An Atomic Magnetometer with Spin-Projection Noise Proportional to \sqrtT_2

There is a common sense view for atomic magnetometers that their spin-projection-noises (SPNs) are inversely proportional to \sqrtT_2, where T_2 is the transverse relaxation time. We analyze the current atomic magnetometer types and give a counter-example of this common sense, which is the all-optical spin precession modulated three-axis atomic magnetometer proposed by our group in 2015. Unlike the other atomic magnetometers, the SPN of this kind of atomic magnetometers is proportional to \sqrtT_2 due to the fact that the scale factor between P_x and B can be unrelated to the transverse relaxation time T_2. We demonstrate this irrelevance experimentally and analyze the SPN theoretically. Using short-pulse ultra-high power laser to fully polarize the atoms, the phenomenon that SPN decreases with T_2 may also be demonstrated experimentally and a new tool for researching SPN in atomic magnetometers may be realized.