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arXiv:1809.10549 · Optica

Rabi oscillations of a quantum dot exciton coupled to acoustic phonons: coherence and population readout

Daniel Wigger, Christian Schneider, Stefan Gerhardt, Martin Kamp, Sven Höfling, Tilmann Kuhn, Jacek Kasprzak

Published Nov 6, 2018• 25 citations
arXivHTMLPDF

Abstract

While the advanced coherent control of qubits is now routinely carried out in low frequency (GHz) systems like single spins, it is far more challenging to achieve for two-level systems in the optical domain. This is because the latter evolve typically in the THz range, calling for tools of ultrafast, coherent, nonlinear optics. Using four-wave mixing micro-spectroscopy, we here measure the optically driven dynamics of a single exciton quantum state confined in a semiconductor quantum dot. In a combined experimental and theoretical approach, we reveal the intrinsic Rabi oscillation dynamics by monitoring both central exciton quantities, i.e., its occupation and the microscopic coherence, as resolved by the four-wave mixing technique. In the frequency domain this oscillation generates the Autler-Townes splitting of the light-exciton dressed states, directly seen in the four-wave mixing spectra. We further demonstrate that the coupling to acoustic phonons strongly influences the FWM dynamics on the picosecond timescale, because it leads to transitions between the dressed states.

DOI
10.1364/optica.5.001442

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While the advanced coherent control of qubits is now routinely carried out in low frequency (GHz) systems like single spins, it is far more challenging to achieve for two-level systems in the optical domain. This is because the latter evolve typically in the THz range, calling for tools of ultrafast, coherent, nonlinear optics. Using four-wave mixing micro-spectroscopy, we here measure the optically driven dynamics of a single exciton quantum state confined in a semiconductor quantum dot. In a combined experimental and theoretical approach, we reveal the intrinsic Rabi oscillation dynamics by monitoring both central exciton quantities, i.e., its occupation and the microscopic coherence, as resolved by the four-wave mixing technique. In the frequency domain this oscillation generates the Autler-Townes splitting of the light-exciton dressed states, directly seen in the four-wave mixing spectra. We further demonstrate that the coupling to acoustic phonons strongly influences the FWM dynamics on the picosecond timescale, because it leads to transitions between the dressed states.
A detailed understanding of the population and coherence dynamics in optically driven individual emitters in solids and their signatures in ultrafast nonlinear-optical signals is of prime importance for their applications in future quantum and optical technologies. In a combined experimental and theoretical study on exciton complexes in single semiconductor quantum dots we reveal a detailed picture of the dynamics employing three-beam polarization-resolved four-wave mixing (FWM) micro-spectroscopy. The oscillatory dynamics of the FWM signals in the exciton-biexciton system is governed by the fine-structure splitting and the biexciton binding energy in an excellent quantitative agreement between measurement and analytical description. The analysis of the excitation conditions exhibits a dependence of the dynamics on the specific choice of polarization configuration, pulse areas and temporal ordering of driving fields. The interplay between the transitions in the four-level exciton system leads to rich evolution of coherence and population. Using two-dimensional FWM spectroscopy we elucidate the exciton-biexciton coupling and identify neutral and charged exciton complexes in a single quantum dot. Our investigations thus clearly reveal that FWM spectroscopy is a powerful tool to characterize spectral and dynamical properties of single quantum structures.
Introduction Quantum dots are often referred to as artificial atoms, since they trap carriers in discrete energy-levels due to the nanoscale three-dimensional finite potential energy well they provide. As such, dots exhibit a coherent light–matter interaction that is similar to an atom. This is evidenced by observations of atom–optics phenomena such as Rabi oscillations [43, 26], power broadening [27], Autler–Townes doublet [14, 42], Mollow triplet [42, 8], and coherent population trapping [6]. In this chapter, Rabi rotation measurements are used to examine how an exciton transition deviates from an ideal two-level atom due to its interaction with a reservoir of phonons. The neutral exciton transition may be regarded as a two-level system, or qubit, composed of the crystal ground-state ∣0〉 and a single electron-hole pair ∣ X 〉. The state-vector of a qubit can be described as a pseudo spin-half. When an oscillating electro-magnetic field resonantly excites the two-level transition it drives an oscillation in the population inversion known as a Rabi oscillation. This results from the oscillations of the driving field and the dipole of the two-level system being synchronous, such that in its rotating frame, the driving field acts as a static magnetic field that causes the pseudo-spin to rotate. Coherent control of the pseudo-spin can be achieved by applying well-defined driving fields, enabling the preparation, and manipulation of superposition states. Such coherent control concepts have found widespread use in electron spin, and nuclear magnetic resonance spectroscopy.
The exact optical response of quantum few-level systems depends crucially on the exact choice of the incoming pulse areas. We use four-wave mixing (FWM) spectroscopy to infer the coherent response and dynamics of single InAs quantum dots (QDs) and study their pulse area dependence. By combining atomic force microscopy with FWM hyperspectral imaging, we show that the retrieved FWM signals originate from individual QDs enclosed in natural photonic defects. The optimized light-matter coupling in these defects allows us to perform our studies in a wide range of driving field amplitudes. When varying the pulse areas of the exciting laser pulses, Rabi rotations of microscopic interband coherences can be resolved by the two-pulse FWM technique. We investigate these Rabi coherence rotations within two- and three-level systems, both theoretically and experimentally, and explain their damping by the coupling to acoustic phonons. To highlight the importance of the pulse area influence, we show that the phonon-induced dephasing of QD excitons depends on the pulse intensity.
A model of semiconductor quantum dots coupled to phonons and laser light, which is relevant in the limit of strong electronic confinement, is investigated. For an arbitrary sequence of excitations by ultrafast pulses, analytical solutions are obtained for all pertinent density-matrix elements. The results are nonperturbative with respect to the coupling to both phonons and laser light. The derivation depends neither on a particular choice of electronic wave functions nor on a particular wave-vector dependence of the phonon interaction or phonon dispersion. All components of the density matrix exhibit oscillatory dependences on the pulse areas of the exciting pulses analogously to the Rabi oscillations known from simple two-level systems. Three typical applications of the general results are worked out: (a) the influence of phonons on four-wave-mixing spectra, (b) the coherent control of electronic dot occupations in the presence of phonons, and (c) the dynamics of phonon correlations including the formation of a stable polaron spatially localized in the dot and the emission of a pulsed phonon wave packet that leaves the dot.
We report picosecond control of excitonic dressed states in a single semiconductor quantum dot. A strong laser pulse couples the exciton and biexciton states, to form an Autler-Townes doublet of the neutral exciton transition. The Rabi-splitting, and hence the admixture of the dressed states follows the envelope of the picosecond control laser. We create a superposition of dressed states, and observe the resulting beat: a direct measurement of a Rabi oscillation in time delay rather than the usual power domain.