Quantum flywheel

In this work we present the concept of a quantum flywheel coupled to a quantum heat engine. The flywheel stores useful work in its energy levels, while additional power is extracted continuously from the device. Generally, the energy exchange between a quantum engine and a quantized work repository is accompanied by heat, which degrades the charging efficiency. Specifically when the quantum harmonic oscillator acts as a work repository, quantum and thermal fluctuations dominate the dynamics. Quantum monitoring and feedback control are applied to the flywheel in order to reach steady state and regulate its operation. To maximize the charging efficiency one needs a balance between the information gained by measuring the system and the information fed back to the system. The dynamics of the flywheel are described by a stochastic master equation that accounts for the engine, the external driving, the measurement, and the feedback operations.

Figure 1

General scheme of a heat engine with a flywheel. (a) The state of two qubits of the heat engine, coupled to heat baths at temperatures $T_h$ and $T_c$, is represented as a two-qubit state with population inversion between the second and third energy levels. The size of the sphere represents the population in each level. (b) The population inversion in the engine corresponds to a heat bath with the inverse negative temperature ${\beta }_e^{-}$. This bath is coupled to the harmonic oscillator (flywheel), increasing exponentially its energy and the width of phase-space probability distribution. (c) Measurement of the quadratures of the harmonic oscillator, resulting in the signal $\overline{c}$. The signal is then fed back to the oscillator to ensure a steady state. (d) Energy flow chart of the different components in the steady state of the flywheel.

Figure 2

Charging efficiency as function of measurement strength ${\gamma }_m$ and feedback strength ${\kappa }_f$. The percentage of useful work out of the entire energy stored in the flywheel has a maximum for the ratio ${\gamma }_m/{\kappa }_f=2$, and it is further maximized for ${\kappa }_f$ approaching its threshold $|{\kappa }_e^{-}|=5\times {10}^{-8}$. Here: ${\omega }_o=1, {\beta }_e^{-}=-{10}^{-1}, {\mathrm{\Gamma }}_e={10}^{-6}$, and ${\epsilon }_d=9\times {10}^{-2}$.