Ultrasensitive Calorimetric Detection of Single Photons from Qubit Decay

We describe a qubit linearly coupled to a heat bath, either directly or via a cavity. The main focus of the paper is on calorimetric detection in a realistic circuit, specifically a solid-state qubit coupled to a resistor as an absorber. The bath in the model is formed of oscillators initially in the ground state with a distribution of energies and coupling strengths. A direct numerical solution of the Schrödinger equation for the full system including up to 106 oscillators in the bath verifies the expected decay process. We address quantitatively the question of separation of the qubit and bath by adding a cavity in between which by detuning allows one to adjust the decay rate into a convenient regime for detection purposes. Most importantly, we propose splitting a quantum to two uncoupled baths and performing a cross-correlation measurement of their temperatures. This technique enhances significantly the signal-to-noise ratio of the calorimeter.