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Frontiers in Optics

Enhanced Phase Estimation using Quantum and Classical Light

Yonatan Israel, Shamir Rosen, I. Afek, O. Ambar, Yaron R. Silberberg

Published Jan 1, 2013• 0 citations
Publisher

Abstract

We show that by mixing quantum spontaneous parametric down-conversion with the classical coherent state we can enhance phase sensitivity in an interferometer, under experimental considerations of photon loss and non ideal detection.
DOI
10.1364/fio.2013.ftu3a.3

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Phase estimation has a wide range of applications. Over the years, several strategies have been studied to improve precision in phase estimation. These strategies include using exotic quantum states to quantum detection schemes. This dissertation summarizes my effort in improving the precision of phase estimation with a linear and nonlinear interferometer. Chapter 1 introduces quantum optics and quantum metrology. I introduce all relevant quantum states of light used. We also look into tools and terminologies of quantum metrology such as Fisher information, shot-noise limit, Heisenberg limit, etc., along with examples of phase estimation with a Mach-Zehnder interferometer. In Chapter 2, I discuss multiple phase estimation using a multimode interferometer. Building upon previous work, our scheme consists of a multimode interferometer with single-photon inputs. By using a quantum Fisher information analysis, we show that our scheme gives a constant improvement over other schemes. We also show that our scheme with photon-number-resolving detection approaches the quantum Cram\'er-Rao bound. Moreover, we also consider the probabilistic nature of photon emission at the input, and we study its effect on phase sensitivity. I discuss phase estimation with SU(1,1) interferometer in Chapter 3. We look at phase sensitivity in this interferometer with different input states. Namely, we consider two different phase estimation scheme, one using thermal and squeezed states, and others using coherent and displaced squeezed states with parity and on-off as a detection scheme. We also look into the effect of photon loss inside the interferometer. In Chapter 4, we revisit phase estimation in SU(1,1) interferometer from the perspective of quantum Fisher information. I discuss in detail a longstanding confusion regarding the use of quantum Fisher information in SU(1,1) interferometer. We show that phase averaging or quantum Fisher information matrix method is needed in general for calculating the phase sensitivity which resolves inconsistencies reported in previously published articles.
Utilizing nonlinear elements, SU(1,1) interferometers demonstrate superior phase sensitivity compared to passive interferometers. However, the precision is significantly impacted by photon losses, particularly internal losses. We propose a theoretical scheme to improve the precision of phase measurement using homodyne detection by implementing a number-conserving operation (NCO), i.e., $a{a}^{\ifmmode\dagger\else\textdagger\fi{}}$ and ${a}^{\ifmmode\dagger\else\textdagger\fi{}}a$, inside the SU(1,1) interferometer, with the coherent state and the vacuum state as the input states. We analyze the effects of the NCO on the phase sensitivity, the quantum Fisher information (QFI), and the quantum Cram\'er-Rao bound under both ideal and photon-loss scenarios. Our findings reveal that the internal non-Gaussian operations can enhance the phase sensitivity and the QFI and effectively improve the robustness of the SU(1,1) interferometer against internal photon losses. Notably, the ${a}^{\ifmmode\dagger\else\textdagger\fi{}}a$ scheme exhibits superior improvement in both the ideal and photon-loss cases in terms of phase sensitivity. Moreover, in the ideal case, the $a{a}^{\ifmmode\dagger\else\textdagger\fi{}}$ scheme slightly outperforms the ${a}^{\ifmmode\dagger\else\textdagger\fi{}}a$ scheme in terms of the QFI. However, in the presence of high photon losses, the ${a}^{\ifmmode\dagger\else\textdagger\fi{}}a$ scheme demonstrates a greater advantage.