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Physics Letters A

Measurement of the helicity of photon pairs using the optical Berry phase

Karsten J. Siebert, Heidrun Schmitzer, Wolfgang Dultz

Published Aug 1, 2002• 3 citations
Publisher
DOI
10.1016/s0375-9601(02)00849-6

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An experimental arrangement is proposed which combines the idea of two-photon interferometry with that of geometric phases. A pair of photons generated by parametric down-conversion is fed into a pair of Mach-Zehnder interferometers, in each of which there is phase shift produced by the helically wound optical fibre in the manner of Tomita and Chiao(1986). If the winding angle is a multiple of 2 pi there is a closed path in parameter space, in accordance with the pioneering analysis of Berry(1984). More general windings are also considered in which the path in parameter space is not closed, and the geometric phase for such open paths is calculated in accordance with the gauge-invariant prescription of Aitchison and Wanelik. If the proposed experiment is realized, it will provide a test for the noncyclic geometric phase for photons and for the set of prescriptions equivalent to that of Aitchison and Wanelik(1992). Furthermore, the geometric phase in this arrangement will be unequivocally quantum mechanical because of the non-classical character of two-photon interferometry.
This chapter presents the derivation of Berry's phase. Many classical phenomena have corresponding quantum mechanical analogue. Therefore, it is natural to identify a classical analogue of Berry's phase. The concept of Berry's phase has been used in the study of quantized Hall Effect, the spin statistics properties of quasiparticle excitations, the rotation of photon polarization in helical optical fibers, etc. The chapter discusses various applications of Berry's phase in solid state physics. The Berry's phase in one-dimension is usually called Zak phase and is used for a better understanding of electric polarization in dielectrics, protected edge states and Wannier–Stark ladders and integer quantum Hall effect. The chapter discusses the Aharonov–Bohm and Sagnac effects. The Aharonov–Bohm experiment consists of splitting an electron beam, passing around both sides of a solenoid and then recombining the beam. The Sagnac effect has been studied in resonant microcavities and light propagation in a wave guide also.
The exact wave function and rigorous solution of Bloch equation for spin-1/2 under the rotating magnetic field are obtained in this paper. Berry's geometric phase can be obtained by taking the adiabatic limit on the exact wave function, and be compared with the slow helical neutron experiment done by Bitter et al. For general cyclic solution, the analytic expressions of AA geometric phase and dynamic phase are obtained, and a perfect explanation to a controversial helical optics fiber experiment done by Chiao et al is given. Another theorem in this paper shows that both Berry's dynamic phase and Berry's geometric phase can be obtained by taking the adiabatic limit on the AA dynamic phase. An orthogonal state method is proposed to reach parallel transport, which is practical for the non-adiabatic geometric quantum computation.