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arXiv:1806.07580 · Optics Express

Super-sensitive angular displacement estimation via an SU(1,1)-SU(2) hybrid interferometer

Jiandong Zhang, Chenfei Jin, Zijing Zhang, Longzhu Cen, Jun-Yan Hu, Yuan Zhe Zhao

Published Dec 4, 2018• 28 citations
arXivHTMLPDF

Abstract

In this paper, we propose a protocol for the estimation of angular displacement based upon orbital angular momentum and an SU(1,1)-SU(2) hybrid interferometer. This interferometer consists of an optical parametric amplifier, a beam splitter, and reflection mirrors; the balanced homodyne detection is used as the detection strategy. The results indicate that super-resolution and super-sensitivity can be achieved with an ideal scenario. Additionally, we study the effect of photon loss on resolution and sensitivity, and the robustness of our protocol is also discussed. Finally, the advantage of our protocol compared with an SU(1,1) protocol is demonstrated, and the merits of orbital angular momentum-enhanced protocol are summarized.

DOI
10.1364/oe.26.033080

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In this paper, we propose a protocol for the estimation of angular displacement based upon orbital angular momentum and an SU(1,1)-SU(2) hybrid interferometer. This interferometer consists of an optical parametric amplifier, a beam splitter, and reflection mirrors; the balanced homodyne detection is used as the detection strategy. The results indicate that super-resolution and super-sensitivity can be achieved with an ideal scenario. Additionally, we study the effect of photon loss on resolution and sensitivity, and the robustness of our protocol is also discussed. Finally, the advantage of our protocol compared with an SU(1,1) protocol is demonstrated, and the merits of orbital angular momentum-enhanced protocol are summarized.
Abstract We theoretically explore the angular rotation measurement sensitivity of SU(1,1) interferometers with a coherent beam and a vacuum beam input by using orbital angular momentum (OAM). Compared with the OAM in an SU(2) interferometer, the SU(1,1) interferometer employing homodyne detection can further surpass the angular rotation shot noise limit 1 2 l N and improve the resolution and sensitivity of angular rotation measurement. Two models are considered, one is that OAM is carried by a probe beam and the other one is a pump beam with the OAM. The sensitivity can be improved by higher OAM and nonlinear process with a large gain. The resolution can be enhanced in the case that the pump beam has OAM. Moreover, we present a brief discussion on the variation of resolution and sensitivity in the presence of photon loss.
Abstract We have theoretically investigated the phase sensitivity of the hybrid interferometer with two coherent beams using the method of balance homodyne detection. The measurement device is a nonlinear–linear hybrid interferometer consisting of an optical parametric amplifier and a beam splitter. We prove that the phase sensitivity can beat the shot noise limit in the optimal conditions. Furthermore, we derive the quantum Cramér–Rao bound of the hybrid interferometer. The effects of transmission loss and detection loss on the measurement accuracy are discussed. The detection accuracy of this scheme is compared with that of the conventional SU (1,1) interferometer. Our results show that this scheme outperforms the conventional SU (1,1) interferometer scheme at high parametric strength. This scheme can be implemented with existing experimental techniques and will have important applications in quantum precision measurements.
We investigate the sensitivity of the angular rotation measurement with the method of homodyne detection in SU(2) and SU(1,1) interferometers by employing orbital angular momentum (OAM). By combining a coherent beam with a vacuum beam in an SU(2) interferometer, we get the sensitivity of the angular rotation measurement as 12Nl. We can surpass the limit of the angular rotation measurement in an SU(1,1) interferometer by combining a coherent beam with a vacuum beam or a squeezed vacuum beam when the probe beam has OAM. Without injection, the sensitivity can reach 12Nl. In addition, by employing another construction of an SU(1,1) interferometer where the pump beam has OAM, with the same injection of an SU(1,1) interferometer, the sensitivity of the angular rotation measurement can be improved by a factor of 2, reaching 14Nl. The results confirm the potential of this technology for precision measurements in angular rotation measurements.
Super-resolved angular displacement estimation is of crucial significance to the field of quantum information processing. Here we report an estimation protocol based on a Sagnac interferometer fed by a coherent state carrying orbital angular momentum. In a lossless scenario, through the use of parity measurement, our protocol can achieve a 4ℓ-fold super-resolved output with quantum number ℓ; meanwhile, a shot-noise-limited sensitivity saturating the quantum Cramér-Rao bound is reachable. We also consider the effects of several realistic factors, including nonideal state preparation, photon loss, and inefficient measurement. Finally, with mean photon number N ¯ = 2.297 and ℓ = 1 taken, we experimentally demonstrate a super-resolved effect of angular displacement with a factor of 7.88.
There has been much recent interest in high precision angular rotation measurement using photon orbital angular momentum to realize super-resolving angular rotation measurement. It is well known that quantum detection strategies can obtain a quantum-enhanced performance. Here, we prove that binary-outcome homodyne detection method can obtain a narrower signal peak, showing better resolution compared with the existing data processing method. Since the photon loss is unavoidable in the actual non-ideal optical system, this paper further discusses the impact of photon loss on the resolution and sensitivity of angular rotation measurement with binary-outcome homodyne detection method.