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Register a new userConserving approximations in cavity quantum electrodynamics: Implications for density functional theory of electron-photon systems
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Authors
I. V. Tokatly
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By analyzing the many-body problem for non-relativistic electrons strongly coupled to photon modes of a microcavity I derive the exact momentum/force balance equation for cavity quantum electrodynamics. Implications of this equation for the electron self-energy and the exchange-correlation potential of quantum electrodynamic time-dependent density functional (QED-TDDFT) are discussed. In particular I generalize the concept of $Phi$-derivability to construct approximations which ensure the correct momentum balance. It is shown that a recently proposed optimized effective potential approximation for QED-TDDFT is conserving and its possible improvements are discussed.
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A relativistic density-functional theory based on a Fock-space effective quantum-electrodynamics (QED) Hamiltonian using the Coulomb or Coulomb-Breit two-particle interaction is developed. This effective QED theory properly includes the effects of vacuum polarization through the creation of electron-positron pairs but does not include explicitly the photon degrees of freedom. It is thus a more tractable alternative to full QED for atomic and molecular calculations. Using the constrained-search formalism, a Kohn-Sham scheme is formulated in a quite similar way to non-relativistic density-functional theory, and some exact properties of the involved density functionals are studied, namely charge-conjugation symmetry and uniform coordinate scaling. The usual no-pair Kohn-Sham scheme is obtained as a well-defined approximation to this relativistic density-functional theory.
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Understanding the interaction between cavity photons and electronic nanocircuits is crucial for the development of Mesoscopic Quantum Electrodynamics (QED). One has to combine ingredients from atomic Cavity QED, like orbital degrees of freedom, with tunneling physics and strong cavity field inhomogeneities, specific to superconducting circuit QED. It is therefore necessary to introduce a formalism which bridges between these two domains. We develop a general method based on a photonic pseudo-potential to describe the electric coupling between electrons in a nanocircuit and cavity photons. In this picture, photons can induce simultaneously orbital energy shifts, tunneling, and local orbital transitions. We study in details the elementary example of a single quantum dot with a single normal metal reservoir, coupled to a cavity. Photon-induced tunneling terms lead to a non-universal relation between the cavity frequency pull and the damping pull. Our formalism can also be applied to multi quantum dot circuits, molecular circuits, quantum point contacts, metallic tunnel junctions, and superconducting nanostructures enclosing Andreev bound states or Majorana bound states, for instance.
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