Abstract
The quantum evolution after a metallic lead is suddenly connected to an electron system contains information about the excitation spectrum of the combined system. We exploit this type of "quantum quench" to probe the presence of Majorana fermions at the ends of a topological superconducting wire. We obtain an algebraically decaying overlap (Loschmidt echo) ${\cal L}(t)=| < \psi(0) | \psi(t) > |^2\sim t^{-\alpha}$ for large times after the quench, with a universal critical exponent $\alpha$=1/4 that is found to be remarkably robust against details of the setup, such as interactions in the normal lead, the existence of additional lead channels or the presence of bound levels between the lead and the superconductor. As in recent quantum dot experiments, this exponent could be measured by optical absorption, offering a new signature of Majorana zero modes that is distinct from interferometry and tunneling spectroscopy.
Highlights
The original example of Anderson’s orthogonality catastrophe [1] was a vanishing overlap between two quantum states of a large number of noninteracting electrons, one with and one without a localized impurity potential VðrÞ
Quantum quenches have been of great interest recently as a basic question about nonequilibrium physics appearing in many contexts [4,5,6,7,8,9]
The boundary entropy droppffiffi[37] associated with this RpGffiffi flow is given by ln 2, where d 1⁄4 gUV=gIR 1⁄4 2 is the quantum dimension of the Majorana fermion γ that was free at high energy and that becomes fully hybridized with the normal lead at low energy
Summary
The original example of Anderson’s orthogonality catastrophe [1] was a vanishing overlap between two quantum states of a large number of noninteracting electrons, one with and one without a localized impurity potential VðrÞ. The behavior of the many-electron wave function at long times after the quench is significantly altered by the presence of the Majorana excitation: The wave-function overlap with the initial state (the Loschmidt echo) decays with a universal power law, unlike in the Anderson orthogonality case where the exponent is nonuniversal This effect of the Majorana fermion can be distinguished. Some of these predictions are verified numerically using DMRG simulations. Assuming that the massive degrees of freedom in the superconductor can be integrated out yields an effective Majorana boundary term for the metallic lead
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