Probing Anderson localization using the dynamics of a qubit

Detecting topological edge states with the dynamics of a qubit

“…However, if the qubit is coupled to an external infinite system (for example, a semi-infinte lead), the oscillations will decay. The decoherence of a qubit can then be evaluated by evaluating the off-diagonal element of the Green's function [4]. The coupling between the qubit and external system can take on different forms.…”

“…In previous work [4], the decay rate of a qubit coupled to another system with or without disorder was studied. The main objective was to investigate under which circumstances the interaction of a qubit with its surroundings can be designed to improve the qubit's performance in a quantum device by increasing the decoherence time.…”

Qubits as edge state detectors: illustration using the SSH model

“…When we couple the TLS to the rest of the system, it will decohere; this will be seen in the Green's function, which will exhibit decaying behavior [1].…”

“…This is not quite correct, since λ ± depend in a highly nontrivial way on E so the Fourier transform cannot be evaluated exactly. An analytical approximation which is justified in the weak-coupling limit (t C 1) [1] indicates that to a good approximation the new (complex) frequencies λ ± can be evaluated at the old frequencies: the time-dependent Green's function has, according to this approximation, frequencies λ ± (λ ± ). According to this analytic approximation, the decay rates are given by the imaginary part of the frequencies, and we conclude that the decoherence time τ φ is given by…”

“…Thus, understanding (and, usually, minimizing) decoherence is critically important to the functioning of quantum devices. As an example, in [1] a tripartite system was studied: a TLS coupled to one end of a finite chain (or channel) whose other end was coupled to a semi-infinite chain; both chains were described by tight-binding Hamiltonians. The question addressed was: how can one reduce the decoherence of the TLS?…”