We study the atom-atom correlation length in an atomic array coupled to a waveguide under the Bragg condition with delayed non-Markovian interactions caused by a finite photon propagation time. Starting from a single excited atom, the excitation partially spreads among all atoms, reaching a steady state. The remaining excitation localizes near the initially excited atom, and the atom-atom correlation length decreases as a power law with the interaction delay. This localization phenomenon reveals how the delay-induced non-Markovian behavior affects the correlation transport in waveguide QED systems.
We study the atom-atom correlation length in an atomic array coupled to a waveguide under the Bragg condition with delayed non-Markovian interactions caused by a finite photon propagation time. Starting from a single excited atom, the excitation partially spreads among all atoms, reaching a steady state. The remaining excitation localizes near the initially excited atom, and the atom-atom correlation length decreases as a power law with the interaction delay. This localization phenomenon reveals how the delay-induced non-Markovian behavior affects the correlation transport in waveguide QED systems.
We study the disentanglement dynamics of two giant atoms coupled to a common one-dimensional waveguide. We focus on the non-Markovian retarded effect in the disentanglement of the two giant atoms by taking the photon transmission time into account. By solving the time-delayed equations of motion for the probability amplitudes, we obtain the evolution of the entanglement of the two giant atoms, which are initially in the maximally entangled states in the single-excitation space. It is found that the retardation-induced non-Markovianity leads to nonexponential decay and revivals of entanglement. Concretely, we consider separate-, braided-, and nested-coupling configurations, and find that the disentanglement dynamics in these configurations exhibits different features. We demonstrate that the steady-state entanglement depends on the time delay under certain conditions in these three coupling configurations. We also study the dependence of the disentanglement of the two giant atoms on both the detuning effect and the initial-state phase effect. In addition, we consider the disentanglement dynamics of the two giant atoms, which are initially in the state superposed by zero-excitation and two-excitation components. This work will pave the way for the generation of stationary entanglement between two giant atoms, which may have potential applications in the construction of large-scale quantum networks based on the giant-atom waveguide-QED systems.
We study the generation of quantum entanglement between two giant atoms coupled to a common one-dimensional waveguide. Here each giant atom interacts with the waveguide at two separate coupling points. Within the Wigner-Weisskopf framework for single coupling points, we obtain the time-delayed quantum master equations governing the evolution of the two giant atoms for three different coupling configurations: separated, braided, and nested couplings. For each coupling configuration, we consider both the Markovian and non-Markovian entanglement dynamics of the giant atoms, which are initially in two different separable states: single- and double-excitation states. Our results show that the generated entanglement depends on the phase shift, time delay, atomic initial state, and the coupling configuration. For the single-excitation initial state, there exists the steady-state entanglement for each coupling in both the Markovian and non-Markovian regimes due to the appearance of the dark state. For the double-excitation initial state, we observe entanglement sudden birth via adjusting the phase shift in both regimes. In particular, the maximally achievable entanglement for the nested coupling is about one order of magnitude larger than those of separate and braided couplings. We also find that the maximal entanglement for these three coupling configurations can be enhanced in the case of small time delays. This work can be utilized for the generation and control of entanglement in quantum networks based on giant-atom waveguide-QED systems, which have wide potential applications in quantum information processing.
Quantum systems are invariably coupled to a surrounding environment. A common theoretical method to simplify the problem is to trace over the environment under a Markov approximation, which assumes that the environment holds no memory over the timescales that the system evolves under. In interacting many-body systems, it is often not trivial to extract which of the multiple collective timescales are relevant. We consider a time-delayed waveguide QED setup with a single excitation. By fixing the maximum propagation time and increasing the number of emitters, we show that, even for small delay times, collective effects are sufficient to cause non-Markovianity. The impact of memory is intrinsically state-dependent. For superradiant states, the relevant system timescale is the superradiant lifetime while the relevant bath timescale is the end-to-end delay time. For subradiant states, both timescales depend on the structure of the specific state. Our results demonstrate the importance of prudently making Markov approximations in quantum many-body systems, and highlight potential pitfalls to avoid in scaling up quantum devices to large system sizes.
We study the quantum dynamics of multiple two-level atoms (qubits) in a waveguide quantum electrodynamics system, with a focus on modified superradiance effects between two or four atoms with finite delay times. Using a numerically exact matrix product approach, we explore both Markovian and non-Markovian regimes, and highlight the significant influence of time-delayed feedback effects and the clear breakdown of assuming instantaneous coupling dynamics. We first show a system composed of two spatially separated qubits, prepared in a doubly excited state (both fully excited), and provide a comprehensive study of how delayed feedback influences the collective system decay rates, as well as the quantum correlations between waveguide photons, atoms, and between atom and photons. The system is then extended to include two additional qubits located next to the initial ones (four qubits in total), and we demonstrate, by manipulating the initial excitations and the time-delay effects, how long-term quantum correlations and light-matter entangled states can be established.
We study the quantum nonlinear dynamics of multiple two-level atoms (qubits) in a waveguide quantum electrodynamics system, with a focus on modified superradiance effects between two or four atoms with finite delay times. Using a numerically exact matrix-product-states approach, we explore both Markovian and non-Markovian regimes and highlight the significant influence of time-delayed feedback effects and the clear breakdown of assuming instantaneous coupling dynamics. We first show a system composed of two spatially separated qubits, prepared in a doubly excited state (both fully excited), and provide a comprehensive study of how delayed feedback influences the collective system decay rates, as well as the quantum correlations between waveguide photons, atoms, and between atoms and photons. The system is then extended to include two additional qubits located next to the initial ones (four qubits in total), and we demonstrate, by manipulating the initial excitations and the time-delay effects, how long-term quantum correlations and light-matter entangled states can be established.
We investigate one- and two-photon scattering in a one-dimensional waveguide coupled to a giant atom within the non-Markovian regime using the resolvent approach. The non-Markovian behavior gives rise to an atom-photon bound state that cannot be excited by a single incident photon. However, the bound state can be excited via the two-photon scattering process described by multichannel scattering theory, from which an analytical trapping probability of a photon in the bound state can be achieved. Additionally, we analyze the two-photon scattering process, obtaining the analytical expressions for scattered states. As non-Markovian effects strengthen, two peaks appear in the incoherent power spectrum, attributed to the system behaving as a leaky cavity formed by the giant atom's coupling points. Through the analysis of second-order correlation functions, we observe the bunching behavior for transmitted photons, antibunching behavior for reflected photons, and the distinctive retrieval behavior at the coupling points' separation.