3 a) b) − π 2 y − π 2 x π x Sensor − π 2 y − π 2 y − π 2 y Bath τ/2 τ/4 τ/4 τ/4 τ/4 0 τ Field |0 〉 |0 〉 |0 〉 I$_{z}$ I$_{z}$ I$_{x}$ I$_{x}$ I$_{z}$ I$_{z}$ I$_{x}$ I$_{x}$ |1 〉 |1 〉 FIG. 2: Method. a) Mach-Zehnder interferometer, showing the central spin state and the effective Hamiltonian of the dark spins along each arm. b) Pulse sequence for environment assisted magnetometry. nal (static) magnetic field that splits the degeneracy be- tween S$_{z}$ = ± 1 states and working on resonance with the (0 ↔ 1) transition, the NV center can be reduced to an effective two-level system [4]. Then, the system compris- ing one NV center and several N spins is well described by Hamiltonian (1). In Fig. 2 we introduce a control sequence that yields an effect equivalent to the circuit in Fig. 1.b. The action of the pulse sequence can be best understood using the well known equivalence between Ramsey spectroscopy and Mach-Zehnder interferometry [18, 19], where the in- terferometer arms describe the central spin state. It is sufficient to consider the evolution of each arm sepa- rately, replacing S$_{z}$ by its eigenvalues m$_{s}$ = { 0 , 1 } and describing the evolution in the interaction frame defined by the control pulses [17]. Hamiltonian (1) becomes time- dependent, with dark spins alternating between I i z and I i x as shown in Fig. 2. Then, for different halves of the spin echo sequence, the coupling Hamiltonian in each arm is zero ( m$_{s}$ = 0) while for the other halves it has identical forms. In the absence of a magnetic field the evolution is thus the same along each arm of the interferometer. Adding an external field creates a phase shift between the two arms. For small field strengths we can then eval- uate the phase difference acquired between the two arms as a perturbation. For a finite polarization P of the dark spins we find looses phase coherence due to interactions with the bath, it is no longer possible to use it for magnetometry. This limits the sensing time and consequently the magnetome- ter sensitivity. Spin echo (as well as more sophisticated decoupling techniques [16, 17, 26, 30]) can be used to prolong the phase coherence of the central spin. Under realistic assumptions the coherence time for the pulse se- quence presented in this Letter is on the same order of the sensor coherence time under spin-echo T s $_{2}$. In essence, the decoherence rate of an entangled state of the form (2) is dictated by the internal evolution of the strongly cou- pled spins, and the relevant decoherence time is thus the time it takes before any of these spins have decohered. The same is, however, the case for spin echo sequences: if a central spin is strongly coupled to n$_{sc}$ dark spins, a spin flip of a single dark spin will lead to different evo- lutions in the two halves of the spin echo sequence, thus decohering the state of the central spin. As the source of both decoherence processes is the dipole-dipole interac- tion among dark spins, the coherence times of spin-echo and our procedure are on the same order and the signal amplification obtained with our strategy (Eq. 4) thus yields a sensitivity enhancement [34]. To be more quantitative, we analyze the evolution due to dipole-dipole couplings in the bath, described by the Hamiltonian with θ$_{s}$ = κ τ [ ∫ τ 2 0 dt b ( t ) − ∫ τ τ 2 dt b ( t ) ] , θ$_{d}$ = ξ τ ∫ 3 τ 4 τ 2 dt b ( t ). Compared to spin-echo based magnetometry [3], the sig- nal is increased by the factor in the square bracket while the measurement noise is the same, as we still read out one spin only. Note that all the dark spins contribute pos- itively. For values of the couplings such that | λ$_{i}$τ | ≥ π , or strongly coupled environment spins, we obtain a con- tribution ∝ 2 n$_{sc}$ 〈 sin $^{2}$( λ i τ 4 ) 〉 ≈ n$_{sc}$ . Each of the n$_{sc}$ strongly coupled spins thus gives a contribution of order one, irrespective of the sign or exact value of the cou- pling. Weakly coupled dark spins ( λ$_{i}$τ ≤ 1) contribute instead with a factor ( λ$_{i}$τ ) $^{2}$/ 8 and we obtain a total phase Φ ≈ θ$_{s}$ [ 1 + θ d θ s P ( n$_{sc}$ + 1 8 ∑ ′ ( λ$_{i}$τ ) 2 )] , where the primed sum is on the weakly coupled spins. In general the sen- sitivity enhancement scales as ∼ P n$_{sc}$ . We thus achieve nearly Heisenberg-limited sensing of the external field. We next take into account decoherence resulting from the interaction with the environment spins as well as de- coherence of the dark spins themselves. To evaluate these effects, we compare the sensitivity achievable with the proposed pulse sequence to that obtained with a spin- echo sequence, considering the same system (a sensor spin surrounded by the same spin bath) and including the effects of decoherence (external perturbations and couplings between the dark spins). Once the central spin H = | 1 〉〈 1 | ∑ λ$_{i}$I i z + ∑ i<j κ$_{ij}$ ( 3 I i $_{z}$I j z − − → I$_{i}$ · − → I$_{j}$ ) (5) A short time expansion shows that the state fidelity at the end of the pulse sequence is given by 1 − τ 4 8 · ∑ i<j ( 1 − P $^{2}$) κ 2 ij ( λ$_{i}$ − λ$_{j}$ ) $^{2}$+ ... , and 1 − τ 4 128 ∑ i<j κ 2 ij × ( 7( λ 2 i + λ 2 $_{j}$) + 12 λ$_{i}$λ$_{j}$ + P $^{2}$( λ$_{i}$ + 2 λ$_{j}$ ) (2 λ$_{i}$ + λ$_{j}$ ) + ... , for the spin-echo and modified pulse sequences, respectively. For experimentally relevant values of polarizations, sim- ilar reductions in fidelity occur for both pulse sequences [35]. To go beyond the short time expansions we have simulated the signal decay for both spin-echo and the proposed pulse sequence (see Fig. 3). We compared these results to the signal decay when no control se- Φ = θ$_{s}$ [ 1 + 2 P ∑ θ$_{d}$ θ$_{s}$ sin $^{2}$( ϕ$_{i}$/ 4) ] , (4)