The experimentally feasible SU (2) and SU (1,1) intelligent states are studied for the parameter values leading to the crescent topography of their quasidistributions. Such states increase the sensitivity of the interferometric measurement based on the photon-number difference and photon-number sum detections.
We study the phase sensitivity of SU(2) and SU(1,1) interferometers fed by two-mode field states which are intelligent states for Hermitian generators of the SU(2) and SU(1,1) groups, respectively. Intelligent states minimize uncertainty relations and this makes possible an essential reduction of the quantum noise in interferometers. Exact closed expressions for the minimum detectable phase shift are obtained in terms of the Jacobi polynomials. These expressions are compared with results for some conventional input states, and some known results for the squeezed input states are reviewed. It is shown that the phase sensitivity for an interferometer that employs squeezing-producing active devices (such as four-wave mixers) should be analyzed in two regimes: (i) fixed input state and variable interferometer, and (ii) fixed interferometer and variable input state. The behavior of the phase sensitivity is essentially different in these two regimes. The use of the SU(2) intelligent states allows us to achieve a phase sensitivity of order 1/N\ifmmode\bar\else\textasciimacron\fi{} (where N\ifmmode\bar\else\textasciimacron\fi{} is the total number of photons passing through the phase shifters of the interferometer) without adding four-wave mixers. This avoids the duality in the behavior of the phase sensitivity that occurs for the squeezed input. On the other hand, the SU(1,1) intelligent states have the property of achieving the phase sensitivity of order 1/N\ifmmode\bar\else\textasciimacron\fi{} in both regimes. \textcopyright{} 1996 The American Physical Society.
The SU(2) group is used in two different fields of quantum optics, the quantum polarization and quantum interferometry.Quantum degrees of polarization may be based on distances of a polarization state from the set of unpolarized states.The maximum polarization is achieved in the case where the state is pure and then the distribution of the photon-number sums is optimized.In quantum interferometry, the SU(2) intelligent states have also the property that the Fisher measure of information is equal to the inverse minimum detectable phase shift on the usual simplifying condition.Previously, the optimization of the Fisher information under a constraint was studied.Now, in the framework of constraint optimization, states similar to the SU(2) intelligent states are treated.