The inverse Mpemba effect has been observed in a quantum bit (qubit). The research was done at the Weizmann Institute in Israel and suggests that under certain conditions a cooler trapped-ion qubit may heat up faster than a similar warmer qubit. The observation could have important implications for quantum computing because many leading qubit types must be maintained at cryogenic temperatures.
The Mpemba effect is the puzzling observation that hot water sometimes freezes faster than cold water. It was first recorded in antiquity and is named after Erasto Mpemba, who as a teenager in Tanzania in the 1960s sought an explanation for the effect – which he first encountered while making ice cream and then confirmed in a series of experiments. Despite the best efforts of physicists over the past six decades, the effect remains poorly understood.
Researchers have also observed the inverse Mpemba effect whereby a cold system heats up faster than a warm system. Theoretical and experimental studies have revealed a range of systems – magnetic, granular, quantum and more – that exhibit Mpemba effects.
Avoiding decoherence
Quantum Mpemba effects are of particular interest to people developing cryogenic qubits. These must be operated at very low temperatures to reduce noise, which destroys quantum calculations in a process called decoherence.
In a new experiment described in Physics Review Letters, Shahaf Aharony Shapira and colleagues observed an inverse Mpemba effect in a single trapped strontium-88 ion coupled to an external thermal bath. This low-temperature ion acted as a qubit that interacted with the thermal bath, causing a slow decoherence of its quantum state over time.
“Most studies are about the direct Mpemba effect, which is easier to understand if you think classically,” says Aharony Shapira.
She offers an intuitive description of the classical Mpemba effect. Imagine, she says, a double-well potential where one well is a global minimum – the system’s most stable state – and the other is a local minimum – a comparatively less stable state.
Uniform energy distribution
When a system is at a high temperature, its energy distribution is relatively uniform, allowing it to transition between the two wells more freely. At lower temperatures, the system’s energy distribution becomes much narrower, concentrating near the bottom of each of the wells.
If the system starts in the local minimum, higher-temperature systems have lower energy barriers between the two wells, allowing them to transition quicker to the global minimum as it cools down.
“However, the inverse effect that we saw has a different intuition,” says Aharony Shapira.
End-state shortcut
To simulate the thermal bath, the team used laser pulses to induce transitions between the qubit states and the higher energy states of the trapped ion. Eventually, the interaction between the thermal photons from the laser caused the qubit to decohere.
The path the system takes as it moves towards its end-state is known as its “relaxation path”. This path is governed by the system’s interactions with the bath and its intrinsic quantum properties, such as coherence and interference effects that can suppress or enhance certain relaxation modes.
Unlike in classical systems, the relaxation rates in quantum systems do not change linearly with temperature. For certain initial conditions, a colder qubit might have a relaxation path that allows it to bypass certain energy barriers more efficiently than a warmer qubit. This shortcut allows it to reach the higher temperature equilibrium state faster than the warmer qubit – which is what the researchers observed.
School bus analogy
Team member Yotam Shapira explains the observation using the analogy of a bus driver waiting for schoolchildren to disembark. The bus driver, he said, finishes work when the last child gets off and is therefore limited by the speed of the slowest child.
“What we saw is that we can find conditions where it’s like the slowest child didn’t show up that morning,” he says, “Now the transition is much faster.”
When cold warms faster than hot
Hisao Hayakawa is a researcher from Kyoto University whose team observed the Mpemba effect in a quantum dot. He says that the mechanisms observed at Weizmann Institute were similar to those seen in previous experiments. However, he suggests that the research may provide more insights into finer control mechanisms for quantum computing systems.
“These experiments suggest that the speed control to reach a desired state in quantum computers might be possible if we know the physics of the quantum Mpemba effect after a quench,” he said. A quench refers to a sudden change in a quantum system’s conditions, such as its temperature or magnetic field.
The research could influence the design of large-scale, temperature-sensitive qubit systems. “Maybe not cooling the system as much as you can would be best in the future,” said Aharony Shapira, “You need to be sensitive to special modes that, like in our case, can heat up very fast.”
