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arXiv:2404.09641 · Physical Review A

Multiple single-photon generations in three-level atoms coupled to a cavity with non-Markovian effects

H. Z. Shen, Y. Chen, T. Z. Luan, X. X. Yi

Published May 8, 2023• 13 citations
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Abstract

In this paper we show how to generate multiple single-photon wave packets of arbitrary temporal shape from an optical cavity coupled with $N$ three-level atoms driven by a driving field in the non-Markovian regime. We derive an exact analytical expression of the optimal driving field to generate such wave packets, which depends on two detunings of the cavity and driving field with respect to the three-level atoms. The cavity we use consists of two mirrors facing each other, where one is perfect and the other includes dissipation (a one-sided cavity), which couples with the corresponding non-Markovian input-output fields. If the first single-photon wave packet generated by the Markovian system is the same as the non-Markovian case, the Markovian system cannot generate the same multiple single-photon wave packets as the non-Markovian system when the spectral widths of the other environments take values different from the spectral width of the first environment, while setting the equal spectral widths for the different environments can generate this. The generated multiple different single-photon wave packets are not independent of each other, which satisfies certain relations with non-Markovian spectral parameters. We analyze the transition from Markovian to non-Markovian regimes and compare the differences between them, where the cavity interacts simultaneously with the multiple non-Markovian environments. Finally, we extend the above results to a general non-Markovian quantum network involving many cavities coupled with driven three-level atoms.

DOI
10.1103/physreva.107.053705

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In this paper we show how to generate multiple single-photon wave packets of arbitrary temporal shape from an optical cavity coupled with NNN three-level atoms driven by a driving field in the non-Markovian regime. We derive an exact analytical expression of the optimal driving field to generate such wave packets, which depends on two detunings of the cavity and driving field with respect to the three-level atoms. The cavity we use consists of two mirrors facing each other, where one is perfect and the other includes dissipation (a one-sided cavity), which couples with the corresponding non-Markovian input-output fields. If the first single-photon wave packet generated by the Markovian system is the same as the non-Markovian case, the Markovian system cannot generate the same multiple single-photon wave packets as the non-Markovian system when the spectral widths of the other environments take values different from the spectral width of the first environment, while setting the equal spectral widths for the different environments can generate this. The generated multiple different single-photon wave packets are not independent of each other, which satisfies certain relations with non-Markovian spectral parameters. We analyze the transition from Markovian to non-Markovian regimes and compare the differences between them, where the cavity interacts simultaneously with the multiple non-Markovian environments. Finally, we extend the above results to a general non-Markovian quantum network involving many cavities coupled with driven three-level atoms.
Taking the non-Markovian effect into account, we study how to store a single photon of arbitrary temporal shape in a single atom coupled to an optical cavity. Our model applies to Raman transitions in three-level atoms, with one branch of the transition controlled by a driving pulse, and the other coupled to the cavity. For any couplings of input field to the optical cavity and detunings of the atom from the driving pulse and cavity, we extend the input-output relation from Markovian to non-Markovian dynamics. For most possible photon shapes, we derive an analytic expression for the driving pulse in order to completely map the input photon into the atom. We find that the amplitude of the driving pulse depends only on the detuning of the atom from the frequency of the cavity, i.e., the detuning of the atom to the driving pulse has no effect on the strength of the driving pulse.
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.
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 concept of non-Markovianity (NM) in quantum dynamics is still an open debate. Understanding how to generate and measure NM in specific models may aid in this quest. In quantum optics, an engineered electromagnetic environment coupled to a single atom can induce NM. The most common scenario of structured electromagnetic environment is an optical cavity, composed by a pair of mirrors. Here, we show how to generate and measure NM on a two-level system coupled to a one-dimensional waveguide with no mirrors required. The origin of the non-Markovian behavior lies in the initial state of the field, prepared as a single-photon packet. NM is shown to depend on two experimentally controllable parameters, namely, the linewidth of the packet and its central frequency. We relate the presence of NM to quantum interference. We also show how the two output channels of the waveguide provide distinct signatures of NM, both experimentally accessible.
Non-Markovian dynamics go beyond the Markovian approximation by capturing memory effects and information backflow in open quantum systems, which are crucial for describing realistic physical processes. In this work, we study the exact non-Markovian dynamics of a driven cavity coupled to an anisotropic three-dimensional photonic-crystal environment via counterrotating-wave interactions. We derive an exact analytical expression for the cavity amplitude satisfying the integro-differential equation, which includes the contributions of the bound states outside the continuum and the dissipative parts with the continuum spectrum. Based on the characteristic function method, we derive the exact non-Markovian master equation for the cavity, which contributes to the gain of the cavity. We give the physical origin of non-Markovian gain in the presence of bound states in the system consisting of cavity and environment, which has no Markovian counterparts due to the nonexponential gain in the non-Markovian structured environment. We find that three different types of bound states can be formed in the system, containing one bound state with no inversion of photon number, two bound states with the periodic equal-amplitude oscillation, and the gain with two complex roots without the bound states formation. We derive a current equation including the source from the driving field, the transient current induced by the change in the number of photons, and the two-photon current caused by the counterrotating-wave term. The results are compared with those given by the rotating-wave interactions and extended to a more general quantum network involving an arbitrary number of coupled cavities. Our findings may pave the way for a deeper understanding of non-Markovian dynamics with gain in quantum networks involving counterrotating-wave effects.
If a two-level system coupled to a single-mode cavity is strongly driven by an external laser, instead of a continuous accumulation of photons in the cavity, oscillations in the mean photon number occur. These oscillations correspond to peaks of finite width running up and down in the photon number distribution, reminiscent of wave packets in linear chain models. A single wave packet is found if the cavity is resonant to the external laser. Here, we show that for finite detuning, multiple packet structures can exist simultaneously, oscillating at different frequencies and amplitudes. We further study the influence of dissipative effects resulting in the formation of a stationary state, which, depending on the parameters, can be characterized by a bimodal photon number distribution. While we give analytical limits for the maximally achievable photon number in the absence of any dissipation, surprisingly, dephasing processes can push the photon occupations towards higher photon numbers.