Up on the jaynes–cummings ladder of a quantum-dot/microcavity system

ABSTRACT In spite of their different natures, light and matter can be unified under the strong-coupling regime, yielding superpositions of the two, referred to as dressed states or

polaritons. After initially being demonstrated in bulk semiconductors1 and atomic systems2, strong-coupling phenomena have been recently realized in solid-state optical microcavities3.

Strong coupling is an essential ingredient in the physics spanning from many-body quantum coherence phenomena, such as Bose–Einstein condensation4 and superfluidity5, to cavity quantum

electrodynamics. Within cavity quantum electrodynamics, the Jaynes–Cummings model6,7,8 describes the interaction of a single fermionic two-level system with a single bosonic photon mode. For

a photon number larger than one, known as quantum strong coupling, a significant anharmonicity is predicted for the ladder-like spectrum of dressed states. For optical transitions in

semiconductor nanostructures, first signatures of the quantum strong coupling were recently reported9. Here we use advanced coherent nonlinear spectroscopy to explore a strongly coupled

exciton–cavity system10,11. We measure and simulate its four-wave mixing response12,13, granting direct access to the coherent dynamics of the first and second rungs of the Jaynes–Cummings

ladder. The agreement of the rich experimental evidence with the predictions of the Jaynes–Cummings model is proof of the quantum strong-coupling regime in the investigated solid-state

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10 August 2020 REFERENCES * Hopfield, J. J. & Thomas, D. G. Polariton absorption lines. _Phys. Rev. Lett._ 15, 22–25 (1965). Article  CAS  Google Scholar  * Kaluzny, Y., Goy, P., Gross,

M., Raimond, J. M. & Haroche, S. Observation of self-induced Rabi oscillations in two-level atoms excited inside a resonant cavity: The ringing regime of superradiance. _Phys. Rev.

Lett._ 51, 1175–1178 (1983). Article  CAS  Google Scholar  * Weisbuch, C., Nishioka, M., Ishikawa, A. & Arakawa, Y. Observation of the coupled exciton–photon mode splitting in a

semiconductor quantum microcavity. _Phys. Rev. Lett._ 69, 3314–3317 (1992). Article  CAS  Google Scholar  * Kasprzak, J. et al. Bose–Einstein condensation of exciton polaritons. _Nature_

443, 409–414 (2006). Article  CAS  Google Scholar  * Amo, A. et al. Superfluidity of polaritons in semiconductor microcavities. _Nature Phys._ 5, 805–810 (2009). Article  CAS  Google Scholar

  * Jaynes, E. & Cummings, F. Comparison of quantum and semiclassical radiation theory with application to the beam maser. _Proc. IEEE_ 51, 89–109 (1963). Article  Google Scholar  *

Laussy, F. P., Glazov, M. M., Kavokin, A. V., Whittaker, D. M. & Malpuech, G. Statistics of excitons in quantum dots and their effect on the optical emission spectra of microcavities.

_Phys. Rev. B_ 73, 115343 (2006). Article  Google Scholar  * del Valle, E., Laussy, F. P. & Tejedor, C. Luminescence spectra of quantum dots in microcavities. II. Fermions. _Phys. Rev.

B_ 79, 235326 (2009). Article  Google Scholar  * Faraon, A. et al. Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade. _Nature Phys._ 4, 859–863

(2008). Article  CAS  Google Scholar  * Reithmaier, J. P. et al. Strong coupling in a single quantum dot-semiconductor microcavity system. _Nature_ 432, 197–200 (2004). Article  CAS  Google

Scholar  * Yoshie, T. et al. Rabi splitting with a single quantum dot in a photonic crystal nanocavity. _Nature_ 432, 200–203 (2004). Article  CAS  Google Scholar  * Langbein, W. &

Patton, B. Heterodyne spectral interferometry for multidimensional nonlinear spectroscopy of individual quantum systems. _Opt. Lett._ 31, 1151–1153 (2006). Article  Google Scholar  * Borri,

P. & Langbein, W. in _Semiconductor Quantum Bits_ (eds Henneberger, F. & Benson, O.) Ch. 12 (Pan Stanford Publishing, 2009). Google Scholar  * Brune, M. et al. Quantum Rabi

oscillation: A direct test of field quantization in a cavity. _Phys. Rev. Lett._ 76, 1800–1803 (1996). Article  CAS  Google Scholar  * Göppl, M. et al. Climbing the Jaynes–Cummings ladder

and observing its nonlinearity in a cavity QED system. _Nature_ 454, 315–318 (2008). Article  Google Scholar  * Khitrova, G., Gibbs, H. M., Kira, M., Koch, S. W. & Scherer, A. Vacuum

Rabi splitting in semiconductors. _Nature Phys._ 2, 81–90 (2006). Article  CAS  Google Scholar  * Löffler, A. et al. Semiconductor quantum dot microcavity pillars with high-quality factors

and enlarged dot dimensions. _Appl. Phys. Lett._ 86, 111105 (2005). Article  Google Scholar  * Reitzenstein, S. et al. AlAs/GaAs micropillar cavities with quality factors exceeding 150.000.

_Appl. Phys. Lett._ 90, 251109 (2007). Article  Google Scholar  * Münch, S. et al. The role of optical excitation power on the emission spectra of a strongly coupled quantum dot–micropillar

system. _Opt. Express_ 17, 12821–12828 (2009). Article  Google Scholar  Download references ACKNOWLEDGEMENTS J.K. and W.L. acknowledge support by the European Commission under the

FP7-PEOPLE-2007-2-1-IEF ‘CUSMEQ’ contract No 219762. E.A.M. acknowledges support of WIMCS and RFBR. S.R., C.K., C.S., M.S., S.H. and A.F. acknowledge support by the Deutsche

Forschungsgemeinschaft through the research group ‘Quantum Optics in Semiconductor Nanostructures’ and the State of Bavaria. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * School of Physics

and Astronomy, Cardiff University, The Parade, Cardiff CF24 3AA, UK J. Kasprzak, E. A. Muljarov & W. Langbein * Technische Physik, Physikalisches Institut, Universität Würzburg and

Wilhelm Conrad Röntgen Research Center for Complex Material Systems, Am Hubland, D-97074 Würzburg, Germany S. Reitzenstein, C. Kistner, C. Schneider, M. Strauss, S. Höfling & A. Forchel

Authors * J. Kasprzak View author publications You can also search for this author inPubMed Google Scholar * S. Reitzenstein View author publications You can also search for this author

inPubMed Google Scholar * E. A. Muljarov View author publications You can also search for this author inPubMed Google Scholar * C. Kistner View author publications You can also search for

this author inPubMed Google Scholar * C. Schneider View author publications You can also search for this author inPubMed Google Scholar * M. Strauss View author publications You can also

search for this author inPubMed Google Scholar * S. Höfling View author publications You can also search for this author inPubMed Google Scholar * A. Forchel View author publications You can

also search for this author inPubMed Google Scholar * W. Langbein View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS Experiments were

designed by W.L. and carried out by J.K., W.L. and S.R. Data were analysed and interpreted by J.K., W.L. and E.A.M. The theory was developed by E.A.M. and W.L. The manuscript was written by

J.K., W.L., E.A.M., S.R. and S.H. The sample was grown and processed by S.R., C.K., C.S., M.S., S.H. and A.F. CORRESPONDING AUTHORS Correspondence to J. Kasprzak or W. Langbein. ETHICS

DECLARATIONS COMPETING INTERESTS The authors declare no competing financial interests. SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION Supplementary Information (PDF 1183 kb) RIGHTS AND

PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Kasprzak, J., Reitzenstein, S., Muljarov, E. _et al._ Up on the Jaynes–Cummings ladder of a quantum-dot/microcavity

system. _Nature Mater_ 9, 304–308 (2010). https://doi.org/10.1038/nmat2717 Download citation * Received: 11 September 2009 * Accepted: 29 January 2010 * Published: 07 March 2010 * Issue

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