Coherence of a dynamically decoupled quantum-dot hole spin

Abstract

A heavy hole confined to an InGaAs quantum dot promises the union of a stable spin and optical coherence to form a near perfect, high-bandwidth spin-photon interface. Despite theoretical predictions and encouraging preliminary measurements, the dynamic processes determining the coherence of the hole spin are yet to be understood. Here, we establish the regimes that allow for a highly coherent hole spin in these systems, recovering a crossover from hyperfine to electrical-noise dominated decoherence with a few-Tesla external magnetic field. Dynamic decoupling allows us to reach the longest ground-state coherence time, T2, of 4.4 µs, observed in this system. The improvement of coherence we measure is quantitatively supported by an independent analysis of the local electrical environment.Self-assembled indium gallium arsenide (InGaAs) quantum dots (QDs) provide an excellent test bed for tackling the implementation challenges of distributed quantum information processing [1,2]. They can be charged deterministically [3] and both electrons and holes can serve as optically active qubits. The outstanding photonic properties [4] in combination with ultrafast spin control [5,6] and efficient state transfer through spinphoton entanglement [7][8][9] have recently allowed for the generation of spin-spin entanglement [10,11]. The first key figure of merit of such a system is the inhomogeneous dephasing time T * 2 relative to the longest operation time, which, in the case of QDs, is the spin-photon state transfer characterized by the optical lifetime Γ −1 . The second figure of merit is the spin coherence time T 2 , which determines for how long the entanglement can be preserved. For the electron spin, T * 2 of a few ns (comparable to Γ −1 , ≈ 0.7 ns) and T 2 of a few µs [12,13] are predominantly limited by the size and dispersion of the QD nuclear spin ensemble, respectively. For the hole spin, the dominant contact interaction term is suppressed due to hole's p-like symmetry, offering an order of magnitude weaker hyperfine interaction [14,15]. Additionally, given the predominantly heavy-hole character of the ground state, the hyperfine interaction is primarily concentrated along the growth axis and can be suppressed by a transverse external magnetic field [14].The coherence of the hole spin has been observed in a number of experiments: Studies using coherent population trapping (CPT) have suggested a promising T * 2 ≥ 100 ns [16,17], whereas direct measurements of the free induction decay through Ramsey interference [6,18,19] and spin-flip Raman scattering [20] could only reach T * 2 of up to 26 ns. While nuclear-spin noise and electrical charge fluctuations have both been suggested as the dominating source of decoherence for the hole spin [6,16,17,19], the understanding of the mechanism governing the coherence and, more importantly, how well it can be protected remains unclear. In this Letter, we study the performance of a single hole spin in an In-GaAs QD experiencing a dynamic nuclear and electric environment. The dependenc...

Hyperfine interaction for holes in quantum dots: k·p model

“…The grey solid lines show the results obtained from Eq. (14). In order to relate our multi-band numerical wave functions to the simple theory we define here the wave function participation number as…”

“…assuming the same envelope shapes for holes and electrons) and all the multi-band effects (including the degree of heavy-light hole mixing), and their relation to QD shape. This includes works on carrier spin coherence (which apart from nuclear effects show influence of charge noise coupling to spin via electric-field dependent g-factors [11,14]), creation of dynamic nuclear polarization [4,5], and optical detection (through changes in Overhauser field-induced spin splitting of electron and holes) of nuclear magnetic resonance of different species of nuclei present in the dot [31]. While such experiments were used to obtain new information on structural properties and strain distribu-tion in QDs [31], the simplicity of some of the abovementioned assumptions casts a certain degree of doubt on the interpretation of measurement results.…”

Generation of Non‐Classical Light Using Semiconductor Quantum Dots

“…In spin echo measurements, coherence times of have been observed for electrons and holes, indicating the presence of charge noise limiting the observed coherence times. To these ends, dynamical decoupling has recently been demonstrated to enhance achievable T 2 times . In addition, it was recently shown that preparing the nuclear spin bath in a subthermal state using optical techniques allows to increase by more than one order of magnitude .…”

“…However, in a temporal or spatial ensemble, the Overhauser field is randomly distributed leading to fast dephasing of electron spins with . Due to their p‐like central cell wavefunction holes have a weaker hyperfine contact interaction and consequently more than one order of magnitude longer have been reported in time domain experiments and in frequency domain measurements (coherent population trapping) for holes times approaching one microsecond were reported . On intermediate timescales of hundreds of ns, the Overhauser field coherently evolves in time due to the quadrupolar moments resulting from the strained nuclei .…”

“…For longer timescales, the mechanism of irreversible dephasing is attributed to nuclear spin co‐flips or other complex many‐body interaction effects . In spin echo measurements, coherence times of have been observed for electrons and holes, indicating the presence of charge noise limiting the observed coherence times. To these ends, dynamical decoupling has recently been demonstrated to enhance achievable T 2 times .…”