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arXiv:1509.01159

Inelastic Confinement-Induced Resonances in Quantum Dots

Maria Troppenz, Simon Sala, Philipp‐Immanuel Schneider, Alejandro Sáenz

Published Sep 3, 2015• 1 citation
arXivHTMLPDF

Abstract

Recently, it was shown that the coupling of center-of-mass and relative motion in atomic systems leads to inelastic confinement-induced resonances (ICIRs) [Phys. Rev. Lett. 109, 073201 (2012)]. In the present work, the possible occurrence of ICIRs in quantum dots is investigated. Particularly, electron-hole and electron-electron two-body systems with long-range Coulomb interaction are considered using the material parameters of GaAs. ICIRs are identified for the electron-hole system verifying the universal nature of the ICIR and, additionally, resonances due to the coupling of center-of-mass and relative motion are found also for the electron-electron system. In analogy to the coherent molecule formation appearing at ICIR in atomic systems a significant change in the mean distance between electrons and holes at the resonance is observed. By using the redistribution of the particle densities at the resonance position in modern quantum-dot experiments, the ICIR can provide a new technique for the control of the electron distribution in quantum dots and for the generation of single photons on demand.

DOI
10.48550/arxiv.1509.01159

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Recently, it was shown that the coupling of center-of-mass and relative motion in atomic systems leads to inelastic confinement-induced resonances (ICIRs) [Phys. Rev. Lett. 109, 073201 (2012)]. In the present work, the possible occurrence of ICIRs in quantum dots is investigated. Particularly, electron-hole and electron-electron two-body systems with long-range Coulomb interaction are considered using the material parameters of GaAs. ICIRs are identified for the electron-hole system verifying the universal nature of the ICIR and, additionally, resonances due to the coupling of center-of-mass and relative motion are found also for the electron-electron system. In analogy to the coherent molecule formation appearing at ICIR in atomic systems a significant change in the mean distance between electrons and holes at the resonance is observed. By using the redistribution of the particle densities at the resonance position in modern quantum-dot experiments, the ICIR can provide a new technique for the control of the electron distribution in quantum dots and for the generation of single photons on demand.
A theoretical model is presented describing the confinement-induced resonances observed in the recent loss experiment of Haller et al. [Phys. Rev. Lett. 104, 153203 (2010)]. These resonances originate from possible molecule formation due to the coupling of center-of-mass and relative motion. A corresponding model is verified by ab initio calculations and predicts the resonance positions in 1D as well as in 2D confinement in agreement with the experiment. This resolves the contradiction of the experimental observations to previous theoretical predictions.
Introduction Quantum optics provides a complete description of the resonant interaction of light and a material system. The light scattered as a result of this interaction – the resonance fluorescence – provides a means to monitor and affect the material system's dynamics and also allows for the generation of nonclassical states of the electromagnetic field. Initial theoretical studies characterizing resonance fluorescence addressed fundamental questions regarding the necessity of quantizing the electromagnetic field. This is a particularly illustrative period in optical physics where multiple theories existed that might describe resonance fluorescence – semi-classical optical Bloch equations [1, 2] or quantum electrodynamics [4, 3] – and experimental evidence was necessary to identify the appropriate theoretical framework. Indeed, experiments in 1974 and 1977 investigating the resonance fluorescence lineshape [5, 6] and the photon statistics of the scattered light [7] vindicated the full quantum electrodynamical description of light-matter interaction over other models. In the subsequent 30 years, resonance fluorescence has been used as a high-resolution spectroscopic probe of a variety of physical systems, as a means to investigate quantum coherence in atomic gases and, with the current interest in quantum information science (QIS), as a tool for quantum-state preparation, measurement and control in trapped ions [8]. During this same time period, advances in material science have ushered in an era where it is possible to grow and fabricate solid-state devices at length scales commensurate with the quantum confinement of electrons and holes. It is only recently that resonance fluorescence has been observed from the prototypical artificial nanostructure exhibiting three-dimensional quantum confinement – a single semiconductor quantum dot (QD) [9].
We study confined scattering of a quantum particle by two centers fixed on the longitudinal axis of a harmonic-waveguide-like trap. The conditions of confinement-induced resonances (CIRs) appearing in these systems, when scattering cross section approaches the unitary limit, are derived for a regularized pseudopotential describing particle interaction with scattering centers. In the limit of a single center, the position of CIR for an even state tends to the well-known result obtained by Olshanii [Phys. Rev. Lett. 81, 938 (1998)]. Our result can be applicable to confined atomic scattering by fixed impurities, such as ions or Rydberg atoms, with possible extension to NNN impurities, or by two-atomic molecules.
We investigate the indistinguishability of single photons generated from strain-free GaAs/AlGaAs quantum dots using pulsed resonance fluorescence techniques. In pulsed two-photon interference measurements we observe a single photon indistinguishability with a raw visibility of 95%. This can be traced back to the short intrinsic lifetime of excitons and trions confined in the GaAs quantum dots and demonstrates that for this material system the generation of single photons is possible with near-unity indistinguishability even without Purcell enhancement.
The discussions in the previous chapters show that already the spontaneous emission, i.e., the simplest manifestation of the quantum-optical fluctuations, exhibits highly nontrivial features as soon as the quantum light is coupled to interacting many-body systems. We have seen, for example, that pronounced resonances in the semiconductor luminescence originate from a nontrivial mixture of exciton and plasma contributions in contrast to the simple transitions between the eigenstates of isolated atomic systems. As a consequence of the conservation laws inherent to the light–matter coupling, the photon emission induces rearrangements in the entire many-body system leading, e.g., to pronounced hole burning in the exciton distribution. As discussed in Chapter 29, this depletion of the optically active excitons leads to a reduction of the total radiative recombination and the appearance of nonthermal luminescence even when the electron–hole system is in quasiequilibrium. Already these observations show that the coupled quantum-optical and many-body interactions induce new intriguing phenomena that are not explainable by the concepts of traditional quantum optics or classical semiconductor physics alone. The foundations of quantum optics are based on systematic investigations of simple systems interacting with few quantized light modes. In this context, one can evaluate and even measure the exact eigenstates or the density matrix with respect to both the photonic and the atomic degrees of freedom. In semiconductor systems, currently the investigations using one or a few quantum dots (QD) are closest to the atomic studies because, due to their discrete eigenstates, one can treat strongly confined quantum dots to some extent like artificial atoms.