Quantum Systems Can Still Generate Power Despite Energy Loss

A new quantum heat engine utilising qubits and qutrits interacting with thermal environments via generalised amplitude damping channels has been investigated by Indrajith VS and Disha Verma at National Institute of Technology. Verma and colleagues show how these quantum channels model heat transfer and work extraction, revealing conditions for achieving positive work output. Their thorough analysis of quantum correlations, emission probability, and system-environment interactions demonstrates that multilevel quantum systems outperform two-level systems in both work extraction and resilience to decoherence, offering key insight into the development of practical quantum thermodynamic devices.

Quantum thermodynamics extends classical principles to nanoscale energy conversion

The coexistence of thermal fluctuations and quantum effects in microscopic systems is currently under investigation. It extends classical thermodynamic principles by incorporating quantum features such as coherence, correlations, and measurement back-action, enabling a consistent description of nonequilibrium processes. As a unifying discipline, quantum thermodynamics bridges fundamental physics and emerging quantum technologies, offering insights into the limits of efficiency, control, and performance of nanoscale devices.

Several quantum-enabled technologies have been proposed, including quantum thermal machines, quantum batteries, and quantum thermodynamic sensors. Indrajith VS and colleagues have proposed quantum thermal machines, quantum batteries, and quantum thermodynamic sensors. Quantum heat engines (QHEs) and quantum batteries have attracted attention due to their potential applications in energy storage, energy conversion, and quantum information processing. QHEs represent an extension of classical heat engines into the quantum regime, where energy exchange and work extraction are governed by quantum mechanics.

These engines serve as platforms for probing the laws of thermodynamics at the quantum level and for assessing the role of quantum resources in energy conversion and information processing. A typical QHE consists of a microscopic working medium, such as a two-level system, harmonic oscillator, or many-body quantum system, that undergoes a thermodynamic cycle while interacting with thermal reservoirs. Unlike classical engines, the performance of QHEs is influenced not only by temperature gradients but also by quantum features like coherence, quantum correlations, and finite-time effects.

Consequently, quantum heat engines offer platforms to explore the laws of thermodynamics at the quantum level. A broad class of models exploits distinct quantum mechanical effects. Squeezed thermal baths, which are non-equilibrium quantum states, enable reduced entropy production and enhanced work extraction. Incorporating non-Markovian dynamics introduces environmental memory effects that preserve coherence and mitigate dissipative losses. Quantum-correlated reservoirs, where entanglement exists between thermal baths, allow for energy extraction beyond classical thermodynamic limits.

Recent studies have investigated the roles of quantum measurements, feedback control, and coherence recycling in optimising engine efficiency. Additional proposals explore many-body working substances, strong system-bath coupling regimes, and the exploitation of quantum phase transitions to enhance power output and efficiency, stressing the rich field of quantum-enhanced thermal machines. Significant efforts have been directed toward developing QHE models based on realistic and experimentally accessible physical systems, bridging the gap between theoretical constructs and practical implementations.

Representative platforms include deformed quantum fields, quantum spin chains, optomechanical systems, and superconducting qubits. Complementing these theoretical advances, experimental realizations of quantum heat engines have been successfully demonstrated across diverse platforms. Notable examples include implementations using single trapped ions, ensembles of nitrogen-vacancy (NV) centres in diamond, and nuclear magnetic resonance systems. These experimental achievements provide insights into quantum thermodynamic processes and validate key theoretical predictions.

More recently, measurement-based quantum heat engines have emerged as a promising model, wherein quantum measurements play an active role in energy exchange and work extraction. Weak measurements enable partial information extraction with minimal disturbance, allowing the system to retain coherence while enabling controlled energy flow. Such engines clarify the fundamental thermodynamic role of information and measurement back-action, opening new avenues for energy conversion beyond conventional thermal cycles.

This work explores quantum heat engines employing qubit and qutrit working media coupled to thermal reservoirs through Generalised Amplitude Damping (GAD) channels. The focus of the study is on the role of quantum channels in describing energy exchange processes such as heat absorption, dissipation, and work generation in quantum heat engines. Special attention is given to the effects of quantum correlations, population dynamics, and system-environment interactions on the overall thermodynamic behaviour of the engine.

The ergotropy of qubit and qutrit systems under dissipative evolution is investigated, analysing how environmental effects influence the amount of extractable work available in these quantum thermal machines. A two-level quantum system is described by two discrete energy eigenstates: the ground state |g⟩, corresponding to lower energy, and the excited state |e⟩, corresponding to higher energy. The Hamiltonian governing the system is given by H = εg 0 0 εe, where e.g. and ee represent the energies of the ground and excited states, respectively.

The statistical populations of these states are denoted by pg and pe, respectively, where pg represents the probability of finding the system in the ground state and pe represents the probability of finding it in the excited state such that pg + pe = 1. The initial state is prepared as ρ = pg 0 0 pe. In the first stage of the cycle, the system interacts with a unitary reservoir and evolves under the action of the unitary operator U1. The unitary evolution is chosen such that the populations of the energy eigenstates remain unchanged during the process, modifying only the coherences of the state while preserving the diagonal elements in the energy basis. The resulting state is ρ1 = U1 ρ U1†. Subsequently, the system is brought into contact with an external environment, allowing energy exchange that modifies the population distribution between the ground and excited states. This stage of the evolution is modelled using the Generalised Amplitude Damping (GAD) channel, capturing the influence of a finite-energy environment on a two-level system.

The corresponding evolution is described by a set of Kraus operators: A0 = pf 1 0 0 √1 −γ, A1 = pf 0 √γ 0 0, A2 = p 1 −f √1 −γ 0 0 1, A3 = p 1 −f 0 0 √γ 0. Here, γ = 1 −e−Γt, where Γ denotes the spontaneous transition rate and t represents the interaction time. The interaction is chosen such that the population of the excited state increases as a result of energy gained from the environment. The parameter f characterizes the relative likelihood of downward transitions, while 1−f corresponds to upward transitions induced by the reservoir.

The value of f depends on the relative energetic configuration of the system and the environment, determining the direction and magnitude of population redistribution. The evolved state under the GAD channel is given by the completely positive trace-preserving map: ρ2 = X k Akρ1A† k, where ρ1 is the state before this interaction. After applying the Kraus operators, the state becomes ρ2 = fγpe + [1 + (f −1)γ]pg 0 0 (1 −fγ)pe −(f −1)γpg 0. For the excited-state population to exceed that of the ground state after the interaction, the following condition must be satisfied: 1 + 2γ(f −1) 1 −2γf pe. The heat rejected in the excitation via amplitude damping channel is Q2 = try(ρ1H′ −ρ3H′) = [(f −1)γpg + fγpe]∆c, which is negative when the ground state population is sharply higher than the excited state. The work done for the protocol using a quantum channel is calculated as W = Q1 + Q2 = [(1 −f)γpg −fγpe](∆h −∆c). The work done in this system is influenced by factors such as the probability of emission, decoherence parameter, and population density.

Qutrit systems enhance efficiency and stability in nanoscale heat engines

Quantum heat engines offer a tantalising route to nanoscale energy conversion, potentially revolutionising fields from sensing to computation. This research highlights the benefits of utilising qutrits, quantum systems with three levels, over traditional two-level qubits, improving both efficiency and durability to environmental disruption. Qutrits demonstrate greater work extraction and durability against environmental ‘noise’, known as decoherence, vital for practical device development.

Employing qutrits within quantum heat engines demonstrably improves performance compared to traditional qubits, offering greater potential for energy conversion at the nanoscale. Scientists have identified conditions for achieving positive work output by modelling energy transfer. This work therefore shifts focus from simply proving quantum heat engines are possible, to optimising their design for real-world application.

Qutrit systems enhance efficiency and stability in nanoscale heat engines. This research demonstrated that multilevel quantum systems, specifically qutrits, are capable of extracting more work and are more robust to decoherence than two-level qubit systems. This finding matters because it suggests a pathway towards building more reliable and effective nanoscale heat engines for energy conversion. The authors analysed how factors like emission probability and system-environment interactions influence work output, providing insight into optimising these devices.