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Europhysics Letters (EPL)

Geometric phase of quantized electromagnetic field in time-dependent linear media

Mustapha Maamache, Nadir Chaabi, J. R. Choi

Published Jun 1, 2010• 2 citations
Publisher
DOI
10.1209/0295-5075/90/59901

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In the Coulomb gauge, the solution to the Maxwell equations for slowly time-varying homogeneous nondispersive conducting linear media without charge source is obtained. We show that the electromagnetic field acquires the extra geometrical Hannay angle associated to the time-dependent generalized harmonic oscillator. The quantization scheme for the electromagnetic field provides a connection between the classical Hannay angle and the quantum adiabatic Berry phase shifts. We confirm that the interference pattern in the optical system is more or less altered by the existence of the geometric phase.
We present a quantization scheme for the electromagnetic field in time-dependent homogeneous nondispersive conducting and nonconducting linear media without sources. Using the Coulomb gauge, we demonstrate this quantization can be mapped into a damped (attenuated) time-dependent quantum harmonic oscillator. Remarkably, we find that the time dependence of the permittivity, for epsilon>0, gives rise to an attenuation of the radiation field. Afterwards, we obtain the exact wave functions for this problem and consider an exponential time accretion of the permittivity as a particular case.