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CRC Press eBooks

To estimate a phase via two-entangled photons with multiple passes

R.Q. Liu L.X. Xia

Published Feb 25, 2015• 0 citations
Publisher

Abstract

This paper is organized as follows. In Section 2, we describe the super stable optical interferometer with multiple passes. In Section 3 and 4, we use single photon and two entangled photons to estimate an unknown phase, respectively. Our scheme enables considerable high precision to beat the SQL. And conclusions and remarks are made in Section 4.

DOI
10.1201/b18167-37

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This paper is organized as follows. In Section 2, we describe the super stable optical interferometer with multiple passes. In Section 3 and 4, we use single photon and two entangled photons to estimate an unknown phase, respectively. Our scheme enables considerable high precision to beat the SQL. And conclusions and remarks are made in Section 4.
It was previously shown that optical networks using only single photon Fock states, passive linear optics, and single photon detection could achieve post-classical sensitivity for singleparameter estimation when the mode number is small. [1] Furthermore, it was shown that multiparameter estimation could achieve similar results with number-resolving detection. [2] Here, we consider an analogous architecture to the Quantum Fourier Transform Interferometer(QuFTI) proposed in [1] for the estimation of multiple phases simultaneously. Thus, we will see that this yields post-classical sensitivity for multiparameter estimation even for an asymptotically large number of modes. This system is also considered for nondeterministic photon sources and a variety of measurement schemes.
The use of quantum resources can provide measurement precision beyond the shot-noise limit (SNL). The task of ab initio optical phase measurement-the estimation of a completely unknown phase-has been experimentally demonstrated with precision beyond the SNL, and even scaling like the ultimate bound, the Heisenberg limit (HL), but with an overhead factor. However, existing approaches have not been able-even in principle-to achieve the best possible precision, saturating the HL exactly. Here we demonstrate a scheme to achieve true HL phase measurement, using a combination of three techniques: entanglement, multiple samplings of the phase shift, and adaptive measurement. Our experimental demonstration of the scheme uses two photonic qubits, one double passed, so that, for a successful coincidence detection, the number of photon-passes is N = 3. We achieve a precision that is within 4% of the HL. This scheme can be extended to higher N and other physical systems.
We derive, and experimentally demonstrate, an interferometric scheme for unambiguous phase estimation with precision scaling at the Heisenberg limit that does not require adaptive measurements. That is, with no prior knowledge of the phase, we can obtain an estimate of the phase with a standard deviation that is only a small constant factor larger than the minimum physically allowed value. Our scheme resolves the phase ambiguity that exists when multiple passes through a phase shift, or NOON states, are used to obtain improved phase resolution. Like a recently introduced adaptive technique [Higgins et al 2007 Nature 450 393], our experiment uses multiple applications of the phase shift on single photons. By not requiring adaptive measurements, but rather using a predetermined measurement sequence, the present scheme is both conceptually simpler and significantly easier to implement. Additionally, we demonstrate a simplified adaptive scheme that also surpasses the standard quantum limit for single passes.
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.