Abstract
Quantum cascade lasers1,2 can be considered the primary achievement of electronic band structure engineering, showing how artificial materials can be created through quantum design to have tailor-made properties that are otherwise non-existent in nature. Indeed, quantum cascade lasers can be used as powerful testing grounds of the fundamental physical parameters determined by their quantum nature, including the intrinsic linewidth of laser emission3, which in such lasers is significantly affected by the optical and thermal photon number generated in the laser cavity. Here, we report experimental evidence of linewidth values approaching the quantum limit4,5 in far-infrared quantum cascade lasers. Despite the broadening induced by thermal photons, the measured linewidth results narrower than that found in any other semiconductor laser to date. By performing noise measurements with unprecedented sensitivity levels, we highlight the key role of gain medium engineering6 and demonstrate that properly designed semiconductor-heterostructure lasers can unveil the mechanisms underlying the laser-intrinsic phase noise, revealing the link between device properties and the quantum-limited linewidth.
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
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Faist, J. et al. Quantum cascade laser. Science 264, 553–556 (1994).
Kohler, R. et al. Terahertz semiconductor heterostructure laser. Nature 417, 156–159 (2002).
Schawlow, A. L. & Townes C. H. Infrared and optical masers. Phys. Rev. 112, 1940–1949 (1958).
Yamanishi, M., Edamura, T., Fujita, K., Akikusa, N. & Kan, H. Theory of the intrinsic linewidth of quantum cascade lasers: hidden reason for the narrow linewidth and line-broadening by thermal photons. IEEE J. Quantum Electron. 44, 12–29 (2008).
Bartalini, S. et al. Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow–Townes limit. Phys. Rev. Lett. 104, 083904 (2010).
Vitiello, M. S. et al. Measurement of subband electronic temperatures and population inversion in THz quantum-cascade lasers. Appl. Phys. Lett. 86, 111115 (2005).
Fathololoumi, S. et al. Terahertz quantum cascade lasers operating up to similar to 200 K with optimized oscillator strength and improved injection tunneling. Opt. Express 20, 3866–3876 (2012).
Williams, B. S., Kumar, S., Hu, Q. & Reno, J. L. High-power terahertz quantum-cascade lasers. Electron. Lett. 42, 89–90 (2006).
Vitiello, M. S. & Tredicucci, A. Tunable emission in a THz quantum cascade lasers. IEEE Trans. Terahertz Sci. Tech. 1, 76–84 (2011).
Reix, J.-M. et al. The Hershel/Planck programme, technical challenges for two science missions, successfully launched. Acta Astronom. 34, 130–148 (2009).
Mittleman, D. M. Sensing with Terahertz Radiation (Springer, 2003).
Tonouchi, M. Cutting edge terahertz technology. Nature Photon. 1, 97–105 (2007).
Capasso, F. et al. Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth and far-infrared emission. IEEE J. Quantum Electron. 38, 511–532 (2002).
Barkan, A. et al. Linewidth and tuning characteristics of terahertz quantum cascade lasers. Opt. Lett. 29, 575–577 (2004).
Betz, A. L. et al. Frequency and phase-lock control of a 3 THz quantum cascade laser. Opt. Lett. 30, 1837–1839 (2005).
Maulini, R. et al. Continuous-wave operation of a broadly tunable thermoelectrically cooled external cavity quantum cascade-laser. Opt. Lett. 30, 2584–2586 (2005).
Hubers, H. et al. Terahertz quantum cascade laser as local oscillator in a heterodyne receiver. Opt. Express 13, 5890–5896 (2005).
Baryshev, A. et al. Phase locking and spectral linewidth of a two-mode terahertz quantum cascade laser. Appl. Phys. Lett. 89, 031115 (2006).
Barbieri, S. et al. Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fiber laser. Nature Photon. 4, 636–640 (2010).
Bartalini, S. et al. Measuring frequency noise and intrinsic linewidth of a room-temperature DFB quantum cascade laser. Opt. Express 19, 17996–18003 (2011).
Wiseman, H. M. Light amplification without stimulated emission: beyond the standard quantum limit to the laser linewidth. Phys. Rev. A 60, 4083–4093 (1999).
Jirauschek, C. Monte Carlo study of intrinsic linewidths in terahertz quantum cascade lasers. Opt. Express 18, 25922–25927 (2010).
Elliott, D. S., Roy, R. & Smith, S. J. Extracavity laser bandshape and bandwidth modification. Phys. Rev. A 26, 12–18 (1982).
Sirtori, C. et al. Resonant tunneling in quantum cascade lasers. IEEE J. Quantum Electron. 34, 1722–1729 (1998).
Lee, S. C. & Wacker, A. Nonequilibrium Green's function theory for transport and gain properties of quantum cascade structures. Phys. Rev. B 66, 245314 (2002).
Callebaut, H., Kumar, S., Williams, B. S., Hu, Q. & Reno, J. L. Importance of electron-impurity scattering for electron transport in terahertz quantum-cascade lasers. Appl. Phys. Lett. 84, 645–647 (2004).
Mahler, L. et al. High-performance operation of single-mode terahertz quantum cascade lasers with metallic gratings. Appl. Phys. Lett. 87, 181101 (2005).
Bartalini, S. et al. Frequency-comb-referenced quantum-cascade laser at 4.4 µm. Opt. Lett. 32, 988–990 (2007).
Hubers, H. W. et al. High-resolution gas phase spectroscopy with a distributed feedback terahertz quantum cascade laser. Appl. Phys. Lett. 89, 061115 (2006).
Gagliardi, G. et al. Sensitive detection of methane and nitrous oxide isotopomers using a continuous wave quantum cascade laser. Eur. Phys. J. D 19, 327–331 (2002).
Tombez, L. et al. Frequency noise of free-running 4.6 µm distributed feedback quantum cascade lasers near room temperature. Opt. Lett. 36, 3109–3111 (2011).
Dunbar, L. A. et al. Small optical volume terahertz emitting microdisk quantum cascade lasers. Appl. Phys. Lett. 90, 141114 (2007).
Walther, C., Scalari, G., Beck, M. & Faist, J. Purcell effect in the inductor–capacitor laser. Opt. Letts 36, 2623–2625 (2011).
Henry, C. H. in Coherence, Amplification, and Quantum Effects in Semiconductor Lasers (ed. Yamamoto, Y.) 5–76 (Wiley, 1991).
Vitiello, M. S. et al. Electron-lattice coupling in bound-to-continuum THz quantum cascade lasers. Appl. Phys. Lett. 88, 241109 (2006).
Vitiello, M. S. et al. Subband electronic temperature and electron lattice energy relaxation in terahertz quantum cascade lasers with different conduction band offsets. Appl. Phys. Lett. 89, 131114 (2006).
Martl, M. et al. Gain and losses in THz quantum cascade laser with metal-metal waveguide. Opt. Express 19, 733–738 (2011).
Walther, C., Scalari, G., Faist, J., Beere, H. E. & Ritchie, D. A. Low frequency terahertz quantum cascade laser operating from 1.6 to 1.8 THz. Appl. Phys. Lett. 89, 231121 (2006).
Vitiello, M. S. et al. Probing quantum efficiency by laser-induced hot-electron cooling. Appl. Phys. Lett. 94, 021115 (2009).
Carr, L. D. & Ye, J. Focus on cold and ultracold molecules. New. J. Phys. 11, 055009 (2009).
Acknowledgements
This work was partly supported by the Italian Ministry of Education, University, and Research (MIUR) through the programme ‘FIRB–Futuro in Ricerca 2010 RBFR10LULP Fundamental Research on Terahertz Photonic Devices’ and by the Ente Cassa di Risparmio di Firenze and Regione Toscana, through project CTOTUS, in the framework of POR–CReO FESR 2007–2013. The authors thank H.E. Beere and D.A. Ritchie for the growth of the QCL structure, J.H. Xu for technical support and J. Faist for useful discussions.
Author information
Authors and Affiliations
Contributions
M.S.V. conceived and performed the experiment, analysed the data, carried out the modelling and wrote the paper. S.B. conceived and performed the experiment, analysed the data and contributed to manuscript preparation. L.C. performed the experiment and analysed the data. P.D. conceived the experiments and contributed to the analysis and manuscript preparation. All authors discussed the results and implications and contributed to the manuscript at various stages.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary information
Supplementary information (PDF 1090 kb)
Rights and permissions
About this article
Cite this article
Vitiello, M., Consolino, L., Bartalini, S. et al. Quantum-limited frequency fluctuations in a terahertz laser. Nature Photon 6, 525–528 (2012). https://doi.org/10.1038/nphoton.2012.145
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nphoton.2012.145
This article is cited by
-
The Heisenberg limit for laser coherence
Nature Physics (2021)
-
Fully phase-stabilized quantum cascade laser frequency comb
Nature Communications (2019)
-
Continuous-wave highly-efficient low-divergence terahertz wire lasers
Nature Communications (2018)
-
Terahertz saturable absorbers from liquid phase exfoliation of graphite
Nature Communications (2017)
-
Terahertz Frequency Metrology for Spectroscopic Applications: a Review
Journal of Infrared, Millimeter, and Terahertz Waves (2017)