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arXiv:0709.1382 · Physical Review B

Hysteretic response of the electron-nuclear spin system in single In 0.75 Al 0.25 As quantum dots: Dependences on excitation power and polarization

R. Kaji, S. Adachi, H. Sasakura, Shunichi Muto

Published Mar 24, 2008• 35 citations
arXivHTMLPDF

Abstract

Optically pumped nuclear spin polarization in single InAlAs quantum dots was investigated in detail with regards to the dependences on the excitation power and electron spin polarization. By increasing (or decreasing) the excitation power at a particular excitation polarization, an abrupt rise (or drop) and a clear hysteretic behavior were observed in the Overhauser shift of the photoluminescence under an external magnetic field of $5\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. Those features appear equivalently for the exciton and exciton complexes of the same quantum dot since the created nuclear field is equally effective. However, the degree of circular polarization shows different behaviors between a positively charged exciton and a neutral exciton or biexciton; further, only the positively charged exciton exhibits the precisely synchronized change and hysteretic behavior. It is suggested that the electron spin distribution is affected by the flip-flop of electron-nuclear spins. Further, the hysteresis is observed as a function of the degree of circular polarization of the excitation light, and its dependence on the excitation power is studied. The saturation of the Overhauser shift indicates the almost complete cancellation of the external magnetic field by the nuclear field.

DOI
10.1103/physrevb.77.115345

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Optically pumped nuclear spin polarization in single InAlAs quantum dots was investigated in detail with regards to the dependences on the excitation power and electron spin polarization. By increasing (or decreasing) the excitation power at a particular excitation polarization, an abrupt rise (or drop) and a clear hysteretic behavior were observed in the Overhauser shift of the photoluminescence under an external magnetic field of 5T5\phantom{\rule{0.3em}{0ex}}\mathrm{T}5T. Those features appear equivalently for the exciton and exciton complexes of the same quantum dot since the created nuclear field is equally effective. However, the degree of circular polarization shows different behaviors between a positively charged exciton and a neutral exciton or biexciton; further, only the positively charged exciton exhibits the precisely synchronized change and hysteretic behavior. It is suggested that the electron spin distribution is affected by the flip-flop of electron-nuclear spins. Further, the hysteresis is observed as a function of the degree of circular polarization of the excitation light, and its dependence on the excitation power is studied. The saturation of the Overhauser shift indicates the almost complete cancellation of the external magnetic field by the nuclear field.
We study a large ensemble of nuclear spins interacting with a single electron spin in a quantum dot under optical excitation and photon detection. At the two-photon resonance between the two electron-spin states, the detection of light scattering from the intermediate exciton state acts as a weak quantum measurement of the effective magnetic (Overhauser) field due to the nuclear spins. In a coherent population trapping state without light scattering, the nuclear state is projected into an eigenstate of the Overhauser field operator, and electron decoherence due to nuclear spins is suppressed: We show that this limit can be approached by adapting the driving frequencies when a photon is detected. We use a Lindblad equation to describe the driven system under photon emission and detection. Numerically, we find an increase of the electron coherence time from 5 to 500 ns after a preparation time of 10 micros.
Summary form only given. Semiconductor quantum dots (QD) offer the current state-of-the-art in intensity and coherence for single photon generation, as well as serving as a testbed for various novel approaches to quantum networking. Their high brightness provides a means to produce high-bandwidth spin-photon entanglement [1]. However, the purity and usefulness of the generated entangled state is severely limited by the coherence time of the QD charge carrier spin, typically on the order of 2ns for electrons in a self-assembled InGaAs QD. This limit is imposed by low-frequency fluctuations of the Overhauser field generated by host nuclear spins, affecting the electron spin resonance frequency.Here, we measure an extension of T2 by over an order of magnitude, enabled by prior preparation of the surrounding nuclear spin bath. The interplay of dynamic nuclear polarization and coherent population trapping (CPT) can lead to a controllable mechanism that locks the nuclear spins, and thereby reduces the Overhauser field fluctuations [2,3]. We use the lambda-scheme formed by an optical transition between bound electron and negatively-charged exciton in Voigt geometry at a field of 5T. There, we use the CPT dark-state resonance as a means to lock the polarization state of the nuclear spins surrounding the electron spin. Using ultrafast optical spin rotations, we perform a Ramsey sequence following a CPT preparation of the nuclear spins, to measure the Free Induction Decay of the electron spin coherence [4]. With a pulse sequence composed of 70μs of CPT preparation, followed by 70μs of repeated Ramsey measurements, as shown in Fig. 1a, we observe coherent electron spin oscillations at a Ramsey delay of 29ns, as shown in Fig. 1b. The oscillations are free of the deleterious effects of nuclear polarization typical in such measurements [5], indicating the stabilization of the mean Overhauser field to a fixed value. The measured T2 of 39ns is over an order of magnitude longer than the Ti of 3ns measured on the system with unprepared nuclear spins, as shown in Fig. 1c.
We investigate the coherent exciton spin dynamics in a single InAlAs/AlGaAs quantum dot using time-resolved quantum state tomography. Under two-LO-phonon quasi-resonant excitation of neutral exciton, we observe pronounced quantum beats in the circular and diagonal polarization components, reflecting the fine-structure splitting (Δ≈19.6 μeVΔ\approx 19.6 \ μ\text{eV}Δ≈19.6 μeV). By employing a global fitting procedure across three orthogonal polarization bases, we demonstrate that the spin evolution is consistently described by a unified Hamiltonian dominated by the anisotropic exchange interaction. While the initial degree of circular polarization is limited to ≈0.28\approx 0.28≈0.28 due to fast relaxation processes during carrier cooling, the subsequent dynamics reveal a long-lived spin coherence (1.1±0.21.1 \pm 0.21.1±0.2 ns) that exceeds the exciton lifetime (∼767\sim 767∼767 ps). Our analysis reveals that the spin-formation time is significantly shorter than the instrument response function, and the absence of a discernible Overhauser shift confirms a negligible influence from the local nuclear environment under the present conditions. These results provide a quantitative benchmark for the three-dimensional reconstruction of spin trajectories using differential polarization signals, demonstrating the feasibility of using quasi-resonant excitation for stable spin initialization in semiconductor nanostructures.
In double quantum dots, the exchange interaction between two electron spins renormalizes the excitation energy of pair flips in the nuclear spin bath, which in turn modifies the non-Markovian bath dynamics. As the energy renormalization varies with the static Overhauser field mismatch between the quantum dots, the electron singlet-triplet decoherence resulting from the bath dynamics depends on sampling of nuclear spin states from an ensemble, leading to the transition from superexponential decoherence in single-sample dynamics to power-law decay under ensemble averaging. In contrast, the decoherence of a single electron spin in one dot is essentially the same for different choices of the nuclear spin configuration.
We report quantum beat phenomena between different polarization states in InAs quantum dots, observed in time-resolved photoluminescence and transient dichroism measurements. The polarization of the emitted light can be changed from linear to circular by applying a small magnetic field. Following quasiresonant excitation the electron and hole spin states remain stable during the exciton lifetime, independent of the applied magnetic field. We show that the exciton spin coherence is partially preserved in the energy relaxation process. These experiments enable us to measure the anisotropic exchange energy $\ensuremath{\Delta}{E}_{XY}$ and the exciton ggg factor. We find $\ensuremath{\Delta}{E}_{XY}\ensuremath{\simeq}30\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{eV}$ and $g\ensuremath{\simeq}2.5$ for the quantum dot excitons.