White Light Cavity Enhanced Spin Squeezing for Creating Schroedinger Cat States to Achieve Heisenberg Limited Sensitivity with Increased Quantum Noise

One axis twist squeezing (OATS) using non-linear interaction in a cavity can increase the sensitivity of metrological devices beyond the standard quantum limit (SQL). When the squeezing parameter is tuned to a critical value, OATS produces the Schroedinger Cat (SC) state, which is an equal superposition of all atoms being spin-up and all atoms being spin-down. However, the orientation of the SC state depends critically on the parity of the number of atoms, N. Changing N by unity causes the orientation to change by ninety degrees. For an experiment employing atoms released from a trap, for example, the parity of N fluctuates between odd and even, thus washing out the SC state. We describe a protocol which, for a given parity, produces a phase magnification by a factor of N, while increasing quantum noise by a factor of root-N, thus reaching the Heisenberg Limit (HL). However, the signal for one parity is filtered out, thus making it possible to achieve the HL within a factor of root-2. The increased quantum noise makes it very robust against classical noise. We also show that the use of a white light cavity for OATS makes it possible to reach the necessary critical value of the squeezing parameter very quickly, before degradation via dissipative processes.