FIG. 2: The dependence of the maximum achievable purity S$_{max}$ of the system (solid line) and the overlapping resonance A$_{+}$$_{−}$ (dashed line; right y-axis) on the coupling strength g$_{r}$/ (2 π ). Here (a) g$_{ph}$ = 2 π × 500 MHz, g$_{nr}$ = 2 π GHz and (b) g$_{ph}$ = 2 π GHz, g$_{nr}$ = 2 π × 500 MHz. The remaining parameters are ω = 2 π GHz, ω$_{0}$ = 2 π × 100 MHz, and the temperature T = 25 mK. The purity is calculated at a time t = 0 . 1 ns. FIG. 3: Variation of purity with time for the initial states ( − 0 . 539998 | + 〉 +0 . 841665 |−〉 ) (solid line), ( | + 〉 + |−〉 ) $_{/}$√$_{2 (dashed line), and}$ | + 〉 (dotted line). Here the interaction strengths g$_{r}$ = 2 π × 400 MHz, g$_{nr}$ = 2 π GHz, and g$_{ph}$ = 2 π × 500 MHz. The other parameters are as in Fig. 2. 14  0.5  0.6  0.7  0.8  0.9  1  0  2e-11  4e-11  6e-11  8e-11  1e-10 S time (sec)  0.5  0.6  0.7  0.8  0.9  1  0  2  4  6  8  10  12  14  100  200  300  400  500  600  700 (a) S max Overlap g$_{r}$/2  (x 10$^{8}$ Hz)  0.5  0.6  0.7  0.8  0.9  1  0  2  4  6  8  10  12  14  100  200  300  400  500  600  700 (b) S max Overlap g$_{r}$/2  (x 10$^{8}$ Hz)