Improvement of measurement accuracy in SU(1,1) interferometers

We consider an SU(1,1) interferometer employing four-wave mixers that is fed with two-mode states which are both coherent and intelligent states of the SU(1,1) Lie group. It is shown that the phase sensitivity of the interferometer can be essentially improved by using input states with a large photon-number difference between the modes. The improvement of measurement accuracy in interferometers is of significant importance in modern experimental physics. Much work has been done on the reduction of the quantum noise in interferometers by using input light fields prepared in nonclassical photon states. It was pointed out by Caves [1] and Bondurant and Shapiro [2] that the quantum fluctuations can be diminished by feeding squeezed states of light into the interferometer. The interferometers considered in [1, 2] employ passive lossless devices, such as beam splitters. Yurke, McCall and Klauder [3] showed that such interferometers can be characterized by the SU(2) group. They also introduced a class of interferometers which employ active lossless devices, such as four-wave mixers, and are characterized by the SU(1,1) group. It was shown [3] that the use of squeezed light in SU(2) interferometers can yield a phase sensitivity ∆φ ∼ 1/N (where N is the total number of photons passing through the interferometer), while SU(1,1) interferometers can achieve a phase sensitivity of 1/N with only vacuum fluctuations entering the input ports. In the present work we study the possibility to improve further the accuracy of SU(1,1) interferometers by using specially prepared states (other than vacuum). We apply the idea of Hillery and Mlodinow [4] who proposed to use intelligent states (IS) [5] for improving the phase sensitivity of interferometers. They analysed [4] the case of SU(2) IS. Since we discuss here interferometers characterized by SU(1,1), it is natural to use IS of this group [6, 7, 8]. There is a problem of generating IS since, in general, they are constructed by nonunitary operators [5, 6]. However, there are some IS which simultaneously are generalized coherent states (CS) [9, 10] of the corresponding Lie group, i.e., an intersection occurs between these two types of states [6]. This intersection is of special importance in physics because IS that also are CS can be created by Hamiltonians for which a given Lie group is the dynamical symmetry group. Recently we developed [7] a general group-theoretical approach to SU(1,1) IS by representing them in the corresponding coherent-state basis. This approach yields the most full characterization of the coherent-intelligent intersection. The above results will be used in the present work for analysing SU(1,1) interferometers fed with states which are both IS and CS of the SU(1,1) Lie group. An SU(1,1) interferometer is described schematically in figure 1. Two light beams represented by mode annihilation operators a1 and a2 enter into the input ports of the first four-wave mixer FWM1. After leaving FWM1, beams accumulate phase shifts φ1 and φ2, respectively, and then they enter E-mail: [email protected]