Abstract
Berry’s approach on “transitionless quantum driving” shows how to set a Hamiltonian which drives the dynamics of a system along instantaneous eigenstates of a reference Hamiltonian to reproduce the same final result of an adiabatic process in a shorter time. In this paper, motivated by transitionless quantum driving, we construct shortcuts to adiabatic passage in a three-atom system to create the Greenberger-Horne-Zeilinger states with the help of quantum Zeno dynamics and of non-resonant lasers. The influence of various decoherence processes is discussed by numerical simulation and the result proves that the scheme is fast and robust against decoherence and operational imperfection.
Highlights
Berry’s approach on “transitionless quantum driving” shows how to set a Hamiltonian which drives the dynamics of a system along instantaneous eigenstates of a reference Hamiltonian to reproduce the same final result of an adiabatic process in a shorter time
To construct shortcuts to speed up adiabatic processes effectively, two methods which are strongly related, and even potentially equivalent to each other[24]: are invariant-based inverse engineering based on Lewis-Riesenfeld invariant[10,25] and Berry’s approach named “transitionless quantum driving” (TQD)[26,27,28,29]
We find that any quantum system whose Hamiltonian is possible to be simplified into the form in eq (15), the corresponding alternative physically feasible (APF) Hamiltonian can be built and the shortcuts to adiabatic passage (STAP) can be constructed with the same approach presented in this paper
Summary
Through performing the unitary transformation UZ = e−i ∑ εk φk φk t and neglecting the terms with high oscillating frequency by setting the condition Ω1/ 3 , Ω3/ 3 λ (the Zeno condition), we obtain an effective Hamiltonian. Which can be seen as a simple three-level system with an excited state φ0 and two ground states ψ1 and ψ7 For this effective Hamiltonian, its eigenstates are obtained n0 (t ). When lπ/2 (l = 0, ± 1, ± 2, ), we β = π, it shows the most common form: |ψ (t f )〉 = (|ψ1〉 + |ψ7〉)/ 2 This process will take quite a long time to obtain the target state, which is undesirable
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
