Phonon-limited detection thresholds for genetically encoded fluorescent-protein spin-qubit relaxometry of neural radicals
The demonstration that enhanced yellow fluorescent protein hosts an optically addressable spin-1 qubit in its metastable triplet state raises the prospect of genetically encoded quantum sensing at molecular length scales. We develop a detection-limit theory for using this fluorescent-protein spin qubit (FPSQ) to sense paramagnetic neural signaling radicals by spin relaxometry. We derive the transition-resolved Redfield relaxation matrix of the zero-field-split triplet coupled to a diffusing radical bath, establish the regime in which it collapses to a single exponential, and validate it against Lindblad simulations and nitrogen-vacancy benchmarks. Propagating the effects of photon shot noise, photobleaching-grounded photon budget, and finite measurement bandwidth, we find that the native room-temperature sensor falls short of physiological sensitivity by six to eight orders of magnitude with the bottleneck being the phonon-limited intrinsic $\Tone$. Analyzing the underlying direct and two-phonon Raman processes, we show that room-temperature relaxation is Raman-dominated by $\sim\!720\!:\!1$ and that, because the Raman coefficient scales as $v^{-10}$ with sound velocity, a $\sim\!2\times$ stiffening of the chromophore environment recovers $\Tone\sim\SI{100}{\micro\second}$, sufficient for micromolar sensing. Nanomolar sensing is obstructed by a direct-process ceiling of \SI{79}{\micro\second} that vibronic decoupling alone cannot breach. We obtain quantitative design rules, identify photon yield as a co-equal bottleneck, and propose a frequency-resolved protocol for chemical specificity.