Optimal signal amplification by weak measurement

The weak measurement proposed by Aharonov and his colleagues extracts information of a physical quantity of the system by the post selection as the shifts of the argument of the probe wavefunction. The shift is called the weak value and is larger for the post-selected state more orthogonal to the initial state. Recently, the signal amplification by the weak measurement has been extensively studied. In the present work, we explicitly obtain the optimal probe wavefunction and the amplification factor for a given weak value, which is calculated from the experimental setup. It is shown that the amplification factor has no upper bound in contrast to the Gaussian probe wavefunction and that the amplified signal is sharp.The weak measurement proposed by Aharonov and his colleagues extracts information of a physical quantity of the system by the post selection as the shifts of the argument of the probe wavefunction. The shift is called the weak value and is larger for the post-selected state more orthogonal to the initial state. Recently, the signal amplification by the weak measurement has been extensively studied. In the present work, we explicitly obtain the optimal probe wavefunction and the amplification factor for a given weak value, which is calculated from the experimental setup. It is shown that the amplification factor has no upper bound in contrast to the Gaussian probe wavefunction and that the amplified signal is sharp.

May 1, 20120 citations

ON SIGNAL AMPLIFICATION FROM WEAK-VALUE AMPLIFICATION

Yutaka Shikano

Apr 1, 20141 citation

Merit of amplification by weak measurement in view of measurement uncertainty

Jaeha Lee, Izumi Tsutsui

arXiv:1305.2721Quantum Studies Mathematics and FoundationsMay 20, 201421 citations

Optimal probe wave function of weak-value amplification

Yuki Susa, Yutaka Shikano, Akio Hosoya

The weak measurement proposed by Aharonov and his colleagues extracts information about a physical quantity of the system by the postselection as shifts of the argument of the probe wave function. The more the postselected state is orthogonal to the preselected state, the larger the shift determined by the weak value becomes. Recently, the signal amplification by the weak measurement has been extensively studied. In the present work, we explicitly obtain the optimal probe wave function and the amplification factor for a given weak value, which is calculated from the experimental setup. It is shown that the amplification factor has no upper bound, in contrast to the Gaussian probe wave function, and that the amplified signal is sharp.The weak measurement proposed by Aharonov and his colleagues extracts information about a physical quantity of the system by the postselection as shifts of the argument of the probe wave function. The more the postselected state is orthogonal to the preselected state, the larger the shift determined by the weak value becomes. Recently, the signal amplification by the weak measurement has been extensively studied. In the present work, we explicitly obtain the optimal probe wave function and the amplification factor for a given weak value, which is calculated from the experimental setup. It is shown that the amplification factor has no upper bound, in contrast to the Gaussian probe wave function, and that the amplified signal is sharp.

arXiv:1203.0827Physical Review AMay 11, 201263 citations

Measuring angular rotation via the rotatory dispersion effect

Chongqi Zhou, Suyi Zhong, Kaijie Ma +3 more

We propose a scheme for an ultrasensitive weak measurement system with an ultrasmall rotatory dispersion effect to measure angular rotation. Estimation of angular rotation is obtained by the shift of the center wavelength. In our scheme, we obtain a continuously adjustable coupling strength and show that our system provides a 13 times higher sensitivity of 38 840 nm/rad compared with previous work. Here we demonstrate that our scheme may offer an optimal weak value ${A}_{w}$ in practice and outperforms conventional measurements in the presence of technical noise. The precision achieved by optimized weak value amplification (WVA) is about three times higher than that of a polarimeter. Our work extends the working regime of WVA. Its simplicity and robustness clear the way for widespread use of WVA involving measurements with commercial cameras and small signals.We propose a scheme for an ultrasensitive weak measurement system with an ultrasmall rotatory dispersion effect to measure angular rotation. Estimation of angular rotation is obtained by the shift of the center wavelength. In our scheme, we obtain a continuously adjustable coupling strength and show that our system provides a 13 times higher sensitivity of 38 840 nm/rad compared with previous work. Here we demonstrate that our scheme may offer an optimal weak value ${A}_{w}$ in practice and outperforms conventional measurements in the presence of technical noise. The precision achieved by optimized weak value amplification (WVA) is about three times higher than that of a polarimeter. Our work extends the working regime of WVA. Its simplicity and robustness clear the way for widespread use of WVA involving measurements with commercial cameras and small signals.

Physical Review ADec 22, 202012 citations

Increase of Signal-to-Noise Ratio in Weak Value Measurements

Courtney L. Byard, Trent Graham, Ariel Danan +3 more

Springer eBooksSep 12, 20132 citations

{A}_{w}

in practice and outperforms conventional measurements in the presence of technical noise. The precision achieved by optimized weak value amplification (WVA) is about three times higher than that of a polarimeter. Our work extends the working regime of WVA. Its simplicity and robustness clear the way for widespread use of WVA involving measurements with commercial cameras and small signals.