Emitters of N-photon bundles

Journal name:
Nature Photonics
Year published:
Published online


Controlling the output of a light emitter is one of the basic tasks in photonics, with landmarks such as the development of the laser and single-photon sources. The ever growing range of quantum applications is making it increasingly important to diversify the available quantum sources. Here, we propose a cavity quantum electrodynamics scheme to realize emitters that release their energy in groups (or ‘bundles’) of N photons (where N is an integer). Close to 100% of two-photon emission and 90% of three-photon emission is shown to be within reach of state-of-the-art samples. The emission can be tuned with the system parameters so that the device behaves as a laser or as an N-photon gun. Here, we develop the theoretical formalism to characterize such emitters, with the bundle statistics arising as an extension of the fundamental correlation functions of quantum optics. These emitters will be useful for quantum information processing and for medical applications.

At a glance


  1. Hamiltonian and dissipative cavity QED.
    Figure 1: Hamiltonian and dissipative cavity QED.

    a, cQED brings QED (the theory of light–matter interactions) under prolonged scrutiny at the level of a few photons and in the presence of a quantum emitter. An external laser can be applied to the emitter to drive its dynamics. We show how peculiar quantum superpositions can be realized and the emission subsequently forced to take place exclusively in bundles of N photons. b, A possible solid-state implementation of our proposal places a quantum dot in a micropillar. With excitation from the side with a conventional laser, one can collect, in the cavity, emission as the output from a quantum laser or a quantum gun, depending on the system parameters. DBR, distributed Bragg reflector.

  2. Energy levels of the two limiting cases of excitation.
    Figure 2: Energy levels of the two limiting cases of excitation.

    a, In the low-excitation regime the Jaynes–Cummings ladder (anticrossing magnified in the inset) is probed by resonantly exciting a given rung of the ladder, with photon blockade at all others. b, In the high-excitation regime, the laser dresses the QE while the cavity Purcell-enhances an N-photon transition from |right fence to |+right fence (here for N = 2). A subsequent emission from the QE brings the system back to a |right fence state.

  3. Resonances in the photon-correlation functions.
    Figure 3: Resonances in the photon-correlation functions.

    a, g(2) as a function of ωL for pumping 0  10−2g, 1  4g and 2  32g. The resonances ωN() are shown in the plane (ωL,). Open circles are the projection of ω2 on g(2). b, Resonant energies to excite the nth rung of the ladder. c, g(n) for n = 2 (solid), 3 (long dash), 4 (short dash) and 5 (dotted) at vanishing pumping with n–1 bunching resonances matching those in b. Δ/g = −60 in all panels.

  4. Dynamics of the emission when probing the two-photon resonance in various regimes of excitation.
    Figure 4: Dynamics of the emission when probing the two-photon resonance in various regimes of excitation.

    a, Wavefunction evolution at the two-photon resonance pictured through the probability of the system to be in any of the states |ng/eright fence. Hamiltonian evolution in the Jaynes–Cummings regime (low pumping). b, Hamiltonian evolution in the Mollow regime (high pumping). c, Quantum trajectory during two-photon emission in the same regime as in b, but in the presence of dissipation. d,e, Cavity-photon clicks as they would be recorded by a streak camera (25 sweeps shown) for pumping values 1 (d) and 2 (e) at ω2(). In d, the emission is highly bunched, although it largely consists of single clicks (g(2) = 3,649 and π2 = 16%). In e, g(2) = 17 with π2 = 98.8%. f, Ideal NPE (N-photon emission) in thick lines and 99% NPE in translucent lines with an envelope to guide the eye. g, Pumping dependence of π2 (left axis) and g(2) (right axis) (from 0 to 3,649) and na (from 0 to 0.03) following ω2(). h,i, Second-order photon correlations at the N = 1 (red) and N = 2 (blue) level, from equation (6) (smooth curve) and from Monte Carlo clicks (data).

  5. Efficiency and characterization of N-photon emission for 2 [le] N [le] 5
    Figure 5: Efficiency and characterization of N-photon emission for 2 ≤ N ≤ 5

    a, Figures of merit for two- and three-photon emission in the space of purity/emission intensity. Almost pure two- and three-photon emission can be achieved with state-of-the-art cQED samples: γσ/g = 0.01 for π2 and 0.001 for π3. b, Full density matrix of the system in the regime of four-photon emission, showing the predominance of the vacuum and the strong coherence between the 2 × 2 sub-blocks of 0 and 4 photons and the 1/n cascade along the diagonal. c, Sketch of two five-photon bundles. Each bundle is composed of photons that pile up together ahead in time due to the mechanism of their production. This structure is not described by the state |5right fence.


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Author information


  1. Condensed Matter Physics Center (IFIMAC), Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, 28049 Madrid, Spain

    • C. Sánchez Muñoz,
    • E. del Valle,
    • C. Tejedor &
    • F. P. Laussy
  2. Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany

    • A. González Tudela
  3. Walter Schottky Institut, Technische Universität München, Am Coulombwall 4, 85748 Garching, Germany

    • K. Müller,
    • S. Lichtmannecker,
    • M. Kaniber &
    • J. J. Finley
  4. E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA

    • K. Müller


F.P.L. and E.d.V. proposed the idea. C.S.M., E.d.V. and F.P.L. developed the theoretical formalism and the conceptual tools. C.S.M. implemented the theoretical methods and analysed the data. A.G.T., K.M., S.L., M.K. and J.J.F. contributed material, analysis tools and expertise. F.P.L., C.S.M., E.d.V., C.T. and J.J.F. wrote the main paper. C.S.M., E.d.V., A.G.T. and F.P.L. wrote the Supplementary Information. F.P.L. supervised the research. All authors discussed the results and its implications and commented on the manuscript.

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