Abstract

While the advanced coherent control of qubits is now routinely carried out in low-frequency (gigahertz) systems like single spins, it is far more challenging to achieve for two-level systems in the optical domain. This is because the latter evolve typically in the terahertz range, calling for tools of ultrafast, coherent, nonlinear optics. Using four-wave mixing microspectroscopy, we here measure the optically driven dynamics of a single exciton quantum state confined in a semiconductor quantum dot. In a combined experimental and theoretical approach, we reveal the intrinsic Rabi oscillation dynamics by monitoring both central exciton quantities, i.e., its occupation and the microscopic coherence, as resolved by the four-wave mixing technique. In the frequency domain, this oscillation generates the Autler–Townes splitting of the light-exciton dressed states, directly seen in the four-wave mixing spectra. We further demonstrate that the coupling to acoustic phonons strongly influences the four-wave mixing dynamics on the picosecond time scale, because it leads to transitions between the dressed states.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (2)

X. Mi, M. Benito, S. Putz, D. M. Zajac, J. M. Taylor, G. Burkard, and J. R. Petta, “A coherent spin-photon interface in silicon,” Nature 555, 599–603 (2018).
[Crossref]

T. Suzuki, R. Singh, M. Bayer, A. Ludwig, A. D. Wieck, and S. T. Cundiff, “Detuning dependence of Rabi oscillations in an InAs self-assembled quantum dot ensemble,” Phys. Rev. B 97, 161301 (2018).
[Crossref]

2017 (7)

D. Wigger, Q. Mermillod, T. Jakubczyk, F. Fras, S. Le-Denmat, D. E. Reiter, S. Höfling, M. Kamp, G. Nogues, C. Schneider, T. Kuhn, and J. Kapsrzak, “Exploring coherence of individual excitons in InAs quantum dots embedded in natural photonic defects: influence of the excitation intensity,” Phys. Rev. B 96, 165311 (2017).
[Crossref]

S. V. Poltavtsev, M. Reichelt, I. A. Akimov, G. Karczewski, M. Wiater, T. Wojtowicz, D. R. Yakovlev, T. Meier, and M. Bayer, “Damping of Rabi oscillations in intensity-dependent photon echoes from exciton complexes in a CdTe/(Cd, Mg) Te single quantum well,” Phys. Rev. B 96, 075306 (2017).
[Crossref]

Y. Zhou, A. Rasmita, K. Li, Q. Xiong, I. Aharonovich, and W. Gao, “Coherent control of a strongly driven silicon vacancy optical transition in diamond,” Nat. Commun. 8, 14451 (2017).
[Crossref]

T. Kaldewey, S. Lüker, A. V. Kuhlmann, S. R. Valentin, A. Ludwig, A. D. Wieck, D. E. Reiter, T. Kuhn, and R. J. Warburton, “Coherent and robust high-fidelity generation of a biexciton in a quantum dot by rapid adiabatic passage,” Phys. Rev. B 95, 161302 (2017).
[Crossref]

T. Kaldewey, S. Lüker, A. V. Kuhlmann, S. R. Valentin, J.-M. Chauveau, A. Ludwig, A. D. Wieck, D. E. Reiter, T. Kuhn, and R. J. Warburton, “Demonstrating the decoupling regime of the electron-phonon interaction in a quantum dot using chirped optical excitation,” Phys. Rev. B 95, 241306 (2017).
[Crossref]

B. Lomsadze and S. T. Cundiff, “Frequency combs enable rapid and high-resolution multidimensional coherent spectroscopy,” Science 357, 1389–1391 (2017).
[Crossref]

S. Lüker, T. Kuhn, and D. E. Reiter, “Phonon impact on optical control schemes of quantum dots: role of quantum dot geometry and symmetry,” Phys. Rev. B 96, 245306 (2017).
[Crossref]

2016 (4)

T. Jakubczyk, V. Delmonte, S. Fischbach, D. Wigger, D. E. Reiter, Q. Mermillod, P. Schnauber, A. Kaganskiy, J.-H. Schulze, A. Strittmatter, S. Rodt, W. Langbein, T. Kuhn, S. Reitzenstein, and J. Kasprzak, “Impact of phonons on dephasing of individual excitons in deterministic quantum dot microlenses,” ACS Photon. 3, 2461–2466 (2016).
[Crossref]

F. Fras, Q. Mermillod, G. Nogues, C. Hoarau, C. Schneider, M. Kamp, S. Höfling, W. Langbein, and J. Kasprzak, “Multi-wave coherent control of a solid state single emitter,” Nat. Photonics 10, 155–158 (2016).
[Crossref]

Q. Mermillod, D. Wigger, V. Delmonte, D. E. Reiter, C. Schneider, M. Kamp, S. Höfling, W. Langbein, T. Kuhn, G. Nogues, and J. Kasprzak, “Dynamics of excitons in individual InAs quantum dots revealed in four-wave mixing spectroscopy,” Optica 3, 377–384 (2016).
[Crossref]

A. M. Barth, S. Lüker, A. Vagov, D. E. Reiter, T. Kuhn, and V. M. Axt, “Fast and selective phonon-assisted state preparation of a quantum dot by adiabatic undressing,” Phys. Rev. B 94, 045306 (2016).
[Crossref]

2015 (3)

W. B. Gao, A. Imamoglu, H. Bernien, and R. Hanson, “Coherent manipulation, measurement and entanglement of individual solid-state spins using optical fields,” Nat. Photonics 9, 363–373 (2015).
[Crossref]

J. H. Quilter, A. J. Brash, F. Liu, M. Glässl, A. M. Barth, V. M. Axt, A. J. Ramsay, M. S. Skolnick, and A. M. Fox, “Phonon-assisted population inversion of a single InGaAs/GaAs quantum dot by pulsed laser excitation,” Phys. Rev. Lett. 114, 137401 (2015).
[Crossref]

S. Bounouar, M. Müller, A. M. Barth, M. Glässl, V. M. Axt, and P. Michler, “Phonon-assisted robust and deterministic two-photon biexciton preparation in a quantum dot,” Phys. Rev. B 91, 161302 (2015).
[Crossref]

2014 (3)

P.-L. Ardelt, L. Hanschke, K. A. Fischer, K. Müller, A. Kleinkauf, M. Koller, A. Bechtold, T. Simmet, J. Wierzbowski, H. Riedl, G. Abstreiter, and J. J. Finley, “Dissipative preparation of the exciton and biexciton in self-assembled quantum dots on picosecond time scales,” Phys. Rev. B 90, 241404 (2014).
[Crossref]

D. Wigger, S. Lüker, D. E. Reiter, V. M. Axt, P. Machnikowski, and T. Kuhn, “Energy transport and coherence properties of acoustic phonons generated by optical excitation of a quantum dot,” J. Phys. Condens. Matter 26, 355802 (2014).
[Crossref]

A. Capua, O. Karni, G. Eisenstein, and J. P. Reithmaier, “Rabi oscillations in a room-temperature quantum dash semiconductor optical amplifier,” Phys. Rev. B 90, 045305 (2014).
[Crossref]

2013 (7)

O. Karni, A. Capua, G. Eisenstein, V. Sichkovskyi, V. Ivanov, and J. P. Reithmaier, “Rabi oscillations and self-induced transparency in InAs/InP quantum dot semiconductor optical amplifier operating at room temperature,” Opt. Express 21, 26786–26796 (2013).
[Crossref]

G. Moody, R. Singh, H. Li, I. A. Akimov, M. Bayer, D. Reuter, A. D. Wieck, A. S. Bracker, D. Gammon, and S. T. Cundiff, “Influence of confinement on biexciton binding in semiconductor quantum dot ensembles measured with two-dimensional spectroscopy,” Phys. Rev. B 87, 041304 (2013).
[Crossref]

S. T. Cundiff and S. Mukamel, “Optical multidimensional coherent spectroscopy,” Phys. Today 66(7), 44–49 (2013).
[Crossref]

D. Wigger, D. E. Reiter, V. M. Axt, and T. Kuhn, “Fluctuation properties of acoustic phonons generated by ultrafast optical excitation of a quantum dot,” Phys. Rev. B 87, 085301 (2013).
[Crossref]

J. Kasprzak, S. Portolan, A. Rastelli, L. Wang, J. D. Plumhof, O. G. Schmidt, and W. Langbein, “Vectorial nonlinear coherent response of a strongly confined exciton-biexciton system,” New J. Phys. 15, 055006 (2013).
[Crossref]

J. R. Schaibley, A. P. Burgers, G. A. McCracken, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Direct detection of time-resolved Rabi oscillations in a single quantum dot via resonance fluorescence,” Phys. Rev. B 87, 115311 (2013).
[Crossref]

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Schöll, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref]

2011 (5)

Y. Wu, I. M. Piper, M. Ediger, P. Brereton, E. R. Schmidgall, P. R. Eastham, M. Hugues, M. Hopkinson, and R. T. Phillips, “Population inversion in a single InGaAs quantum dot using the method of adiabatic rapid passage,” Phys. Rev. Lett. 106, 067401 (2011).
[Crossref]

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Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1. Schematic picture of the experiment and the theory. (a) Experimental setup. AOMs label the excitation pulses with radio frequencies Ωi. The signal beam after the sample is mixed in an AOM with the reference beam into channels A and B to generate the stationary spectral interference at the CCD camera. FWM is detected background free by subtracting A and B. Note that the actual experiment is working in reflection from the sample. To keep the picture as simple as possible, the figure shows transmission geometry. (b), (c) Schematic picture of the theoretical simulation of the exciton state on the Bloch sphere. After each pulse with pulse area θi the state is filtered with respect to phase factor ϕi corresponding to the final FWM phase ϕFWM. (b) For two-pulse FWM where τ12 is scanned and (c) for three-pulse FWM where τ23 changes.
Fig. 2.
Fig. 2. Normalized two-pulse FWM generated with subps pulses on a QD exciton embedded in a low-Q cavity. (a), (b) FWM amplitude as a function of the delay τ12 for increasing pulse area of the first pulse from bottom to top. The FWM delay dependence probes the optically driven evolution of the exciton polarization, performing Rabi oscillations for excitations with high pulse areas. (a) Experiment, the P1 impinging the sample surface are (0.14,1.1,2.3,2.7)  μW, P2=1  μW, temperature T=23  K. The dots indicate the noise level. (b) Theory, solid lines with phonon coupling dotted lines without phonons. θ1 as given in the plot. The circles mark maxima of the FWM signal. (c), (d) Schematic pictures of the FWM signal on the Bloch sphere; (c) for small pulse areas θ1; (d) for pulse areas θ1 exceeding π.
Fig. 3.
Fig. 3. Micropillar cavity system. (a) Scanning electron microscopy image of an exemplary micropillar cavity system with a diameter of 1.8 μm and a height around 10 μm; (b) FWM spectra for varying temperatures, demonstrating operation in the weak coupling regime: exciton and cavity resonances shift in energy and cross at T27  K; (c) schematic picture of the driving laser pulses and the measured FWM dynamics. The effective pulse duration τ is increased by a factor of 30 inside the cavity. Green trace is the measured time-resolved FWM field (vertical logarithmic scale), illustrating its buildup owing to the high Q factor.
Fig. 4.
Fig. 4. Normalized two-pulse FWM with τ12  ps pulses in a micropillar cavity. (a), (b) FWM amplitude as a function of the delay τ12 for increasing pulse area of the first pulse from bottom to top. (a) Experiment, P1=(0.02,0.24,0.35,0.55)  μW, P2=0.08  μW; (b) theory, with θ1 as given in the plot and θ2=π; solid/dotted lines with/without coupling to phonons; (c), (d) FWM spectral amplitudes as a function of excitation power for τ12=0 illustrating emergence of the AT splitting with increasing θ1. Experiment in (c) against P1 and theory in (d) against θ1.
Fig. 5.
Fig. 5. Normalized three-pulse FWM with τ12  ps pulses in a micropillar cavity. (a), (b) Schematic pictures of the FWM signal on the Bloch sphere. (a) For small pulse areas θ2; (b) for pulse areas θ2 exceeding π; solid/dotted lines with/without coupling to phonons; (c), (d) FWM amplitude as function of the delay τ23 for increasing pulse area of the second pulse from bottom to top. The FWM delay dependence probes the optically driven evolution of the exciton occupation, performing Rabi oscillations for excitations with high pulse areas. (c) Experiment, T=27  K, τ12=10  ps, P1=0.05  μW, P3=0.1  μW, P2=(0.13,0.3,0.56,1)  μW; (d) theory, with θ1=0.2π, θ3=0.4π and θ2 as given in the plot.
Fig. 6.
Fig. 6. Entire complex FWM signal. Real and imaginary part of the FWM signal SFWM. The delays are color-coded; the dotted lines show simulations without phonon coupling, and the solid lines with phonon coupling. (a), (b) For two-pulse FWM. The corresponding dynamics of the FWM amplitude are given in Fig. 4(b). (c), (d) For three-pulse FWM. The corresponding dynamics of the FWM amplitude is given in Fig. 5(d).

Equations (1)

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Ei(t)=22πθiμτexp[12(ttiτ)2iωLt+iϕi],