Reimagining the Mpemba effect at the atomic scale

In a new Nature Communications study, scientists have demonstrated the quantum version of the strong Mpemba effect (sME) in a single trapped ion system.

The Mpemba effect is a counterintuitive phenomenon in which—under certain conditions—hotter water cools faster than colder water.

It was first described by Tanzanian high school student Erasto Bartholomeo Mpemba in 1963. However, according to early scientific literature, it was observed much earlier, as far as Aristotelian times.

While the classical effect remains incompletely understood, researchers have now shown they can create and control a quantum version that works fundamentally differently.

Phys.org spoke to some members behind the research, including Associate Professors Yan-Li Zhou and Jie Zhang, Professors Hui Jing and Ping-Xing Chen from the National University of Defense Technology in China and Associate Professor Weibin Li from the University of Nottingham.

The researchers shared their motivation behind the collaboration, “One common theme shared by all of us is about quantum control.”

“A few years ago, we were engaged in research related to relaxation acceleration and noticed Carollo et al.’s theoretical work on the quantum Mpemba effect, which inspired us to investigate the acceleration effects of the strong Mpemba effect from an experimental and theoretical joint perspective.”

The strong Mpemba effect (sME)

Relaxation describes the process of a system returning to its equilibrium or steady state. During this, a system can choose any path to reach equilibrium, with the path taking the most time being the slowest decaying mode (SDM).

In the classical Mpemba effect, a hotter system naturally has less overlap with the SDM, allowing it to reach equilibrium faster than a colder system.

While this happens naturally with temperature differences in classical systems, the quantum Mpemba effect works differently—it focuses on relaxation dynamics through quantum states and their evolution towards equilibrium.

In the quantum sME, an exponentially fast relaxation can be achieved by preparing a special quantum state that completely avoids the SDM, as shown theoretically by Carollo and colleagues.

However, their study demonstrated this was theoretically possible in quantum systems, but until now, no one had shown it working in practice.

The team explained, “The underlying principles that allow the strong Mpemba effect to be observed in a quantum system is devising an optimal initial state to prohibit excitation of the slowest decaying mode of the system.”

“This optimal initial state can be a quantum superposition state, representing a fundamental difference from the classic Mpemba effect, and thus the resulting dynamical behavior cannot be captured by semi-classical approaches.”

Liouvillian exceptional point

The preparation of this optimal initial state, however, will not always lead to exponential speedup. The team identified a critical point in the system when this exponential acceleration is possible—Liouvillian exceptional point (LEP).

“LEP is the boundary between the quantum strong Mpemba effect and weak Mpemba effect, which means we build a link between the Mpemba effect and the LEP,” explained the team.

At the LEP, the decay rates (eigenvalues) and paths (eigenmodes) of the systems “coalesce” into a single new rate and its associated path.

Before the LEP, the system can achieve exponential speedup because the optimal state can be prepared to avoid the slow decay path. However, at and after the LEP, exponential speedup is impossible since all paths merge, marking a boundary between the weak and strong Mpemba effect.

The team was the first to experimentally demonstrate the coalescence of eigenvalues and eigenmodes, and they did so using a single trapped ion system.

Single ion system

The team’s experimental setup consisted of a single trapped Calcium (⁴⁰Ca⁺) ion, focusing on three energy levels, ground state |0⟩ and two excited states |1⟩ and |2⟩.

A 729 nanometer (nm) laser ensures coherent decay between energy states using two frequency components with precisely controlled Rabi frequencies. The laser and quantum gate operations helped prepare the system’s initial state.

An additional 854 nm laser created a tunable decay channel, enabling the researchers to engineer specific relaxation dynamics. A 397 nm optical pumping beam was also introduced to prevent unwanted population leakage between quantum states.

The system was then allowed to evolve in this controlled environment, with researchers using quantum state tomography to measure the system’s quantum state and precisely track the relaxation dynamics.

The experimental approach not only represents the first realization and observation of the quantum sME, but also the observation of the coalescence of eigenvalues and eigenmodes at the LEP.

“We demonstrate, for the first time, the coalescence of the LEP clearly in the experiment from both eigenvalues and eigenmodes perspectives. Thus, our work builds a new bridge between such two active fields as the Mpemba effect and non-Hermitian physics, through which more exciting physics can be uncovered in the near future,” said the researchers.

Beyond the sME

The study of the Mpemba effect has attracted interest beyond fundamental physics. Energy dissipation, which in this case is the relaxation process, is central to all processes.

Optimizing or engineering this process is central to many fields, including quantum technologies. The researchers explained, “If the dissipation of the quantum system is engineered to prepare a specific steady state, then one might use this effect to speed up the relaxation.”

“In the context of quantum computing, our findings are expected to improve the efficiency of quantum state preparation and enhance the instantaneous bandwidth of quantum sensors.”

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