Quantum nondemolition measurement of microwave photons using engineered quadratic interactions

We present a quantum electrical circuit with Josephson junctions formed of two anharmonic oscillators coupled with an interaction $g{\gamma }_1^2{\gamma }_2^2$, where ${\gamma }_1$ and ${\gamma }_2$ are positionlike coordinates. This type of coupling allows the quantum nondemolition measurement of the energy of one oscillator by monitoring the frequency of the second oscillator. Despite the fundamental tradeoff between the coupling strength $g$ and maximum photon-storage capacity of the oscillators, it is possible to achieve high-fidelity detection of up to ten photons over time scale on the order of microseconds. We discuss the possibility of observing quantum jumps in the number of photons and related applications.

Figure 1

(Color online) (a) dc-SQUID-based resonator: the cross symbols represent Josephson junctions. (b) Screening current $I_s$ versus transport current $I_t$ for $f=0$, $\beta =0$ (continuous line), $f=0.4$, $\beta =0$ (dashed line), and $f=0.4$, $\beta =0.2$ (dotted line), see text for details.

Figure 2

Diagram of the measurement scheme (see text for details). The presence of $n$ photons in the $N$ resonator causes an $n$-dependent shift of the frequency of the $D$ resonator, which is monitored in a reflection measurement.

Figure 3

(Color online) (a) The SNR as a function of $L_D/L_N$. (b) The maximum number of photons that can be store in each resonator $n_{\text{max},N}$ and $n_{\text{max},D}$ versus $L_D/L_N$.