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Physical Review B

Interference with coupled microcavities: Optical analog of spin 2π rotations

Omar Di Stefano, Roberto Stassi, A. Ridolfo, Salvatore Patanè, Salvatore Savasta

Published Aug 29, 2011• 5 citations
Publisher

Abstract

It is well known that spinor wave functions change their sign under $2\ensuremath{\pi}$ rotation. Several experiments have used magnetic precession of neutrons to implement rotations. Here we propose an all-optical analog of this effect based on time-resolved optical interference in coupled optical microcavities. We show that feeding the coupled-microcavity system with a pair of phase-locked probe pulses, separated by precise delay times, provides direct information on the sign change of the transmitted field after one complete Rabi-like oscillation period.

DOI
10.1103/physrevb.84.085324

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It is well known that spinor wave functions change their sign under 2\ensuremathπ2\ensuremath{\pi}2\ensuremathπ rotation. Several experiments have used magnetic precession of neutrons to implement rotations. Here we propose an all-optical analog of this effect based on time-resolved optical interference in coupled optical microcavities. We show that feeding the coupled-microcavity system with a pair of phase-locked probe pulses, separated by precise delay times, provides direct information on the sign change of the transmitted field after one complete Rabi-like oscillation period.
The observation of the 4π symmetry of spinor wave functions was one of the first and highly debated neutron interference experiments. Polarized neutrons have been used to verify the spin-superposition principle on a macroscopic level when the spin in one beam path is inverted with respect to the other one. This results in a spin polarization perpendicular to both initial spins. When a Rabi flipper is used the final spin polarization rotates in this perpendicular plane with the Larmor frequency of the flipper field. Thus, it produces a “frozen” Larmor spin rotation in free space. In this case the spin-flip is associated with an energy (photon) transfer which causes this effect. A magnetic Josephson effect-like situation exists when spin-flippers with slightly different resonance frequencies are used in both beam paths. When such a spin reversal is done in both beam paths a magnetic Josephson effect analog has been realized which shows a remarkably high energy resolution. Multiphoton exchange can be achieved when off-resonance fields are used.
The effect of spin–rotation coupling is measured for the first time with neutrons. The coupling of spin with the angular velocity of a rotating spin turner can be observed as a phase shift in a neutron polarimeter set-up. After the neutron's spin is rotated by 2 π through a rotating magnetic field, different phase shifts are induced for 'up' and 'down' spin eigenstates. This phase difference results in the rotation of the neutron's spin-vector, which turns out to depend solely on the frequency of the rotation of the magnetic field. The experimental results agree well with the solutions acquired by the Pauli–Schrödinger equation.
A fully quantized theory of optical interactions with semiconductors reveals quantum correlations between the field and carrier density. These quantum correlations lead to intraband coherences which live much longer than the interband dephasing time; the correlations are observed as oscillations in the time-resolved reflectivity in a pump-probe experiment on a normal-mode microcavity. Coherent control of the microcavity normal modes using phase-locked pump pulses enables considerable enhancement of the intraband oscillations due to quantum interference; the detailed phase dependence is well reproduced by the theory.