Wigner-molecularization-enabled dynamic nuclear polarization

Article https://doi.org/10.1038/s41467-023-38649-5 Wigner-molecularization-enabled dynamic nuclear polarization Received: 3 August 2022 Accepted: 10 May 2023 1234567890():,; 1234567890():,; Check for updates Wonjin Jang 1, Jehyun Kim1, Jaemin Park1, Gyeonghun Kim 1, Min-Kyun Cho Hyeongyu Jang1, Sangwoo Sim 1, Byoungwoo Kang1, Hwanchul Jung2, Vladimir Umansky3 & Dohun Kim 1 1 , Multielectron semiconductor quantum dots (QDs) provide a novel platform to study the Coulomb interaction-driven, spatially localized electron states of Wigner molecules (WMs). Although Wigner-molecularization has been confirmed by real-space imaging and coherent spectroscopy, the open system dynamics of the strongly correlated states with the environment are not yet well understood. Here, we demonstrate efficient control of spin transfer between an artificial three-electron WM and the nuclear environment in a GaAs double QD. A Landau–Zener sweep-based polarization sequence and low-lying anticrossings of spin multiplet states enabled by Wigner-molecularization are utilized. Combined with coherent control of spin states, we achieve control of magnitude, polarity, and site dependence of the nuclear field. We demonstrate that the same level of control cannot be achieved in the non-interacting regime. Thus, we confirm the spin structure of a WM, paving the way for active control of correlated electron states for application in mesoscopic environment engineering. Semiconductor quantum dot (QD) systems facilitate investigations of the interaction between electron spins and nuclear environments, which is known as the central-spin problem1,2. Although the fluctuation of nuclear fields, which is quantified by the effective Overhauser field Bnuc3,4, often acts as a magnetic-noise source for spin qubits3, the hyperfine electron–nuclear spin interaction allows achieving dynamic nuclear polarization (DNP)5–8. DNP is used for enhancing the signal-tonoise ratio in nuclear magnetic resonance6 and prolonging coherence times in QD-based spin qubits9,10. Gate-defined semiconductor QDs have been used to achieve the fast probing of nuclear environments8,11,12, bidirectional DNP11, and active feedback control of nuclear fields10. While the DNP achieved by spin-flip mediated transport with an applied bias13,14 allows large DNP13, the QD - reservoir tunnel rate needs to be large enough to allow the finite spin-flip current. On the contrary, the DNP based on the pulsed-gate technique can be demonstrated while maintaining the small tunnel rates ~101 kHz. Because the qubit control typically requires small QD-reservoir tunnel rates transition from the pulsed-gate DNP to qubit experiments is straightforward without additional parameter modulation via the gate voltages. However, spin qubit control combined with DNP has been limited to twoelectron singlet–triplet (ST0) spin qubits9–12,15. Despite the versatility of gate-defined QD systems16–19, the large singlet–triplet energy splitting EST (~102 h·GHz; h is Planck’s constant) in particular in GaAs limits the access to higher spin states20 in multielectron QDs at moderate external magnetic fields B0 < 1 T or within a typical frequency bandwidth of experimental setups. Coulomb-correlation-driven Wigner molecules (WMs) in confined systems21–25 may provide new directions for expanding nuclear control to multielectron systems. Recent studies on QDs in various systems have shown clear evidence of WM formation22,23,25–29. It has been demonstrated that the EST can reach down to ~100 h·GHz upon the WM formation27,29 because of strong electron–electron interactions confirmed by full-configuration interaction (FCI)-based theories23,25,28,30. 1 Department of Physics and Astronomy, and Institute of Applied Physics, Seoul National University, Seoul 08826, Korea. 2Department of Physics, Pusan National University, Busan 46241, Korea. 3Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, e-mail: Rehovot 76100, Israel. Nature Communications | (2023)14:2948 1 Article https://doi.org/10.1038/s41467-023-38649-5 However, most studies have focused on the spectroscopic confirmation of WM formation, and studies on the open system dynamics using correlated states have not been reported to date. Here, we demonstrate the formation of a WM in semiconductor QDs, which helps achieving efficient spin environment control. We use gate-defined QDs in GaAs and exploit the quenched energy spectrum of the WM (EST ~ 0.9 h·GHz) to enable mixing between different spin subspaces within B0 < 0.3 T. Furthermore, we demonstrate DNP by pulsed-gate control of the electron spin states. Leakage spectroscopy and Landau–Zener–Stuckelberg (LZS) oscillations confirm a sizable bidirectional change in Bnuc ~ 80 mT and the spatial Overhauser field gradient ΔBnuc ~ 35 mT due to the long nuclear spin diffusion time a. V V τN ~ 62 s. Further, we demonstrate on-demand control of Bnuc combined with coherent LZS oscillations, providing a new route for realizing controllable DNP using correlated electron states. Results Figure 1a shows a gate-defined QD device fabricated on a GaAs/AlGaAs heterostructure, where a 2D electron gas (2DEG) is formed ~70 nm below the surface (see Methods). We focus on the left double QD (DQD) containing three electrons. We designed the V2 gate to form an anisotropic potential, which is predicted to promote WM formation22. An electrostatic simulation of the electric potential at the QD site near V2 shows an oval-shaped confinement potential with anisotropy [110] (1,2) Ground State Elec. Potential (2,1), EST 500 nm B0 100 nm Wigner molecule ground state Exc. State 0.17 rf refl. (V) 0.21 b. CDS Amp. High Low c. (2,1) -0.40 2 0 time -0.42 FFT amp. High Low 3 (1,1) -0.44 Charge Qubit (1,2) 1 -1.16 -1.12 400 -1.08 V2 (V) d. 600 800 ( eV) 100 Non-interacting EQ Energy (h GHz) Energy (h GHz) Frequency (GHz) V1 (V) tevol (ns) 4 -0.38 100 0 Strong e-e interaction (This work) EQ 0 -100 Energy (mV) DS(2,1) EQ 1 Charge qubit DS(1,2) Fig. 1 | Wigner molecule formation in a GaAs double quantum dot. a Scanning electron microscope image of a GaAs quantum dot (QD) device similar to the one used in the experiment. Green dots denote the double QD defined for Wigner molecule (WM) formation which is aligned along the [110] crystal axis (black arrow). The inner plunger gate V2 is designed to have anisotropic confinement potential as shown in the right panel to facilitate the localization of the electronic ground state. Yellow circle: a radio-frequency (rf) single-electron transistor (rf-SET) charge sensor for rf-reflectometry. External magnetic field B0 is applied along the direction denoted by the yellow arrow. b Charge stability diagram of the double QD near the three-electron region spanned by V1 and V2 gate voltages. Green-shaded region: the Nature Communications | (2023)14:2948 -1 1 (mV) Energy -1 EQ Q(1,2) DT(1,2) energy- (...truncated)