Distributed phase sensing using four-mode entanglement

In quantum interferometry it is well known that employing single-mode squeezed states can allow for sensitivities below the standard quantum limit. Besides squeezing it has also been shown that quantum entanglement between... [ view full abstract ]

In quantum interferometry it is well known that employing single-mode squeezed states can allow for sensitivities below the standard quantum limit. Besides squeezing it has also been shown that quantum entanglement between modes allows for increased sensitivities in certain settings.

Here we present a distributed quantum sensing scheme for multimode phase estimation. By utilizing the correlations of a continuous-variable entangled four-mode probe state we experimentally show that our scheme achieves an improved sensitivity and resource scaling with respect to an equivalent approach using separable probe states.

A probe state for phase sensing is generated at a sideband frequency by phase modulating a seed beam with an EOM before injecting it into an optical parametric oscillator (OPO) locked to deamplification. The result is an amplitude squeezed displaced state |α,r>  at 4 MHz, where α and r can be controlled experimentally by the modulation depth and pump power respectively. After the OPO the carrier field is combined with a LO field in an orthogonal polarization and their relative phases locked by tapping off a small part of the beam and interfering them. The beam is then split into four spatial modes, where a relative phase shift between the probe and LO field in each mode is introduced by the combination of a ¼ and ½ waveplate. The average phase shift is then estimated by performing homodyne detection of each individual mode and looking at the correlations (fig 1+2).

We establish entanglement between the four modes by directly measuring a squeezing level of 0.8 dB below the shot noise in each individual mode while regaining a 5.0 dB squeezing level in the correlated (HD₁+HD₂+HD₃+HD₄) homodyne detector output. From this entanglement we show a factor 2 improved sensitivity scaling, compared to a separable approach using the same resources.

In conclusion we show how entanglement together with squeezing can be used as a resource in distributed sensing scenarios. Our protocol could also be used to boost the sensitivity of phase sensing in situations where multiple fragile samples needs to be addressed such as photo-sensitive molecules or to avoid heating of ultra-cold atomic clouds during read-out.