Can Anomalous Amplification be Attained without Postselection?

Abstract

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.Introduction Anomalous amplification [1] has been shown to be advantageous for precision metrology. Such an amplification provides a way to increase a signal while decreasing [2] or retaining the technical-noise floor [3,4]. As a result, the sensitivity and precision of measurements limited by technical noise can be effectively improved, facilitating the saturation of the standard quantum limit. Anomalous amplification was first proposed for metrology with the introduction of the Weak Value (WV) of an observable [1,5], and parameter estimation protocols defined after it are usually known as Weak-ValueAmplification (WVA) techniques. The WV of an observable is obtained by post-selecting the state of a system after a weak interaction with a meter system. In WVA, such measurements in the system induce a discarding of data counts in the measurements of the meter. In addition to the notion that the state of the system is post-selected after the weak interaction, we consider post-selection as the process of selecting and processing desired events, which, for WVA, results in discarding data in the meter. Due to the interference of the pre-and post-selection states of the system the WV can take large complex values outside the eigenvalue spectrum of the observable, which defines the anomalous amplification in WVA. Discussion about the quantum interpretation of such a phenomenon can be found in Refs. [6][7][8][9]. Many recent applications of WVA for metrology have been done in classical optics, where the interference can be understood using standard wave mechanics [10,11].

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.…”

“…Experimental demonstration of the robustness "against not only misalignment errors but also the wavelength dependence of the optical components" of such a protocol was soon demonstrated [41]. It was also shown than a WVAlike response can be obtained in the difference signal of the two-detector protocol [42]. Simulating an anomalous amplification in a Homodyne detection procedure, the technique has been dubbed Almost-Balanced Weak Values (ABWV).…”

“…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].…”

Quantum-enhanced sensing from hyperentanglement

“…In this case, the information on θ is contained mainly in the relative phase. Though this effect has been exploited by a few authors [26,27], it is not present in implementations using colinear Sagnac configurations [28][29][30]32]. Furthermore, we rely in the present scheme on a simple binary polarization measurement.…”

“…Estimation of tilt angles of mirrors is important in several fields of science [22][23][24][25]. A common procedure consists in detecting the spatial or phase displacement of a laser beam reflected by the mirror [26][27][28][29][30][31][32]. Our method, on the other hand, is based solely on a binary polarization measurement at the output of an interferometer with a displaced input beam.…”