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Nature Communications

Observing the dynamics of quantum states generated inside nonlinear optical cavities

Seou Choi, Yannick Salamin, Charles Roques‐Carmes, Jamison Sloan, Michael Horodynski, Marin Soljacic A

Published Aug 14, 2025• 6 citations
Publisher

Abstract

Observing non-classical properties of light is a long-standing interest to advance a wide range of quantum applications. Optical cavities are essential to generate and manipulate non-classical light. However, detecting changes in cavity properties induced by the quantum state remains a critical challenge in the optical domain due to the weak material nonlinearity. Here, we propose a framework for observing the dynamics of quantum states generated inside nonlinear optical cavities. We leverage the symmetry-breaking process of a bistable system, which is highly sensitive to the initial state, enabling detection of quantum state displacement through an asymmetric equilibrium of a macroscopic observable. With a nonlinear response at the single photon level, our approach directly imprints the cavity field distribution onto the statistics of bistable cavity steady-states. We experimentally demonstrate our approach in a degenerate optical parametric oscillator, generating and reconstructing different quantum states. As a validation, we reconstruct the Husimi Q function of the cavity squeezed vacuum state. In addition, we observe the evolution of the quantum vacuum state inside the cavity as it undergoes phase-sensitive amplification. By enabling generation and measurement of quantum states in a single nonlinear optical cavity, our method paves a way for studying exotic dynamics of quantum optical states in nonlinear driven-dissipative systems. Characterising an optical quantum state confined in a cavity is not an easy task, as standard tomographic techniques works by interfering propagating fields and therefore encounters the problems relative to outcoupling the state. Here, the authors fill this gap for states generated within a nonlinear cavity featuring multiple steady states.

DOI
10.1038/s41467-025-63035-8

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Observing non-classical properties of light is a long-standing interest to advance a wide range of quantum applications. Optical cavities are essential to generate and manipulate non-classical light. However, detecting changes in cavity properties induced by the quantum state remains a critical challenge in the optical domain due to the weak material nonlinearity. Here, we propose a framework for observing the dynamics of quantum states generated inside nonlinear optical cavities. We leverage the symmetry-breaking process of a bistable system, which is highly sensitive to the initial state, enabling detection of quantum state displacement through an asymmetric equilibrium of a macroscopic observable. With a nonlinear response at the single photon level, our approach directly imprints the cavity field distribution onto the statistics of bistable cavity steady-states. We experimentally demonstrate our approach in a degenerate optical parametric oscillator, generating and reconstructing different quantum states. As a validation, we reconstruct the Husimi Q function of the cavity squeezed vacuum state. In addition, we observe the evolution of the quantum vacuum state inside the cavity as it undergoes phase-sensitive amplification. By enabling generation and measurement of quantum states in a single nonlinear optical cavity, our method paves a way for studying exotic dynamics of quantum optical states in nonlinear driven-dissipative systems. Characterising an optical quantum state confined in a cavity is not an easy task, as standard tomographic techniques works by interfering propagating fields and therefore encounters the problems relative to outcoupling the state. Here, the authors fill this gap for states generated within a nonlinear cavity featuring multiple steady states.
Abstract Observing non-classical properties of light is a long-standing interest to advance a wide range of quantum application from computing to metrology. Optical cavities are essential to generate and manipulate non-classical light. However, detecting changes in cavity properties induced by the quantum state remains a critical challenge in the optical domain due to the weak material nonlinearity, limiting our ability to observe quantum states generated in optical cavities. Here, we propose a framework for observing the dynamics of quantum states generated inside nonlinear optical cavities. We utilize symmetry-breaking to obtain high sensitivity to small perturbations introduced to the quantum state, resulting in an asymmetric equilibrium of a macroscopic observable. With a nonlinear response at the single photon level, our approach directly imprints the field distribution of the cavity quantum state onto the statistics of bistable cavity steady-states. We experimentally demonstrate our approach in a degenerate optical parametric oscillator, generating and reconstructing the quasi-probability distribution of different quantum states. As a validation, we reconstruct the Husimi Q function of the cavity squeezed vacuum state. In addition, we observe the evolution of the quantum vacuum state inside the cavity as it undergoes phase-sensitive amplification. By enabling generation and measurement of quantum states in a single nonlinear optical cavity, our method paves a way for studying exotic dynamics of quantum optical states in nonlinear driven-dissipative systems such as soliton generation and Kerr frequency combs.
Quantum states at optical frequencies are often generated inside cavities to facilitate strong nonlinear interactions. However, measuring these quantum states with traditional homodyne techniques poses a challenge, as outcoupling from the cavity disturbs the state's quantum properties. Here, we propose a framework for reconstructing quantum states generated inside nonlinear optical cavities and observing their dynamics. Our approach directly imprints the field distribution of the cavity quantum state onto the statistics of bistable cavity steady-states. We propose a protocol to fully reconstruct the cavity quantum state, visualized in 2D phase-space, by measuring the changes in the steady-state statistics induced by a probe signal injected into the cavity under different condition. We experimentally demonstrate our approach in a degenerate optical parametric oscillator, generating and reconstructing the quasi-probability distribution of different quantum states. As a validation, we reconstruct the Husimi Q function of the cavity squeezed vacuum state. In addition, we observe the evolution of the quantum vacuum state inside the cavity as it undergoes phase-sensitive amplification. By enabling generation and measurement of quantum states in a single nonlinear optical cavity, our method realizes an "end-to-end" approach to intracavity quantum tomography, facilitating studies of quantum optical phenomena in nonlinear driven-dissipative systems.
We propose and experimentally demonstrate a method to study intracavity quantum states and their dynamics in an optical parametric oscillator (OPO). By measuring the OPO steady state’s sensitivity to an external bias field, we show how intracavity quantum states can be reconstructed. Our method includes precise control over the pump phase, facilitating arbitrary quadrature reconstruction and enabling complete visualization of cavity states using Husimi Q-function representations. We experimentally demonstrate the quantum tomography of an intracavity squeezed vacuum state generated by an OPO pumped below threshold. Additionally, by controlling the bias time delay and amplitude relative to the pump it allows for the reconstruction of the intracavity state at various times, offering insights into the temporal evolution of the OPO intracavity state. This approach provides a powerful tool for exploring and understanding the intricate behavior of quantum states within optical cavities.
Engineering non-classical states of the electromagnetic field is a central quest for quantum optics(1,2). Beyond their fundamental significance, such states are indeed the resources for implementing various protocols, ranging from enhanced metrology to quantum communication and computing. A variety of devices can be used to generate non-classical states, such as single emitters, light-matter interfaces or non-linear systems(3). We focus here on the use of a continuous-wave optical parametric oscillator(3,4). This system is based on a non-linear χ(2) crystal inserted inside an optical cavity and it is now well-known as a very efficient source of non-classical light, such as single-mode or two-mode squeezed vacuum depending on the crystal phase matching. Squeezed vacuum is a Gaussian state as its quadrature distributions follow a Gaussian statistics. However, it has been shown that number of protocols require non-Gaussian states(5). Generating directly such states is a difficult task and would require strong χ(3) non-linearities. Another procedure, probabilistic but heralded, consists in using a measurement-induced non-linearity via a conditional preparation technique operated on Gaussian states. Here, we detail this generation protocol for two non-Gaussian states, the single-photon state and a superposition of coherent states, using two differently phase-matched parametric oscillators as primary resources. This technique enables achievement of a high fidelity with the targeted state and generation of the state in a well-controlled spatiotemporal mode.
We theoretically investigate the response of a coherently-driven nonlinear optical cavity to an additional incident single photon. Using a quantum description of the nonlinear dynamics that fully accounts for the quantum fluctuations of the cavity field and for the discrete nature of the incident photon, we characterize the quantum dynamics of single-photon-stimulated jumps from the low-photon-number to the high-photon-number state of the optical bistability loop. We find that the system can exhibit a giant response to this single quantum of excitation, rooted in the phase-transition picture of optical bistability. In addition to shedding light on the role of quantum fluctuations in the non-equilibrium dynamics of a nonlinear optical cavity, our results suggest a strategy for an all-optical single-photon avalanche detector.