. This demonstrates a convincing observation of the photon-dressed Bloch-Siegert shift in the ultrastrongly coupled quantum system. Moreover, our results show that the photon-dressed Bloch-Siegert shift becomes more pronounced as the photon number increases, which is a characteristic of the quantum Rabi model.

Abstract We experimentally investigate a superconducting circuit composed of two flux qubits ultrastrongly coupled to a common LC resonator. Owing to the large anharmonicity of the flux qubits, the system can be correctly described by a generalized Dicke Hamiltonian containing spin-spin interaction terms. In the experimentally measured spectrum, an avoided level crossing provides evidence of the exotic interaction that allows the simultaneous excitation of two artificial atoms by absorbing one photon from the resonator. This multi-atom ultrastrongly coupled system opens the door to studying nonlinear optics where the number of excitations is not conserved. This enables novel processes for quantum-information processing tasks on a chip.

Light-matter interaction between an atom and an electromagnetic resonator is ubiquitous in quantum technologies. Although linear light-matter coupling

g{\hat{\sigma }}_{x}(\hat{a}+{\hat{a}}^{{{\dagger}} })

can reach the ultrastrong regime g/ω > 10−1, nonlinear light-matter coupling

\frac{\chi }{2}{\hat{\sigma }}_{z}{\hat{a}}^{{{\dagger}} }\hat{a}

is typically perturbative and limited to χ/ω < 10−2. Nonlinear coupling has the advantage of commuting with the atomic

{\hat{\sigma }}_{z}

and photonic

{\hat{a}}^{{{\dagger}} }\hat{a}

Hamiltonian, allowing for fundamental operations such as quantum-non-demolition measurement. Here, we use a superconducting circuit to demonstrate the experimental realization of near-ultrastrong χ/ω = (4.852 ± 0.006) × 10−2. We also show signatures of light-light nonlinear coupling (

\chi {\hat{a}}^{{{\dagger}} }\hat{a}{\hat{b}}^{{{\dagger}} }\hat{b}

) and χ/2π = 580.3 ± 0.4 MHz matter-matter nonlinear coupling (

\frac{\chi }{4}{\hat{\sigma }}_{z,a}{\hat{\sigma }}_{z,b}

), representing the largest reported ZZ interaction between two coherent qubits. Such advances in the nonlinear coupling strength of light, matter modes enable new physical regimes and could lead to orders of magnitude faster qubit readout and gates. Nonlinear light-matter coupling has applications in quantum technologies, for instance in quantum-non-demolition measurements, but its strength is typically limited. Here the authors demonstrate near-ultrastrong nonlinear light-matter coupling in a superconducting circuit with two transmons and a quarton coupler.

We propose a scheme for realizing a deterministic two-photon controlled-

Z

(cz) gate based on variants of the two-photon quantum Rabi model, which is feasible within the framework of circuit QED. We begin by utilizing the two-photon interaction to implement the nonlinear sign gate and subsequently we construct the cz gate following the Knill-Laflamme-Milburn scheme [Nature (London) 409, 46 (2001)]. We consider three different regimes: the strong-coupling regime, the perturbative ultrastrong-coupling regime, and the large-detuning regime. Our results indicate that the cz gate operates fast with high fidelity. We also show that the photonic state in the waveguide can be input into the circuit QED system through a variable coupler and released after interaction with almost the same waveform except for a $\ensuremath{\pi}$-phase shift. Our scheme offers a suitable approach for achieving fast and deterministic two-photon quantum gates via light-matter interactions.