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Tunable photon-photon correlations in waveguide QED systems with giant atoms

Wenju Gu, Lei Chen, Zhen Yi, Sujing Liu, and Gao-xiang Li
Phys. Rev. A 109, 023720 – Published 26 February 2024
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Abstract
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  • INTRODUCTION
  • PHYSICAL MODEL
  • SINGLE-PHOTON SCATTERING EIGENSTATES
  • TWO-PHOTON INTERACTING SCATTERING…
  • INCOHERENT POWER SPECTRUM
  • SECOND-ORDER CORRELATION FUNCTION
  • CONCLUSIONS AND DISCUSSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    We investigate the scattering processes of two photons in a one-dimensional waveguide coupled to two giant atoms. By adjusting the accumulated phase shifts between the coupling points, we are able to effectively manipulate the characteristics of these scattering photons. Utilizing the Lippmann-Schwinger formalism, we derive analytical expressions for the wave functions describing two-photon interaction in separate, braided, and nested configurations. Based on these wave functions, we also obtain analytical expressions for the incoherent power spectra and second-order correlation functions. In contrast to small atoms, the incoherent spectrum, which is defined by the correlation of the bound state, can exhibit more tunability due to the phase shifts. Additionally, the second-order correlation functions in the transmission and reflection fields could be tuned to exhibit either bunching or antibunching upon resonant driving. These unique features offered by the giant atoms in waveguide QED could benefit the generation of nonclassical itinerant photons in quantum networks.

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    • Received 9 November 2023
    • Accepted 8 February 2024

    DOI:https://doi.org/10.1103/PhysRevA.109.023720

    ©2024 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Nonlinear opticsQuantum optics
    Quantum Information, Science & TechnologyAtomic, Molecular & Optical

    Authors & Affiliations

    Wenju Gu*, Lei Chen, Zhen Yi, and Sujing Liu

    • School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China

    Gao-xiang Li†

    • Department of Physics, Huazhong Normal University, Wuhan 430079, China

    • *guwenju@yangtzeu.edu.cn
    • †gaox@mail.ccnu.edu.cn

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    Vol. 109, Iss. 2 — February 2024

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    Images

    • Figure 1
      Figure 1

      Schematic illustration of two two-level giant atoms with a one-dimensional (1D) waveguide in three distinct configurations: (a) separate, (b) braided, (c) nested. The coupling between the atomic transitions and the waveguide modes occurs at four specific points denoted as lk, where k=1,2,3,4. The strength of the coupling is represented by V. Additionally, the phase shifts acquired between neighboring points are represented by ϕ1 and ϕ2.

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    • Figure 2
      Figure 2

      Incoherent power spectra in the three different configurations as a function of frequency ω with different values of ϕ1 and ϕ2. The first row corresponds to the separate case, the second row corresponds to the braided case, and the third row corresponds to the nested case. In addition, the black solid lines denote the total incoherent power spectra, the red dashed lines denote the incoherent power spectra in transmission, and the blue dotted lines denote the incoherent power spectra in reflection. The other parameters are k=ω0=100Γ.

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    • Figure 3
      Figure 3

      The total inelastic flux in the three different configurations as a function of k with different values of ϕ1 and ϕ2. The first row corresponds to the separate case, the second row corresponds to the braided case, and the third row corresponds to the nested case. The other parameter is ω0=100Γ.

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    • Figure 4
      Figure 4

      Second-order differential correlation functions in the three different configurations as functions of ϕ1 and ϕ2. The first row corresponds to the separate configuration, the second row corresponds to the braided configuration, and the third row corresponds to the nested configuration. Moreover, the first column represents the transmission, and the second column represents the reflection. The white lines indicate that the differential correlation functions equal to zero. The other parameters are k=ω0=100Γ.

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    • Figure 5
      Figure 5

      Normalized second-order correlation functions in the three different configurations as a function of x with different values of ϕ1 and ϕ2. The first row corresponds to the transmission, and the second row corresponds to the reflection. Additionally, the first column represents the separate case, the second column represents the braided case, and the third column represents the nested case. The other parameters are k=ω0=100Γ.

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    • Figure 6
      Figure 6

      Energy diagram illustrating the inelastic power spectra in the three configurations. (a) Independent transitions in the symmetric and antisymmetric basis for the separate and braided configurations. (b) Correlated transitions in the eigenbasis for the nested configuration.

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    • Figure 7
      Figure 7

      The numerical simulation of the incoherent power spectra and total inelastic flux using the master equation approach. Here, ϕ1=0.25π, ϕ2=0.85π, ω0=100Γ, and the coherent drive amplitude fulfills α2=0.01Γ.

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    • Figure 8
      Figure 8

      Two-photon differential correlation function calculated from the master equation approach. Here, ω0=100Γ and the coherent drive amplitude fulfills α2=0.01Γ.

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