Detection Loss Tolerant Supersensitive Phase Measurement with an SU(1,1) Interferometer

In an unseeded SU(1,1) interferometer composed of two cascaded degenerate parametric amplifiers, with direct detection at the output, we demonstrate a phase sensitivity overcoming the shot noise limit by 2.3 dB. The interferometer is strongly unbalanced, with the parametric gain of the second amplifier exceeding the gain of the first one by a factor of 2, which makes the scheme extremely tolerant to detection losses. We show that by increasing the gain of the second amplifier, the phase supersensitivity of the interferometer can be preserved even with detection losses as high as 80%. This finding can considerably improve the state-of-the-art interferometry, enable sub-shot-noise phase sensitivity in spectral ranges with inefficient detection, and allow extension to quantum imaging.

Figure 1

Unbalanced unseeded SU(1,1) interferometer formed by coherently pumped DOPA1 and DOPA2. Squeezed vacua with phases ${\varphi }_{1,2}$ are distinguishable if their Wigner functions do not fully overlap. After DOPA2, the phase information is encoded into the photon number, or into the antisqueezed quadrature, which is tolerant to loss. A low detection efficiency $\eta$ almost destroys the squeezing but, with the DOPA2 gain high enough, the states remain distinguishable.

Figure 2

The unseeded SU(1,1) interferometer is made of two cascaded BBO crystals, BBO1 and BBO2. The generated PDC light is spatially filtered by a pinhole placed in the focal plane of the lens $L$ and spectrally filtered by an interference filter. The number of photons contained in a given PDC pulse is measured by the photodiode PD1. A second photodiode PD2 is used for postselecting a pump intensity interval. For finding the SNL, BBO2 is removed and an APD registers the number of photons emitted by BBO1 within the $\mathrm{\Delta }\lambda$, $\mathrm{\Delta }\theta$ bandwidths.

Figure 3

Phase sensitivity measurements with $\mathrm{\Delta }\theta =0.9\mathrm{mrad}$ and $\mathrm{\Delta }\lambda =3.1\mathrm{nm}$. (a) Phase sensitivity for strongly differing gain values of BBO1: $r_1=1.5$, $⟨N(\mathrm{\Delta }\lambda ,\mathrm{\Delta }\theta )⟩=1.7$ photons (blue), and $r_1=2.7$, $⟨N(\mathrm{\Delta }\lambda ,\mathrm{\Delta }\theta )⟩=11$ photons (red). The values of $|r_2|$ are 4.9 and 5.2, respectively. The dashed lines mark the SNL $\mathrm{\Delta }{\varphi }_{\mathrm{SNL}}$ for the two cases. (b) Phase sensitivity for strongly differing gain values of BBO2: $|r_2|=3.9$ (blue), $|r_2|=5.2$ (red). The values of $r_1$ are 2.5 and 2.1, respectively. $⟨N(\mathrm{\Delta }\lambda ,\mathrm{\Delta }\theta )⟩=4.8$ photons is the same in both cases and the corresponding $\mathrm{\Delta }{\varphi }_{\mathrm{SNL}}$ is given by the dashed red line. The insets show the $⟨N_f(\varphi )⟩$ dependences.

Figure 4

Best phase sensitivity $\mathrm{\Delta }{\varphi }_{\min }$ normalized to $\mathrm{\Delta }{\varphi }_{\mathrm{SNL}}$ against the detection transmission $\eta$, reduced by adding neutral density filters. The number of photons is kept constant for all presented cases, with $⟨N(\mathrm{\Delta }\lambda ,\mathrm{\Delta }\theta )⟩=4.5\pm 0.5$. Red: $r_1=2.1$, $|r_2|=5.2$. Blue: $r_1=2.5$, $|r_2|=4.7$. Green: $r_1=2.6$, $|r_2|=4$.