Quantum nondemolition microwave photon counter based on the cross-Kerr nonlinearity of a Josephson junction embedded in a superconducting circuit

1. A microwave device comprising:

a dispersive nonlinear element;

a pump resonator, at a first pump resonator end, connected to both the dispersive nonlinear element and a first stub, the pump resonator, at a second pump resonator end, being capacitively coupled to a pump port, wherein the first stub is terminated in an open circuit; and

a quantum signal resonator, at a first quantum signal resonator end, connected to both the dispersive nonlinear element and a second stub, the quantum signal resonator, at a second signal resonator end, being capacitively coupled to a signal port, wherein the second stub is connected to ground.

2. The microwave device of claim 1 , wherein the dispersive nonlinear element is at least one Josephson junction.

3. The microwave device of claim 1 , wherein the dispersive nonlinear element is an array of Josephson junctions.

4. The microwave device of claim 1 , wherein the pump resonator comprises a pump resonance mode, the pump resonance mode having a pump resonance frequency and a pump wavelength;

wherein a length of the pump resonator corresponds to a quarter wavelength of the pump wavelength;

wherein the quantum signal resonator comprises a signal resonance mode, the signal resonance mode having a signal resonance frequency and a signal wavelength;

wherein a length of the quantum signal resonator corresponds to a quarter wavelength of the signal wavelength; and

wherein the pump resonance mode and the signal resonance mode are coupled to the dispersive nonlinear element.

5. The microwave device of claim 4 , wherein by having the pump port and the signal port spatially separated and by having the pump resonance mode and the signal resonance mode isolated from each other via the first and second stubs, no direct power leakage occurs between the pump and signal ports;

wherein the pump resonator and the quantum signal resonator are configured such that pump resonance mode acquires a frequency shift according to a number of photons in an input quantum signal at the signal resonance frequency.

6. The microwave device of claim 5 , wherein the pump resonator and the quantum signal resonator are configured such that a cross-Kerr nonlinear effect is generated in the dispersive nonlinear element in response to an input pump signal, thereby creating a nonlinear interaction between the pump resonance mode and the signal resonance mode.

7. The microwave device of claim 6 , wherein the cross-Kerr nonlinear effect causes a reflected pump signal at the pump resonance frequency to be dependent on the number of the photons in the input quantum signal at the signal resonance frequency.

8. The microwave device of claim 7 , wherein the pump resonator is configured such that the reflected pump signal at the pump resonance frequency carries information about a presence or absence of the photons in the input quantum signal.

9. The microwave device of claim 6 , wherein the cross-Kerr nonlinear effect causes a reflected quantum signal at the signal resonance frequency to be dependent on a number of photons in the input pump signal at the pump resonance frequency.

10. The microwave device of claim 5 , wherein the pump resonator is configured such that a size of the frequency shift in the pump resonance frequency is determinative of the number of the photons in the input quantum signal.

11. The microwave device of claim 5 , wherein the pump resonator, the quantum signal resonator, the first and second stubs, and the dispersive nonlinear element are configured to neither destroy nor absorb the photons in the input quantum signal while the frequency shift of the pump resonance mode counts the number of the photons in the input quantum signal.