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AI and Optical Data Sciences

Quantum tomography and intracavity dynamics with a biased optical parametric oscillator

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

Published Mar 21, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.3043893

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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.
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.
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.
We have carried out a linearized quantum analysis of the steady-state operation of an optical parametric oscillator (OPO) without cavity detunings; our analysis emphasizes the effects of pump quantum noise and pump excess noise. We show that pump excess noise reduces the observable signal/idler intensity correlation at low frequencies only in the presence of a cavity-loss mismatch between these subharmonic waves. This effect is so strong that the combination of pump excess noise and cavity-loss mismatch explains the rapid low-frequency noise increase well above the shot-noise level that has been seen in recent signal/idler correlation measurements. Moreover, the critical dependence of intensity correlation on cavity-loss mismatch opens a new possibility for ultrasensitive intracavity absorption spectroscopy. Specifically, sinusoidal amplitude modulation of the OPO pump beam with lock-in amplification of the signal/idler photocurrent affords a sensitive probe of subharmonic cavity-loss mismatch. Although this robust measurement capability exploits the strong intracavity correlation between the signal and idler waves, it does not require that nonclassical correlation be externally observable, nor is it limited to near-threshold OPO operation.