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arXiv:2002.02195 · Applied Physics Letters

Quantum dense metrology by an SU(2)-in-SU(1,1) nested interferometer

Wei Du, J. F. Chen, Z. Y. Ou, Weiping Zhang

Published Jul 13, 2020• 22 citations
arXivHTMLPDF

Abstract

With the help of quantum entanglement, quantum dense metrology (QDM) is a technique that can make joint estimates of two conjugate quantities such as phase and amplitude modulations of an optical field, with an accuracy beating the standard quantum limit simultaneously. SU(1,1) interferometers (SUIs) can realize QDM with detection loss tolerance but is limited in absolute sensitivity. Here, we present a QDM scheme with a linear or SU(2) interferometer nested inside an SUI. By using a degenerate SUI and controlling the phase angle of the phase-sensitive amplifiers in the SUI, we can achieve the optimum quantum enhancement in the measurement precision of an arbitrary mixture of phase and amplitude modulation.

DOI
10.1063/5.0012304

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With the help of quantum entanglement, quantum dense metrology (QDM) is a technique that can make joint estimates of two conjugate quantities such as phase and amplitude modulations of an optical field, with an accuracy beating the standard quantum limit simultaneously. SU(1,1) interferometers (SUIs) can realize QDM with detection loss tolerance but is limited in absolute sensitivity. Here, we present a QDM scheme with a linear or SU(2) interferometer nested inside an SUI. By using a degenerate SUI and controlling the phase angle of the phase-sensitive amplifiers in the SUI, we can achieve the optimum quantum enhancement in the measurement precision of an arbitrary mixture of phase and amplitude modulation.
Quantum entanglement is a resource in quantum metrology that can be distributed to two conjugate physical quantities for the enhancement of their measurement sensitivity. This is demonstrated in the joint measurement of phase and amplitude modulation signals in quantum dense metrology schemes. We can also devote all the quantum resource to phase measurement only, leading to the optimum sensitivity enhancement. In this paper, we experimentally implement a dual-beam sensing scheme in an SU(1,1) interferometer for the optimum quantum enhancement of phase measurement sensitivity. We demonstrate a 3.9-dB improvement in signal-to-noise ratio over the optimum classical method, and this is 3-dB better than the traditional single-beam scheme. Furthermore, such as cheme also realizes a quantum optical tap of quantum entangled fields and has the full advantages of an SU(1,1) interferometer, such as detection loss tolerance, making it more suitable for practical applications in quantum metrology and quantum information.
We present experimental and theoretical results on a new interferometer topology that nests a SU(2) interferometer, e.g., a Mach-Zehnder or Michelson interferometer, inside a SU(1,1) interferometer, i.e., a Mach-Zehnder interferometer with parametric amplifiers in place of beam splitters. This SU(2)-in-SU(1,1) nested interferometer (SISNI) simultaneously achieves a high signal-to-noise ratio (SNR), sensitivity beyond the standard quantum limit (SQL) and tolerance to photon losses external to the interferometer, e.g., in detectors. We implement a SISNI using parametric amplification by four-wave mixing (FWM) in Rb vapor and a laser-fed Mach-Zehnder SU(2) interferometer. We observe path-length sensitivity with SNR 2.2 dB beyond the SQL at power levels (and thus SNR) 2 orders of magnitude beyond those of previous loss-tolerant interferometers. We find experimentally the optimal FWM gains and find agreement with a minimal quantum noise model for the FWM process. The results suggest ways to boost the in-practice sensitivity of high-power interferometers, e.g., gravitational wave interferometers, and may enable high-sensitivity, quantum-enhanced interferometry at wavelengths for which efficient detectors are not available.
The use of squeezing and entanglement allows advanced interferometers to detect signals that would otherwise be buried in quantum mechanical noise. High sensitivity instruments including magnetometers and gravitational wave detectors have shown enhanced signal-to-noise ratio (SNR) by injecting single-mode squeezed light into SU(2) interferometers, e.g. the Mach-Zehnder or Michelson topologies. The quantum enhancement in this approach is sensitive to losses, which break the fragile quantum correlations in the squeezed state. In contrast, SU(1,1) interferometers achieve quantum enhancement by noiseless amplification; they noiselessly increase the signal rather than reducing the quantum noise. Prior work on SU(1,1) interferometers has shown quantum-enhanced SNR11 and insensitivity to losses but to date has been limited to low powers and thus low SNR. Here we introduce a new interferometer topology, the SU(2)-in-SU(1,1) nested interferometer, that combines quantum enhancement, the high SNR possible with a SU(2) interferometer, and the loss tolerance of the SU(1,1) approach. We implement this interferometer using four-wave mixing in a hot atomic vapor and demonstrate 2:2(5) dB of quantum SNR enhancement, in a system with a phase variance nearly two orders of magnitude below that of any previous loss-tolerant enhancement scheme. The new interferometer enables new possibilities such as beyond-shot-noise sensing with wavelengths for which efficient detectors are not available.