⚛️ quantum physics

Observation of a power transfer controlled by the phase of a quantum superposition

This paper demonstrates that a driven superconducting transmon qubit can transfer power between two spatially separated transmission lines with directionality controlled solely by the phase of the qubit's quantum superposition, achieving a routing efficiency of 63% for maximal coherence.

Original authors: Nathanaël Cottet, Sébastien Jezouin, Bogdan Reznychenko, Alexia Auffèves, Benjamin Huard

Published 2026-07-22

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CC BY 4.0

Original authors: Nathanaël Cottet, Sébastien Jezouin, Bogdan Reznychenko, Alexia Auffèves, 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

The Quantum Traffic Cop

Imagine a world where energy isn't just a static fuel tank, but a flowing river that can be redirected, pumped, and steered. In the strange and wonderful realm of quantum physics, scientists study how tiny particles like atoms or artificial atoms (called qubits) interact with light and electricity. Usually, we think of these interactions as simple: you push a button, energy flows one way, and the machine does its job. But when you zoom in to the quantum level, things get weird. A key concept here is "superposition," which is like a coin spinning on a table. While it's spinning, it isn't just heads or tails; it's a blur of both at the same time. Another crucial idea is "phase," which is like the timing of that spin. If you have two spinning coins, their phases determine whether they are spinning in sync or out of sync.

Why does this matter? Because controlling how energy moves is the heart of all technology, from your phone to future quantum computers. If we can learn to steer energy not just with big switches and wires, but with the invisible, ghostly properties of quantum states, we could build machines that are incredibly efficient or perform tasks we thought were impossible. The big question scientists have been asking is: Can the "spinning coin" nature of a particle itself act as the steering wheel for energy, rather than just a classical dial we turn?

The Quantum Pump That Listens to a Ghost

In this paper, a team of researchers built a tiny, high-tech playground to answer that question. They used a superconducting "artificial atom" called a transmon qubit, which acts like a tiny, two-level switch that can be in a "ground" state (off) or an "excited" state (on). They connected this qubit to two separate highways for microwave signals, which we'll call Line A and Line B.

Here is the magic trick they performed: They blasted the qubit with signals from both Line A and Line B at the exact same time. But they set the signals up so that they perfectly canceled each other out. Imagine two people pushing a heavy box from opposite sides with equal force; the box doesn't move. In the quantum world, this meant the qubit felt no net push, so it shouldn't have done anything. It should have just sat there, inert.

But the qubit wasn't just sitting there. The researchers found that the qubit was acting like a pump, stealing energy from Line A and dumping it into Line B (or vice versa), even though the net force on it was zero. How? The direction of this energy flow wasn't controlled by a knob or a switch. Instead, it was controlled by the phase of the qubit's quantum superposition.

Think of the qubit's state as a spinning coin. If the coin is spinning with a specific "phase" (let's say, heads-up), the energy flows from Line A to Line B. If you flip the phase (making it tails-up), the flow instantly reverses, going from Line B to Line A. The researchers measured this by watching the power coming out of the lines. They saw that when they changed the phase of the qubit's superposition, the power flow changed direction, following a smooth curve like a cosine wave. It's as if the qubit was a traffic cop that didn't look at the cars (the signals) but listened to the rhythm of its own internal dance to decide which way the traffic should go.

The Efficiency of the Quantum Dance

Of course, nature is rarely perfect. The researchers had to deal with some "noise" in the system. Even though the qubit was pumping energy, some of it was just bouncing back (reflected) or leaking out randomly (spontaneous emission), which doesn't care about the direction. This meant the pump wasn't 100% efficient.

To figure out how good their quantum pump really was, they calculated an "efficiency" score. They found that when the qubit was in a perfect, balanced superposition (the most "quantum" state possible), it managed to route 63% of the energy in the desired direction. This is very close to the theoretical limit of 69% that the laws of physics (specifically the qubit's own stability times) say is possible.

The team also checked how this worked with different amounts of incoming energy. If the incoming signal was too weak, the random leakage (spontaneous emission) drowned out the directed flow. If the signal was too strong, the reflection took over, and the pump got overwhelmed. The sweet spot was right in the middle, where the directed flow was strongest.

Why This Is a Big Deal

This experiment is a big deal because it proves that quantum coherence—the ability of a particle to exist in a superposition—is a real, usable resource for moving energy. In the past, scientists used classical controls (like magnetic fields or engineered phases) to direct energy. Here, the direction was set by a purely quantum property: the phase of the superposition.

The researchers even compared their qubit to a simple, classical wave (like a vibrating guitar string). They showed that while a classical wave can also be steered, it relies on classical interference. The qubit, however, relies on a superposition of energy states that has no classical equivalent. It's a duality: the qubit's "on" and "off" states map to the classical "zero" and "one" of a wave, but the qubit's "spinning" superposition maps to the classical wave's amplitude. The paper concludes that this directional power transfer is a genuine quantum effect, opening the door to new types of thermodynamic machines that operate in the quantum regime, where the "knob" for controlling energy is the very fabric of quantum reality itself.

Technical Summary: Observation of a power transfer controlled by the phase of a quantum superposition

Problem and Motivation
In open quantum systems, drives are typically modeled as classical parameters. However, conservation of energy dictates that when a quantum system's internal energy changes under a drive, the energy of the driving mode must also change. While previous work has demonstrated energy flows between environmental modes controlled by classical parameters (e.g., magnetic flux, engineered control field phases, or adiabatic modulation), a gap remains in understanding whether the direction of energy flow can be governed by a genuinely quantum parameter. Specifically, this study addresses whether the direction of power transfer between two propagating modes can be set by the phase of a coherent superposition of qubit states, rather than by a classical "which-state" bit or external control knob.

Methodology
The authors realized an experiment using a superconducting transmon qubit ( $\omega_q/2\pi = 7.088$ GHz) coupled to two spatially separated transmission lines, $a$ and $b$ , via a far-detuned microwave cavity. The coupling rates were asymmetric ( $\gamma_b \approx \gamma_a/100$ ) to maximize fluorescence collection in line $a$ .

The experimental protocol involved:

Dual-Drive Configuration: The qubit was driven simultaneously by two modes with complex amplitudes set such that their net effect on the qubit's dynamics vanishes (i.e., $\Omega_a = -\Omega_b = \Omega$ ). In this "cancelling" configuration, the qubit Hamiltonian in the rotating frame is zero ( $H=0$ ), and the qubit state evolves only due to decoherence.
Phase Control: The qubit was initialized in a superposition state $|\psi\rangle = \cos(\theta/2)|g\rangle + e^{i\phi}\sin(\theta/2)|e\rangle$ . The phase $\phi$ of this superposition was the primary control variable.
Measurement: The output fields were measured using continuous heterodyne detection after quantum-limited amplification. The time-resolved output power in line $a$ was recorded to determine the net power flow.
Characterization: The Purcell rate ( $\gamma_a$ ) and qubit coherence times ( $T_1, T_2$ ) were independently characterized via fluorescence measurements under non-cancelling drives to establish theoretical bounds.

Key Contributions and Theoretical Framework
The paper derives the outgoing photon flux in each line, showing that the power consists of three terms: reflected input power, spontaneous emission, and stimulated emission/absorption.

Stimulated Emission as the Routing Mechanism: The directionality arises from the interference between the input drive and the fluorescence field emitted by the qubit. This term is proportional to the qubit coherence $\langle \sigma_x \rangle$ .
Phase-Dependent Directionality: When drives cancel ( $\Omega_a = -\Omega_b$ $Ω_{a} = - Ω_{b}$ ), the net power transfer is proportional to $\langle \sigma_x \rangle \propto \sin(\theta)\cos(\phi)$ $⟨ σ_{x} ⟩ \propto sin (θ) cos (ϕ)$ .
- If $\phi = 0$ , $\langle \sigma_x \rangle > 0$ , and energy is transferred from line $a$ to line $b$ .
- If $\phi = \pi$ , $\langle \sigma_x \rangle < 0$ , and energy is transferred from line $b$ to line $a$ .
Quantum vs. Classical Distinction: The authors highlight that while a linear harmonic oscillator driven by cancelling fields exhibits directional transfer proportional to the real part of its coherent state amplitude (a classical effect), the qubit's directional transfer relies on the superposition of energy eigenstates ( $|g\rangle$ and $|e\rangle$ ), a resource with no classical counterpart.

Results

Observation of Directional Transfer: Time-resolved measurements confirmed that the net power flow reverses direction as the superposition phase $\phi$ is tuned from $0$ to $\pi$ . The transfer amplitude follows a $\cos(\phi)$ dependence, matching theoretical predictions without adjustable fit parameters for the phase dependence.
Decoherence Dynamics: The power transfer decays over time as the qubit loses coherence. The stimulated emission term (proportional to $\langle \sigma_x \rangle$ ) decays at the rate $\gamma_2 = 1/T_2$ , while the spontaneous emission term (proportional to $\langle \sigma_z \rangle$ ) decays at $\gamma_1 = 1/T_1$ .
Routing Efficiency: The authors defined a routing efficiency $\eta$ $η$ based on the on/off ratio of photon flux in line $a$ $a$ for phases $\phi=\pi$ $ϕ = π$ and $\phi=0$ $ϕ = 0$ .
- For an equal superposition ( $\theta = \pi/2$ ), the maximum measured efficiency was 63%.
- This is close to the theoretical limit of 69% derived from the measured coherence times ( $T_1 = 2.22$ $\mu$ s, $T_2 = 3.21$ $\mu$ s).
- The efficiency is limited by the competition between the directional stimulated emission and the non-directional contributions of the reflected drive and spontaneous emission.
- At an input flux of 1 photon (on average), the efficiency drops to 46% (experimental) vs. 54% (ideal).

Significance and Claims
The paper claims to demonstrate that quantum coherence acts as a "non-classical knob" for power routing. The direction of energy flow between two modes is determined solely by the phase of the qubit's superposition, a genuinely quantum parameter.

Thermodynamic Context: The results contribute to the study of quantum thermodynamic machines, specifically those operating in the regime where a qubit acts as an energy pump or a measurement-powered engine.
Fundamental Insight: The work establishes a direct link between the efficiency of power transfer and the information leakage to the environment (decoherence).
Duality: The authors note a duality between the qubit and a harmonic oscillator: the qubit's superposition states map to the oscillator's classical coherent states, suggesting that what appears as classical interference in a linear system relies on quantum superposition in a two-level system.

The study does not propose immediate applications but situates the findings within the broader framework of chiral quantum optics and quantum energetics, demonstrating a fundamental mechanism for controlling energy flow using quantum coherence.

The Quantum Traffic Cop

The Quantum Pump That Listens to a Ghost

The Efficiency of the Quantum Dance

Why This Is a Big Deal

Technical Summary: Observation of a power transfer controlled by the phase of a quantum superposition

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