Weak measurement has been proven to amplify the detection of changes in meters while discarding most photons due to the low probability of postselection. Previous power-recycling schemes enable the failed postselection photons to be repeatedly selected, thus overcoming the inefficient postselection and increasing the precision of detection. In this study, we focus on the polarization-based weak value angular-velocity measurement and introduce three cyclic methods to enhance the accuracy of detecting time shifts in a Gaussian beam: power-recycling, signal-recycling, and dual-recycling schemes. By incorporating one or two partially transmitting mirrors into the system, both the power and the signal-to-noise ratio of the detected light are substantially enhanced. Compared to nonpolarization schemes, polarization-based approaches offer several advantages, including lower optical loss, unique cyclic directions, and a wider optimal region. These features effectively reduce crosstalk among different light paths and theoretically eliminate the walk-off effect, thus yielding improvements in both theoretical performance and application.
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.
We experimentally evaluate five estimators for weak-value amplification (WVA) using a position pointer to measure birefringence time delays. Two general approaches are considered: measuring the position shift
Δx and measuring the probability change
ΔPw of successful postselection. Specifically, five estimators are investigated: CCD-detected fringe shift
Δx, quadrant photodiode (PDQ) transversal voltage difference (XDIFF), and lock-in amplifier output phase
η (for
Δx measurement), as well as PDQ total output voltage (SUM) and CCD-detected average photon number
Nr (for
ΔPw measurement). The measurement precision is characterized by the Allan deviation over a range of input laser powers
P0. Generally, measuring the position shift
Δx yields higher precision than measuring the probability change
ΔPw. At
P0=0.5~mW, corresponding to a laser-power-limited regime, direct measurement of the fringe displacement with the CCD achieves a minimum Allan deviation of
(5.30±0.10)×10−3~as, approaching the corresponding photon-statistical Cramér--Rao bound (CRB). At
P0=50~mW, corresponding to a detector-limited regime, PDQ detection combined with lock-in demodulation provides the best precision, reaching
(1.80±0.06)×10−3~as and remaining close to the corresponding CRB. These results demonstrate that the optimal readout depends on the available optical power, detector dynamic range, and technical noise, providing practical guidance for selecting readout strategies in high-precision WVA-based metrology.
In a recent letter, Brunner and Simon propose an interferometric scheme using imaginary weak values with a frequency-domain analysis to outperform standard interferometry in longitudinal phase shifts [N. Brunner and C. Simon, Phys. Rev. Lett {\bf105} (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 Cramer-Rao bound.
By choosing more orthogonality between preselection and postselection states, one can significantly improve the sensitivity in general optical quantum metrology based on the weak-value amplification (WVA) approach. However, increasing the orthogonality decreases the probability of detecting photons and makes the weak measurement difficult, especially when the weak measurement is disturbed by strong noise and the pointer is drowned in noise with a negative-decibel signal-to-noise ratio (SNR). In this article we introduce and numerically evaluate a modified weak-measurement protocol with a temporal pointer, namely, the autocorrelative weak-value amplification (AWVA) approach. Specifically, a small longitudinal time delay (tiny phase shift) $\ensuremath{\tau}$ of a Gaussian pulse is measured by implementing two simultaneous autocorrelative weak measurements under Gaussian white noise with different SNRs. The small quantities $\ensuremath{\tau}$ are obtained by measuring the autocorrelation coefficient of the pulses instead of fitting the shift of the mean value of the probe in the standard WVA technique. Simulation results show that the AWVA approach outperforms the standard WVA technique in the time domain with smaller statistical errors, remarkably increasing the precision of weak measurement under a strong noise background.
Background: Weak measurement involves weak coupling between the system and the measuring device (pointer) enables large amplification and high precision measurement of small physical parameters. The outcome of this special measurement procedure involving nearly mutually orthogonal pre- and post-selection of states in such weakly interacting systems leads to weak value that can become exceedingly large and lie outside the eigenvalue spectrum of the measured observable. This unprecedented ability of weak value amplification of small physical parameters has been successfully exploited for various metrological applications in the optical domain and beyond. Even though it is a quantum mechanical concept, it can be understood using the classical electromagnetic theory of light and thus can be realized in classical optics. Objective: Here, we briefly review the basic concepts of weak measurement and weak value amplification, provide illustrative examples of its implementation in various optical domains. The applications involve measuring ultra-sensitive beam deflections, high precision measurements of angular rotation, phase shift, temporal shift, frequency shift and so forth, and expand this extraordinary concept in the domain of nano-optics and plasmonics. Methods: In order to perform weak value amplification, we have used Gaussian beam and spectral response as the pointer subsequently. The polarization state associated with the pointer is used as pre and post-selection device. Results: We reveal the weak value amplification of sub-wavelength optical effects namely the Goos-Hänchen shift and the spin hall shift. Further, we demonstrate weak measurements using spectral line shape of resonance as a natural pointer, enabling weak value amplification beyond the conventional limit, demonstrating natural weak value amplification in plasmonic Fano resonances and so forth. The discussed concepts could have useful implications in various nano-optical systems to amplify tiny signals or effects. Conclusion: The emerging prospects of weak value amplification towards the development of novel optical weak measurement devices for metrological applications are extensively discussed.