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.
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.
Abstract Quantum metrology is being gradually studied for weak measurement systems. For weak measurement systems with a thermal state pointer, we find that in the displacement space corresponding to imaginary weak values, the maximal quantum Fisher information (QFI) after the postselection for an accepted event (conversely, the postselection for a rejected event) can attain a level of thermal fluctuation, without surpassing the total QFI, and further, that QFI which increases with increasing temperature can constantly improve measurement precision. These results are much better than those of weak measurement with a pure state (i.e. Gaussian state) pointer. On the other hand, in Kerr nonlinear interaction systems with weak measurement, and by using a thermal state pointer, we obtain in the phase space the accepted postselection and the postselected measurement both achieving the Heisenberg limit of quantum metrology, and showing that weak measurement with thermal states only obtain classical Fisher information (CFI) which increases with increasing temperature and achieves classical-enhanced scaling of N 2 . Moreover, weak measurement with thermal states has an advantage over that with coherent states or mixed states of light because generating these states with larger uncertainty is limited under current technology, but thermal states with larger uncertainly are very easy to achieve with increasing temperature in nature, such as for optical systems and optomechanical systems.
Quantum metrology is being gradually studied for weak measurement systems. For weak measurement systems with thermal state pointer, we find that in the displacement space corresponding to imaginary weak values, the maximal QFI after successful postselection can attain the level of thermal fluctuations, without surpassing total QFI, and that QFI which increases with increasing temperature can constantly improve the measurement precision. These results are much better than that of weak measurement with pure state (i.e., Gaussian state) pointer. On the other hand, in Kerr nonlinear interaction systems with weak measurement, and by using thermal state pointer, we obtain in the phase space successful postselection and postselected measurements both achieve the Heisenberg limit of quantum metrology, and show weak measurement with thermal states only obtain classical Fisher information (CFI) which increases with increasing temperature and achieves classical enhanced scaling of N^2. Moreover, weak measurement with thermal states has an advantage over that with coherent states or mixed states of the light because generating these states with more large uncertainty are limited under the current technology, but thermal states with more large uncertainly are very easy to achieve with increasing temperature in nature, regardless of thermal states of the light or the matter.
An experimental proposal is presented in which dark port postselection 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-P\'erot cavity and initialized in the ground state. By preparing and postselecting the photon (the system) in two quasiorthogonal 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 can be amplified as compared to the effect caused by a photon without postselection, 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 can reach the level of the zero-point fluctuations, but the postselection probabilities are smaller. Finally, the situation in which the oscillator starts in a thermal equilibrium state is studied. In this case, the amplification of the average position remains the same, i.e., proportional to the weak value, but the signal-to-noise ratio is reduced by a factor that depends on the average number of thermal phonons.
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.