🔬 mesoscale physics

Engineering multi-photon dissipation with a dc-voltage-biased Josephson junction

This paper demonstrates that a dc-voltage-biased SQUID can engineer multi-photon dissipation (converting one, two, or four photons into a single lossy photon) while suppressing parasitic nonlinearities, offering a viable route for stabilizing cat qubits and reservoir engineering.

Original authors: Marco Paradina, Ambroise Peugeot, Roberto Negrin, Oscar Novat, Tristan Villain, Anil Murani, Jean-Loup Ville, Sébastien Jezouin, Raphaël Lescanne, Audrey Bienfait, Benjamin Huard

Published 2026-09-01

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Marco Paradina, Ambroise Peugeot, Roberto Negrin, Oscar Novat, Tristan Villain, Anil Murani, Jean-Loup Ville, Sébastien Jezouin, Raphaël Lescanne, Audrey Bienfait, Benjamin Huard

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the quiet world of quantum computing, where machines operate at the very edge of reality, the biggest enemy is often the environment itself. Quantum bits, the fundamental units of information in these machines, are incredibly fragile. The slightest touch from the outside world causes them to lose their information, a process known as decoherence. For decades, scientists have tried to isolate these bits completely, building shields to keep the noise out. However, a more recent and counterintuitive idea has emerged: instead of fighting the environment, one can learn to use it. By carefully designing how a quantum system interacts with its surroundings, researchers can turn the inevitable loss of energy into a tool. This technique, called quantum reservoir engineering, allows scientists to steer a system toward a specific, stable state, effectively using the environment to clean up errors and protect information.

The challenge has been finding a way to do this without introducing new problems. In superconducting circuits, which are a leading platform for building quantum computers, scientists have traditionally used a method involving rapid, rhythmic pulses of energy to create these protective states. While effective, this approach is messy. The very pulses used to create the desired effect also generate unwanted side effects, like tiny, unpredictable shifts in the system's behavior that become worse as the pulses get stronger. These side effects limit how well the system can be controlled, acting as a ceiling on performance. The question remained: could there be a cleaner way to engineer this dissipation, one that avoids these parasitic side effects entirely?

A team of researchers in France and at the company Alice & Bob has now demonstrated a solution. They built a circuit that uses a steady, constant voltage to control the flow of energy, rather than the usual rapid pulses. Their device consists of two main parts: a high-quality storage resonator, which acts as a memory for quantum information, and a lossy resonator, which acts as a drain. These two are connected by a tiny electronic component called a SQUID, which behaves like a controllable valve for quantum energy. By applying a direct current voltage across this SQUID, the researchers created a new pathway for energy to flow.

The mechanism relies on a fundamental property of superconductors where pairs of electrons, known as Cooper pairs, tunnel across the junction. When a voltage is applied, these pairs gain or lose a precise amount of energy. The researchers tuned this voltage so that the energy gained by a tunneling pair exactly matched the energy required to convert two photons (particles of light) from the memory resonator into a single photon in the lossy drain. This process is highly specific. Because the energy balance is set by the voltage itself, the system naturally filters out the messy, unwanted interactions that plague pulsed methods. The researchers showed that this setup could not only remove two photons at a time but could also be tuned to remove one, four, or even more photons in a single step, all while keeping the unwanted side effects virtually zero.

To prove their method worked, the team filled their memory resonator with a specific quantum state containing an average of four photons. They then switched on the voltage bias and watched what happened. In a standard system, the photons would leak out slowly and randomly. In their engineered system, the photons vanished in pairs at a rapid rate. Within about 50 nanoseconds, the complex state collapsed into a simple state containing either zero or one photon. This rapid, targeted removal of energy pairs is exactly what is needed to stabilize a special type of quantum bit known as a cat qubit, which is designed to be immune to certain types of errors.

The researchers also measured how well their system avoided the unwanted side effects that usually come with such strong interactions. They found that the memory's natural frequency remained stable and did not shift unpredictably, a sign that the parasitic terms were indeed averaging out to zero. They also confirmed that the system could handle the conversion of four memory photons into one drain photon, a high-order process that is notoriously difficult to isolate with traditional pulsed methods. While the system still showed some minor losses due to imperfections in the wiring and filtering, the team calculated that these could be reduced significantly with better engineering.

This work provides a clear path forward for building more robust quantum computers. By replacing complex, noisy pulses with a simple, steady voltage, the researchers have shown that it is possible to create a clean, efficient channel for removing errors. The ability to engineer the loss of multiple photons at once without the usual baggage of side effects suggests a new way to protect quantum information. The researchers conclude that with modest improvements to their filtering, this approach could become a standard tool for stabilizing the next generation of quantum bits, turning the unavoidable interaction with the environment from a source of error into a powerful resource for control.

Technical Summary: Engineering Multi-Photon Dissipation with a dc-Voltage-Biased Josephson Junction

Problem Statement
Quantum reservoir engineering utilizes dissipation to steer open quantum systems toward desired states, a resource critical for stabilizing bosonic qubits (e.g., cat qubits) and performing autonomous quantum error correction. Standard approaches employ parametrically pumped Josephson couplers to isolate specific multi-photon interaction terms (e.g., $\hat{a}^n \hat{b}^\dagger + \text{h.c.}$ ). However, these designs suffer from unavoidable parasitic nonlinear terms arising from the Josephson Hamiltonian, such as self-Kerr and cross-Kerr effects. These terms are difficult to suppress completely due to stray inductances and fabrication uncertainties, particularly at high pump powers, limiting the fidelity of state stabilization. Furthermore, parametric pumping can excite spurious higher modes via harmonics. The paper addresses the need for a coupling mechanism where these parasitic terms vanish by construction rather than by mitigation.

Methodology
The authors propose and experimentally demonstrate a circuit where a high-Q memory resonator (mode $a$ ) is coupled to a lossy buffer resonator (mode $b$ ) via a dc-voltage-biased Superconducting Quantum Interference Device (SQUID).

Mechanism: Unlike parametric pumping, which uses microwave drive photons, this system utilizes the energy $2eV$ gained or lost by Cooper pairs tunneling across the junction biased at voltage $V$ . By setting $2eV = n\hbar\omega_a - \hbar\omega_b$ , the system enables the conversion of $n$ memory photons into a single buffer photon (and vice versa).
Parasitic Suppression: The dc-bias modulation at the Josephson frequency $\omega_J = 2e\bar{V}/\hbar$ dresses all spurious terms (self-Kerr, cross-Kerr, bias-induced detunings). In the rotating wave approximation, these terms rotate at $\omega_J$ and average to zero at first order, unlike in pumped couplers where they remain static.
Experimental Setup: The device consists of coplanar-waveguide resonators galvanically connected to a SQUID on a sapphire substrate with a tantalum film. A stepped-impedance filter isolates the memory from the bias line while ensuring a high coupling rate for the buffer ( $\kappa_b/2\pi \approx 85$ MHz). A transmon qubit dispersively coupled to the memory is used for quantum state tomography (Wigner functions).
Noise Management: The authors address voltage noise, which could smear the energy matching condition. They demonstrate that proper filtering reduces voltage noise to levels where the resulting Josephson frequency linewidth ( $\sigma_J$ ) remains well below the buffer decay rate ( $\kappa_b$ ), preserving the engineered dissipation.

Key Contributions and Results

Activation of Multi-Photon Swaps: The team successfully demonstrated the conversion of 1, 2, and 4 memory photons into a single buffer photon by tuning the dc bias voltage.
- 1-to-1 Swap: Characterized via buffer reflectometry, showing hybridization of modes with a swap rate $g_1/2\pi \approx 4.8$ MHz at critical coupling.
- 2-to-1 and 4-to-1 Swaps: Confirmed by observing absorption features in the buffer spectrum that follow the energy matching conditions $\hbar\omega + 2eV = n\hbar\omega_a$ . The 4-to-1 process highlights the capability to reach high-order processes difficult to isolate with pumped couplers.
Characterization of Two-Photon Dissipation: Using a "deflate" experiment, the authors prepared the memory in a coherent state and monitored its decay under a 2-to-1 swap condition ( $2eV = 2\hbar\omega_a - \hbar\omega_b$ $2 e V = 2ℏ ω_{a} - ℏ ω_{b}$ ).
- The coherent state collapsed rapidly (within $\sim 50$ ns) toward the manifold spanned by $|0\rangle$ and $|1\rangle$ , followed by slower relaxation to vacuum.
- Fitting the average photon number decay yielded an effective two-photon loss rate $\kappa_2/2\pi = 0.51$ MHz, consistent with the theoretical prediction $\kappa_2 = 4g_2^2/\kappa_b$ in the adiabatic elimination regime.
- The maximum two-photon coupling rate was extracted as $g_2^{\text{max}}/2\pi = 18.5 \pm 0.5$ MHz.
Suppression of Nonlinearities:
- Self-Kerr: The memory self-Kerr rate was measured to be bounded by $K/2\pi < 3$ kHz at zero Josephson energy and did not visibly increase with $E_J$ , confirming the suppression of this parasitic term.
- Parasitic Losses: The authors identified that at large $E_J$ , memory lifetime is limited by parasitic 1-photon swaps with spurious modes in the bias line (specifically a standing wave mode at $\sim 227$ MHz). They attribute the observed extra loss scaling as $E_J^2$ to these processes and propose that adding filter periods could mitigate this by orders of magnitude.
- Dephasing: A voltage-bias-dependent dephasing rate was observed, attributed to the ac-Stark shift induced by environmental modes driven by the biased SQUID. This dephasing scales with $E_J$ and the voltage noise.

Significance and Claims
The paper claims to demonstrate a viable route for reservoir engineering that inherently suppresses parasitic nonlinear terms (self-Kerr, cross-Kerr) through the dynamical averaging provided by a dc-voltage bias. This approach offers practical advantages, including the absence of pump harmonics and easier scalability compared to microwave drives.
The authors conclude that while modest improvements in radiofrequency filtering are required to suppress spurious resonances limiting coherence at high swap rates, dc-voltage-biased Josephson junctions are a robust resource for engineering pure multi-photon dissipation. This capability is presented as a direct path toward stabilizing cat qubits and implementing quantum error correction schemes that rely on high-order parametric processes, such as four-legged cat qubits, without the detrimental nonlinearities that plague parametrically pumped systems.

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