Converting coherence into work with a fully quantum engine

Abstract

Heat engines convert thermal energy into mechanical work. We here report the experimental realization of a fully quantum engine that converts quantum coherence into work. A single solid-state spin in diamond is fueled by a coherent bath and cyclically stores energy in a spin quantum battery. We establish quantum-enhanced performance by showing that almost 200$\%$ more work is produced after a few cycle compared to the corresponding classical engine. We obtain concrete criteria for successful coherence-to-work conversion, and highlight the importance of a coherent motor-battery interaction. This device harnesses nonclassical features during all stages of its cycle, and demonstrates the functionality of a nanomachine whose parts are all quantum coherent.

Figures (3)

• Figure 1: Coherent engine. a) Otto-like cycle for a spin-1/2 quantum working medium (motor) consisting of four steps: coherent heating, expansion, cooling and compression. The expansion and compression phases of the engine represent the adiabatic interaction stages, wherein the motor coherently exchanges energy with a spin-$1/2$ quantum battery, resulting in a power stroke. b) The quantum engine is experimentally implemented using the electron spin of a nitrogen-vacancy (NV) center in diamond (motor) and two nuclear carbon atoms ($\textsuperscript{13}$C$_{1}$ for the battery and $\textsuperscript{13}$C$_{2}$ for the cold bath). Heating is achieved by applying microwave fields, whereas coherent flip-flop interactions between motor and battery is realized with the help of Hamiltonian engineering. c) The subpanels display the measured one and two-qubit density matrices during initialization and power stroke stages that verify the nonclassicality of the medium state as well as the joint medium-battery state (see SI).
• Figure 2: Engine performance over one cycle. a) The work $W$ deposited into the battery during the first cycle, with increasing duration of the power stroke. Work is the same for incoherent (blue) and coherent (orange) heating, indicating that coherence-to-work conversion is ineffective when the battery is classical. b) By contrast, coherence is converted into work when the battery is also quantum, demonstrating quantum-enhanced work production (coherent spins are highlighted in yellow). c) The battery spin polarization $P_B^y(t)$ increases with the interaction time, showing that the quantum motor-battery coupling transfers coherence from the working medium to the flywheel. Good agreement with theoretical simulations (solid lines) is observed in all cases. Error bars correspond to one standard deviation.
• Figure 3: Performance of the coherent engine over many cycles. a) After the first few cycles, work production is significantly enhanced for coherent heating (orange) compared to incoherent heating (blue), demonstrating coherence-to-work conversion and quantum advantage, as well as effective work storage. Maximum work production is achieved after $N=8$ cycles, with an enhancement of almost 200$\%$ compared to the classical case, through coherence-preserving reset of the hot and cold baths. b) Coherence-to-work conversion is facilitated by the transfer of coherence from the motor to the battery, leading to an increase of the battery polarization $P_B^y$. c) The ergotropy $\cal E$ of the battery is equally increased in the presence of a coherent hot bath. The coherent part of the ergotropy ${\cal E}_q$ is shown in purple. d) The coherent ergotropy is related to the relative entropy of coherence $C_B$ of the battery, which quantifies its amount of quantum coherence, and exhibits a similar behavior as a function of the cycle number. Error bars correspond to one standard deviation.