We investigated the spontaneous emission of a giant atom coupled with a semi-infinite waveguide. Our model considers the giant atom a two-level system coupled to the semi-infinite waveguide at two points. Based on the Hamiltonian in real space, the first-order delay-differential equation for the atomic excitation amplitude is obtained using the Schrödinger equation. Furthermore, the dynamics of spontaneous emission controlled by quantum coherent feedback due to the semi-infinite waveguide in the non-Markov regime are discussed in two cases, with the coupling strengths between the giant atom and the semi-infinite waveguide at the two coupling points being identical in one case and having a phase difference in the other case. The spontaneous emission exhibits partial decay due to multiple excitations from the quantum feedback and two-point coupling. When the coupling strengths are identical, the decay of the atomic excitation can be either increased or inhibited substantially, even forming a steady state, due to the self-interference due to the two-point coupling. The quantum coherent feedback can either further increase the decay of the excited state or maintain the steady state formed by self-interference. Moreover, a new steady state can be built due to quantum coherent feedback, which cannot exist in the self-interference system. The decay rates can also be increased or decreased by manipulating the phase difference between the coupling strengths at the two coupling points. It can destroy the steady state formed by self-interference or build a steady state based on the chosen phase difference. One can leverage quantum coherent feedback to manipulate the steady state value of the population of the excited states by adjusting the phase difference. The dissipation can increase the decay rates of the excited states. Furthermore, it also destroys steady states. Our results may find applications in developing quantum devices such as quantum memory based on giant atom-waveguide systems.
We investigated the spontaneous emission of a giant atom coupled with a semi-infinite waveguide. Our model considers the giant atom a two-level system coupled to the semi-infinite waveguide at two points. Based on the Hamiltonian in real space, the first-order delay-differential equation for the atomic excitation amplitude is obtained using the Schrödinger equation. Furthermore, the dynamics of spontaneous emission controlled by quantum coherent feedback due to the semi-infinite waveguide in the non-Markov regime are discussed in two cases, with the coupling strengths between the giant atom and the semi-infinite waveguide at the two coupling points being identical in one case and having a phase difference in the other case. The spontaneous emission exhibits partial decay due to multiple excitations from the quantum feedback and two-point coupling. When the coupling strengths are identical, the decay of the atomic excitation can be either increased or inhibited substantially, even forming a steady state, due to the self-interference due to the two-point coupling. The quantum coherent feedback can either further increase the decay of the excited state or maintain the steady state formed by self-interference. Moreover, a new steady state can be built due to quantum coherent feedback, which cannot exist in the self-interference system. The decay rates can also be increased or decreased by manipulating the phase difference between the coupling strengths at the two coupling points. It can destroy the steady state formed by self-interference or build a steady state based on the chosen phase difference. One can leverage quantum coherent feedback to manipulate the steady state value of the population of the excited states by adjusting the phase difference. The dissipation can increase the decay rates of the excited states. Furthermore, it also destroys steady states. Our results may find applications in developing quantum devices such as quantum memory based on giant atom-waveguide systems.
We study the non-Markovian dynamics of a two-level giant atom interacting with a one-dimensional semi-infinite waveguide through multiple coupling points, where a perfect mirror is located at the endpoint of the waveguide. The system enters a non-Markovian process when the travel time of the photon between adjacent coupling points is sufficiently large compared to the inverse of the bare relaxation rate of the giant atom. The photon released by the spontaneous emission of the atom transfers between multiple coupling points through the waveguide or is reabsorbed by the atom with the photon emitted via the atom having completed the round trip after reflection of the mirror, which leads to the photon being trapped and forming bound states. We find that three different types of bound states can be formed in the system, containing the static bound states with no inversion of population, the periodic equal amplitude oscillation with two bound states, and the periodic nonequal amplitude oscillation with three bound states. The physical origins of the three bound states' formation are revealed. Moreover, we consider the influences of the dissipation of unwanted modes and dephasing on the bound states. Finally, we extend the system to a more general case involving many giant atoms coupled into a one-dimensional semi-infinite waveguide. The obtained set of delay differential equations for the giant atoms might open a way to better understand the non-Markovian dynamics of many giant atoms coupled to a semi-infinite waveguide.
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.
Abstract. In this paper, we demonstrate the application of quantum feedback control in creating desired states for atomic and photonic systems utilizing a semi-infinite waveguide coupled with multiple two-level atoms. In this approach, an initially excited atom can emit one photon into the waveguide, and the photon can be reflected by either the terminal mirror of the waveguide or other atoms, establishing various feedback loops through the coherent interactions between the atom and photon. When there are no more than two excitations in the waveguide quantum electrodynamics (QED) system, the evolution of quantum states can be effectively elucidated through the lens of random graph theory. However, this process is influenced by the environment. We propose that the environment-induced dynamics in the coherent feedback loop can be eliminated by measurement-based feedback control or coherent drives. Consequently, in the atom-waveguide interactions in open quantum systems, measurement-based feedback has the potential to modulate the quantum steady states. Additionally, the homodyne detection noise during the measurement process can induce errors upon quantum states, which can be influenced by the coherent feedback parameter designs.
Controlling radiative dynamics of a giant Λ-type atom via interference induced by the vacuum of a waveguide
We investigate the dynamics of a Λ-type giant atom (GA) whose both transition coupled to the guided modes of a one-dimensional (1D) waveguide at two spatially separated points with the GA initially excited and the electromagnetic (EM) modes of waveguide in vacuum. The spontaneous emission properties of this GA is investigated by solving the delay-differential equation for the amplitude of the 3GA in its excited state. Signatures of non-Markovian behavior is manifested in a population trapping in the excited state of the GA in the regime where the distance d of the coupling points is smaller or comparable to the coherent length L characterizing the width of the emitted wave packet. And an exact Markovian dynamics is also found when d≥L via the inference by adjusting the energy spacing and the inherent time delay besides the complex phases in the atom-light coupling, matching the behavior of a small atom coupled to a waveguide.
The non-Markovian effects of open quantum systems subjected to external environments are deemed to be valuable resources in quantum optics and quantum information processing. In this work, we construct the model Hamiltonian of three-level giant atom with multiple coupling points in the semi-infinite photonic waveguide via complex coupling coefficients and investigate the non-Markovian dynamics of the three-level giant atom driven by a classical laser field. In the non-Markovian regime, the traveling time of a photon between different coupling points is sufficiently large compared to the inverse of the bare relaxation rate of the giant atom. We derive the analytical expressions for the probability amplitudes of the driven three-level giant atom by solving a set of delay differential equations and obtain two independent conditions of bound states' formation that can inhibit the dissipation. We find two different types of bound states (including the static bound states and the periodic equal-amplitude oscillating bound states) and discuss the physical origins of the bound states' formation. Moreover, we discuss the case of the driven three-level giant atom interacting with the infinite photonic waveguide, where there is only one purely imaginary solution (i.e., only one bound-state condition exists) for its complex frequency (coming from the absence of mirror at one end of the waveguide) compared to that of a driven three-level giant atom coupling with a semi-infinite photonic waveguide. With this, we also find two different types of bound states, including the static bound state and the periodic equal-amplitude oscillating bound states. We study the influences of the phase in the coupling strength on the bound states in semi-infinite and infinite photonic waveguides. The presented protocol might open a way to better understand exactly the non-Markovian dynamics of driven multilevel giant atoms interacting with semi-infinite (or infinite) photonic waveguides.
We propose a stochastic Schrödinger equation (SSE) approach to investigate the dynamics of giant atoms coupled to a waveguide, addressing two critical gaps in existing research, namely insufficient exploration on continuous coupling and multiple excitations. A key finding is that continuous coupling, unlike discrete coupling at finite points, breaks the constant phase difference condition, thereby weakening the interference effects in giant atom-waveguide systems. In addition, a key technical advantage of the SSE approach is that auto- and cross-correlation functions can directly reflect the complex photon emission/absorption processes and time-delay effects in giant atom-waveguide systems. Moreover, the SSE approach also naturally handles multiple excitations, without increasing equation complexity as the number of excitations grows. This feature enables the investigation of multi-excitation initial states of the waveguide, such as thermal and squeezed initial states. Overall, our approach provides a powerful tool for studying the dynamics of giant atoms coupled to waveguide, particularly for continuous coupling and multi-excitation systems.