Thursday, May 9, 2013

1305.1800 (Lingzhen Guo et al.)

Phase Space Crystals: A new way to create a quasienergy bandstructure    [PDF]

Lingzhen Guo, Michael Marthaler, Gerd Schön
The space periodicity of crystals leads to the energy bandstructure. Systems driven periodically in time show a discrete time translation symmetry, which in the frame of the Floquet theory leads to the concept of quasienergy. Here we propose a novel way to create a bandstructure of the quasienergy spectrum. The system, e.g. an ion trapped in a potential, shows no spatial periodicity, but it is driven by a time-dependent field coupling highly nonlinearly to one of its degrees of freedom (e.g., ~ q^n). The bandstructure in quasienergy arises as a consequence of the n-fold discrete periodicity in phase space induced by this driving field. We propose an explicit model to realize such a phase space crystal and analyze its bandstructure in the frame of a tigh-binding approximation. In spite of an orbital circular symmetry the quasienergy bandstructure shows a peculiar asymmetry. It arises due to the loss of phase reflection symmetry of the quantum system which renders the clockwise and anti-clockwise motion in phase space non-equivalent. The resulting bandstructure of the quasienergy spectrum determines the emission spectrum, which shows resonant peaks grouping together into several clusters due to intra-band and inter-band transitions. The phase space crystal opens new ways to engineer energy bandstructures and emission spectra, with the added advantage that its properties can be changed in situ by tunning the driving field's parameters.
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