Quantum metrology with molecular ensembles

The field of quantum metrology promises measurement devices that are fundamentally superior to conventional technologies. Specifically, when quantum entanglement is harnessed, the precision achieved is supposed to scale more favorably with the resources employed, such as system size and time required. Here, we consider measurement of magnetic-field strength using an ensemble of spin-active molecules. We identify a third essential resource: the change in ensemble polarization (entropy increase) during the metrology experiment. We find that performance depends crucially on the form of decoherence present; for a plausible dephasing model, we describe a quantum strategy, which can indeed beat the standard strategy.

Figure 1

(a) Schematic of a sensor molecule with five satellites. (b) Quantum circuit employed in the quantum strategy.

Figure 2

Simulation of the FID of the classical (upper) and quantum strategy (lower); see Eqs. (4) and (9). The simulated measurement points (crosses) were chosen randomly from a Gaussian distribution with a standard deviation of 0.05. In the classical strategy, we observe uncoupled precessing spins, and the strength of the probe field is given by the oscillation frequency. In the quantum strategy, a GHZ state senses the field for a time $T_w$ without producing a signal but acquiring phase $K$ times faster than a single spin and dephasing at a rate $\beta$. The acquired phase is mapped onto the central spin, and the FID is measured. The strength of the magnetic field can now be estimated from the phase and the oscillation frequency.

Figure 3

The maximal ${\mathcal{R}}_{\infty }$ for a given $K$ as a function of $K$ and $p$. ${\mathcal{R}}_{\infty }>1$ implies that the quantum strategy outperforms the standard strategy.

Figure 4

(a) Minimal (optimized over $T$ and $T_w$) uncertainty of the parameter estimation for the quantum strategy per $\sqrt{\mathrm{Hz}}$ [i.e., $S_{\mathrm{GHZ}}^{*}/(\sqrt{t_s}|\alpha |{}^{3/2}\frac{\sigma }{c})$ in dependence of $K$ and $p$]. (b) The corresponding optimal times $T^{*}$ (upper surface) and $T_w^{*}$ (lower surface) as units of $T_2^{*}$ for which the minimum in (a) is attained in dependence of $K$ and $p$.