Aided by quantum sources, quantum metrology helps to enhance measurement precision. Here, we introduce a method to enhance the measurement of a rotation angle. As a proof of principle, assisted by a quantum state called the squeezed orbital-angular-position (OAP) state and balance homodyne detection, we demonstrate in experiments 3 dB-enhanced measurements of a rotation-angle beyond the shot noise limit. A precision of up to 17.7 nrad/Hz is obtained. Furthermore, we discuss means to further improve the measurement with a high-order precision OAP squeezed state. The method holds promise for future practical applications, such as in high-sensitive Sagnac interferometry.

Nonclassical beams in high order spatial modes have attracted much interest but they exhibit much less squeezing and entanglement than the fundamental spatial modes, limiting their applications. We experimentally demonstrate the relation between pump modes and entanglement of first-order HG modes (HG10 entangled states) in a type II OPO and show that the maximum entanglement of high order spatial modes can be obtained by optimizing the pump spatial mode. To our knowledge, this is the first time to report this. Utilizing the optimal pump mode, the HG10 mode threshold can be reached easily without HG00 oscillation and HG10 entanglement is enhanced by 53.5% over HG00 pumping. The technique is broadly applicable to entanglement generation in high order modes.

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The continuous-variable (CV) orbital angular momentum (OAM) entanglement is very different to the traditional quadrature entanglement. The Stokes-operators directly reflect the character of OAM light. Here, we report the first direct experimental demonstration the Stokes-operator entanglement of continuous-variable OAM entanglement. Generated by transforming quadrature entanglement in the HG mode onto the orbital Stokes-operator basis, the entanglement is measured in the Stokes-operator basis using a self-designed detection scheme. An inseparability of I(O^,O^)<1 is achieved over a wide analyzing frequency of 1-10 MHz. Moreover, experimental fluctuations at 5.0 MHz are visualized using the quantum orbital Poincaré sphere representation. The OAM entanglement with Stokes-operators measurement has a promising application in certain nonlocal quantum information protocols and rotational optomechanics by interacting with nanoparticle or atoms.