An atomic magnetometer with quantum sensitivity limited by the longitudinal relaxation time T₁

It is usually assumed that fundamental sensitivity of any quantum measurement is limited by the coherence relaxation time T₂. We demonstrate a simple measurement scheme with sensitivity limited by the population relaxation time T₁. The quantum sensitivity for magnetic fields δB exhibits a Heisenberg linear scaling with number of atoms N until it reaches the standard quantum limit except with T₂ time replaced by T₁, δB ∝ (NT₁)^-1/2. Since the longitudinal relaxation time T₁ is longer than T₂ in most systems, it provides a general advantage for quantum measurements. We derive these results based on a simple Bloch-equation model and demonstrate them experimentally with a ⁸⁷Rb atomic magnetometer. A key requirement for implementing this approach is high optical density on resonance of the atomic vapor, which enables quantum non-demolition measurements of the collective atomic spin state with high fidelity.