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  • Letter
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Ultrafast Rabi flopping and coherent pulse propagation in a quantum cascade laser

Abstract

Pulse propagation phenomena are central to ultrashort pulse generation and amplification in lasers1,2,3,4,5. In the coherent regime, the phase relationship between the pulse and the material transition is preserved, allowing both optical fields and material states to be controlled6. The most prominent form of coherent manipulation is Rabi flopping7, a phenomenon well established in few-level absorbers, including atoms and single quantum dots8,9,10,11,12,13,14,15,16,17,18,19. However, Rabi flopping is generally much weaker in semiconductors because of strong dephasing in the electronic bands, in contrast to discrete-level systems. Although low-density induced coherent oscillations have been observed in semiconductor absorbers11,13,14,15,16,17,18,19,20, coherent pulse propagation phenomena in active semiconductor devices have not been observed. In this Letter, we explore coherent pulse propagation in an operating quantum cascade laser and directly observe Rabi flopping and coherent pulse reshaping. This work demonstrates the applicability of few-level models for quantum cascade lasers and may stimulate novel approaches to short pulse generation21,22.

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Figure 1: Experimental scheme.
Figure 2: Pulse envelope and lasing dynamics.
Figure 3: Dynamics of population inversion and polarization, and Bloch vectors.

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References

  1. Icsevgi, A. & Lamb, W. E. Propagation of light pulses in a laser amplifier. Phys. Rev. 185, 517–545 (1969).

    Article  ADS  MathSciNet  Google Scholar 

  2. Lamb, G. L. Analytical descriptions of ultrashort optical pulse propagation in a resonant medium. Rev. Mod. Phys. 43, 99–124 (1971).

    Article  ADS  MathSciNet  Google Scholar 

  3. Nakazawa, M., Suzuki, K., Kimura, Y. & Kubota, H. Coherent π-pulse propagation with pulse breakup in an erbium-doped fiber waveguide amplifier. Phys. Rev. A 45, R2682–R2685 (1992).

    Article  ADS  Google Scholar 

  4. Zhang, J.-Z. & Galbraith, I. Rabi oscillations of ultrashort optical pulses in 1.55 µm InGaAs/InGaAsP quantum-well amplifiers. J. Appl. Phys. 96, 922–924 (2004).

    Article  ADS  Google Scholar 

  5. Wang, C. Y. et al. Coherent instabilities in a semiconductor laser with fast gain recovery. Phys. Rev. A 77, 031802 (2007).

    Article  ADS  Google Scholar 

  6. Mosseini, M. et al. Coherent optical pulse sequencer for quantum applications. Nature 461, 241–245 (2009).

    Article  ADS  Google Scholar 

  7. Rabi, I. I. On the process of space quantization. Phys. Rev. 49, 324–328 (1936).

    Article  ADS  Google Scholar 

  8. Gibbs, H. M. Incoherent resonance fluorescence from a Rb atomic beam excited by a short coherent optical pulse. Phys. Rev. A 8, 446–455 (1973).

    Article  ADS  Google Scholar 

  9. Binder, R., Koch, S. W., Lindberg, M., Peyghambarian, N. & Schafer, W. Ultrafast adiabatic following in semiconductors. Phys. Rev. Lett. 65, 899–902 (1990).

    Article  ADS  Google Scholar 

  10. da Silva, V. L. & Silberberg, Y. Photon echoes in an optical amplifier. Phys. Rev. Lett. 70, 1097–1100 (1993).

    Article  ADS  Google Scholar 

  11. Cundiff, S. T. et al. Rabi flopping in semiconductors. Phys. Rev. Lett. 73, 1178–1181 (1994).

    Article  ADS  Google Scholar 

  12. Hughes, S. Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses. Phys. Rev. Lett. 81, 3363–3366 (1998).

    Article  ADS  Google Scholar 

  13. Giessen, H. et al. Self-induced transmission on a free exciton resonance in a semiconductor. Phys. Rev. Lett. 81, 4260–4263 (1998).

    Article  ADS  Google Scholar 

  14. Dynes, J. F., Frogley, M. D., Beck, M., Faist, J. & Phillips, C. C. AC stark splitting and quantum interference with intersubband transitions in quantum wells. Phys. Rev. Lett. 94, 157403 (2005).

    Article  ADS  Google Scholar 

  15. Mücke, O. D., Tritschler, T., Wegener, M., Morgner, U. & Kärtner, F. X. Signatures of carrier-wave Rabi flopping in GaAs. Phys. Rev. Lett. 87, 057401 (2001).

    Article  ADS  Google Scholar 

  16. Stievater, T. H. et al. Rabi oscillations of excitons in single quantum dots. Phys. Rev. Lett. 87, 133603 (2001).

    Article  ADS  Google Scholar 

  17. Schülzgen, A. et al. Direct observation of excitonic Rabi oscillations in semiconductors. Phys. Rev. Lett. 82, 2346–2349 (2004).

    Article  ADS  Google Scholar 

  18. Luo, C. W. et al. Phase-resolved nonlinear response of a two-dimensional electron gas under femtosecond intersubband excitation. Phys. Rev. Lett. 92, 047402 (2004).

    Article  ADS  Google Scholar 

  19. Khitrova, G., Gibbs, H. M., Kira, M., Koch, S. W. & Scherer, A. Vacuum Rabi splitting in semiconductors. Nature Phys. 2, 81–90 (2006).

    Article  ADS  Google Scholar 

  20. Gunter, G. et al. Sub-cycle switch-on of ultrastrong light–matter interaction. Nature 458, 178–181 (2009).

    Article  ADS  Google Scholar 

  21. Menyuk, C. R. & Talukder, M. A. Self-induced transparency modelocking of quantum cascade lasers. Phys. Rev. Lett. 102, 023903 (2009).

    Article  ADS  Google Scholar 

  22. Talukder, M. A. & Menyuk, C. R. Analytical and computational study of self-induced transparency mode locking in quantum cascade lasers. Phys. Rev. A 79, 063841 (2009).

    Article  ADS  Google Scholar 

  23. McCall, S. L. & Hahn, E. L. Self-induced transparency. Phys. Rev. 183, 457–485 (1969).

    Article  ADS  Google Scholar 

  24. Allen, L. & Eberly, J. H. Optical Resonance and Two Level Atoms (Dover, 1987).

    Google Scholar 

  25. Liu, H. & Capasso, F. Intersubband Transitions in Quantum Wells: Physics and Device Application II (Academic Press, 2000).

    Google Scholar 

  26. Choi, H. et al. Time-domain upconversion measurements of group-velocity dispersion in quantum cascade lasers. Opt. Express 15, 15898–15907 (2007).

    Article  ADS  Google Scholar 

  27. Choi, H. et al. Gain recovery dynamics and photon-driven transport in quantum cascade lasers. Phys. Rev. Lett. 100, 167401 (2008).

    Article  ADS  Google Scholar 

  28. Choi, H. et al. Time-resolved investigations of electronic transport dynamics in quantum cascade lasers based on diagonal lasing transition. IEEE J. Quantum Electron. 45, 307–321 (2009).

    Article  ADS  Google Scholar 

  29. Gordon, A. et al. Multimode regimes in quantum cascade lasers: from coherent instabilities to spatial hole burning. Phys. Rev. A 77, 053804 (2008).

    Article  ADS  Google Scholar 

  30. Wang, C. Y. et al. Mode-locked pulses from mid-infrared quantum cascade lasers. Opt. Express 17, 12929–12943 (2009).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

Studies at the University of Michigan and MIT were supported by US Army Research Office. The authors acknowledge support from the Center for Nanoscale System (CNS) at Harvard University (Harvard–CNS is a member of the National Nanotechnology Infrastructure Network, NNIN). The Nanoscale Science and Engineering Center (NERC) at Harvard University, funded by the National Science Foundation, is also gratefully acknowledged.

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Contributions

H.C. designed and performed the experiments. V.-M.G. and H.C. carried out modelling, simulations and interpretation of the measurement results. L.D. calculated the band structure and fabricated the sample. S.C., J.Z. and G.H. grew the sample wafer. F.C., F.X.K. and T.B.N. initiated the work, managed the project and interpreted the data. All authors discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to Franz X. Kärtner or Theodore B. Norris.

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The authors declare no competing financial interests.

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Choi, H., Gkortsas, VM., Diehl, L. et al. Ultrafast Rabi flopping and coherent pulse propagation in a quantum cascade laser. Nature Photon 4, 706–710 (2010). https://doi.org/10.1038/nphoton.2010.205

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