Single Photon Detection by a Photoreceptive Molecule and a Quantum Coherent Spin Center

The long spin coherence times in ambient conditions of color centers in solids, such as nitrogen-vacancy (NV−) centers in diamond, make these systems attractive candidates for quantum sensing. Quantum sensing provides remarkable sensitivity at room temperature to very small external perturbations, including magnetic fields, electric fields, and temperature changes. A photoreceptive molecule, such as those involved in vision, changes its charge state or conformation in response to the absorption of a single photon.

In arXiv:1906.01800 we have shown that the resulting change in local electric field modifies the properties of a nearby quantum coherent spin center in a detectable fashion. Using the formalism of positive operator values measurements (POVMs), we analyzed the photo-excited electric dipole field and, by extension, the arrival of a photon based on a measured readout, using a fluorescence cycle, from the spin center. We determined the jitter time of photon arrival and the probability of measurement errors. We predict that configuring multiple independent spin sensors around the photoreceptive molecule would dramatically suppresses the measurement error.

This material is based on work supported by the DARPA DETECT program.

Figure 1

Toy model of single photon detection using a photoreceptor and a nitrogen vacancy (NV−) center in diamond. Also shown are the ground state (triplet) energy levels for the NV spin with a magnetic field in the axial direction (zˆ, pointing from N to V) and including zero-field splitting. The separations of energy levels are not drawn to scale. (a) No photon is absorbed so the spin evolves according to the photoreceptor’s electric dipole field in the photoreceptor’s ground state. (b) Photon is absorbed which i

Toy model of single photon detection using a photoreceptor and a nitrogen vacancy (NV−) center in diamond. Also shown are the ground state (triplet) energy levels for the NV spin with a magnetic field in the axial direction (zˆ, pointing from N to V) and including zero-field splitting. The separations of energy levels are not drawn to scale. (a) No photon is absorbed so the spin evolves according to the photoreceptor’s electric dipole field in the photoreceptor’s ground state. (b) Photon is absorbed which induces an altered electric dipole field (in magnitude and direction) and modifies the coherent preces- sion of the NV− spin within the three ground-state sublevels. The two configurations are, in general, non-orthogonal, suggesting that POVM’s provide the optimal framework for measurement.

Figure 3

(a, b) Error probability calculated using POVMs (black solid line using Eq. 25) and the standard measurement basis (blue dashed line using Eq. 28) for electric fields Ex,0 = 107 V/m and Ex,1 = Ex,0 + ∆Ex. (a) ∆Ex is odd multiple of Ex,0: for certain times, the minimum Perr in the standard basis is equivalent to the minimum Perr in the POVM calculation. Vertical gray lines denote local minima in the error probability. (b) ∆Ex is even multiple of Ex,0: the minimum Perr in the standard basis is significantly w

(a, b) Error probability calculated using POVMs (black solid line using Eq. 25) and the standard measurement basis (blue dashed line using Eq. 28) for electric fields Ex,0 = 107 V/m and Ex,1 = Ex,0 + ∆Ex. (a) ∆Ex is odd multiple of Ex,0: for certain times, the minimum Perr in the standard basis is equivalent to the minimum Perr in the POVM calculation. Vertical gray lines denote local minima in the error probability. (b) ∆Ex is even multiple of Ex,0: the minimum Perr in the standard basis is significantly worse than the minimum Perr in the POVM calculation. (c) Difference in Perr when an axial magnetic field is applied: ∆Pe = Perr(Bz)−Perr(0) using the POVM calculation and the same electric fields as in (a). The arrow on the bottom left of (c) points to tmin corresponding to (a) — the time at which the minimum error probability exists so the optimal time for a measurement to take place.

Figure 2

Minimum error probability, P , with (T = 10 μs) and err 2 without decoherence for two electric fields. Light/dark blue curves: ∆Ex = 106 V/m. Orange/brown curves: ∆Ex = 3 × 106 V/m. Ey,0 = 0=∆Ey,Bz =0forallcurves.

Minimum error probability, P , with (T = 10 μs) and err 2
without decoherence for two electric fields. Light/dark blue curves: ∆Ex = 106 V/m. Orange/brown curves: ∆Ex = 3 × 106 V/m. Ey,0 = 0=∆Ey,Bz =0forallcurves.

Figure 4

Error probability, Perr, at the best time for N=1,7,15 (red, orange, black) number of independent NV spin sensors. Vertical gray line denotes the best time for the measurement. (b) Error probability, Perr, evaluated at tmin for increasing number of independent NV spin sensors. Symbols are result of calculations; line is guide to eye.

Error probability, Perr, at the best time for N=1,7,15 (red, orange, black) number of independent NV spin sensors. Vertical gray line denotes the best time for the measurement. (b) Error probability, Perr, evaluated at tmin for increasing number of independent NV spin sensors. Symbols are result of calculations; line is guide to eye.