Weak-value amplification of photon-number operators in the optomechanical interaction

Abstract

An experimental proposal is presented in which dark port post-selection together with weak measurements are used to enlarge the radiation pressure effect of a single photon on a mechanical oscillator placed in the middle of a Fabry-Pérot cavity and initialized in the ground state. By preparing and post-selecting the photon (the system) in two quasi orthogonal states, the weak value of the radiation force operator can lie outside the eigenvalue spectrum, producing a large shift on the wave function of the mechanical oscillator (the measuring device) in the position representation. Consequently, the effect of a single photon on the average position of the oscillator in its final state can be amplified as compared to the effect caused by a photon without post-selection, i.e. only preselected. The strong measurement scenario is also analyzed. In this case, a higher amplification effect is achieved and the mean position of the oscillator reaches the level of the zero-point fluctuation, but the back-action on the system is increased and the post-selection probabilities are smaller.

Implementation of weak measurement amplification with the weak coherent light and optomechanical system

“…However, outside the WVA regime, if the optomechanical coupling parameter k range is selected appropriately, i.e., 0.001 ≤ k ≤ 0.01, and when δ tends to and is equal to k, P f at the strong coupling limit can be improved by |α| 2 , and is in the range 0.02 − 0.4%. In [20,25] an implementation of WVA with one photon and optomechanical system was proposed as a method for measuring the small coupling constant between a single photon and the mechanical oscillator. In the same condition, P f at the strong coupling limit is in the range 2 × 10 −6 − 2 × 10 −4 .…”

“…Its important characteris-tic is used to amplify tiny physical effects, such as ultrasensitive beam deflection [13], the transverse separation of an optical beam due to birefringence [14,15], longitudinal phase shifts [16], and angular rotations of a classical beam [17], and to measure small physical quantities, such as the direct measurement of wave functions [18], and observation of the average trajectories in a two slit interferometer [19]. Li et al [20][21][22][23][24][25] showed that the mirror's displacement of a single photon in optomechanical system [26,27] can be amplified and observed using weak measurements when the initial states of the mirror are in the different quantum states. These schemes require single-photon sources, and the successful postselection probability is very low.…”

“…These schemes require single-photon sources, and the successful postselection probability is very low. However, the conditions for preparing an ideal single photon are very harsh and the economic cost is very high, so these schemes [20,25] are difficult to be verified by experiments. Feizpour et al [28][29][30] showed that the nonlinear cross-Kerr effect of a single photon can be amplified using weak measurements.…”

“…Hence, we were able to maintain a substantial set of postselections even for small the postselection parameter (i.e., the inner product of the preselection and the postselection states) simply by adjusting the mean photon number accordingly. Outside the WVA regime, the amplification limit can reach the level of the vacuum fluctuations, and when the mean photon number and the optomechanical coupling parameter range are selected appropriately, its successful postselection probability becomes higher, as compared to the studies of weak measurement with one photon and optomechanical system [20,25], which is beneficial to observe the maximum amplification value under the current experimental conditions. This result is unexpected and it breaks the constraint that it is difficult to detect outside the WVA regime.…”

Pragmatic Implementation With Non-Gaussian Devices of Noise-Limited Weak Value Amplification

“…We propose a solution by means of fitting the initial wave function with multiple Gaussian distributions, an approach when viewed as a general expansion in a series of Gaussians, can faithfully represent most broadband devices, which improves the measurement accuracy and reduces the implementation difficulty of WVA phase measurement. Moreover, the WVA scheme entails an inherent dilemma: a higher sensitivity is obtained at the expense of greatly reduced probability of post-selection [14] [17]. Dominated by technical noise associated with the number of detected photons, a common WVA scheme of higher sensitivity does not necessarily result in better precision [18]- [19], because the decrease in the post-selection probability will increase the measurement uncertainty.…”