Fig. 1
From: Dynamics of a qubit while simultaneously monitoring its relaxation and dephasing
Measurement setup and quantum trajectory resulting from its outputs. a Bloch vector representation of a qubit whose state is described by a density matrix ρt = (1 + x(t)σx + y(t)σy + z(t)σz)/2. A quantum trajectory ρt is represented as a blue line. The qubit decoherence can be modeled as originating from a relaxation channel at a rate Γ1 and a dispersive measurement channel at a rate Γd. b A superconducting qubit in a cavity is driven by two microwave signals at the weakly coupled input. The one at qubit frequency fq = 5.353 GHz (orange) induces Rabi oscillations of the qubit at frequency Ω. The one at cavity frequency fd = 7.761 GHz (purple) leads to a dispersive measurement of the qubit state along σz. A diplexer at the strongly coupled output port separates the outgoing signals depending on their frequency. The radiation at fq that is spontaneously emitted by the qubit is processed by a Josephson Parametric Converter (JPC)39, 40 so that a following heterodyne measurement reveals the two quadratures u(t) and v(t) of the fluorescence field10, 14, 41. The transmitted signal at fd is processed by a doubly pumped Josephson Parametric Amplifier (JPA)4, 42 with a pump phase such that a following homodyne measurement reveals the quadrature w(t) of the field at fd. c Measurement records u (blue), v (red), and w (yellow) as a function of time for one realization of the experiment. These records feed the stochastic master equation, Eq. (3), which leads to the trajectory in a
