Abstract:
This thesis addresses the search for quantum enhanced metrology with system that do not require all-to-all interactions, upon investigation it was identified that isotropic central spin model(CSM), which has a single ancilla spin interacting with N bath spins through a star-graph topology requiring only O(N) connectivity, as the bath spins do not interact within themselves but rather the information exchange is mediated via the central spin. In the dispersive regime (Ω ≫ ˜g√N), it reduces to effective OAT (one-axis twisting) Hamiltonian, which is a well established model time-reversal protocols, since the structure of OAT is preserved in high detuning limits, it enables Heisenberg-scaled metrology through the SATIN (Signal Amplification Through Time Reversed INteraction), further to generalize and enable sensing in unknown direction the CSM via Butterfly Echo protocol is implemented, enabling the axis-agnostic de tection. Systematically characterizing various parameters such as peak gain, optimal sensing time and robustness to detector noise and how they change as the number of bath spins (N), central spin detuning (Ω), and central spin value (Scen) change, thus establishing the CSM as a robust platform to perform echo based protocols with less resources. It is proved through numerical calculations that both the pro tocols achieve the Heisenberg-scaled metrological gain, and providing a control knob through Scen and Ω deciding the time scale of the protocol just with O(N) couplings instead of O(N^2) couplings as required by the ideal echo protocols to achieve such scaling. Crucially, both protocols achieve the same N^2 quantum Fisher information scaling as the Heisenberg exponent with only O(N) physical connections: the stan dard echo reaches FQ = N^2/e (4.34dB below the Heisenberg Limit) and the butterfly echo reaches FQ = N^2/4 (6dB below), with the additional gap between them being the sole fundamental cost of axis-agnosticity. The results demonstrate that the star graph central spin architecture is sufficient to implement both protocols, establishing a resource-efficient, experimentally natural route to near-Heisenberg precision sensing in NV centres, cavity QED, and trapped-ion platforms.
