Abstract
We study the generation and evolution of entanglement between two qubits coupled through one-dimensional waveguide modes. By using a complete quantum electrodynamical formalism we go beyond the Markovian approximation. The diagonalization of the Hamiltonian is carried out, and a set of quasi-localized eigenstates is found. We show that when the qubit–waveguide coupling is increased, the Markov approximation is no longer valid, and the generation of entanglement is worsened.
Highlights
We call the dynamics Markovian when the system is well described by a master equation formalism, being the EM modes traced out
We have presented a full quantum electrodynamical solution to the qubit–qubit system coupled to a waveguide in the single excitation case
A complete set of eigenstates has been obtained for the first time, allowing us to study the population dynamics for every combination of parameters
Summary
The system under study is composed of two quantum emitters coupled to a 1D infinite waveguide (figure 1). The coefficients t0, j and αj are different from zero, and are given by t0, j These states are localized in the region between emitters, as shown in figure 2(b). The appearance of these states can be understood by noticing that, when a photon with energy is scattered by a single emitter, the transmission probability is zero [33]. This quantity represents the qubit part of the state in the resonant subspace This overlap can be expressed as P0 = Psc + Ploc, in which scattering and localized state contributions appear separately. After solving the more realistic lossy Hamiltonian, we will observe that the effective coupling to additional decay channels induces the localized state to become not a single, discrete state but a whole new continuous branch
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