Single hole spin relaxation probed by fast single-shot latched charge sensing

ARTICLE https://doi.org/10.1038/s42005-019-0113-0 OPEN 1234567890():,; Single hole spin relaxation probed by fast singleshot latched charge sensing Alex Bogan1,2, Sergei Studenikin1,2, Marek Korkusinski1, Louis Gaudreau1, Piotr Zawadzki1, Andy Sachrajda1, Lisa Tracy3, John Reno4 & Terry Hargett4 Hole spins have recently emerged as attractive candidates for solid-state qubits for quantum computing. Their state can be manipulated electrically by taking advantage of the strong spinorbit interaction (SOI). Crucially, these systems promise longer spin coherence lifetimes owing to their weak interactions with nuclear spins as compared to electron spin qubits. Here we measure the spin relaxation time T1 of a single hole in a GaAs gated lateral double quantum dot device. We propose a protocol converting the spin state into long-lived charge configurations by the SOI-assisted spin-flip tunneling between dots. By interrogating the system with a charge detector we extract the magnetic-field dependence of T1 ∝ B−5 for fields larger than B = 0.5 T, suggesting the phonon-assisted Dresselhaus SOI as the relaxation channel. This coupling limits the measured values of T1 from ~400 ns at B = 1.5 T up to ~60 μs at B = 0.5 T. 1 Security and Disruptive Technologies Research Centre, National Research Council of Canada, Ottawa, ON K1A0R6, Canada. 2 Department of Physics and Astronomy, University of Waterloo, Waterloo N2L3G1 ON, Canada. 3 Sandia National Laboratories, Albuquerque, NM 87185, USA. 4 Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, NM 87185, USA. Correspondence and requests for materials should be addressed to S.S. (email: ) COMMUNICATIONS PHYSICS | (2019)2:17 | https://doi.org/10.1038/s42005-019-0113-0 | www.nature.com/commsphys 1 ARTICLE C COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-019-0113-0 oherence of solid-state spins is of crucial importance in the context of their utilization in quantum computation and communication1–3. This property is quantified by the spin relaxation time T1 and the decoherence time T2
3. While both of them are essentially material parameters, T2
can be extended dynamically by refocusing techniques4. On the other hand, 1/T1 measures the spin relaxation rate from an arbitrary linear superposition to the ground state, by which the quantum information is lost irreversibly. Extending T1 is thus essential. Here, solid-state holes offer an advantage, as they interact much weaker than the electrons with the nuclei in the crystal lattice5. Two mechanisms of the spin relaxation process in quantum dots have been identified3,6. The first involves flip–flop interactions with nuclear spins of the crystal lattice and is active at magnetic fields B up to several mT. The resulting T1 was measured to be 10–100 ns at very small fields for electrons in gated GaAs quantum dots3, rising to ~70 μs at B = 100 mT7. It can be radically enhanced by moving to 28Si samples where nuclear spins are absent8. However, GaAs hole spins have a competitive edge, since their hyperfine interaction strength in bulk was predicted9–12 and measured13–15 to be an order of magnitude weaker than that of the electrons. This suppression translates into improved values of T1, reaching 1 ms for holes in InGaAs samples16,17. In the second mechanism, dominant at higher magnetic fields, the spin relaxation occurs via the phonon-mediated spin–orbit interaction (SOI). Crossover into this regime occurs when the spin Zeeman energy exceeds the hyperfine interaction strength18 and is marked by a large increase of T13. In Si/SiGe dots, T1 was reported to reach ~3 s at B = 1–2 T19,20; in GaAs systems at similar fields T1 ~ 1 s3,21, whereas in InGaAs T1 ~ 20 ms at B = 2 T22 and T1 ~ 1 ms at B = 5 T23. The trend follows the strength of the SOI, which is weaker in centrosymmetric materials such as Si, and strongest in III–V In-based systems. The importance of the phonon component is revealed in the dependence of T1 on the magnetic field, as the increasing spin Zeeman energy tracks the increasing phonon density of states. The dependence of T1 ∝ B−5 was predicted theoretically24,25 and confirmed experimentally in GaAs quantum dots3,22,23,26–28, revealing values of T1 ~ 100 μs at B ~ 10 T. For hole spins, theory also predicts a decrease of T1 with increasing magnetic field, with T1 ∝ B−5 for the Dresselhaus SOI, or T1 ∝ B−9 for the Rashba SOI29,30. Moreover, the exact functional relationship depends on the structural properties of the dots, such as size, thickness, shape, and strain, characteristic for the strong SOI experienced by holes in solids31–33. However, there has been little systematic experimental analysis of T1 in p-type quantum dots at higher magnetic fields. Measurements in Ge/Si samples suggest T1 of hundreds of microseconds34 to submicrosecond values35 at B ~ 1 T. In the Ge hut wire system, values of tens to a hundred microseconds were recorded for magnetic fields from 0.5 T to 1.5 T36. T1 times of several microseconds in hole Si Complementary Metal Oxide Semiconductor (CMOS) devices37, and several nanoseconds in gated GaAs samples at similar fields38 have been reported. Two-axis coherent control of the hole spin has been demonstrated both in the Ge hut sample39 and in the Si dots40. With the exception of the Si device, however, all measurements mentioned above involved systems with several holes. Here we report on the detailed experimental study of the single-hole T1 as a function of the magnetic field. We show that, in the range of B = 0.5–1.5 T, T1 changes from 60 μs down to 400 ns along the power law of T1 ∝ B−5. This result, in agreement with theory29,30, reveals the dominance of the Dresselhaus SOI in spin relaxation. Although our values of T1 are lower than those for electrons in GaAs at similar fields, extrapolation to very small magnetic fields is consistent with previous optical 2 measurements16,17, showing holes to be superior (T1 potentially in tens of milliseconds at B ~ 100 mT) owing to the reduced hyperfine interactions. We also report on the development of a technique to read out a single-hole spin qubit in one quantum dot by converting the spin state into a latched charge state in a secondary dot. Charge-latching techniques involving spin-to-charge mapping have been applied to a variety of qubits41–44. In the gated electronic double dot, the latching technique proposed by our group42 involved the mapping of the spin of a singlet–triplet qubit onto the charge states differing by one electron charge, rather than by the charge distribution of different spin states. The technique relies on a long-lived (latched) nature of the ground and excited charge states allowing for a high-contrast charge sensor readout. The latched technique was used to demonstrate single-shot high-fidelity spin measurements44,45 and to extend the sensitivity of the spin detection at large magnetic-field gradients46. The spin-to-charge conversion allows measuring T1 by fitting the (...truncated)