Mapping quantum state dynamics in spontaneous emission

Abstract

The evolution of a quantum state undergoing radiative decay depends on how its emission is detected. If the emission is detected in the form of energy quanta, the evolution is characterized by a quantum jump to a lower energy state. In contrast, detection of the wave nature of the emitted radiation leads to different dynamics. Here, we investigate the diffusive dynamics of a superconducting artificial atom under continuous homodyne detection of its spontaneous emission. Using quantum state tomography, we characterize the correlation between the detected homodyne signal and the emitter's state, and map out the conditional back-action of homodyne measurement. By tracking the diffusive quantum trajectories of the state as it decays, we characterize selective stochastic excitation induced by the choice of measurement basis. Our results demonstrate dramatic differences from the quantum jump evolution associated with photodetection and highlight how continuous field detection can be harnessed to control quantum evolution.

Homodyne monitoring of postselected decay

“…In Fig. 2c, we display our experimental results V , testing the predicted average signal V for different θ. V oscillates as a function of θ and reaches a maximum (minimum) at θ = π 2 (θ = − π 2 ) as expected [3]. The experimental and theoretical curves are in good agreement and show that the average homodyne signal | V | without post-selection never exceeds the maximum value √ ηγdt (dashed horizontal lines).…”

“…3b-d diffuse through the Bloch sphere, but are confined to different deterministic curves for different evolution times (blue dashed lines in Fig. 3) [3,5]. In a similar way, the trajectories for E t diffuse backwards in time through the Bloch sphere from the post-selected state and they are also, for different evolution times, confined to different deterministic curves.…”

Dynamics of a qubit while simultaneously monitoring its relaxation and dephasing

“…Any measurement record is a stochastic process and the corresponding quantum trajectories follow a random walk in the Bloch sphere with a state dependent diffusion constant. The inherent backaction of a quantum measurement is thus better discussed by representing distributions of states at a given time [4,5,8,[10][11][12]20] or distributions of trajectories for a given duration [7,[21][22][23][24]. Figure 4 gives a different perspective to the Rabi oscillation of Fig.…”

Quantum Trajectories and Their Statistics for Remotely Entangled Quantum Bits

“…Continuous measurements [28] in superconducting systems have only recently been realized, owing to the challenge associated with high-fidelity detection of microwave signals near the single-photon level. In particular, experimental achievements include continuous feedback control [29,30] and the tracking of trajectories in individual experiments in the plain measurement case [31][32][33][34] as well as with a concurrent Rabi drive [35].…”