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

Abstract

The technique of almost-balanced weak values amplification (ABWV) was recently proposed [Phys. Rev. Lett. 116: 100803 (2016)]. We demonstrate this technique using a modified Sagnac interferometer, where the counter-propagating beams are spatially separated. The separation between the two beams provides additional amplification, with respect to using colinear beams in a Sagnac interferometer. As a demonstration of the technique, we perform measurements of the angular velocity in one of the mirrors of the 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 × 10 7 . In addition, the amplification factor monotonically increases with decreasing post-selection phase for the ABWV case in our experiments, which is not the case for weak-value amplification at small post-selection phases.

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

“…larger time shifts) than WVA, and second, the amplification monotonically grows for small values of (WVA breaks down for ≲ 0.2 rad). The former was noted when the technique was originally proposed [42], and the latter was subsequently experimentally demonstrated [43]. For a given frequency f r (and velocity v), the smaller the phase the larger the time shift.…”

“…Simulating an anomalous amplification in a Homodyne detection procedure, the technique has been dubbed Almost-Balanced Weak Values (ABWV). The ABWV technique has been used to measure angular velocities of the linear polarization of laser pulses with a precision of 22 nrad/s after ∼11 hours of integration time [42], and more recently, to measure angular velocities of a rotating mirror with a precision of ∼4.9 nrad/s with one minute of collection time [43].…”

“…The ABWV protocol has proven to offer larger amplification than the WVA approach [43], however it is still an open question if it offers noise-mitigation advantages or not. We perform the velocities measurements under equal conditions for both techniques (WVA and ABWV) and for six different frequencies on the driving mirror.…”

Scheme and experimental demonstration of fully atomic weak-value amplification

“…A single ion 40 Ca + trapped in a blade-shaped linear Paul trap is used in the experiment. In the first part of the experimental sequence, all the motional modes of the single ion are cooled down to a phonon number of about 20 using Doppler cooling method with lasers at 397 and 866 nm.…”

“…In the experiment, we use a single 40 Ca + ion trapped in a blade-shaped linear Paul trap with radial and axial trapping frequencies ω r = 2π × 1.6 MHz and ω z = 2π × 1.41 MHz, respectively. Fig.…”