Pronounced non-Markovian features in multiply excited, multiple emitter waveguide QED: Retardation induced anomalous population trapping

Abstract

The Markovian approximation is widely applied in the field of quantum optics due to the weak frequency dependence of the vacuum field amplitude, and in consequence non-Markovian effects are typically regarded to play a minor role in the optical electron-photon interaction. Here, we give an example where non-Markovianity changes the qualitative behavior of a quantum optical system, rendering the Markovian approximation quantitatively and qualitatively insufficient. Namely, we study a multiple emitter, multiple excitation waveguide quantum electrodynamic (waveguide QED) system and include propagation time delay. In particular, we demonstrate anomalous population trapping as a result of the retardation in the excitation exchange between the waveguide and three initially excited emitters. Allowing for local phases in the emitter-waveguide coupling, this population trapping cannot be recovered using a Markovian treatment, proving the essential role of non-Markovian dynamics in the process. Furthermore, this time-delayed excitation exchange allows for a novel steady state in which one emitter decays entirely to its ground state while the other two remain partially excited.

Intermittent decoherence blockade in a chiral ring environment

“…3 ). We emphasize that such an intermittent suppression of decoherence arising from delayed coherent quantum feedback does not require the existence of dark states, contrary to other decoherence suppression methods based on delayed feedback 34 , 44 , 45 . Indeed, as shown in the Methods, the full Hamiltonian does not sustain eigenmodes localized near the emitter.…”

Cavitylike strong coupling in macroscopic waveguide QED using three coupled qubits in the deep non-Markovian regime

“…).-To represent the time evolution of the probe qubit in the non-Markovian regime, and to confirm our semiclassical results in the frequency domain, we next solve the same system using MPSs [37][38][39]. To do this, we first consider the Hamiltonian for three qubits [29], dependent boson operator. The interaction term,…”

“…We show explicitly how a non-Markovian delay time significantly improves the cavity-QED resonances. We also study this problem from the viewpoint of matrix products states (MPS), which allows us to solve the quantum Hamiltonian also in the non-Markovian regime [29]. We directly show how the lifetimes improve dramatically for long delay times when the retardation is considered, giv-ing a method to precisely control the coherence times of these novel polariton states.…”

Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

“…For all coherent dynamics with pure states, however, the more efficient Schrödinger picture allows for the full access of expectation values and may be applied on systems with Markovian as well as non-Markovian dynamics, which has already successfully been demonstrated for open few-level systems [ 43 , 75 , 76 , 77 ]. For this, the picture of the quantum stochastic Schrödinger equation serves as a numerical basis.…”

“…The first term models the free evolution of N single spin systems, where governs the free evolution of each single site and creates/annihilates a fermionic excitation in the i th two-level system which is equivalent to a flip of the spin on site i [ 76 , 85 , 86 , 87 , 88 , 89 ]. The second term describes the isotropic Heisenberg spin chain, a chain with N single sites and a three-dimensional nearest-neighbor interaction in x , y and z direction, where , represent the Pauli matrices interacting with strength J .…”