High-accuracy Su(1,1) interferometers with minimum-uncertainty input states

Mark S. Hillery, Leonard D. Mlodinow

Minimum-uncertainty states in variables which are quadratic in mode creation and annihilation operators can be used to increase the accuracy of interferometric measurements. For a general interferometer we show how to find the relevant uncertainty relation. We consider two specific examples, a Mach-Zehnder interferometer and a Mach-Zehnder interferometer in which the first beam splitter has been replaced by a four-wave mixer. For both devices su(2) squeezed minimum-uncertainty states can be used to achieve phase-measurement accuracies of 1/N, where N is the total photon number at the input. We also describe a method of producing approximate versions of these states.

Bernard Yurke, S. L. McCall, John R. Klauder

Constantin Brif, A. Mann

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.

Shuai Wang, Jiandong Zhang, Xue-xiang Xu

Yadong Wu, Chun-Hua Yuan

We theoretically investigate an interferometer composed of four four-wave-mixers by Lie group method. Lie group SU(1,2) characterizes the mode transformations of this kind of interferometer. With vacuum state inputs, the phase sensitivity of SU(1,2) interferometer achieves the Heisenberg limit, and the absolute accuracy beats SU(1,1) interferometer because of higher intensity of light inside the interferometer. For different input cases, the optimal combination of output photon number for detection to obtain the best phase sensitivity is calculated. Our research on SU(1,2) interferometer sheds light on the performance of SU(1,n) interferometer in quantum metrology.

Leyang Cao, Qingqian Kang, Zekun Zhao +5 more