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Simulating a one-half spin
MSC : Martin Devaud, Thierry Hocquet, Valentin Leroy, Jean-Claude Bacri
The dynamics of Harmonic Oscillators (HOs) can be described very smartly thanks to Glauber’s variables. Using this formalism, it was shown that the motion of two quasi identical and weakly coupled HOs – a situation referred to as quasi-degeneracy – is analogous to that of a one-half spin in a magnetic field, ruled by a Schrödinger equation. The latter motion can also be regarded as that of a pseudo magnetic moment, moving in a R3-isomorphous Larmor space, and ruled by Bloch equations. In the free motion, the Larmor precession is observed. Should an adiabatic (in the Ehrenfest sense) parametric excitation be implemented, the Rabi precession is then observed.
PUBLICATIONS:
V. Leroy, J.-C. Bacri, T. Hocquet, and M. Devaud, "A Hamiltonian approach to the parametric excitation", Eur. J. Phys. 27 469 (2006)
V. Leroy, J.-C. Bacri, T. Hocquet, and M. Devaud, "Simulating a one-half spin with two coupled pendula: the free Larmor precession ", Eur. J. Phys. 27 1363 (2006)
M. Devaud, V. Leroy, J.-C. Bacri, and T. Hocquet, "The adiabatic invariant of the n-degree-of-freedom harmonic oscillator", Eur. J. Phys. 29 831 (2008)
V. Leroy, J.-C. Bacri, T. Hocquet, and M. Devaud, "Simulating a one-half spin with two coupled pendula: II. The parametrically induced Rabi precession", Eur. J. Phys. 31 157 (2010)
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LEROY Valentin, DEVAUD Martin, HOCQUET Thierry
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