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arXiv:quant-ph/9604016 · Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Improvement of measurement accuracy inSU(1, 1) interferometers

Constantin Brif, Y. Ben-Aryeh

Published Feb 1, 1996• 26 citations
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Abstract

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.

DOI
10.1088/1355-5111/8/1/001

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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.
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.
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.
A Lie-group-theoretical approach to the analysis of interferometers is presented. Conventional interferometers such as the Mach-Zehnder and Fabry-Perot can be characterized by SU(2). We introduce a class of interferometers characterized by SU(1,1). These interferometers employ active elements such as four-wave mixers or degenerate-parametric amplifiers in their construction. Both the SU(2) and SU(1,1) interferometers can in principle achieve a phase sensitivity \ensuremath{\Delta}\ensuremath{\varphi} approaching 1/N, where N is the total number of quanta entering the interferometer, provided that the light entering the input ports is prepared in a suitable quantum state. SU(1,1) interferometers can achieve this sensitivity with fewer optical elements.
Abstract To improve the phase sensitivity, multi-photon subtraction schemes (multi-PSS) within the SU(1,1) interferometer are proposed. The input states are the coherent state and the vacuum state, and the detection method is homodyne detection. The effects of multi-photon subtraction on phase sensitivity, quantum Fisher information (QFI), and quantum Cramér-Rao bound (QCRB) are analyzed under both ideal and photon losses situations. It is shown that the internal subtraction operation can improve the phase sensitivity, which becomes better performance by increasing subtraction number. It can also efficiently improve the robustness of the SU(1,1) interferometer against internal photon losses. By comparing separatively arbitrary photon subtraction on the two-mode inside SU(1,1) interferometer, the performance differences under different conditions are analyzed, including the asymmetric properties of non-Gaussian operations on the phase precision and the QFI. Our proposed scheme represents a valuable method for achieving quantum precision measurements.
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.