High Resolution Coherent Population Trapping on a Single Hole Spin in a Semiconductor Quantum Dot

Julien Houel, Jonathan H. Prechtel, Andreas V. Kuhlmann, Daniel Brunner, Christopher E. Kuklewicz, Brian D. Gerardot, Nick G. Stoltz, Pierre M. Petroff, and Richard J. Warburton

Phys. Rev. Lett. 112, 107401 – Published 12 March 2014

Abstract

We report high resolution coherent population trapping on a single hole spin in a semiconductor quantum dot. The absorption dip signifying the formation of a dark state exhibits an atomic physicslike dip width of just 10 MHz. We observe fluctuations in the absolute frequency of the absorption dip, evidence of very slow spin dephasing. We identify the cause of this process as charge noise by, first, demonstrating that the hole spin $g$ factor in this configuration (in-plane magnetic field) is strongly dependent on the vertical electric field, and second, by characterizing the charge noise through its effects on the optical transition frequency. An important conclusion is that charge noise is an important hole spin dephasing process.

Received 8 July 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.107401

Authors & Affiliations

Julien Houel^1,5, Jonathan H. Prechtel^1,*, Andreas V. Kuhlmann¹, Daniel Brunner², Christopher E. Kuklewicz³, Brian D. Gerardot³, Nick G. Stoltz⁴, Pierre M. Petroff⁴, and Richard J. Warburton¹

¹Department of Physics, University of Basel, Klingelbergstrasse 82, CH 4056 Basel, Switzerland
²Instituto de Fisica Interdisciplinar y Sistemas Complejos, IFISC (UIB-CSIC), Campus Universitat de les Illes Balears, Palma de Mallorca E-07122, Spain
³SUPA, Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
⁴Materials Department, University of California, Santa Barbara, California 93106, USA
⁵Institut Lumière Matière (ILM), UMR5306 Université Lyon 1/CNRS, Université de Lyon, 69622 Villeurbanne Cedex, France

^*jonathan.prechtel@unibas.ch;http://nano-photonics.unibas.ch/

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Vol. 112, Iss. 10 — 14 March 2014

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Figure 1
(a) Layer sequence of the semiconductor heterostructure. The tunnel barrier is 25 nm, capping layer 10 nm and short-period superlattice 120 nm. Postgrowth, Ohmic contacts along with a semitransparent surface gate electrode are fabricated. (b) Schematic of the optical setup.
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Figure 2
Probe absorption in the presence of a close-to-resonant pump laser on a single InGaAs quantum dot containing a single hole spin at $B = 0.5 T$ and $T = 4.2 K$ , 10 s integration per point. The absorption (here, differential reflectivity $Δ R / R$ ) shows an absorption dip signifying coherent population trapping. The solid line shows the result of a 3-level density matrix model ( $ℏ Ω_{1} = 0.17$ , $ℏ Ω_{2} = 0.35$ , $ℏ δ_{2} = - 2.5 μ eV$ , $ℏ / τ_{r} = 0.8 μ eV$ , $T_{2} \geq 1 μ s$ , $T_{1} ≫ T_{2}$ ) convoluted with a Lorentzian with FWHM $Γ_{X} = 5 μ eV$ (1.22 GHz) to describe slow exciton dephasing, and then with a Lorentzian with FWHM 8.3 neV (2.0 MHz) to account for the mutual coherence of the lasers.
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Figure 3
(a) Probe absorption versus probe detuning on the same quantum dot as Fig. 2 in the regime $ℏ Ω_{2} ≫ ℏ / τ_{r}$ showing an Autler-Townes splitting. The solid curve is a fit to the data, $ℏ Ω_{2} = 4.7 μ eV$ , $ℏ δ_{2} = 0.0 μ eV$ , as fit parameters. $Γ_{X} = 7.5 μ eV$ is taken from $Δ R / R$ at $B = 0$ . (b) Probe absorption versus probe detuning on the same quantum dot in the regime $ℏ Ω_{2} ≪ ℏ / τ_{r}$ . Three curves are shown under close-to-identical conditions showing a shift in the location of the dip in one case by 4 MHz (17 neV), and in another case by 23 MHz (95 neV).
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Figure 4
(a) The quantum states of a single hole spin in an in-plane magnetic field. $↑$ , $↓$ denotes an electron spin, $⇑$ , $⇓$ a hole spin. (b) Photoluminescence on a single InGaAs quantum dot (different quantum dot from Figs. 2 and 3 but from the same wafer) at $B = 9.0 T$ and $T = 4.2 K$ as a function of $V_{g}$ over the extent of the single hole Coulomb blockade plateau. Four transitions are visible, labeled 1–4, and identified in (a). The width of each peak is determined by the spectrometer detector (system resolution $50 μ eV$ ). The apparent steps are an artifact arising from the pixelated detector. (c) Electron and hole $g$ factors, $g_{e}$ and $g_{h}$ , versus $V_{g}$ . $V_{g}$ is converted into vertical electric field $F$ with $F = - e (V_{g} + V_{o}) / D$ with $D = 155 nm$ and Schottky barrier $V_{o} = 0.62 V$ . Under the assumption of a negative $g_{e}$ , $g_{h}$ is positive. The error on each point is $\sim 2 μ eV$ using a routine which corrects for the detector pixelation.
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