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Physical Review A

Exceptional-point-engineered dispersive readout of a driven three-level atom weakly interacting with coupled cavities in non-Markovian environments

Ji-Feng Yang, H. Z. Shen

Published May 16, 2024• 13 citations
Publisher

Abstract

In this paper we study the dispersive readout of a driven three-level atom weakly interacting with a passive cavity that couples to an active cavity. The system excluding the three-level atom exhibits a parity-time ($\mathcal{P}\mathcal{T}$) symmetric phase transition at the exceptional point (EP), which originates from the balance between dissipation of the passive cavity and gain of the active cavity. The perturbation to the passive cavity induced by the three-level atom can be amplified near the EP, where the eigenvalues of the effective Hamiltonian have significant differences when the three-level atom is in the excited, metastable, and ground states, respectively. Applying the modified Laplace transformation and input-output theory near the EP, we can realize the dispersive readout of the three-level atom weakly interacting with coupled cavities, which can be characterized through the different distributions of the transmission spectrum of the passive cavity and the ratio of the active cavity excitation number to the input photon number corresponding to the different levels of the three-level atom. Moreover, we generalize the dispersive readout method to the non-Markovian regime, which is in good agreement with that obtained by the Markovian approximation. We find that the non-Markovian effects of the environment backacting on the system dynamics can lead to the enhancement of the dispersive readout for the three-level atom, which is revealed by the excitation backflow generated in the interaction between the passive cavity and environment. The dispersive readout proposed is conducive to understanding the influences of $\mathcal{P}\mathcal{T}$ symmetry and the non-Markovian effect on dispersive readout, which offers the possibility of an alternative field of possible applications for quantum information and quantum communication.

DOI
10.1103/physreva.109.053712

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In this paper we study the dispersive readout of a driven three-level atom weakly interacting with a passive cavity that couples to an active cavity. The system excluding the three-level atom exhibits a parity-time (PT\mathcal{P}\mathcal{T}PT) symmetric phase transition at the exceptional point (EP), which originates from the balance between dissipation of the passive cavity and gain of the active cavity. The perturbation to the passive cavity induced by the three-level atom can be amplified near the EP, where the eigenvalues of the effective Hamiltonian have significant differences when the three-level atom is in the excited, metastable, and ground states, respectively. Applying the modified Laplace transformation and input-output theory near the EP, we can realize the dispersive readout of the three-level atom weakly interacting with coupled cavities, which can be characterized through the different distributions of the transmission spectrum of the passive cavity and the ratio of the active cavity excitation number to the input photon number corresponding to the different levels of the three-level atom. Moreover, we generalize the dispersive readout method to the non-Markovian regime, which is in good agreement with that obtained by the Markovian approximation. We find that the non-Markovian effects of the environment backacting on the system dynamics can lead to the enhancement of the dispersive readout for the three-level atom, which is revealed by the excitation backflow generated in the interaction between the passive cavity and environment. The dispersive readout proposed is conducive to understanding the influences of PT\mathcal{P}\mathcal{T}PT symmetry and the non-Markovian effect on dispersive readout, which offers the possibility of an alternative field of possible applications for quantum information and quantum communication.
For some cavity-quantum-electrodynamics systems, such as a single-electron spin coupled to a passive cavity, it is challenging to reach the strong-coupling regime. In such a weak-coupling regime, the conventional dispersive readout technique cannot be used to resolve the quantum states of the spin. Here we propose an improved dispersive readout method to measure the quantum states of a weakly coupled qubit by harnessing either one or two auxiliary cavities linearly coupled to the passive cavity containing the qubit. With appropriate parameters in both cases, the system excluding the qubit can exhibit a parity-time-symmetric phase transition at the exceptional point (EP). Because the EP can amplify the perturbation induced by the qubit and the parity-time symmetry can narrow the linewidths of the peaks in the transmission spectrum of the passive cavity, we can measure the quantum states of the weakly coupled qubit via this transmission spectrum. Owing to the weak coupling between the qubit and the passive cavity, the backaction due to the measurement of the qubit can also be reduced in comparison with the conventional dispersive readout technique in the strong-coupling regime.
We study the non-Markovian dispersive readout of a single-mode bosonic (SMB) quantum system coupled to the open cavity with two non-Markovian environments. Assuming that the SMB quantum system is initially prepared in a thermal equilibrium state, the susceptibility of the measured SMB quantum system to the cavity can be obtained by the nonequilibrium linear response theory, which provides the dispersive frequency shift of the cavity. We analytically derive the transmission and reflection of the cavity in the non-Markovian regime and discuss the non-Markovian dispersive readout of the SMB quantum system, which is in good agreement with that obtained by the Markovian approximation. We show that the effect of non-Markovian dynamics on the system's behavior leads to the decrease of the transmission and shifts of the frequency corresponding to the peak of the transmission in the dispersive regime compared with the Markovian case and the increase of the sum of the transmission and reflection due to the excitation backflowing induced by the couplings of the cavity and two non-Markovian environments, which could be applied to quantum secure direct communication with quantum memory. Finally, we generalize the readout theory to the periodically driven SMB quantum system based on the Floquet theory and quantum network, which contain all influences from the non-Markovian environments. The formalism presented in this paper opens an alternative field of possible applications in quantum information and quantum communication with non-Markovianity by manipulating the spectral densities of the environments.
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 an alternative scheme for nonreciprocal light propagation in two coupled cavities system, in which a two-level quantum emitter is coupled to one of the optical microcavities. For the case of parity-time (\textrm{PT}) system (i.e., active-passive coupled cavities system), the cavity gain can significantly enhance the optical nonlinearity induced by the interaction between a quantum emitter and cavity field beyond weak-excitation approximation. The giant optical nonlinearity results in the non-lossy nonreciprocal light propagation with high isolation ratio in proper parameters range. In addition, our calculations show that nonreciprocal light propagation will not be affected by the unstable output field intensity caused by optical bistability and we can even switch directions of nonreciprocal light propagation by appropriately adjusting the system parameters.
Quantum entanglement is one of most remarkable features of quantum mechanics,and in recent years it has played a more and more important role in quantum information.However,real quantum system inevitably interacts with the environment,resulting in the entanglement decay or even entanglement sudden death,so it is necessary to study the entanglement dynamical properties of an open system under different environments.In this paper,we investigate the entanglement dynamic behaviors of three interacting two-level atoms in an optical cavity which is coupled to a structured zero-temperature bosonic reservoir.Laplace transform,LBC and other methods are utilized,through numerical method we analyze the entanglement dynamic behavios of tripartite of three atoms and bipartite of cavity and reservoir.We also discuss how the coupling parameters affect the entanglement dynamics.Results show that in a short time,the entanglement of tripartite increases with coupling strength of three atoms increasing,and a periodic oscillation appears, but entanglement of bipartite decreases.The entanglement of tripartite decreases with the coupling strength between atoms and cavity increasing and damping oscillation appears,but the entanglement of bipartite increases.In a long-time limit,the entanglement approaches to a steady value.The non-Markovian dynamics of the qubits is determined by both the coupling strength and the spectral width.The strong system-reservoir coupling regime results in the non-Markovian dynamics of system.As the spectral width increases,the system of three atoms transforms from non-Markovian regime to Markovian regime.The increasing of spectral width results in the Markovian dynamic behavior of system,but the system of the atoms falls into the non-Markovian regime once more.When the coupling between the cavity and reservoir is weak,the entanglement of three atoms increases as the detuning of the cavity and reservoir increases,but it is not obvious.When the coupling between the cavity and reservoir is strong,the entanglement of three atoms increases and a periodic oscillation appears with increasing the detuning between the cavity and reservoir,so we can effectively restrain the effects of dissipation of reservoir on entanglement decay by adjusting the detuning between the cavity and reservoir.
We propose a scheme for nonreciprocal light propagation in two coupled cavities system, in which a two-level quantum emitter is coupled to one of the optical microcavities. For the case of parity-time ([Formula: see text]) symmetric system (i.e., coupled active-passive cavities system), the cavity gain can significantly enhance the optical nonlinearity induced by the interaction between a quantum emitter and cavity field beyond weak-excitation approximation. The increased optical nonlinearity results in the non-lossy nonreciprocal light propagation with high isolation ratio in proper parameters range. In addition, our calculations show that nonreciprocal light propagation will not be affected by the unstable output field intensity caused by optical bistability, and we can even switch directions of nonreciprocal light propagation by appropriately adjusting the system parameters.