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Generation of single- and two-mode multiphoton states in waveguide QED

V. Paulisch, H. J. Kimble, J. I. Cirac, and A. González-Tudela
Phys. Rev. A 97, 053831 – Published 22 May 2018
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  • INTRODUCTION
  • ATOM-WAVEGUIDE QED
  • GUIDELINES TO ANALYZE THE PROTOCOLS
  • GENERATING SINGLE-MODE MULTIPHOTON…
  • EXTENSION TO TWO-MODE PHOTONIC STATES
  • CONCLUSIONS AND OUTLOOK
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    Single- and two-mode multiphoton states are the cornerstone of many quantum technologies, e.g., metrology. In the optical regime, these states are generally obtained combining heralded single photons with linear optics tools and post-selection, leading to inherent low success probabilities. In a recent paper [A. González-Tudela et al., Phys. Rev. Lett. 118, 213601 (2017)], we design several protocols that harness the long-range atomic interactions induced in waveguide QED to improve fidelities and protocols of single-mode multiphoton emission. Here, we give full details of these protocols, revisit them to simplify some of their requirements, and also extend them to generate two-mode multiphoton states, such as Yurke or NOON states.

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    • Received 14 February 2018

    DOI:https://doi.org/10.1103/PhysRevA.97.053831

    ©2018 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Cavity quantum electrodynamicsCollective effects in quantum opticsPhoton pairs & parametric down-conversionPhoton statisticsQuantum metrologyQuantum opticsSuperradiance & subradiance
    Quantum Information, Science & TechnologyAtomic, Molecular & Optical

    Authors & Affiliations

    V. Paulisch1, H. J. Kimble1,2, J. I. Cirac1, and A. González-Tudela1

    • 1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
    • 2Norman Bridge Laboratory of Physics 12-33, California Institute of Technology, Pasadena, California 91125, USA

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    Vol. 97, Iss. 5 — May 2018

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    Images

    • Figure 1
      Figure 1

      (a) General setup of atoms coupled to a one-dimensional photonic waveguide. We depict the splitting into source, target, and detector ensembles with 1, N, and Nd emitters, respectively, which can be controlled by external fields independently. (b) Internal level structure of emitters in which the transitions g−e1 and s−e2 are coupled to a waveguide mode. The Rabi coupling between atomic states α and β, denoted by Ωαβ, can be obtained through laser or microwave fields. (c) The suppression of the decay rate corresponding to one transition can be implemented by using a far-off-resonance two-photon transition via a metastable state.

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    • Figure 2
      Figure 2

      (a) Exact population dynamics of step (c) of protocol 1 of the states {|e1〉s|ϕms1〉t,|g〉sSe1g(t)|ϕms1〉t,|g〉sScg(t)|ϕms1〉t} in black squares, blue circles, and red triangles, respectively, for Nm=P1d=100. In black and red solid lines we compare with the approximated results from the restricted evolution obtained under quantum Zeno dynamics. (b) Optimal probability of step (c) of protocol 1 as a function of P1d for Nm=100. The markers correspond to the exact numerical evolution, whereas the solid line is the analytical expression of Eq. (18) obtained under quantum Zeno dynamics.

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    • Figure 3
      Figure 3

      (a) Exact (markers) and estimated upper bound (solid lines) of the errors from spontaneous emission, pc,*, as a function of the Purcell factor P1d for different Nm=N−m and fixed α=1. The exact calculation is obtained from integrating populations in Eq. (21), whereas for the analytical upper bound we use Eq. (22).

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    • Figure 4
      Figure 4

      (a) The repumping scheme contains three steps for pumping any excitation in the metastable states c or s back to the ground state g. (b) Schemes to build up m excitations in a metastable state by beam-splitter operations and post-selection on zero detection in one of the modes. By doubling the number of excitations at each step, one can achieve a subexponential scaling.

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    • Figure 5
      Figure 5

      (a) Level structure required for protocol 3: Λ system for which two different waveguide modes are coupled to the transitions s−e, g−e, with rates Γ1ds,g, respectively.

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    • Figure 6
      Figure 6

      (a) Populations for Nm=100=P1d calculated with exact non-Hermitian Hamiltonian (markers) of Eq. (46), together with the analytical approximations (solid lines) within quantum Zeno dynamics using the optimal Ωge(d)=NmΓ1dΓ*/3. (b) Exact (markers) and approximated (solid line) optimal probability pm→m+1 obtained at time Toptb≈π3/Γ*Γ1d. (c) Exact (markers) and asymptotic bound (solid lines) of p* as a function of the Purcell factor P1d. The exact calculation is obtained from integrating populations of Eq. (48), whereas for the analytical upper bound we use Eq. (50).

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    • Figure 7
      Figure 7

      The level structure for the generation of two-mode states is obtained by mirroring the level structure of Fig. 1 around the ground state g.

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    • Figure 8
      Figure 8

      For the generalized Zeno Step we consider two ensembles with three-level atoms with one transition coupled to a waveguide mode.

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