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Physics Letters A

4π spinor symmetry — some new observations

Rajendra Bhandari

Published Aug 1, 1993• 24 citations
Publisher
DOI
10.1016/0375-9601(93)90487-k

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Since its advent in 1974, the neutron interferometry technique is a powerful tool for tests of quantum mechanics by matter waves. High order interference pattern could be observed and an upper limit for nonlinear terms in the Schroedinger equation has been given. The 4..pi..-symmetry of a spinor wave function was verified in 1975. Afterwards a precision measurement of this 4..pi..-symmetry effect has been performed which yields, after corrections for the new values of the fundamental constants, a periodicity factor of ..cap alpha.. = 715.87 +- 3.8 deg which does not include the expected 720 deg within its simple error limits. Alternative formulations of quantum mechanics predict a deviation of the 4..pi..-periodicity factor in the region of strong interaction. Therefore, a precision measurement of the influence of strong interactions is proposed where the spinor rotation is observed within the region of additional strong interactions caused by a nonmagnetic material of heavy nuclei inserted alternatively into the beam paths of the interferometer. It is expected to reach an accuracy concerning the additional phase shift in the range of 10/sup -5/ which corresponds to deviation factors within the region of strong interactions of about 20% from the standard formulation. Various factors limiting themore » accuracy are discussed.« less
We report the observation of coherent circulation in a macroscopic Bose-Einstein condensate of polaritons in a ring geometry. Because they are spinor condensates, half-quanta are allowed in where there is a phase rotation of π in connection with a polarization vector rotation of π around a closed path. This half-quantum behavior is clearly seen in the experimental observations of the polarization rotation around the ring. In our ring geometry, the half-quantum state that we see is one in which the handedness of the spin flips from one side of the ring to the other side in addition to the rotation of the linear polarization component; such a state is allowed in a ring geometry but will not occur in a simply connected geometry. This state is lower in energy than a half-quantum state with no change of the spin direction and corresponds to a superposition of two different elementary half-quantum states. The direction of circulation of the flow around the ring fluctuates randomly between clockwise and counterclockwise from one shot to the next; this fluctuation corresponds to spontaneous breaking of time-reversal symmetry in the system. This type of macroscopic polariton ring condensate allows for the possibility of direct control of the circulation to excite higher quantized states and the creation of Josephson junction tunneling barriers.