Towards quantum telescopes: demonstration of a two-photon interferometer for precision astrometry.

Classical optical interferometry requires maintaining live, phase-stable links between telescope stations. This requirement greatly adds to the cost of extending to long baseline separations and limits on baselines will in turn limit the achievable angular resolution. Here we describe a novel type of two-photon interferometer for astrometry, which uses photons from two separate sky sources and does not require an optical link between stations. Such techniques may make large increases in interferometric baselines practical, even by orders of magnitude, with a corresponding improvement in astrometric precision benefiting numerous fields in astrophysics. We tested a benchtop analogue version of the two-source interferometer and unambiguously observe correlated behavior in detections of photon pairs from two thermal light sources, in agreement with theoretical predictions. This work opens new possibilities in future astronomical measurements.

Distributed quantum sensing with mode-entangled spin-squeezed atomic states.

Quantum sensors are used for precision timekeeping, field sensing and quantum communication1-3. Comparisons among a distributed network of these sensors are capable of, for example, synchronizing clocks at different locations4-8. The performance of a sensor network is limited by technical challenges as well as the inherent noise associated with the quantum states used to realize the network9. For networks with only spatially localized entanglement at each node, the noise performance of the network improves at best with the square root of the number of nodes10. Here we demonstrate that spatially distributed entanglement between network nodes offers better scaling with network size. A shared quantum nondemolition measurement entangles a clock network with up to four nodes. This network provides up to 4.5 decibels better precision than one without spatially distributed entanglement, and 11.6 decibels improvement as compared to a network of sensors operating at the quantum projection noise limit. We demonstrate the generality of the approach with atomic clock and atomic interferometer protocols, in scientific and technologically relevant configurations optimized for intrinsically differential comparisons of sensor outputs.

Free Space Ramsey Spectroscopy in Rubidium with Noise below the Quantum Projection Limit.

We demonstrate the utility of optical cavity generated spin-squeezed states in free space atomic fountain clocks in ensembles of 390 000 ^{87}Rb atoms. Fluorescence imaging, correlated to an initial quantum nondemolition measurement, is used for population spectroscopy after the atoms are released from a confining lattice. For a free fall time of 4 milliseconds, we resolve a single-shot phase sensitivity of 814(61) microradians, which is 5.8(0.6) decibels (dB) below the quantum projection limit. We observe that this squeezing is preserved as the cloud expands to a roughly 200 µm radius and falls roughly 300 µm in free space. Ramsey spectroscopy with 240 000 atoms at a 3.6 ms Ramsey time results in a single-shot fractional frequency stability of 8.4(0.2)×10^{-12}, 3.8(0.2) dB below the quantum projection limit. The sensitivity and stability are limited by the technical noise in the fluorescence detection protocol and the microwave system, respectively.

Femtometer displacement resolution with phase-insensitive Doppler sensing.

The measurement of extremely small displacements is of utmost importance for fundamental studies and practical applications. One way to estimate a small displacement is to measure the Doppler shift generated in light reflected off a moving object, converting a displacement measurement into a frequency measurement. Here we show a sensitive device capable of measuring µHz/Hz Doppler frequency shifts corresponding to tens of femtometer displacements for a mirror oscillating at 2 Hz. While the Doppler shift measured is comparable to other techniques, the position sensitivity is orders of magnitude better, and operates over several orders of magnitude of Doppler frequency range. In addition, unlike other interferometric techniques, our device is phase insensitive, making it unusually robust to noise.

Anomalous vibration suppression in a weak-value-emulated heterodyne roll interferometer.

We experimentally validate the vibration suppression capabilities of a weak-value-like protocol. The phase-sensitive heterodyne technique exhibits advantageous characteristics of a weak measurement including anomalous amplification in sensitivity and technical noise suppression. It does not, however, leverage the entanglement between the system and meter to amplify the signal of interest, as is typical in a weak measurement. In this formalism, we demonstrate an amplification in sensitivity to the roll angle of over 700 times. High precision roll experiments anchor numerical simulations to show that the interferometer outperforms standard interferometry by a factor of 500 in terms of peak-to-peak noise amplitude. During the measurement of a rolling stage, technical noise - primarily in the form of vibrations - is substantially attenuated. This is the first demonstration of vibration suppression capabilities that are inherent to the light from a metrology instrument instead of achieved via mechanical damping. The emulation presented in this work also identifies an avenue to achieve anomalous amplification outside of the standard weak measurement protocol.

Ultrasensitive inverse weak-value tilt meter.

We present an interferometric technique for measuring ultrasmall tilts. The information of a tilt in one of the mirrors of a modified Sagnac interferometer is carried by the phase difference between the counter-propagating laser beams. Using a small misalignment of the interferometer, orthogonal to the plane of the tilt, a bimodal (or two-fringe) pattern is induced in the beam's transverse power distribution. By tracking the mean of such a distribution, using a split detector, a sensitive measurement of the phase is performed. With 1.2 mW of continuous-wave laser power, the technique has a shot noise limited sensitivity of 56 frad/Hz and a measured noise floor of 200 frad/Hz for tilt frequencies above 2 Hz. A tilt of 200 frad corresponds to a differential displacement of 4.0 fm in our setup. The novelty of the protocol relies on signal amplification due to the misalignment and on good performance at low frequencies. A noise floor of about 70 prad/Hz is observed between 2 and 100 mHz.

Anomalous amplification of a homodyne signal via almost-balanced weak values.

We propose precision measurements of ultra-small angular velocities of a mirror within a modified Sagnac interferometer, where the counter-propagating beams are spatially separated, using the recently proposed technique of almost-balanced weak values amplification (ABWV) [Phys. Rev. Lett.116, 100803 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.100803]. The separation between the two beams provides additional amplification with respect to using collinear beams in a Sagnac interferometer. Within the same setup, the weak-value amplification technique is also performed for comparison. Much higher amplification factors can be obtained using the almost-balanced weak values technique, with the best one achieved in our experiments being as high as 1.2×107. In addition, the amplification factor monotonically increases with decreasing of the post-selection phase for the ABWV case in our experiments, which is not the case for weak-value amplification (WVA) at small post-selection phases. Both techniques consist of measuring the angular velocity. The sensitivity of the ABWV technique is ∼38 nrad/s per averaged pulse for a repetition rate of 1 Hz and ∼33 nrad/s per averaged pulse for the WVA technique.

Can Anomalous Amplification be Attained without Postselection?

We present a parameter estimation technique based on performing joint measurements of a weak interaction away from the weak-value-amplification approximation. Two detectors are used to collect full statistics of the correlations between two weakly entangled degrees of freedom. Without discarding of data, the protocol resembles the anomalous amplification of an imaginary-weak-value-like response. The amplification is induced in the difference signal of both detectors allowing robustness to different sources of technical noise, and offering in addition the advantages of balanced signals for precision metrology. All of the Fisher information about the parameter of interest is collected. A tunable phase controls the strength of the amplification response. We experimentally demonstrate the proposed technique by measuring polarization rotations in a linearly polarized laser pulse. We show that in the presence of technical noise the effective sensitivity and precision of a split detector is increased when compared to a conventional continuous-wave balanced detection technique.

Weak-values technique for velocity measurements.

In a recent Letter, Brunner and Simon proposed an interferometric scheme using imaginary weak values with a frequency-domain analysis to outperform standard interferometry in longitudinal phase shifts [Phys. Rev. Lett105, 010405 (2010)]. Here we demonstrate an interferometric scheme combined with a time-domain analysis to measure longitudinal velocities. The technique employs the near-destructive interference of non-Fourier limited pulses, one Doppler shifted due to a moving mirror in a Michelson interferometer. We achieve a velocity measurement of 400 fm/s and show our estimator to be efficient by reaching its Cramér-Rao bound.