Noise suppression in inverse weak value based phase detection

We examine the effect of different sources of technical noise on inverse weak value-based precision phase measurements. We find that this type of measurement is similarly robust to technical noise as related experiments in the weak value regime. In particular, the measurements considered here are robust to additive Gaussian white noise and angular jitter noise commonly encountered in optical experiments. Additionally, we show the same techniques used for precision phase measurement can be used with the same technical advantages for optical frequency measurements.Comment: 6 pages, 4 figure

Technical advantages for weak value amplification: When less is more

The technical merits of weak value amplification techniques are analyzed. We consider models of several different types of technical noise in an optical context and show that weak value amplification techniques (which only use a small fraction of the photons) compare favorably with standard techniques (which uses all of them). Using the Fisher information metric, we demonstrate that weak value techniques can put all of the Fisher information about the detected parameter into a small portion of the events and show how this fact alone gives technical advantages. We go on to consider a time correlated noise model, and find that a Fisher information analysis indicates that while the standard method can have much larger information about the detected parameter than the postselected technique. However, the estimator needed to gather the information is technically difficult to implement, showing that the inefficient (but practical) signal-to-noise estimation of the parameter is usually superior. We also describe other technical advantages unique to imaginary weak value amplification techniques, focusing on beam deflection measurements. In this case, we discuss combined noise types (such as detector transverse jitter, angular beam jitter before the interferometer and turbulence) for which the interferometric weak value technique gives higher Fisher information over conventional methods. We go on to calculate the Fisher information of the recently proposed photon recycling scheme for beam deflection measurements, and show it further boosts the Fisher information by the inverse postselection probability relative to the standard measurement case

Gravitational sensing with weak value based optical sensors

Using weak values amplification angular resolution limits, we theoretically investigate the gravitational sensing of objects. By inserting a force-sensing pendulum into a weak values interferometer, the optical response can sense accelerations to a few 10's of $\mathrm{zepto}\text{-}\mathrm{g}/\sqrt{\mathrm{Hz}}$, with optical powers of $1~\mathrm{mW}$. We convert this precision into range and mass sensitivity, focusing in detail on simple and torsion pendula. Various noise sources present are discussed, as well as the necessary cooling that should be applied to reach the desired levels of precision.Comment: 9 pages, 4 figures, Quantum Stud.: Math. Found. (2018

Precision frequency measurements with interferometric weak values

We demonstrate an experiment which utilizes a Sagnac interferometer to measure a change in optical frequency of 129 kHz per root Hz with only 2 mW of continuous wave, single mode input power. We describe the measurement of a weak value and show how even higher frequency sensitivities may be obtained over a bandwidth of several nanometers. This technique has many possible applications, such as precision relative frequency measurements and laser locking without the use of atomic lines.Comment: 4 pages, 3 figures, published in PR

Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification

We report on the use of an interferometric weak value technique to amplify very small transverse deflections of an optical beam. By entangling the beam's transverse degrees of freedom with the which-path states of a Sagnac interferometer, it is possible to realize an optical amplifier for polarization independent deflections. The theory for the interferometric weak value amplification method is presented along with the experimental results, which are in good agreement. Of particular interest, we measured the angular deflection of a mirror down to 560 femtoradians and the linear travel of a piezo actuator down to 20 femtometers

Optimizing the Signal to Noise Ratio of a Beam Deflection Measurement with Interferometric Weak Values

The amplification obtained using weak values is quantified through a detailed investigation of the signal to noise ratio for an optical beam deflection measurement. We show that for a given deflection, input power and beam radius, the use of interferometric weak values allows one to obtain the optimum signal to noise ratio using a coherent beam. This method has the advantage of reduced technical noise and allows for the use of detectors with a low saturation intensity. We report on an experiment which improves the signal to noise ratio for a beam deflection measurement by a factor of 54 when compared to a measurement using the same beam size and a quantum limited detector

Power-recycled weak-value-based metrology

We improve the precision of the interferometric weak-value-based beam deflection measurement by introducing a power recycling mirror, creating a resonant cavity. This results in \emph{all} the light exiting to the detector with a large deflection, thus eliminating the inefficiency of the rare postselection. The signal-to-noise ratio of the deflection is itself magnified by the weak value. We discuss ways to realize this proposal, using a transverse beam filter and different cavity designs.Comment: 5 pages, 1 figur

Continuous phase amplification with a Sagnac interferometer

We describe a weak value inspired phase amplification technique in a Sagnac interferometer. We monitor the relative phase between two paths of a slightly misaligned interferometer by measuring the average position of a split-Gaussian mode in the dark port. Although we monitor only the dark port, we show that the signal varies linearly with phase and that we can obtain similar sensitivity to balanced homodyne detection. We derive the source of the amplification both with classical wave optics and as an inverse weak value.Comment: 5 pages, 4 figures, previously submitted for publicatio