Abstract
This chapter presents autonomous quantum engines that generate work in the form of directed motion for a rotor. We first formulate a prototypical clock-driven model in a time-dependent framework and demonstrate how it can be translated into an autonomous engine with the introduction of a planar rotor degree of freedom. The rotor plays both the roles of internal engine clock and of work repository. Using the example of a single-qubit piston engine, the thermodynamic performance is then reviewed. We evaluate the extractable work in terms of ergotropy, the kinetic energy associated to net directed rotation, as well as the intrinsic work based on the exerted torque under autonomous operation; and we compare them with the actual energy output to an external dissipative load. The chapter closes with a quantum-classical comparison of the engine’s dynamics. For the single-qubit piston example, we propose two alternative representations of the qubit in an entirely classical framework: (i) a coin flip model and (ii) a classical magnetic moment, showing subtle differences between the quantum and classical descriptions
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Notes
- 1.
To ensure a consistent quantum description of the rotor angle, the operator \(\hat{\varphi }\) will appear only in the form of strictly \(2\pi \)-periodic functions.
- 2.
We assume that the hot and cold dissipators do not themselves contribute to a net boost of angular momentum through their angular dependence. In the present case of thermal dissipators (9.10), this is ensured for real-valued modulation functions \(f_\mathrm{h,c}\).
- 3.
A passive state is a state whose energy content cannot be reduced further by means of another unitary. This implies that this state must be diagonal in the energy eigenbasis and its eigenvalues must decrease with growing energy.
- 4.
Notice that we choose to keep the contribution of spontaneous emission.
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Acknowledgements
This research is supported by the Singapore Ministry of Education through the Academic Research Fund Tier 3 (Grant No. MOE2012-T3-1-009); and by the same MoE and the National Research Foundation, Prime Minister’s Office, Singapore, under the Research Centres of Excellence programme. In addition, this work was financially supported by the Swiss SNF and the NCCR Quantum Science and Technology.
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Seah, S., Nimmrichter, S., Roulet, A., Scarani, V. (2018). Quantum Rotor Engines. In: Binder, F., Correa, L., Gogolin, C., Anders, J., Adesso, G. (eds) Thermodynamics in the Quantum Regime. Fundamental Theories of Physics, vol 195. Springer, Cham. https://doi.org/10.1007/978-3-319-99046-0_9
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