A laser pulse can reshape the behavior of a superconducting microwave cavity, even though optical photons carry far more energy than microwave photons. This experiment shows that the control can remain remarkably coherent at millikelvin temperatures.

Interfaces based on cryogenic cavity electro-optic systems are particularly promising because microwave and optical fields interact directly in the quantum regime. Quantum optical control of superconducting microwave circuits has been precluded so far by weak electro-optical coupling and quasiparticles induced by the pump laser.

The experiment reports coherent control of a superconducting microwave cavity using laser pulses in a multimode electro-optical device at millikelvin temperature with near-unity cooperativity. Both stationary and instantaneous responses of the microwave and optical modes comply with coherent electro-optical interaction and reveal only a minuscule amount of excess back-action with an unanticipated time delay.

The experiment demonstrates coherent electro-optic dynamical back-action in a multimode cavity electro-optical device. The stationary and instantaneous electro-optic back-action includes the optical spring effect and microwave linewidth narrowing or broadening, with negligible excess back-action.

The optical-probing field shows electro-optically induced absorption or transparency, opening possibilities for dispersion engineering of propagating optical and microwave pulses. This coherent electro-optical response confirms the feasibility of direct quantum optical control and sensing of microwave fields in the quantum back-action dominant regime.

The device uses a crystalline lithium niobate whispering gallery mode optical resonator coupled to the azimuthal-number-one mode of a superconducting aluminum microwave cavity inside a dilution refrigerator at about ten millikelvin. The optical resonator provides transverse-electric modes with the same optical loss rate: the Stokes, pump, and anti-Stokes modes.

When the optical free spectral range matches the microwave frequency, resonant three-wave mixing arises between the microwave and adjacent optical modes through cavity-enhanced electro-optic interaction. An on-resonance optical pump enhances the electro-optic interaction, with the enhancement set by the mean intracavity photon number of the pump mode.

The interaction includes two-mode squeezing between the Stokes and microwave modes, and a beam-splitter interaction between the anti-Stokes and microwave modes. The multiphoton cooperativity is a figure of merit for the cavity electro-optic device, determined by the pump photon number, the vacuum electro-optical coupling rate, and the optical and microwave loss rates.

Mode engineering chooses the two-mode-squeezing or beam-splitter interaction by selectively suppressing the counterpart through coupling to an optical transverse-magnetic mode of different polarization. The measurements examine temporal and spectral coherent dynamical responses in the pulsed regime.

A strong optical pump pulse is sent to the electro-optic device together with a weak continuous probing field around either the microwave or optical resonance, so the dynamical back-action can be probed during the pulse. The normalized probing-field reflection compares the pump pulse on and off using reflection scattering parameters, defined as the output-to-input field amplitude ratio for the microwave or optical mode.

Figure one introduces the multimode cavity electro-optic platform: a lithium niobate optical resonator is integrated into an aluminum three-dimensional microwave cavity, with a microwave mode coupled to Stokes, pump, and anti-Stokes optical modes. The reflection data in panel c characterize a family of transverse-electric modes with similar optical loss, identifying modes two, three, and five for the pump, Stokes, and anti-Stokes configurations.

This setup matters because it provides the mode structure needed to control electro-optic dynamical back-action in the pulsed regime. In the symmetric case, no evident microwave frequency or linewidth change is observed because the back-action is evaded. In the anti-Stokes case, the microwave linewidth increases linearly with cooperativity, while in the Stokes case it decreases.

The theoretical curves for both asymmetric cases match the experimental results very well using a full dynamical back-action model. Figure two shows how the microwave response changes under three pump configurations.

In panel a, the symmetric configuration leaves the stationary response essentially unchanged, while the Stokes and anti-Stokes configurations produce opposite changes in the resonance lineshape and reconstructed reflection. Panel b tracks the fitted microwave frequency and linewidth changes across pump power, showing the absence of evident back-action in the symmetric case and contrasting linewidth trends for Stokes versus anti-Stokes pumping.

Figure three maps stationary electro-optically induced absorption and transparency across four probing configurations. In panel a, measured reflection responses are jointly fit with the full dynamical back-action model, while the lower plots reconstruct optical reflection efficiency with the pump on and off, revealing absorption or transparency features.

Panel b summarizes how the fitted response changes with cooperativity, with solid curves showing fits and dashed curves showing theory; this matters because it connects the observed spectra to the extracted coupling and optical parameters. When the optical pump pulse arrives, the fitted cooperativity increases smoothly, reaches a stationary value in the middle, and slowly decreases to zero after the pulse.

The microwave linewidth change follows the predicted coherent electro-optical dynamical back-action: narrowing in the Stokes case and broadening in the anti-Stokes case. In the symmetric case, a very slight excess frequency drift and linewidth change appear at the beginning and end of the pulse because the optical pump field is loaded and unloaded.

Similar instantaneous excess back-action also appears in the optical coherent response, producing an estimated sub-megahertz detuning jiggle during the pulse. Figure four tracks how the microwave mode responds during and after optical pump pulses.

In panel a, the fitted cooperativity rises during the pulse and the microwave frequency and linewidth shifts follow corresponding dynamical-back-action curves across different pump configurations. Panel b compares resonant and off-resonant conditions, revealing delayed excess back-action after the pulse; panel c plots the extracted delay time against pulse length.

This matters because transient and lingering microwave perturbations are important for designing pulsed quantum transduction and entanglement protocols. The experiment demonstrates coherent optical control of a microwave cavity in the pulsed regime, using a multimode electro-optical device at millikelvin temperature with near-unitary cooperativity.

The stationary and instantaneous microwave and optical-probing responses agree very well with coherent dynamical back-action theory, apart from very small excess back-action. That excess back-action is surprisingly small given the large optical photon energy compared with the small superconducting gap of aluminum.

The central result is coherent optical control of a superconducting microwave cavity with near-unitary cooperativity and only very small excess back-action, supporting future quantum control and sensing applications.