Coherent Polariton Laser

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Coherent Polariton Laser

Seonghoon Kim, Bo Zhang, Zhaorong Wang, Julian Fischer, Sebastian Brodbeck, Martin Kamp, Christian Schneider, Sven Höfling, and Hui Deng

Phys. Rev. X 6, 011026 – Published 11 March 2016

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Abstract

The semiconductor polariton laser promises a new source of coherent light, which, compared to conventional semiconductor photon lasers, has input-energy threshold orders of magnitude lower. However, intensity stability, a defining feature of a coherent state, has remained poor. Intensity noise many times the shot noise of a coherent state has persisted, attributed to multiple mechanisms that are difficult to separate in conventional polariton systems. The large intensity noise, in turn, limits the phase coherence. Thus, the capability of the polariton laser as a source of coherence light is limited. Here, we demonstrate a polariton laser with shot-noise-limited intensity stability, as expected from a fully coherent state. This stability is achieved by using an optical cavity with high mode selectivity to enforce single-mode lasing, suppress condensate depletion, and establish gain saturation. Moreover, the absence of spurious intensity fluctuations enables the measurement of a transition from exponential to Gaussian decay of the phase coherence of the polariton laser. It suggests large self-interaction energies in the polariton condensate, exceeding the laser bandwidth. Such strong interactions are unique to matter-wave lasers and important for nonlinear polariton devices. The results will guide future development of polariton lasers and nonlinear polariton devices.

Received 25 July 2015

DOI:https://doi.org/10.1103/PhysRevX.6.011026

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Laser-system design Lasers Polaritons Semiconductor lasers

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Focus

Polariton Laser Upgrade

Published 11 March 2016

The emission from a polariton laser shows the coherence that is common to conventional lasers, a step toward using them as high-efficiency alternative light sources.

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Authors & Affiliations

Seonghoon Kim¹, Bo Zhang², Zhaorong Wang¹, Julian Fischer³, Sebastian Brodbeck³, Martin Kamp³, Christian Schneider³, Sven Höfling^3,4, and Hui Deng^2,*

¹Department of Electrical Engineering and Computer Science, University of Michigan, 1301 Beal Avenue, Ann Arbor, Michigan 48109-2122, USA
²Department of Physics, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109-1040, USA
³Technische Physik, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
⁴SUPA, School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS, United Kingdom

^*Corresponding author. dengh@umich.edu

Popular Summary

Semiconductor polaritons are half-light, half-matter particles formed in a high-quality optical cavity. They can condense into their ground state via a thermodynamic phase transition and form a coherent matter wave, and they can produce coherent light emission known as polariton lasing. Polariton lasers do not require electronic population inversion, and they therefore hold promise as a new source of coherent light with energy thresholds orders of magnitude lower than those of traditional semiconductor lasers. However, intensity stability and phase coherence, the defining properties of laser light, have been poor in polariton systems, which will limit the utility of polariton lasers. It has remained unclear whether such properties are intrinsic to polariton lasers. Here, using an optical cavity with high-mode selectivity, we achieve a polariton laser with full intensity stability and, based on its phase coherence properties, confirm its matter-wave origin.

We create a single-mode polariton laser using a cavity that integrates a high-reflectance, polarization-selective mirror a few microns across in size. With this system, which we maintain at 10 degrees above absolute zero, we demonstrate polariton lasing with Poisson-intensity noise over a wide range of condensate occupancies, as expected of a fully coherent state. We also expand our analyses to multimode polariton lasers. At high occupancies, the strong condensate nonlinearity is manifested in the Gaussian decay of the intrinsic phase coherence, which is characteristic of matter-wave lasers.

This work provides the proof of principle of a polariton condensate as a matter-wave-based source of coherent light. We expect that our findings will guide the future development of polariton lasers and nonlinear polariton devices.

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Vol. 6, Iss. 1 — January - March 2016

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Images

Figure 1
The cavity system and experimental setup. (a) A schematic of the SWG-based microcavity. (b) The spectrally resolved real-space image of polariton states at a low excitation power. $E_{cav}$ is the cavity resonance, and $E_{ex}$ is the exciton resonance. $E_{cav}$ is estimated by using lower polariton, upper polariton, and exciton energies. (c) A schematic of the experimental setup. OL: objective lens; BS: beam splitter, P: polarizer; M: mirror; MC: monochromator; and APD: avalanche photodetector. For the $g^{(2)}$ measurements, a monochromator followed by two mechanical slits was used to spectrally filter the discrete polariton states. Examples are shown for the spectrally resolved real-space images of the lowest two LP states right after the monochromator (bottom), the spectrally filtered ground state (top left), and the spectrally filtered first excited state (top right). The resolution of the spectral filter was about 0.08 nm, determined by the monochromator resolution.
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Figure 2
Intensity and spectral properties of the single-mode polariton laser. (a) The occupation number vs $P / P_{th}$ for pulsed excitation. $P_{th}$ indicates the threshold for polariton lasing, and $P_{th, 2}$ indicates the threshold for photon lasing. The $\bar{n}$ is estimated from the independently measured PL intensity from the ground state, collection and detection efficiencies of the setup, and the polariton lifetime [4, 6]. (b) Energy and blueshift of the polariton ground state (dots) and lasing photon mode (squares) vs the normalized pump powers $P / P_{th}$ for pulsed excitation. Here, $P_{th}$ is the pump power at the polariton lasing threshold. The solid vertical line marks the polariton lasing threshold, and the dashed vertical line marks the photon lasing threshold. (c) The linewidth (full width at half maximum) of the polariton ground state vs $P / P_{th}$ for pulsed excitation. (d)–(f) The occupation number, blueshift, and linewidth of the polariton ground state vs $P / P_{th}$ for CW excitation. The dashed line in (f) represents the spectral resolution of the monochromator of about 0.08 nm.
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Figure 3
Second-order coherence properties of the single-mode polariton laser. (a) $\bar{g^{(2)}} (τ)$ vs $τ$ below and above the threshold for pulsed excitation. (b) $\bar{g^{(2)}} (τ)$ vs $τ$ below and above the threshold for CW excitation. (c) $\bar{g^{(2)}} (0)$ vs $P / P_{th}$ for pulsed (dots) and CW (rectangles) excitations. The error bars indicate statistical error of 1 standard deviation. The grey-shaded area shows where the polariton and photon lasing coexist. Inset: $g^{(2)} (0)$ vs $\bar{n}$ of pulsed excitation corrected for the relaxation time of the ground state [40]. The solid line shows a theoretical fit by Eq. (2), yielding $n_{s} = 37.3 \pm 0.9$ .
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Figure 4
Second-order correlations of the two-mode polariton laser. (a) The occupation numbers of the ground state (dots) and the excited state (squares) vs $P / P_{th}$ . GS: ground state; ES: first excited state. (b) $\bar{g^{(2)}} (0)$ vs $P / P_{th}$ . $\bar{g_{00}^{(2)}} (0)$ : autocorrelation of GS; $\bar{g_{11}^{(2)}} (0)$ : autocorrelation of ES; and $\bar{g_{01}^{(2)}} (0)$ : cross-correlation between GS and ES.
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Figure 5
First-order coherence properties of the single-mode polariton laser. (a) A spatial interference image of the polariton laser at zero time delay. (b) The interference fringe along $x$ axis obtained from (a) by integration along the $y$ axis. The dots are data, and the solid line is a fit by Eq, (a1) with $g^{(1)} (0) = 0.94$ (see the Appendix). (c,d) The measured $g^{(1)} (τ)$ vs $τ$ (dots), exponential fits (red solid lines), and Gaussian fits (black dashed lines), for $\bar{n} = 2.66$ and 968, respectively. (e) The phase coherence time $τ_{c}$ of the polariton laser vs $\bar{n}$ . The dots are taken from the measured $g^{(1)} (τ)$ for each value of $\bar{n}$ . The line is calculated from Eq. (3) using the fitted parameters. Inset: Comparison between the interaction energy $U$ (dots) and decay rate $γ$ (yellow-shaded region) of the condensate vs $\bar{n}$ . The error bars and thickness of the shaded area are determined by fitting errors with a 95% confidence interval. The rectangle and diamond marks represent $\bar{n} = 2.66$ and $\bar{n} = 968$ , respectively.
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