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.
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 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.
In this work, we investigate the non-Markovian (NM) dynamical evolution of a three-level atom coupled to a semi-infinite one-dimensional photonic waveguide and driven by a classical driving field. The single-end of waveguide behaves as a perfect mirror while light can pass through the opposite end with no backreflection. We derive the exact analytical expressions for the wave function of the driven three-level atom by solving a set of delay differential equations and give the conditions of atom-photon bound state formation that can inhibit the dissipation, which appears in the atom-mirror interspace in order to trap a considerable amount of initial atomic excitation. We show that when the evolution time of the system is shorter than the time delay taken by a photon to perform a round trip between the atom and mirror, the atomic dynamics exhibits Markovian properties, which depend on the driving strength and rescaled parameters. If the evolution time of the system exceeds the time delay, the photon can be reabsorbed by the atom with the photon emitted by the atom having completed the round trip, which exhibits NM memory effects, where the population eventually convergences to the finite-steady values. We also study the influence of the loss and dephasing on the formation of a bound state. Finally, the above results are extended to a more general quantum system involving single-end photonic waveguide coupled to an arbitrary number of noninteracting three-level atoms driven by the driving fields. The presented formalism might open a way to better understand exactly the NM dynamics of driven multilevel atoms coupled to a semi-infinite waveguide.
Non-Markovian dynamics with Λ-type atomic systems in a single end photonic waveguide
In this work, we investigate the non-Markovian dynamical evolution of a Λ-type atom interacting with a semi-infinite one-dimensional photonic waveguide via two atomic transitions. The waveguide terminates at a perfect mirror, which reflects the light and introduces boundary effects. We derive exact analytical expressions and show that, under suitable conditions, the instantaneous and retarded decay rates reach equilibrium, leading to the formation of an atom-photon bound state that suppresses dissipation. Consequently, the atom retains a long-lived population in the asymptotic time limit. Furthermore, we analyze the output field intensity and demonstrate that blocking one of the coupling channels forces the atomic system to emit photons of a single frequency. Finally, we extend the model to a two-atom system and examine the disentanglement dynamics of the two spatially separated atoms. These findings elucidate the dynamic process of spontaneous emission involving multi-frequency photons from multi-level atoms and provide insights into the complex interference between different decay pathways.
Quantum optics with giant atoms provides a new approach for implementing optical memory devices at the atomic scale. Here, we theoretically investigate the relaxation dynamics of a single driven three-level atom interacting with a one-dimensional waveguide via two coupling points. Under certain conditions, after long-time dynamics, we find that the population of the giant atom can either remain stable or exhibit regular periodic oscillations, while photons are trapped within the region of the giant atom. This phenomenon cannot be realized using a two-level atom configured with two coupling points. It is noteworthy that the atomic excitation probability of a stable bound state is a constant value, which is determined by the size of the atom. Importantly, the size of the atom, defined as the distance between the two coupling points, is significantly larger than the wavelength of the light field, which is a necessary condition for the existence of oscillating bound states.
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.
Coherent Control of Spontaneous Emission for a giant driven Λ-type three-level atom
Quantum optics with giant atoms provides a new approach for implementing optical memory devices at the atomic scale. Here, we theoretically study the relaxation dynamics of a single driven three-level atom interacting with a one-dimensional waveguide, via two coupling points. Under certain conditions, after the long-time dynamics, we found that the population of giant atom can either maintain stable values or exhibit regular periodic oscillation behavior, while photons can be trapped in the region of giant atoms. This phenomenon is not achievable using a two-level atom with two legs. It is worth noting that the atomic excitation probability of a stable bound state is a constant value, which is determined by the size of the atom. Crucially, the size of the atom (the distance between the two coupling points) is much larger than the wavelength of the light field, which is a necessary condition for the existence of oscillating bound states.