Fig. 1. Scheme for the angular rotation measurement uses a coherent beam carrying OAM and a vacuum beam. The coherent beam comes from input-port a and has an OAM of lℏ and is detected by the method of HD. M, mirror; DP, Dove prism; LO, local beam.

Fig. 2. SU(1,1) interferometer for the angular rotation measurement uses a coherent beam and a vacuum beam. The beam comes from input-port a carries an OAM of lℏ. Note that two PA processes replace two BS compared with Fig. 1.

Fig. 3. SU(1,1) interferometer for the angular rotation measurement uses a coherent beam and a vacuum beam. The pump beam has an OAM of lℏ, and the probe beam has no OAM.