Quantum Enhancement of Phase Sensitivity for the Bright-Seeded SU(1,1) Interferometer with Direct Intensity Detection

An SU(1,1) interferometer can be realized by replacement of the beam splitters in the Mach-Zehnder interferometer with parametric amplifiers. This interferometer scheme was proposed more than 30 years ago [Yurke et al., Phys. Rev. A 33, 4033 (1986)] and the enhancement of its signal-to-noise ratio was experimentally demonstrated in our recent work [Hudelist et al., Nat. Commun. 5, 3049 (2014)]. The sensitivity of any interferometer increases with increasing internal photon number. Therefore, the bright-seeded SU(1,1) interferometer has an advantage of boosted sensitivity. However, the phase sensitivity used to characterize the bright-seeded SU(1,1) interferometer has not been shown yet. In this article, with direct intensity detection, we experimentally demonstrate the phase-sensitivity enhancement of such a bright-seeded SU(1,1) interferometer compared with the phase-sensitivity scaling given by $1/\sqrt{N_s}$, known as the “shot-noise limit,” where $N_s$ is the average photon number inside the interferometer. It is this direct intensity detection that brings about the major advance of quantum enhancement for the bright-seeded SU(1,1) interferometer in real time, which is substantially different from our previous work. Our results may find applications in quantum metrology.

Figure 1

The two types of interferometer. (a) MZI and (b) bright-seeded SU(1,1) interferometer. $G$ and $g$ are the amplitude gains of the amplifier, $\varphi$ is the internal phase difference, $S_{1-2}$ is the interference fringe obtained by subtraction of the two arms in the MZI, and $S_c$ is the interference fringe of the conjugate arm in the bright-seeded SU(1,1) interferometer.

Figure 2

Detailed experimental arrangement. AMP, amplifier; AOM, acousto-optic modulator; FM, flip mirror; GT, Glan-Thompson polarizer; HRM, high reflectivity mirror; HWP, half-wave plate; L1, lens 1; L2, lens 2; OS, oscilloscope.

Figure 3

Typical experimental data and corresponding phase sensitivity for the MZI and the bright-seeded SU(1,1) interferometer. (a) Traces i and ii represent the dc and rf components of the interference fringe for the MZI. (b) Traces i and ii represent the dc and rf components of the interference fringe for the bright-seeded SU(1,1) interferometer. (c) The phase sensitivity of the MZI (trace ii) versus the phase inside the interferometer; trace i represents the corresponding SNL. (d) The phase sensitivity of the bright-seeded SU(1,1) interferometer (trace ii) versus the phase inside the interferometer. The dashed blue lines are the corresponding theoretical predictions. Trace i represents the corresponding SNL. The parts below the SNL are enlarged. The error bars are obtained from the standard deviations of multiple repeated measurements.

Figure 4

The phase-sensitivity scaling of the bright-seeded SU(1,1) interferometer and the SNL. (a) Traces i and ii represent the phase sensitivity of the SNL and the bright-seeded SU(1,1) interferometer versus the average intensity ($I_{\mathrm{av}}$) of the fields inside the interferometers. The error bars are obtained from the standard deviations of multiple repeated measurements. (b) The theoretical prediction corresponding to (a).