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Optics Express

Ultra-sensitive phase measurement based on an SU(1,1) interferometer employing external resources and substract intensity detection

Jun Liu, Yuanxiang Wang, Mingming Zhang, Jinwen Wang, Dong Wei, Hong Gao

Published Dec 6, 2020• 22 citations
Publisher

Abstract

A new scheme has been proposed to realize the enhancement of phase sensitivity based on an SU(1,1) interferometer. Compared with the classical Mach-Zehnder interferometer, the SU(1,1) interferometer is splitted and recombined by an optical parametric amplifier and the phase sensitivity can beat shot noise limit by adjusting the parametric strength. In this model, the inputs of the SU(1,1) interferometer are bright entangled twin beams generated from four wave mixing and the detection method is substract intensity difference with one of the twin beams entering into the interferometer. The detection efficiency of the detector is taken into consideration. This scheme also proves that when one of the inputs of an SU(1,1) interferometer is an vacuum beam, the phase sensitivity can beat shot noise limit by employing substract intensity detection and external resources.

DOI
10.1364/oe.413179

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A new scheme has been proposed to realize the enhancement of phase sensitivity based on an SU(1,1) interferometer. Compared with the classical Mach-Zehnder interferometer, the SU(1,1) interferometer is splitted and recombined by an optical parametric amplifier and the phase sensitivity can beat shot noise limit by adjusting the parametric strength. In this model, the inputs of the SU(1,1) interferometer are bright entangled twin beams generated from four wave mixing and the detection method is substract intensity difference with one of the twin beams entering into the interferometer. The detection efficiency of the detector is taken into consideration. This scheme also proves that when one of the inputs of an SU(1,1) interferometer is an vacuum beam, the phase sensitivity can beat shot noise limit by employing substract intensity detection and external resources.
We theoretically study the phase sensitivity of an SU(1,1) interferometer with a coherent state in one input port and a squeezed-vacuum state in the other input port using the method of homodyne detection. In this interferometer, beam splitting and recombination are generated by the parametric amplifiers instead of the beam splitters. Compared with the traditional Mach–Zehnder interferometer, the phase sensitivity of this interferometer can be improved due to the amplification process of the parametric amplifiers. Combined with the squeezed state input, the sensitivity can be improved further due to the noise reduction. The phase sensitivity of our scheme can approach the Heisenberg limit and the associated optimal condition is analyzed. The scheme can be implemented with current experimental technology.
The SU(1,1) interferometer can be thought of as a Mach-Zehnder interferometer with its linear beam splitters replaced with parametric nonlinear optical processes. We consider the cases of bright- and vacuum-seeded SU(1,1) interferometers using intensity or homodyne detectors. A simplified truncated scheme with only one nonlinear interaction is introduced, which not only beats conventional intensity detection with a bright seed, but can saturate the phase-sensitivity bound set by the quantum Fisher information. We also show that the truncated scheme achieves a sub-shot-noise phase sensitivity in the vacuum-seeded case, despite the phase-sensing optical beams having no well-defined phase.
Abstract A novel scheme for the enhancement of phase sensitivity based on a Mach–Zehnder interferometer (MZI) and intensity detection is proposed. With the input of bright entangled twin beams from four wave mixing (FWM), the phase sensitivity can beat shot noise limit (SNL) and approach Heisenberg limit. This scheme is special due to that only one of bright entangled twin beams enters into the MZI and the other one is employed for measurement. In addition, by altering the parametric strength of FWM and the implementation of maximum quantum squeezing, the optimal phase sensitivity can reach sub-SNL. Optical intensity depletion of photon detectors and internal intensity depletion of the MZI are also discussed. The scheme displays that by employing external resources, while one input of the MZI is an vacuum beam, the phase sensitivity still can beat SNL.
Introducing squeezed states of light into interferometers can increase the phase sensitivity of the device beyond the standard quantum limit (SQL). We discuss an SU(1,1) interferometer, where nonlinear optical elements replace the beam splitters in a Mach-Zehnder interferometer. A two-mode squeezed state of light is generated inside of such an interferometer. We talk about the phase sensitivities of an SU(1,1) interferometer with different detection schemes and their improvement over the SQL. We also discuss the concept of an optimal detection scheme for phase measurement in an interferometer. We describe a modification of the SU(1,1) interferometer which reduces the experimental complexities while giving the same phase sensitivity. We call the design a truncated SU(1,1) interferometer. We show our experimental results of 4 dB improvement in phase sensitivity over the SQL using a truncated SU(1,1) interferometer. We also compare the theoretical sensitivities of vacuum-seeded configurations of a conventional and a truncated SU(1,1) interferometer, and show our experimental results for the phase sensitivity of the truncated version. We explain the dependence of phase sensitivity on the measurement of squeezing. We talk about the methods to improve the measurement of squeezing in a 4-wave mixing experiment, and our efforts in implementing them. Finally, we mention our progress in measuring a big phase shift using an adaptive algorithm in the truncated SU(1,1) interferometer, and discuss the technicalities involved in big phase measurements.
We focus on the Mach–Zehnder interferometer (MZI) with the input of a coherent beam and one of the bright entangled twin beams with an external power reference beam employed for measurement. The results show that the phase sensitivity can reach sub-Heisenberg limit and approach quantum Cramér–Rao bound by changing the squeezing parameters and the photon number of the coherent beam, under the phase-matching condition. The absence of the external power reference beam will degrade the performance of the phase sensitivity. Meanwhile, this scheme shows good robustness against the losses of the photon detectors. We present a detailed discussion about the phase sensitivities when the inputs are two coherent beams, or a coherent beam plus a single-mode squeezed vacuum beam based on the MZI. This scenario can be applied in the field of phase precision measurements and other optical sensors.
Phase sensitivity of an SU⁡(1,1)\operatorname{SU}(1,1)SU(1,1) interferometer via product detection
Abstract We theoretically analyze the phase sensitivity of an SU⁡(1,1)\operatorname{SU}(1,1)SU(1,1) SU ( 1 , 1 ) interferometer with various input states by product detection in this paper. This interferometer consists of two parametric amplifiers that play the role of beam splitters in a traditional Mach–Zehnder interferometer. The product of the amplitude quadrature of one output mode and the momentum quadrature of the other output mode is measured via balanced homodyne detection. We show that product detection has the same phase sensitivity as parity detection for most cases, and it is even better in the case with two coherent states at the input ports. The phase sensitivity is also compared with the Heisenberg limit and the quantum Cramér–Rao bound of the SU⁡(1,1)\operatorname{SU}(1,1)SU(1,1) SU ( 1 , 1 ) interferometer. This detection scheme can be easily implemented with current homodyne technology, which makes it highly feasible. It can be widely applied in the field of quantum metrology.