Since spin dynamics leads to a pairwise transfer to atoms to the Zeeman levels mF = +1 and mF = -1 we expect the number of atoms in these levels to be identical N+1 = N-1 in the absence of losses and other technical noise sources. For a fixed total number of atoms N = N+1 + N-1, the created state is a so-called twin-Fock state and can be depicted as a ring on the equator of the multi-particle Bloch sphere (b) which indicates its completely undefined phase difference and its precisely defined population difference N+1 - N-1 = 0. This state can be used for interferometry with increased precision compared to an ideal classical interferometer.
The operation of an interferometer can be depicted as a rotation on the Bloch sphere and the final measurement corresponds to a projection on the z-axis. For a classical input state, the output signal is given by a Gaussian distribution (a). The center of this distribution can be used to estimate the turning angle, which corresponds to the acquired phase shift. The precision of this phase estimation is limited by the width of the distribution.
If the interferometer is operated with the twin-Fock state as an input state, the output signal corresponds to double-wing distribution as depicted in (b). For a small phase shift the width of this distribution can be much smaller compared to the Gaussian distribution of the classical output signal. For an increasing phase, however, the double-wing distribution spreads out quickly (c). Hence, the width of the distribution can be used for an estimation of the interferometer phase with an increased precision compared to the classical operation which we demonstrated in our experiments. Ideally, this non-standard interferometer scheme enables a phase sensitivity close to the absolute optimum which is given by the so-called Heisenberg limit. Thus, our experiments demonstrate a new strategy to increase the precision of atom interferometers beyond the classical limit.
Read More in our Publication
B. Lücke, M. Scherer, J. Kruse, L. Pezzé, F. Deuretzbacher, P. Hyllus, O. Topic, J. Peise, W. Ertmer, J. Arlt, L. Santos, A. Smerzi, C. Klempt (2011): Twin matter waves for interferometry beyond the classical limit, Science 334, 773 (2011). More