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arXiv:1511.07742 · Physical Review Letters

Signatures of Quantum Coherences in Rydberg Excitons

P. Grünwald, Marc Aßmann, Julian Heckötter, D. Fröhlich, M. Bayer, H. Stolz, Stefan Scheel

Published Sep 22, 2016• 48 citations
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Abstract

Coherent optical control of individual particles has been demonstrated both for atoms and semiconductor quantum dots. Here we demonstrate the emergence of quantum coherent effects in semiconductor Rydberg excitons in bulk Cu_{2}O. Because of the spectral proximity between two adjacent Rydberg exciton states, a single-frequency laser may pump both resonances with little dissipation from the detuning. As a consequence, additional resonances appear in the absorption spectrum that correspond to dressed states consisting of two Rydberg exciton levels coupled to the excitonic vacuum, forming a V-type three-level system, but driven only by one laser light source. We show that the level of pure dephasing in this system is extremely low. These observations are a crucial step towards coherently controlled quantum technologies in a bulk semiconductor.

DOI
10.1103/physrevlett.117.133003

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Coherent optical control of individual particles has been demonstrated both for atoms and semiconductor quantum dots. Here we demonstrate the emergence of quantum coherent effects in semiconductor Rydberg excitons in bulk Cu_{2}O. Because of the spectral proximity between two adjacent Rydberg exciton states, a single-frequency laser may pump both resonances with little dissipation from the detuning. As a consequence, additional resonances appear in the absorption spectrum that correspond to dressed states consisting of two Rydberg exciton levels coupled to the excitonic vacuum, forming a V-type three-level system, but driven only by one laser light source. We show that the level of pure dephasing in this system is extremely low. These observations are a crucial step towards coherently controlled quantum technologies in a bulk semiconductor.
Semiconductor quantum dots tightly confine excited electron-hole pairs, called excitons, resulting in discrete energy levels similar to those of single atoms. Transition energies in the visible or near-infrared make quantum dots suitable for many applications in quantum optics and quantum information science, but to take advantage of all the properties of quantum dot emission, it is necessary to excite them coherently which has been a great challenge due to background scattering of the excitation laser. This dissertation presents the first coherent control of a single quantum dot with observation of its resonance fluorescence and decoherence phenomena. Strong continuous-wave excitation causes the dot to undergo several Rabi oscillations before emitting. These are visible as oscillations in the first- and second-order correlation functions of the emission, and the quantum dot states are "dressed", resulting in a Mollow triplet in the emission spectrum. Some resonantly excited dots, in addition to resonance fluorescence, also emit light from excited states several meV higher in energy. Such up-conversion fits existing theories of decoherence but has never been directly observed before. The up-conversion intensity is shown to be described well by a fairly simple three-level model with single-phonon absorption. The coherent phenomena of resonance fluorescence and the decoherence due to up-conversion paint a dual picture of single quantum dots wherein they can sometimes be treated as an ideal two-level system, but their interactions with the host crystal can lead to many complex behaviors.
The coherent response of a semiconductor three-state system to one or two intense light pulses is investigated experimentally on a 100 fs time scale. Three experiments constitute this dissertation: observation of excitonic Rabi oscillations, measurement of two-exciton coupled Stark shifting, and an attempt to observe dark states. Basic concepts of time-resolved ultrafast semiconductor spectroscopy are explained, followed by an analysis of semiconductor two- and three-state systems. Pure two- and three-state dynamics are derived from first principles, followed by the development of the appropriate semiconductor Bloch equations (SBE). Two-color pump-probe, two-color pump-pump, and pump-pump-probe techniques are explained in the context of three-state semiconductor experiments. The experimental setup is explained in detail. Resonant two-color pump-probe measurements resulted in the first observation of multiple excitonic Rabi oscillations. The common conduction band shared by the light-hole and heavy-hole excitons of an InGaAs multiple quantum well allowed us to measure hh-exciton density (Rabi) oscillations by probing lh-exciton absorption. By studying the intensity dependence of the Rabi frequency, we showed the important role of many-body effects in renormalizing the dipole energy. The shared conduction band also causes the lh-exciton resonance to Stark shift when the hh exciton is Stark shifted. We measured a transient Stark shifting of both resonances due to virtual hh-exciton transitions. We observed that the ratio of the hh-exciton shift to lh-exciton shift was 2:1 at large pump-exciton detuning, as predicted from a simple three-state dressed exciton picture. For smaller detunings we saw an increase in the ratio and a redshift of the non-dipole coupled exciton state. Both of these observations are consistent with the most recent theories and experiments on excitonic Stark shifting. For strong near-resonant pumping of both lh- and hh-exciton transitions, an intervalence-band Raman-type coherence follows from the SBE that results in a transparent eigenstate (dark state) when both pumps are equally detuned from resonance. The existence of this coherence is well-known in atomic-optical systems, but has been elusive in semiconductors. Our inconclusive experimental result is presented along with an evaluation of experimental shortcomings. In brief, the expected change is absorption was too small to see.
Highly excited Rydberg states of excitons in Cu_{2}O semiconductors provide a promising approach to explore and control strong particle interactions in a solid-state environment. A major obstacle has been the substantial absorption background that stems from exciton-phonon coupling and lies under the Rydberg excitation spectrum, weakening the effects of exciton interactions. Here, we demonstrate that two-photon excitation of Rydberg excitons under conditions of electromagnetically induced transparency (EIT) can be used to control this background. Based on a microscopic theory that describes the known single-photon absorption spectrum, we analyze the conditions under which two-photon EIT permits separating the optical Rydberg excitation from the phonon-induced absorption background, and even suppressing it entir7ely. Our findings thereby pave the way for the exploitation of Rydberg blockade with Cu_{2}O excitons in nonlinear optics and other applications.
We report on coherent control of the resonantly driven exciton state in a single quantum dot in the strong coupling regime. With picosecond laser pulses, the two-level system undergoes Rabi oscillations and a given coherent superposition of states can be addressed. Using a pair of phase-locked pulses, optical manipulation is achieved during the coherence time of the qu-bit. The dephasing processes are also studied and we show that in typical quantum dots, the coherence time T 2 can be of the same order of magnitude as the effective lifetime of the exciton T 1 (a few hundreds of ps) although not reaching the upper theoretical limit of 2T 1 . We conclude that energy relaxation and pure dephasing processes due to virtual scattering with phonons contribute on an equal footing to the loss of coherence.
Summary form only given. In the excitonic ac Stark shift in quantum wells the excitonic absorption line is blueshifted by shining on the sample an intense laser pulse, whose frequency is lower than the exciton transition frequency. The effect is bigger when the laser spectrum approaches the resonance with the excitonic absorption. But if the laser and excitonic absorption spectra sensibly overlap, a great amount of electronic population is excited and consequently the Coulomb nonlinearities due to the interaction between excited carries or excitons dramatically increase. One prominent effect under these conditions is the excitation- induced dephasing which can destroy the coherence of the electronic system and therefore the coupling between excitons and light, which is inherently coherent. Some evidence for the resonant Stark effect was already reported, but the direct observation of the spectral splitting was still missing. This observation demonstrates that the coherent exciton light coupling in semiconductors can be strong enough to survive the fast dephasing, and that therefore an efficient ultrafast manipulation of the exciton absorption in the coherent transient is possible. In order to magnify the ac Stark effect and its visibility a special sample was designed: a single In/sub 0.04/Ga/sub 0.96/As quantum well is grown on the top of an AlAs/AlGaAs distributed Bragg reflector; two /spl lambda//2 spacers separate the quantum well from the mirror and from the air. In this configuration the light field incident on the sample and the one reflected by the mirror constructively interfere at the quantum well position, giving a high effective absorption.
The interaction of a resonant light field with a quantum two-level system is of key interest both for fundamental quantum optics and quantum technological applications employing resonant excitation. While emission under resonant continuous-wave excitation has been well studied, the more complex emission spectrum of dynamically dressed states-a quantum two-level system driven by resonant pulsed excitation-has so far been investigated in detail only theoretically. Here, we present the first experimental observation of the complete resonance fluorescence emission spectrum of a single quantum two-level system, in the form of an excitonic transition in a semiconductor quantum dot, driven by finite Gaussian pulses. We observe multiple emerging sidebands as predicted by theory, with an increase of their number and spectral detuning with excitation pulse intensity and a dependence of their spectral shape and intensity on the pulse length. Detuning-dependent measurements provide additional insights into the emission features. The experimental results are in excellent agreement with theoretical calculations of the emission spectra, corroborating our findings.