⚛️ quantum physics

Experimental observation and application of the genuine Quantum Mpemba Effect

This paper presents an experimental demonstration of the genuine Quantum Mpemba Effect in a spin-1/2 system, revealing how coherence accelerates thermalization and enhancing the cooling power of a quantum Otto refrigerator.

Original authors: Bruno P. Schnepper, Jefferson L. D. de Oliveira, Yan A. C. Avó, Carlos H. S. Vieira, Krissia Zawadzki, Roberto M. Serra

Published 2026-08-18

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Bruno P. Schnepper, Jefferson L. D. de Oliveira, Yan A. C. Avó, Carlos H. S. Vieira, Krissia Zawadzki, Roberto M. Serra

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 world of heat and energy, there is a long-held intuition that things cool down at a rate determined by how hot they are. A cup of boiling water takes longer to reach room temperature than a cup of lukewarm water simply because it has more heat to lose. This seems like a fundamental rule of nature, yet for centuries, a few curious observers have noted exceptions. They reported that under specific conditions, a hotter object could actually reach the temperature of its surroundings faster than a warmer one. This counterintuitive phenomenon, known as the Mpemba effect, has been debated since the time of Aristotle and was famously named after a Tanzanian student in the 1960s. While scientists have studied this in everyday materials like water and colloidal suspensions, a deeper question remained: does this strange behavior exist in the realm of quantum mechanics, where particles behave according to the laws of the very small? Understanding this is crucial because quantum systems are the building blocks of future technologies, from ultra-fast computers to highly sensitive sensors. If these systems can be made to settle into their desired states more quickly, even if they start in a more chaotic or energetic condition, it could revolutionize how we build and operate quantum devices.

A team of researchers in Brazil and China has now provided the first experimental proof that this effect is real in a genuine quantum system. They worked with a single quantum bit, or qubit, which acts like a tiny magnet that can point in different directions. In their experiment, they used a liquid sample containing carbon and hydrogen atoms, manipulating the spins of these atomic nuclei with radio waves. The researchers set up a scenario where this quantum system was allowed to exchange heat with a neighboring system acting as a heat sink, essentially a reservoir that absorbs energy. They prepared the quantum system in two different starting states. In the first scenario, the system began in a state that was relatively close to its final, calm equilibrium. In the second scenario, they applied a precise sequence of radio pulses to transform the system into a different state that was actually further away from equilibrium and possessed higher energy.

According to standard thermodynamic expectations, the system starting with more energy should take longer to cool down. However, the researchers observed the opposite. The system that began in the more energetic, transformed state reached its final equilibrium temperature significantly faster than the one that started closer to equilibrium. This was not a trick of measurement; the team tracked the energy of the system continuously as it cooled. They found that the two cooling paths crossed each other at a specific moment in time. After this crossing point, the system that started with the "worse" initial condition was always closer to the final state than the one that started with the "better" condition. This crossing of paths is the definitive signature of the quantum Mpemba effect.

To understand why this happened, the scientists looked inside the mechanics of the cooling process. They discovered that the speed at which a quantum system relaxes depends on how its internal properties interact with the environment. The system has different modes of behavior, some of which decay very quickly and others that decay very slowly. The researchers found that the initial state which cooled faster was carefully engineered to avoid the slow-decaying modes entirely. Instead, it was composed almost entirely of the fast-decaying modes. By using a specific transformation, they effectively removed the "slow" part of the system's behavior, allowing it to slide rapidly into equilibrium. The system that started closer to equilibrium, by contrast, still contained a significant amount of the slow-decaying behavior, which acted as a bottleneck, dragging out the cooling process.

The team did not stop at observing this phenomenon; they also demonstrated how it could be used to improve a machine. They applied this effect to a quantum refrigerator, a theoretical device designed to pump heat out of a cold space to cool it down. In a standard cycle, the refrigerator has to wait for the working fluid to cool down completely before it can move to the next step. By using the quantum Mpemba effect to prepare the working fluid in the special, transformed state before the cooling phase, the researchers were able to speed up the entire cycle. This allowed the refrigerator to extract heat more quickly, increasing its cooling power by about six percent. While this percentage might seem small, in the context of quantum technologies where cycles happen in microseconds, such an improvement is significant. It proves that by understanding and manipulating the internal structure of quantum states, scientists can bypass natural bottlenecks to make quantum machines more efficient and powerful. This work confirms that the strange rules of the quantum world can be harnessed to solve practical problems, turning a counterintuitive curiosity into a useful tool for the future of technology.

Technical Summary: Experimental Observation and Application of the Genuine Quantum Mpemba Effect

Problem Statement
Accelerating the relaxation of quantum systems toward a steady state is a critical objective in non-equilibrium quantum thermodynamics, with implications for rapid state preparation, qubit engineering, and enhancing the power of quantum thermal cycles. The Quantum Mpemba Effect (QME) offers a theoretical pathway to achieve this speed-up. Unlike the classical Mpemba effect, where a "hotter" system cools faster than a "warmer" one, the genuine QME in the quantum regime is defined by a system starting from a state with higher non-equilibrium free energy (further from equilibrium) reaching the steady state faster than a system starting from a state with lower free energy. While theoretical frameworks based on Davies maps and Markovian open dynamics have recently described this phenomenon, experimental verification has been limited. A primary challenge lies in the need for high-level quantum control and the complete characterization of relaxation dynamics to distinguish the genuine QME from simple thermodynamic expectations or passive state relaxation.

Methodology
The authors employed Nuclear Magnetic Resonance (NMR) techniques on a liquid sample of 99% $^{13}$ C-labeled chloroform ( $CHCl_3$ ) diluted in acetone- $d_6$ . The experimental setup utilized the nuclear spin of $^1$ H as the working substance and the nuclear spin of $^{13}$ C as a heat sink.

System Preparation and Control: Using a 600 MHz Bruker NMR spectrometer, the team prepared an effective thermal state for the $^{13}$ C spin and initialized the $^1$ H spin into a non-equilibrium state ( $\hat{\rho}(0) \approx |x_+\rangle\langle x_+|$ ) exhibiting maximum coherence in the energy eigenbasis.
Heat Exchange Protocol: The relaxation dynamics were governed by a Davies map, realized experimentally through a sequence of radio-frequency (rf) pulses and free evolution periods under scalar coupling ( $J = 215.1$ Hz). The interaction Hamiltonian was $\hat{H}_{int} = 2\pi\hbar J \hat{\sigma}_z \otimes \hat{\sigma}_z$ .
Genuine QME Implementation: Two scenarios were compared:
- Direct Cooling: The heat exchange protocol was applied immediately to the initial state $\hat{\rho}(0)$ .
- Mpemba Cooling: Before heat exchange, a unitary transformation $\hat{U}$ was applied to generate the "Mpemba state" $\hat{\rho}_{mb}(0) = \hat{U}\hat{\rho}(0)\hat{U}^\dagger$ . This transformation diagonalized the state in the energy eigenbasis with a population inversion, ensuring minimal overlap with the slowest-decaying eigenmode of the Lindbladian super-operator.
Characterization: The authors performed Quantum Process Tomography (QPT) to verify that the heat exchange protocol satisfied the structural conditions of a Davies map (separability of populations and coherences, and Quantum Detailed Balance). They tracked the non-equilibrium free energy ( $F_{neq}$ ) and the trace distance to the steady state over time.
Application: The QME was integrated into a quantum Otto refrigerator cycle. The cycle included energy gap expansion, a cooling stroke (with or without the QME preparation), energy gap compression, and thermalization with a cold bath.

Key Results

Verification of Genuine QME: The experiment demonstrated that the transformed state $\hat{\rho}_{mb}(0)$ , despite possessing a higher initial non-equilibrium free energy than $\hat{\rho}(0)$ , reached thermal equilibrium faster. This was evidenced by the crossing of the free-energy trajectories over time, a signature of the genuine QME.
Mechanism Unveiled: Through QPT and analysis of the Lindbladian eigenmodes, the authors identified the physical mechanism: the original state $\hat{\rho}(0)$ had a significant projection onto the slowest-decaying coherence modes (eigenmodes 2 and 3), which acted as a bottleneck. In contrast, the Mpemba state $\hat{\rho}_{mb}(0)$ minimized this overlap, relying instead on the fastest-decaying population mode (eigenmode 4), thereby accelerating relaxation.
Refrigerator Performance: When applied to a quantum Otto refrigerator, the use of the QME preparation step resulted in a measurable increase in cooling power. The power gain ratio $R(\delta)$ reached approximately 6% at optimal conditions, demonstrating that the QME can be harnessed to improve the performance of quantum thermal machines.
Thermodynamic Consistency: The experimental process matrix confirmed the system behaved as a Davies map, satisfying the Quantum Detailed Balance condition and the decoupling of populations and coherences.

Significance and Claims
The paper presents a proof-of-concept experiment that successfully observes the genuine Quantum Mpemba Effect in a controlled spin-1/2 system. The authors claim that their work:

Unveils the Mechanism: It provides the first experimental identification of the specific role of Lindbladian eigenmodes in the QME, showing how suppressing slow coherence modes accelerates thermalization.
Bridges Theory and Experiment: It validates recent theoretical frameworks regarding the QME in the Markovian regime (specifically those by Moroder et al.) using NMR techniques.
Practical Application: It demonstrates a tangible advantage in quantum thermal tasks, specifically showing that the QME can be used to increase the cooling power of a quantum refrigerator.
Power-Efficiency Trade-off: The authors note that while the QME increases power, the preparation of the Mpemba state incurs an intrinsic cost (difference in non-equilibrium free energy), integrating the effect into the broader paradigm of power-efficiency trade-offs in quantum devices.

The study concludes that the QME represents a new mechanism for balancing power against efficiency, offering a pathway for optimizing quantum thermal machines, while acknowledging that further research is needed to explore these trade-offs across different scenarios.

More like this