Practical advantages of almost-balanced-weak-value metrological techniques

Abstract

Precision measurements of ultra-small linear velocities of one of the mirrors in a Michelson interferometer are performed using two different weak-values techniques. We show that the technique of Almost-Balanced Weak Values (ABWV) offers practical advantages over the technique of WeakValue Amplification (WVA), resulting in larger signal-to-noise ratios and the possibility of longer integration times due to robustness to slow drifts. As an example of the performance of the ABWV protocol we report a velocity sensitivity of 60 fm/s after 40 hours of integration time. The sensitivity of the Doppler shift due to the moving mirror is of 150 nHz.

Universality of local weak interactions and its application for interferometric alignment

“…If the pointer is a Gaussian in the position variable Q it is of course also a Gaussian in the conjugate momentum PQ representation. Therefore, [20] and [21], in analogy to the above, become exact formulas with ∆PQ = 1 2∆Q . There are corresponding exact formulas for the effect of a shift in momentum δPQ with…”

“…To test the universality of modifications of effects for various degrees of freedom one could either perform complete tomographies of the final pointer states [14] and [15] or, more clearly, show the modification of the effects of the three couplings according to [20] and [21]. We follow the second approach.…”

Femtometer displacement resolution with phase-insensitive Doppler sensing

“…One way to estimate a small displacement is to measure the Doppler shift generated in light reflected off an object moving with a known periodic frequency. This remote sensing technique converts a displacement measurement into a frequency measurement, and has been considerably successful [8][9][10][11][12][13][14]. The displacement sensitivity of this technique is limited by the Doppler frequency noise floor and by the velocity of the moving object.…”

“…Other primary limitations are hours of integration time [12,13] and optimal operation only in a narrow Doppler frequency range.Here we show a sensitive device capable of measuring µHz/ √ Hz Doppler frequency shifts corresponding to tens of fm displacements for a mirror oscillating at 2 Hz. While the Doppler shift measured is comparable to other techniques [12,13], the position sensitivity is orders of magnitude better, and operates over several orders of magnitude of Doppler frequency range. In addition, unlike other techniques which often rely on interferometric methods, our device is phase insensitive, making it unusually robust to noise.…”

“…The displacement sensitivity of this technique is limited by the Doppler frequency noise floor and by the velocity of the moving object. Other primary limitations are hours of integration time [12,13] and optimal operation only in a narrow Doppler frequency range.…”