Virtual Qubit Reduces Thermodynamic Uncertainty, Enabling Enhanced Nanoscale System Performance

The fundamental relationship between energy fluctuations and entropy production is being re-examined, with implications for the efficiency of nanoscale technologies. Yang Li and Fu-Lin Zhang, from Tianjin University, alongside their colleagues, investigate this connection using a novel approach involving a ‘virtual qubit’ , a system created by coherent coupling between energy levels. Their research demonstrates that this virtual qubit can reduce thermodynamic uncertainty, potentially allowing for optimisation of thermal machines and surpassing classical limitations. By analysing steady-state currents and entropy production, the team reveals a decomposition of uncertainty into classical and coherent components, with the latter reaching a minimum at conditions that maximise coherence. This work identifies specific criteria for exceeding established thermodynamic bounds, bringing us closer to more efficient and powerful micro- and nanoscale devices.

Quantum thermal-machines require understanding transient universal responses to optimise performance and enable technological advancement. This work analyses these responses in quantum thermal-machine models utilising coherent coupling between two energy levels, effectively creating a virtual qubit. Steady-state coherences are restricted to this virtual-qubit subspace, and without coherent coupling, the system adheres to detailed balance with thermal reservoirs, exhibiting no steady-state heat currents. The research demonstrates that steady-state currents and entropy production are fully reproducible by an effective classical Markov process, while current fluctuations exhibit an additional purely quantum contribution.

Coherence Drives Entropy Production in Nanoscale Engines

Scientists have demonstrated a novel thermodynamic uncertainty relation applicable to micro- and nanoscale systems, revealing genuinely new effects crucial for optimising technological performance. Their work centres on analysing this relation within thermal-machine models utilising coherent coupling between two energy levels, effectively creating a virtual qubit. Steady-state coherences are confined to this virtual-qubit subspace, and the absence of coherent coupling results in detailed balance with thermal reservoirs, preventing steady-state heat currents. Experiments revealed that these steady-state currents and entropy production are fully reproducible by an effective classical Markov process, while current fluctuations exhibit a correction originating from coherence.

The research team meticulously measured the decomposition of the uncertainty into classical and coherent contributions, discovering that the coherent component becomes negative under resonant conditions. This negative coherence reaches a minimum at the coupling strength that maximises steady-state coherence, a critical finding for system optimisation. Further analysis identified the conditions necessary to surpass the classical bound, specifically in the vicinity of the reversible limit, suggesting pathways to enhanced efficiency. The researchers mapped the time-dependent driven model onto an equivalent stationary coupling system through a rotating reference frame, ensuring identical photon number currents.

Introducing a rotating transformation, the density matrix evolution was governed by a master equation with a time-independent Hamiltonian, simplifying analysis. Measurements confirm that the detuning parameter, representing the energy-level splitting and driving frequency difference, is crucial for the stationary-coupling case, with thermodynamic consistency requiring these values to be equal. The team restricted their focus to the relation expressed in terms of heat current and variance for reservoirs participating in transitions between energy levels, establishing that currents are fully correlated between reservoirs. Data shows that the photon-number current from the system into a reservoir can be calculated by evaluating the action of jump operators on the density matrix.

The researchers constructed a classical counterpart of the system, replacing coherent interaction with an effective dissipator, and demonstrated that the classical model reproduces the steady-state currents and entropy production of the original quantum system. Specifically, they found that the steady-state current in the classical model is equal to the net number of transitions induced by the original interaction, with a relationship established between currents and reservoir properties. The entropy production rate was found to be identical for both the quantum and classical systems, confirming the effectiveness of the classical approximation. Through a counting-field approach, scientists calculated the variance of the current and the thermodynamic uncertainty.

Coherence Minimises Thermodynamic Uncertainty in Virtual Qubits

This research presents a comprehensive analysis of the thermodynamic uncertainty relation within quantum thermal machines operating via coherent coupling between energy levels, effectively forming a virtual qubit. By examining these models, the authors demonstrate that while steady-state currents and entropy production align with classical Markovian processes, current fluctuations exhibit a distinct quantum contribution originating from coherence. This allows for a natural decomposition of the relation into classical and coherent components, with the latter potentially becoming negative under resonant conditions. The study identifies specific coupling strengths that minimise the coherent contribution to thermodynamic uncertainty, simultaneously maximising steady-state coherence within the virtual qubit.

This reveals a direct relationship between coherence as a quantum resource and the precision of energy transport. Although the analysis relies on a local master equation, the authors confirm its equivalence to a global approach under resonant conditions, and acknowledge a limitation in extending the current framework to systems with coherence across multiple energy levels. Future work could investigate the role of other quantum correlations, such as entanglement, in contributing to thermodynamic uncertainty and potentially establishing a hierarchical relationship between these effects.