Optimal work-to-work conversion of a nonlinear quantum Brownian duet

Performances of work-to-work conversion are studied for a dissipative nonlinear quantum system with two isochromatic phase-shifted drives. It is shown that for weak Ohmic damping simultaneous maximization of efficiency with finite power yield and low power fluctuations can be achieved. Optimal performances of these three quantities are accompanied by a shortfall of the tradeoff bound recently introduced for classical thermal machines. This bound can be undercut down to zero for sufficiently low temperature and weak dissipation, where the non-Markovian quantum nature dominates. Analytic results are given for linear thermodynamics. These general features can persist in the nonlinear driving regime near a maximum of the power yield and a minimum of the power fluctuations. This broadens the scope to an operation field beyond linear response.

Figure 1

Efficiency (a) and power fluctuations (b) in the LR regime as function of $P^{*}$ (see text). Blue (red) color refers to the $+$ ($-$) branch. The solid curve is $\alpha =4\kappa$ and the dashed curve $\alpha =0.2\kappa$. Other parameters are $\beta \omega =6,\omega =5{\mathrm{\Delta }}_{\mathrm{r}},{\mathrm{\Delta }}_{\mathrm{r}}=1,K=0.1$, and $F_2=0.1\omega$.

Figure 2

Maximum efficiency ${\eta }_{\mathrm{ME}}^{}$ (a) and tradeoff criterion $Q_{1,\mathrm{ME}}$ (b) versus $\beta \omega$ in the LR regime for $\alpha =5$ and different $K$ [in both (a) and (b)]. See text. Shortfall of the bound 2 occurs for $K⪅0.4$. The gradual increase of $Q_{1,\mathrm{ME}}$ in the range $1/4<K⪅0.4$ takes place at higher $\beta \omega$ than shown in (b).

Figure 3

Nonlinear regime. (a) and (b) Mean power and power fluctuations at maximum efficiency versus $F_2/\omega$. (c) Efficiency ${\eta }_{\mathrm{ME}}$ versus $F_2/\omega$. (d) Tradeoff criterion $Q_{1,\mathrm{ME}}$ versus $\beta \omega$ for different $F_2/\omega$. See text. The solid curves are those of nonlinear response (NLR), and the dashed curves pertain to linear response (LR). The parameters are $K=0.1,\alpha =5,\omega =5{\mathrm{\Delta }}_{\mathrm{r}}$, and ${\mathrm{\Delta }}_{\mathrm{r}}=1$. The parameter range covered by the plots is experimentally accessible in QPC transport experiments in the FQH regime [58, 59].

Figure 4

Sketch of the two-terminal setup of a fractional quantum Hall bar with a quantum point contact (QPC). The QPC is placed at $x=0$, and the two time-dependent voltages are applied at $x=-d$ and $x=d$.