Coherent coupling of individual quantum dots measured with phase-referenced two-dimensional spectroscopy: Photon echo versus double quantum coherence

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Coherent coupling of individual quantum dots measured with phase-referenced two-dimensional spectroscopy: Photon echo versus double quantum coherence

Valentin Delmonte, Judith F. Specht, Tomasz Jakubczyk, Sven Höfling, Martin Kamp, Christian Schneider, Wolfgang Langbein, Gilles Nogues, Marten Richter, and Jacek Kasprzak

Phys. Rev. B 96, 041124(R) – Published 26 July 2017

Abstract

We employ two-dimensional (2D) coherent, nonlinear spectroscopy to investigate couplings within individual InAs quantum dots (QDs) and QD molecules. Swapping pulse ordering in a two-beam sequence permits one to distinguish between rephasing and nonrephasing four-wave mixing (FWM) configurations. We emphasize the nonrephasing case, allowing one to monitor two-photon coherence dynamics. Respective Fourier transform yields a double quantum 2D FWM map, which is corroborated with its single quantum counterpart, originating from the rephasing sequence. We introduce referencing of the FWM phase with the one carried by the driving pulses, overcoming the necessity of its active stabilization, as required in 2D spectroscopy. Combining single and double quantum 2D FWM provides a pertinent tool in detecting and ascertaining coherent coupling mechanisms between individual quantum systems, as exemplified experimentally.

Received 9 March 2017

DOI:https://doi.org/10.1103/PhysRevB.96.041124

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International 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)

Excitons Optical coherence Optical transient phenomena Photonics

III-V semiconductors Quantum dots Semiconductor microcavities

Four-wave mixing Homodyne & heterodyne detection Optical microscopy

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Valentin Delmonte^1,2, Judith F. Specht³, Tomasz Jakubczyk^1,2, Sven Höfling^4,5, Martin Kamp⁴, Christian Schneider⁴, Wolfgang Langbein⁶, Gilles Nogues^1,2, Marten Richter³, and Jacek Kasprzak^1,2,*

¹Université Grenoble Alpes, F-38000 Grenoble, France
²CNRS, Institut Néel, “Nanophysique et Semiconducteurs” Group, F-38000 Grenoble, France
³Institut für Theoretische Physik, Nichtlineare Optik und Quantenelektronik, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
⁴Technische Physik, University of Würzburg, Würzburg 97074, Germany
⁵SUPA, School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS, United Kingdom
⁶School of Physics and Astronomy, Cardiff University, The Parade, Cardiff CF24 3AA, United Kingdom

^*jacek.kasprzak@neel.cnrs.fr

Article Text

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Supplemental Material

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References

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Issue

Vol. 96, Iss. 4 — 15 July 2017

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Images

Figure 1
Rephasing and nonrephasing pathways in two-beam four-wave mixing of individual quantum dots. (a) Two possible pulse sequences in the so-called positive (negative) delays $τ_{12}$ , corresponding to the rephasing (nonrephasing) FWM pathways. The nonrephasing pathway involves a two-photon coherence between the ground state ( $G$ ) and a two-particle state, here, a quantum dot biexciton ( $B$ ). (b) Measured FWM amplitude as a function of $τ_{12}$ on a few InAs QDs embedded in a low- $Q$ microcavity. Impinging $E_{1}, E_{2}$ intensities of $(150, 600) nW$ correspond to pulse areas of around $(0.4 π, 0.8 π)$ , significantly beyond the $χ^{(3)}$ limit, generating a pronounced exciton-biexciton beating.
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Figure 2
Photon-echo formation on a single QD exciton measured upon a FWM rephasing pathway. The delay $τ_{R 2}$ , between the reference $E_{R}$ and $E_{2}$ , is scanned for different values of $τ_{12}$ , as indicated. Formation of the photon echo is observed: A Gaussian form of the FWM transient is fully recovered for $τ_{12} > ℏ / σ$ . Temporal width of the echo yields the inhomogeneous broadening $σ$ . Inset: By adjusting $τ_{R 2}$ , one shifts the temporal detection window towards the echo, such that the FWM signal can be retrieved via spectral interference even for delays exceeding the temporal resolution of the setup, defined by the spectrometer. This is here exemplified for $τ_{12} = 1 ns$ and $τ_{R 2} = - 0.85 ns$ .
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Figure 3
Coherent dynamics of an exciton-biexciton system measured at the nonrephasing FWM configuration, $τ_{12} < 0$ . (a), (b) Time-resolved FWM transient measured at $G X_{1}$ and $X_{1} B_{1}$ for negative delays. Due to the nonrephasing configuration, the FWM decay becomes more pronounced when increasing delay. (c), (d) Two-photon coherence dynamics, induced between $G$ and $B$ (also known as a biexciton coherence), measured at the nonrephasing FWM configuration. The two-photon dephasing time is retrieved from the exponential decay of $G X_{1}$ and $X_{1} B_{1}$ transitions.
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Figure 4
Two-dimensional FWM spectroscopy of exciton complexes in a few InAs QDs probed along the (a) rephasing and (b) nonrephasing pathways. Four exciton-biexciton systems in different QDs are indicated dashed-dotted, dotted, dashed, and solid lines, respectively.
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Figure 5
Quantum dot molecule, consisting of two electrostatically coupled InAs QDs, observed in single and double quantum 2D FWM. Measured (a) rephasing and (c) nonrephasing 2D FWM spectra revealing coherent couplings between two QDs. Corresponding simulations (see Sec. I C of the Supplemental Material [36] for details regarding the model parameters) are shown in (b) and (d). The signatures belonging to this QD molecule are marked by dashed lines. An additional exciton-biexciton pair in (a) and (c) at $(1360.3, 1356.8) meV$ occurs in other QDs not involved in the molecule formation, thus not included in the calculated spectra.
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