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.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Rent or buy this article
Prices vary by article type
from$1.95
to$39.95
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Icsevgi, A. & Lamb, W. E. Propagation of light pulses in a laser amplifier. Phys. Rev. 185, 517–545 (1969).
Lamb, G. L. Analytical descriptions of ultrashort optical pulse propagation in a resonant medium. Rev. Mod. Phys. 43, 99–124 (1971).
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).
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).
Wang, C. Y. et al. Coherent instabilities in a semiconductor laser with fast gain recovery. Phys. Rev. A 77, 031802 (2007).
Mosseini, M. et al. Coherent optical pulse sequencer for quantum applications. Nature 461, 241–245 (2009).
Rabi, I. I. On the process of space quantization. Phys. Rev. 49, 324–328 (1936).
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).
Binder, R., Koch, S. W., Lindberg, M., Peyghambarian, N. & Schafer, W. Ultrafast adiabatic following in semiconductors. Phys. Rev. Lett. 65, 899–902 (1990).
da Silva, V. L. & Silberberg, Y. Photon echoes in an optical amplifier. Phys. Rev. Lett. 70, 1097–1100 (1993).
Cundiff, S. T. et al. Rabi flopping in semiconductors. Phys. Rev. Lett. 73, 1178–1181 (1994).
Hughes, S. Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses. Phys. Rev. Lett. 81, 3363–3366 (1998).
Giessen, H. et al. Self-induced transmission on a free exciton resonance in a semiconductor. Phys. Rev. Lett. 81, 4260–4263 (1998).
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).
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).
Stievater, T. H. et al. Rabi oscillations of excitons in single quantum dots. Phys. Rev. Lett. 87, 133603 (2001).
Schülzgen, A. et al. Direct observation of excitonic Rabi oscillations in semiconductors. Phys. Rev. Lett. 82, 2346–2349 (2004).
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).
Khitrova, G., Gibbs, H. M., Kira, M., Koch, S. W. & Scherer, A. Vacuum Rabi splitting in semiconductors. Nature Phys. 2, 81–90 (2006).
Gunter, G. et al. Sub-cycle switch-on of ultrastrong light–matter interaction. Nature 458, 178–181 (2009).
Menyuk, C. R. & Talukder, M. A. Self-induced transparency modelocking of quantum cascade lasers. Phys. Rev. Lett. 102, 023903 (2009).
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).
McCall, S. L. & Hahn, E. L. Self-induced transparency. Phys. Rev. 183, 457–485 (1969).
Allen, L. & Eberly, J. H. Optical Resonance and Two Level Atoms (Dover, 1987).
Liu, H. & Capasso, F. Intersubband Transitions in Quantum Wells: Physics and Device Application II (Academic Press, 2000).
Choi, H. et al. Time-domain upconversion measurements of group-velocity dispersion in quantum cascade lasers. Opt. Express 15, 15898–15907 (2007).
Choi, H. et al. Gain recovery dynamics and photon-driven transport in quantum cascade lasers. Phys. Rev. Lett. 100, 167401 (2008).
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).
Gordon, A. et al. Multimode regimes in quantum cascade lasers: from coherent instabilities to spatial hole burning. Phys. Rev. A 77, 053804 (2008).
Wang, C. Y. et al. Mode-locked pulses from mid-infrared quantum cascade lasers. Opt. Express 17, 12929–12943 (2009).
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.
Author information
Authors and Affiliations
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
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nphoton.2010.205
This article is cited by
-
Short pulse generation from a graphene-coupled passively mode-locked terahertz laser
Nature Photonics (2023)
-
Study of ultrafast Rabi flopping in colloidal quantum dots at room temperature
Communications Physics (2021)
-
Population difference gratings created on vibrational transitions by nonoverlapping subcycle THz pulses
Scientific Reports (2021)
-
Coherent master equation for laser modelocking
Nature Communications (2020)
-
Population density gratings induced by few-cycle optical pulses in a resonant medium
Scientific Reports (2017)