Approaching Quantum-Limited Metrology with Imperfect Detectors by Using Weak-Value Amplification

Abstract

Weak value amplification (WVA) is a metrological protocol that amplifies ultra-small physical effects. However, the amplified outcomes necessarily occur with highly suppressed probabilities, leading to the extensive debate on whether the overall measurement precision is improved in comparison to that of conventional measurement (CM). Here, we experimentally demonstrate the unambiguous advantages of WVA that overcome practical limitations including noise and saturation of photo-detection and maintain a shot-noise-scaling precision for a large range of input light intensity well beyond the dynamic range of the photodetector. The precision achieved by WVA is six times higher than that of CM in our setup. Our results clear the way for the widespread use of WVA in applications involving the measurement of small signals including precision metrology and commercial sensors.

Beating Standard Quantum Limit with Weak Measurement

“…The uncertainty in the meter is determined as the standard deviation σ ν for ν times measurement of p √ . The achieved precision is defined as the ratio of σ ν and s, and the results shown in Figure 7a are consistent with the theoretical prediction in Equation (26). The amount of extracted Fisher information (FI) for different n. The n 2 scaling also indicates that the Heisenberg limit is approached in this measurement.…”

“…Other practical factors may also confer WM the ability to outperform CM, e.g., when detector saturation occurs, WM maintains a considerable amount of metrology information while detecting an ultra-small fraction of probes. Vaidman proposed the conjecture about this advantage [24], which was then rigorously verified in theory [25] and demonstrated in experiment [26].…”

Improving the precision of optical metrology by detecting fewer photons with biased weak measurement

“…Based on this point, Vaidman conjectured that SWM can effectively alleviate DSE and outperform CM with incident photon number above the saturation threshold of detectors 33 . Recently, several theoretical and experimental studies have confirmed this advantage of SWM and proved that SWM offers an improved precision compared to CM in the presence of DSE 34 .…”

“…SWM satisfies these two premises by increasing the strength of post-selection, and eventually, an improved precision can be acquired 35 . In an ideal case, a stronger postselection in SWM necessarily results in a larger factor of amplification; however, in practice, this simple postselection cannot be arbitrarily strong, and SWM can only alleviate DSE to a limited extent 34 . By contrast, biased weak measurement (BWM) employs an additional reduction of photons in the post-selection by introducing a pre-coupling, and the remaining photons have shown to be extremely sensitive to the estimated parameter both in theory and experiments [36][37][38] .…”

Fisher information analysis on post-selection involved quantum precision measurements using optical coherent states

“…Actually, theoretical analysis has pointed out that the WVA technique can outperform conventional measurement in the presence of detector saturation [18]. This advantage of the WVA technique was recently illustrated by achieving a precision of 6 times higher than that of the conventional measurement [19]. Other improvements along the line of the WVA technique include such as strengthening the WVA via photon recycling [20][21][22] and applying a technique called dual WVA (DWVA) which allows for a precision metrology with sensitivity several orders of magnitude higher than the standard approach [23].…”