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arXiv:2401.05830

The inverse Mpemba effect demonstrated on a single trapped ion qubit

Shahaf Aharony Shapira, Yotam Shapira, Jovan Markov, Gianluca Teza, Nitzan Akerman, Oren Raz, Roee Ozeri

Published Jan 11, 2024• 0 citations
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Abstract

The Mpemba effect is a counter-intuitive phenomena in which a hot system reaches a cold temperature faster than a colder system, under otherwise identical conditions. Here we propose a quantum analog of the Mpemba effect, on the simplest quantum system, a qubit. Specifically, we show it exhibits an inverse effect, in which a cold qubit reaches a hot temperature faster than a hot qubit. Furthermore, in our system a cold qubit can heat up exponentially faster, manifesting the strong version of the effect. This occurs only for sufficiently coherent systems, making this effect quantum mechanical, i.e. due to interference effects. We experimentally demonstrate our findings on a single $^{88}\text{Sr}^+$ trapped ion qubit. The existence of this anomalous relaxation effect in simple quantum systems reveals its fundamentality, and may have a role in designing and operating quantum information processing devices.

DOI
10.48550/arxiv.2401.05830

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The Mpemba effect is a counter-intuitive phenomena in which a hot system reaches a cold temperature faster than a colder system, under otherwise identical conditions. Here we propose a quantum analog of the Mpemba effect, on the simplest quantum system, a qubit. Specifically, we show it exhibits an inverse effect, in which a cold qubit reaches a hot temperature faster than a hot qubit. Furthermore, in our system a cold qubit can heat up exponentially faster, manifesting the strong version of the effect. This occurs only for sufficiently coherent systems, making this effect quantum mechanical, i.e. due to interference effects. We experimentally demonstrate our findings on a single 88Sr+^{88}\text{Sr}^+88Sr+ trapped ion qubit. The existence of this anomalous relaxation effect in simple quantum systems reveals its fundamentality, and may have a role in designing and operating quantum information processing devices.
The Mpemba effect is a counterintuitive phenomena in which a hot system reaches a cold temperature faster than a colder system, under otherwise identical conditions. Here, we propose a quantum analog of the Mpemba effect, on the simplest quantum system, a qubit. Specifically, we show it exhibits an inverse effect, in which a cold qubit reaches a hot temperature faster than a hot qubit. Furthermore, in our system a cold qubit can heat up exponentially faster, manifesting the strong version of the effect. This occurs only for sufficiently coherent systems, making this effect quantum mechanical, i.e., due to interference effects. We experimentally demonstrate our findings on a single ^{88}Sr^{+} trapped ion qubit. The existence of this anomalous relaxation effect in simple quantum systems reveals its fundamentality, and may have a role in designing and operating quantum information processing devices.
The Mpemba effect, where a hotter system cools faster than a colder one under otherwise identical conditions, has been extensively studied in classical systems. In this work, we present the quantum analogue of the Mpemba effect using a dissipative qubit, which is referred to as the canonical quantum Mpemba effect. We demonstrate that, under the identical conditions, the relaxation dynamics of a qubit initialized in a thermal state with a higher temperature can be exponentially faster than those of a colder thermal state. Strikingly, this acceleration is determined solely by the initial temperature of the system, independent of other parameters. The relaxation is confirmed to be a genuine cooling process via the effective steady state temperature, mirroring its classical counterpart. Last, we propose a practical classical quantum hybrid algorithmic quantum circuit to realize this effect using superconducting qubits experimentally.
An ancient and counterintuitive phenomenon known as the Mpemba effect (water can cool faster when initially heated up) showcases the critical role of initial conditions in relaxation processes. How to realize and utilize this effect for speeding up relaxation is an important but challenging task in purely quantum system till now. Here, we experimentally study the strong Mpemba effect in a single trapped ion system in which an exponentially accelerated relaxation in time is observed by preparing an optimal quantum initial state with no excitation of the slowest decaying mode. Also, we demonstrate that the condition of realizing such effect coincides with the Liouvillian exceptional point, featuring the coalescence of both the eigenvalues and the eigenmodes of the systems. Our work provides an efficient strategy to engineer the dynamics of open quantum system, and suggests a link unexplored yet between the Mpemba effect and the non-Hermitian physics. The Mpemba effect is an archetype for various anomalous relaxation phenomena. Here, the authors experimentally study a quantum version of the Mpemba effect in a single trapped ion system, where relaxation is exponentially accelerated by removing the excitation of the slowest decaying mode. This phenomenon, seen in Markovian open quantum systems containing Liouvillian exceptional points, indicates a link between the Mpemba effect and non-Hermitian physics.
Passive qubit reset is a key primitive for quantum information processing, whereby qubits are initialized by allowing them to relax to their ground state through natural dissipation, without the need for active control or feedback. However, passive reset occurs on timescales that are much longer than those of gate operations and measurements, making it a significant bottleneck for algorithmic execution. Here, we show that this limitation can be overcome by exploiting the Mpemba effect, originally indicating the faster cooling of hot systems compared to cooler ones. Focusing on the regime where coherence times exceed energy relaxation times (T2>T1T_2 > T_1T2​>T1​), we propose a simple protocol based on a single entangling two-qubit gate that converts local single-qubit coherences into fast-decaying global two-qubit coherences. This removes their overlap with the slowest decaying Liouvillian mode and enables a substantially faster relaxation to the ground state. For realistic parameters, we find that our protocol can reduce reset times by up to 50%50\%50% compared to standard passive reset. We analyze the robustness of the protocol under non-Markovian noise, imperfect coherent control and finite temperature, finding that the accelerated reset persists across a broad range of realistic error sources. Finally, we present an experimental implementation of our protocol on an IQM superconducting quantum processor. Our results demonstrate how Mpemba-like accelerated relaxation can be harnessed as a practical tool for fast and accurate qubit initialization.
The Mpemba effect (ME)—where hot systems cool faster than colder ones—has intrigued both classical and quantum thermodynamics. Compared to classical systems, quantum systems add complexity due to quantum correlations. Recent works have explored anomalous relaxation and Mpemba-like effects in several quantum systems, considering isolated systems at zero temperature or open systems in contact with reservoirs under Markovian or non-Markovian dynamics. However, these models typically assume an initial unentangled system–bath state, overlooking the role of initial system–environment correlations. Here we propose a type of quantum ME, distinct from the strong ME, originating solely from initial system–bath entanglement. It is shown that the degree of initial entanglement significantly influences the early relaxation dynamics, with certain conditions causing backflow and retarded thermalization. As an example, we investigate the spontaneous emission of a two-level atom in a photonic waveguide at zero temperature, where an initial atom-photon entangled state results in delayed relaxation and a pronounced ME. These findings highlight the crucial role of quantum correlations in thermalization processes and open new avenues for identifying and engineering quantum Mpemba phenomena. Controlling relaxation dynamics through system–environment entanglement may have potential applications in quantum thermal machines, state initialization protocols, and quantum information processing, where precise control over thermalization is essential.