Abstract
We evaluate the exact dipole coupling strength between a single emitter and the radiation field within an optical cavity, taking into account the effects of multilayer dielectric mirrors. Our model allows one to freely vary the resonance frequency of the cavity, the frequency of light or atomic transition addressing it, and the design wavelength of the dielectric mirror. The coupling strength is derived for an open system with unbound frequency modes. For very short cavities, the effective length used to determine their mode volume and the lengths defining their resonances are different, and also found to diverge appreciably from their geometric length, with the radiation field being strongest within the dielectric mirror itself. Only for cavities much longer than their resonant wavelength does the mode volume asymptotically approach that normally assumed from their geometric length.
Highlights
The development of universal quantum computation remains a key endeavour in the coherent control and manipulation of quantum states of light and matter
We evaluate the exact dipole coupling strength between a single emitter and the radiation field within an optical cavity, taking into account the effects of multilayer dielectric mirrors
The effective length used to determine their mode volume and the lengths defining their resonances are different, and found to diverge appreciably from their geometric length, with the radiation field being strongest within the dielectric mirror itself
Summary
The development of universal quantum computation remains a key endeavour in the coherent control and manipulation of quantum states of light and matter. To achieve the mirror reflectivity required for coherent atom-cavity interactions, highly reflective dielectric coatings, or Bragg stacks are used as standard [14] These comprise layer pairs of quarter-wavelength optical thickness dielectric material, with alternating refractive indices. We consider an open cavity system, where the electric field is able to propagate through the dielectric mirror and couples to external free-space modes This departs from the standard notion of having a mode volume and well defined frequency modes of the resonator, suitably modifying our calculation of the Purcell Factor. We expand it into a multilayer stack, repeating our analysis.
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