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arXiv:0804.4631 · Physical Review Letters

Andreev Reflection in Bosonic Condensates

Ivar Zapata, Fernando Sols

Published May 8, 2009• 40 citations
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Abstract

We study the bosonic analog of Andreev reflection at a normal-superfluid interface where the superfluid is a boson condensate. We model the normal region as a zone where nonlinear effects can be neglected. Against the background of a decaying condensate, we identify a novel contribution to the current of reflected atoms. The group velocity of this Andreev reflected component differs from that of the normally reflected one. For a three-dimensional planar or two-dimensional linear interface Andreev reflection is neither specular nor conjugate.

DOI
10.1103/physrevlett.102.180405

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A theory describing a one-dimensional Luttinger liquid in contact with a superconductor is developed. Boundary conditions for the fermion fields describing Andreev reflection at the contacts are derived and used to construct a bosonic representation of the fermions. The Josephson current through a superconductor/Luttinger liquid/superconductor junction is considered for both perfectly and poorly transmitting interfaces. In the former case, the Josephson current at low temperatures is found to be essentially unaffected by electron-electron interactions. In the latter case, significant renormalization of the Josephson current occurs. The profile of the (induced) condensate wave function in a semi-infinite Luttinger liquid in contact with a superconductor is shown to decay as a power law, the exponent depending on the sign and strength of the interactions. In the case of repulsive (attractive) interactions the decay is faster (slower) than in their absence. An equivalent method of calculating the Josephson current through a Luttinger liquid, which employs the bosonization of the system as a whole (i.e., superconductor, as well as Luttinger liquid) is developed and shown to give the results equivalent to those obtained via boundary conditions describing Andreev reflection. \textcopyright{} 1996 The American Physical Society.
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Abstract It is found that Andreev reflection provides a deterministic teleportation process at an ideal normal-superconductor interface, making it behave like an information mirror. However, it is challenging to control the Andreev reflection in a spatially-separated junction due to the mode mixing at the interface. We theoretically propose the laser-induced Andreev reflection between two-component Fermi superfluid and normal states without mode mixing via spatially-uniform Rabi couplings. By analyzing the tunneling current up to the fourth order, we find that the Andreev current exhibits unconventional non-Ohmic transport at zero temperature. The Andreev current gives the only contribution in the synthetic junction system at zero detunings regardless of the ratio of the chemical potential bias to the superfluid gap, which is in sharp contrast to that in conventional junctions. Our result may give a potential impact on theoretical and experimental study of quantum many-body phenomena, and also pave a way for understanding the black hole information paradox through the Andreev reflection as a quantum-information mirror.