Injection Locking of Quantum-Dot Microlasers Operating in the Few-Photon Regime

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Injection Locking of Quantum-Dot Microlasers Operating in the Few-Photon Regime

Elisabeth Schlottmann, Steffen Holzinger, Benjamin Lingnau, Kathy Lüdge, Christian Schneider, Martin Kamp, Sven Höfling, Janik Wolters, and Stephan Reitzenstein

Phys. Rev. Applied 6, 044023 – Published 31 October 2016

Abstract

We experimentally and theoretically investigate injection locking of quantum-dot microlasers in the regime of cavity quantum electrodynamics. We observe frequency locking and phase locking where cavity-enhanced spontaneous emission enables simultaneous stable oscillation at the master frequency and at the solitary frequency of the slave microlaser. Measurements of the second-order autocorrelation function prove this simultaneous presence of both master and slavelike emission, where the former has coherent character with $g^{(2)} (0) = 1$ , while the latter has thermal character with $g^{(2)} (0) = 2$ . Semiclassical rate equations explain this peculiar behavior by cavity-enhanced spontaneous emission and a low number of photons in the laser mode.

Received 11 April 2016

DOI:https://doi.org/10.1103/PhysRevApplied.6.044023

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics Control & applications of chaos Optical & microwave phenomena Photonics

VCSELs

Condensed Matter, Materials & Applied PhysicsNonlinear Dynamics

Authors & Affiliations

Elisabeth Schlottmann^1,*, Steffen Holzinger¹, Benjamin Lingnau², Kathy Lüdge², Christian Schneider³, Martin Kamp³, Sven Höfling^3,4, Janik Wolters^1,*, and Stephan Reitzenstein¹

¹Institut für Festkörperphysik, Quantum Devices Group, Technische Universität Berlin, Hardenbergstraße 36, EW 5-3, 10623 Berlin, Germany
²Institut für Theoretische Physik, AG Nichtlineare Laserdynamik, Technische Universität Berlin, Hardenbergstraße 36, EW 7-1, 10623 Berlin, Germany
³Technische Physik, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
⁴SUPA, School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS, United Kingdom

^*janik.wolters@tu-berlin.de

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Vol. 6, Iss. 4 — October 2016

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Images

Figure 1
The microlaser and its optical characteristics. (a) Sketch of the optical setup used in the experiments. SPCM means single photon counting module and PZT indicates a piezo moveable mirror. (b),(c) Average photon number $⟨ \hat{n} ⟩$ and linewidth $δ ν_{0}$ (FWHM) obtained from the measured output characteristics and numerical simulations, respectively, as a function of normalized current $I / I_{thr}$ . The investigated CQED microlaser exhibits $β \sim 10^{- 2}$ , while for comparison, the calculation for $β \sim 10^{- 6}$ corresponds to a conventional low- $β$ laser. (d) Calculated normalized gain $⟨ G ⟩ = 2 Z g_{0}^{2} (2 ⟨ \hat{ρ} ⟩ - 1)$ . (e) Amplitude of the phase-locked slave oscillation as a function of detuning $Δ$ between the master and slave, and injection strength $K_{eff}$ measured at high electrical current. (f) Simulation result corresponding to (e).
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Figure 2
Partial injection locking of the QD microlaser. (a) High-resolution spectra of the emission at $I = 1.6 I_{thr}$ under optical injection with $K_{eff} \sim 0.17$ for various detunings. The frequency axis is relative to the free-running slave frequency of $ν_{0} = 352 THz$ . The microlaser shows a large region of partial injection locking, where phase-locked oscillation at the master frequency $ν_{0} + Δ$ and nonlocked oscillation at the slave frequency $ν_{0}$ occur simultaneously. (b) Upper panel: Intensity of the phase-locked (masterlike) and the nonlocked (slavelike) oscillation as obtained from the measurements shown in (a). All error bars correspond to one standard deviation as obtained from fitting the data with Lorentzian curves. Lower panel: Ratio between locked and total oscillation intensity indicating that despite the comparable large injection strength, perfect locking is not achieved. (c) Numerical simulations corresponding to (b). For the used microlaser with $β \sim 2 %$ (solid lines), partial locking is reproduced, while for a conventional laser with $β = 0$ (dashed lines), complete locking is predicted.
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Figure 3
Signatures of partial injection locking in the time domain. (a) Time-dependent second-order autocorrelation measurements for $Δ = - 1.45 GHz$ (top) and $Δ = - 0.88 GHz$ (bottom). Both show an exponentially decaying oscillatory behavior caused by the beat note between the simultaneously present spectrally narrow locked and the spectrally broad nonlocked oscillation modes. (b) Frequency-selective measured photon statistics of the locked and nonlocked emission, with absolute value of $Δ$ comparable to the lower panel in (a). The latter one undergoes a transition from coherent to thermal emission $g^{(2)} (0) = 2$ with increasing injection strength $K_{eff}$ . Solid lines are numerical simulations.
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Figure 4
Mode intensities and gain under variation of the injection strength with $Δ = 500 MHz$ . (a) High-resolution emission spectra of the CQED microlaser at $I = 1.4 I_{thr}$ under optical injection. Locked oscillation at frequency $ν_{0} + Δ$ and nonlocked oscillation near frequency $ν_{0}$ is visible within a large range of $K_{eff}$ values. (b) Intensity of locked (red) and nonlocked (yellow) oscillation for varying $K_{eff}$ . Dots are measured values extracted from (a), while solid lines correspond to numerical simulations of the device. (c) Contribution of the locked emission to the overall emission $⟨ {\hat{n}}_{lock} ⟩ / ⟨ {\hat{n}}_{tot} ⟩$ for various $β \sim 1 - 10^{- 4}$ corresponding to $⟨ {\hat{n}}_{0} ⟩ \sim 5 - 7000$ . Dark blue squares correspond to the measurement shown in (b). (d) Calculated gain $⟨ G ⟩$ as a function of $K_{eff}$ corresponding to the $β$ values in (c).
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