From computers to medicine, miniaturization approaches the atomic scale, where device operation can be dominated by quantum effects that are strongly coupled to the local environment. These influences may be seen not as a nuisance, but rather a nearly untapped source of information about physical or biochemical processes playing out nearby. How can one extract maximum information from such fluctuations with an atomic probe, under typical experimental constraints? The authors use quantum estimation theory to outline a general strategy for dynamical measurement of a broad class of environmental processes.
Simulation of an experimental real-time adaptive-estimation protocol for realistic conditions with a NVC spin probe. (a),(b) Convergence of the real-time adaptive-estimation protocol to the theoretically predicted values for estimating τc. Free evolution of the probe (blue circles) is contrasted with that of a dynamically controlled probe under a CPMG (green square) sequence with N=8 pulses in the presence of an Ornstein-Uhlenbeck process with Lorentzian spectrum with τc=10μs, a coupling with the environment g=1 MHz consistently with the spectral density of a HPHT diamond sample. The simulated curves derived from exact analytical results are averaged over 600 realizations. In (a), the optimal measurement time tm as a function of the number of measurements Nm converges to the optimal value to perform the measurements t^{opt} for the CPMG case. Similar curves converging to the corresponding t^{opt} are observed for other controls and free evolution. In (b), the minimal relative error ϵ(τc,t^{opt}) converges to the (Cramer-Rao) bound. Under free evolution, the regime where ϵ∝(1/√Nm) is attained for Nm≫100. The ultimate bound (ϵ0/√Nm dashed line, α=β−1) is attained only by optimal control. (c) Convergence to the minimal relative error ϵ(g,t^{opt}) to the (Cramer-Rao) bound for estimating g by N=500 consecutive projective measurements in the Zeno regime (green triangle) compared to the estimation under free evolution (blue circle). In this case, G_{β=2}(g=0.03 MHz,ω), with τc=10 μs, consistently with the spectral density of a 12C diamond sample. Here too the ultimate bound (ϵ0/2√Nm dashed line, α=2) is attained only by optimal control. (d) Proposed scheme for using a NVC as a qubit probe for its environment. The ms=0 (|0⟩) state is fully populated by laser irradiation (dashed curly arrow). Microwave (MW) pulses are selectively applied between the states with ms=0 and −1 (|0⟩ and |−1⟩) of the electronic ground states to initialize the spin probe in a |+⟩=(1/√2)(|0⟩+|−1⟩) state and effect the π pulse CPMG sequence for estimating τc. For estimating g, projective measurements are emulated by combining MW π/2 pulses on the 0↔−1 transition and laser-induced relaxation between the ground and exited electronic states that conserve the spin components (solid curly arrows). The readout is done at the end of the N-pulse sequence by detecting the laser-induced fluorescence signal.
From computers to medicine, miniaturization approaches the atomic scale, where device operation can be dominated by quantum effects that are strongly coupled to the local environment. These influences may be seen not as a nuisance, but rather a nearly untapped source of information about physical or biochemical processes playing out nearby. How can one extract maximum information from such fluctuations with an atomic probe, under typical experimental constraints? The authors use quantum estimation theory to outline a general strategy for dynamical measurement of a broad class of environmental processes.
Gonzalo Agustin Alvarez 