T_1 \gg 1$, the output populations of each quantum interferometer are then preserved (frozen) until the subsequent interferometer is reached in the following period; therefore, although the resonance condition is lost, the Mach-Zehnder quantum interference remains. This behavior can be contrasted with driven Rabi oscillations, for which there would be no signature of coherence in the limit $\nu T_2^* \sim 1$.

![image](Fig4_Oliver_final_red_size.png){width="5in"}

Microwave Cooling {#sec:Cooling}
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The previous discussion involved driving transitions in the lowest two energy levels in the double-well potential of our artificial atom (Fig. \[fig:4\]A), which constitute the two-level qubit subsystem of a more complex energy level diagram (Fig. \[fig:5\]C). When higher-excited states are accessed, the driven system behavior can be markedly different from the population saturation observed when only two levels are involved. For example, at least three levels are required to achieve population inversion, and such a multi-level artificial atom coupled to a microwave cavity has been used to demonstrate masing (microwave lasing) [@Astafiev07a]. In that work, Josephson quasi-particle states were driven to achieve inversion. Alternatively, population inversion can be established by accessing an ancilliary excited state via direct or LZS transitions. This will be briefly discussed in the next section.

Here, by reversing the 