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Register a new userOrbital-angular-momentum-enhanced estimation of sub-Heisenberg-limited angular displacement with two-mode squeezed vacuum and parity detection
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We report on an orbital-angular-momentum-enhanced scheme for angular displacement estimation based on two-mode squeezed vacuum and parity detection. The sub-Heisenberg-limited sensitivity for angular displacement estimation is obtained in an ideal situation. Several realistic factors are also considered, including photon loss, dark counts, response-time delay, and thermal photon noise. Our results indicate that the effects of the realistic factors on the sensitivity can be offset by raising orbital angular momentum quantum number $ell$. This reflects that the robustness and the practicability of the system can be improved via raising $ell$ without changing mean photon number $N$.
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We study the sensitivity and resolution of phase measurement in a Mach-Zehnder interferometer with two-mode squeezed vacuum (<n> photons on average). We show that super-resolution and sub-Heisenberg sensitivity is obtained with parity detection. In particular, in our setup, dependence of the signal on the phase evolves <n> times faster than in traditional schemes, and uncertainty in the phase estimation is better than 1/<n>.
A proposed phase-estimation protocol based on measuring the parity of a two-mode squeezed-vacuum state at the output of a Mach-Zehnder interferometer shows that the Cram{e}r-Rao sensitivity is sub-Heisenberg [Phys. Rev. Lett. {bf104}, 103602 (2010)]. However, these measurements are problematic, making it unclear if this sensitivity can be obtained with a finite number of measurements. This sensitivity is only for phase near zero, and in this region there is a problem with ambiguity because measurements cannot distinguish the sign of the phase. Here, we consider a finite number of parity measurements, and show that an adaptive technique gives a highly accurate phase estimate regardless of the phase. We show that the Heisenberg limit is reachable, where the number of trials needed for mean photon number $bar{n}=1$ is approximately one hundred. We show that the Cram{e}r-Rao sensitivity can be achieved approximately, and the estimation is unambiguous in the interval ($-pi/2, pi/2$).
A recently proposed phase-estimation protocol that is based on measuring the parity of a two-mode squeezed-vacuum state at the output of a Mach-Zehnder interferometer shows that Cram{e}r-Rao bound sensitivity can be obtained [P. M. Anisimov, et al., Phys. Rev. Lett. {bf104}, 103602 (2010)]. This sensitivity, however, is expected in the case of an infinite number of parity measurements made on an infinite number of photons. Here we consider the case of a finite number of parity measurements and a finite number of photons, implemented with photon-number-resolving detectors. We use Bayesian analysis to characterize the sensitivity of the phase estimation in this scheme. We have found that our phase estimation becomes biased near 0 or $pi/2$ phase values. Yet there is an in-between region where the bias becomes negligible. In this region, our phase estimation scheme saturates the Cram{e}r-Rao bound and beats the shot-noise limit.
We present an optomechanical device designed to allow optical transduction of orbital angular momentum of light. An optically induced twist imparted on the device by light is detected using an integrated cavity optomechanical system based on a nanobeam slot-mode photonic crystal cavity. This device could allow measurement of the orbital angular momentum of light when photons are absorbed by the mechanical element, or detection of the presence of photons when they are scattered into new orbital angular momentum states by a sub-wavelength grating patterned on the device. Such a system allows detection of a $l = 1$ orbital angular momentum field with an average power of $3.9times10^3$ photons modulated at the mechanical resonance frequency of the device and can be extended to higher order orbital angular momentum states.
The interference between coherent and squeezed vacuum light can produce path entangled states with very high fidelities. We show that the phase sensitivity of the above interferometric scheme with parity detection saturates the quantum Cramer-Rao bound, which reaches the Heisenberg-limit when the coherent and squeezed vacuum light are mixed in roughly equal proportions. For the same interferometric scheme, we draw a detailed comparison between parity detection and a symmetric-logarithmic-derivative-based detection scheme suggested by Ono and Hofmann.
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