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arXiv:1509.00636 · Physical Review A

Amplification effects in optomechanics via weak measurements

Gang Li, Tao Wang, He‐Shan Song

Published Jul 21, 2014• 23 citations
arXivHTMLPDF

Abstract

We revisit the scheme of single-photon weak-coupling optomechanics using postselection, proposed by Pepper, Ghobadi, Jeffrey, Simon, and Bouwmeester [Phys. Rev. Lett. 109, 023601 (2012)], by analyzing the exact solution of the dynamical evolution. Positive and negative amplification effects of the displacement of the mirror's position can be generated when the Kerr phase is considered. This effect occurs when the postselected state of the photon is orthogonal to the initial state, which cannot be explained by the usual weak measurement results. The amplification effect can be further modulated by a phase shifter, and the maximal displacement state can appear within a short evolution time.

DOI
10.1103/physreva.90.013827

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We revisit the scheme of single-photon weak-coupling optomechanics using postselection, proposed by Pepper, Ghobadi, Jeffrey, Simon, and Bouwmeester [Phys. Rev. Lett. 109, 023601 (2012)], by analyzing the exact solution of the dynamical evolution. Positive and negative amplification effects of the displacement of the mirror's position can be generated when the Kerr phase is considered. This effect occurs when the postselected state of the photon is orthogonal to the initial state, which cannot be explained by the usual weak measurement results. The amplification effect can be further modulated by a phase shifter, and the maximal displacement state can appear within a short evolution time.
Abstract Most studies for postselected weak measurement in optomechanical system focus on using a single photon as a measured system. However, we find that using weak coherent light instead of a single photon can also amplify the mirror’s position displacement of one photon. In the weak value amplification (WVA) regime, the weak value of one photon can lie outside the eigenvalue spectrum, proportional to the difference of the mirror’s position displacement between the successful and failed postselection and its successful postselection probability is dependent of the mean photon number of the coherent light and improved by adjusting it 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 are selected appropriately, its successful postselection probability becomes higher, which is beneficial to observe the maximum amplification value under the current experimental conditions. This result breaks the constraint that it is difficult to detect outside the WVA regime. This opens up a new regime for the study of a single photon nonlinearity in optomechanical system.
Abstract We have studied the amplification in displacement of the mechanical mirror in a simple optomechanical system. Here photon number acts as system and the mirror acts as the meter. In the weak coupling condition, post selection of the photon number operator enhance the value of mirror displacement. The displacement of the mirror depends on the weak value of the photon number operator and on the value of relative phase(φ) between the pre and post selected states. Amplification of the mirror can be seen for maximum coupling strength(.25Ω m ) in weak coupling criteria for optomechanical systems, Ωm being the mechanical frequency.
Most studies for postselected weak measurement focus on using pure Gaussian state as a pointer, which can only give an amplification limit reaching the ground state fluctuation. In this paper we use the thermal state pointer. We find that its amplification limit can reach thermal fluctuations and we also give the amplification mechanism different from the one with pure Gaussian state pointer. To illustrate the results, we propose two schemes to implement room temperature amplification of the mechanical oscillator's displacement caused by one photon in optomechanical system. The two schemes can both enhance the original displacement by nearly seven orders of magnitude, attaining sensitivity to displacements of ~ 0.26 nm. Such amplification effect can be used to observe the impact of a single photon on a room temperature mechanical oscillator which is impossible to detect in traditional measurement.
Abstract Most studies for postselected weak measurement focus on using the pure Gaussian state as a pointer, which can only give an amplification limit reaching the level of the ground state fluctuation. When the pointer is initialized in a thermal state, we find that the amplification limit after the postselection can reach the level of thermal fluctuation, indicating that the amplification effect achieving the level of thermal fluctuation is also increased with the temperature growth, and also that the amplification mechanism is different from that with pure Gaussian-state pointer. To illustrate these results, we propose two schemes to implement room temperature amplification of the mechanical oscillator’s displacement caused by a single photon in the optomechanical system. The two schemes both enhance the mechanical oscillator’s original displacement by nearly seven orders of magnitude, attaining sensitivity to displacements of ∼0.26 nm. Such amplification effect can be used to observe the impact of a single photon on a room temperature mechanical oscillator, which is hard to detect in traditional measurement.