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arXiv:2604.24689

Singlet-triplet oscillations in multivalley Si double quantum dots

Łukasz Cywiński, Mats Volmer, Tom Struck, Giordano Scappucci, Lars R. Schreiber

cond-mat.mes-hallquant-phSubmitted Apr 27, 2026• Announced Apr 28, 2026
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Abstract

Charge separation from the $(4,0)$ to the $(3,1)$ state in a Si/SiGe double quantum dot is commonly used for initialization of spin qubits and Pauli-spin-blockade readout. It was used in recent experiments involving creation of the $(3,1)$ singlet, and subsequent shuttling of one of the electrons. We present a theoretical description of the process of charge separation and singlet-triplet mixing, arriving at expressions for the singlet return probability that take into account experimentally observed finite probabilities of the creation of singlets with various patterns of valley occupations. In our analysis we focus on magnetic fields for which the electron spin Zeeman splitting is close to the valley splitting in one of the dots, when the spin-valley coupling causes a strong renormalization of the frequency of oscillations of singlet return probability. The latter effect has been recently used to perform valley splitting mapping by shuttling of one quantum dot to various locations with respect to the other. We give a detailed description of singlet-triplet dynamics near these spin-valley resonances and compare the results of calculations with measurements on double quantum dots in two distinct Si/SiGe heterostructures. Comparison of theory with experiments in which the presence of a few valley occupation patterns is visible, gives insight into the valley dependence of $g$-factors in these structures, providing support for a recently proposed theoretical model of this dependence. We also discuss how dephasing of singlet return probability oscillations near the spin-valley resonances is affected by valley splitting fluctuations caused by electric field noise.

Comments
21 pages, 10 figures

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Charge separation from the (4,0)(4,0)(4,0) to the (3,1)(3,1)(3,1) state in a Si/SiGe double quantum dot is commonly used for initialization of spin qubits and Pauli-spin-blockade readout. It was used in recent experiments involving creation of the (3,1)(3,1)(3,1) singlet, and subsequent shuttling of one of the electrons. We present a theoretical description of the process of charge separation and singlet-triplet mixing, arriving at expressions for the singlet return probability that take into account experimentally observed finite probabilities of the creation of singlets with various patterns of valley occupations. In our analysis we focus on magnetic fields for which the electron spin Zeeman splitting is close to the valley splitting in one of the dots, when the spin-valley coupling causes a strong renormalization of the frequency of oscillations of singlet return probability. The latter effect has been recently used to perform valley splitting mapping by shuttling of one quantum dot to various locations with respect to the other. We give a detailed description of singlet-triplet dynamics near these spin-valley resonances and compare the results of calculations with measurements on double quantum dots in two distinct Si/SiGe heterostructures. Comparison of theory with experiments in which the presence of a few valley occupation patterns is visible, gives insight into the valley dependence of ggg-factors in these structures, providing support for a recently proposed theoretical model of this dependence. We also discuss how dephasing of singlet return probability oscillations near the spin-valley resonances is affected by valley splitting fluctuations caused by electric field noise.
We study the singlet-triplet relaxation due to the spin-orbit coupling assisted by the electron-phonon scattering in two-electron SiGe/Si/SiGe double quantum dots in the presence of an external magnetic field in either Faraday or Voigt configuration. By explicitly including the electron-electron Coulomb interaction and the valley splitting induced by the interface scattering, we employ the exact-diagonalization method to obtain the energy spectra and the eigenstates. Then, we calculate the relaxation rates with the Fermi golden rule. We find that the transition rates can be effectively tuned by varying the external magnetic field and the interdot distance. Especially in the vicinity of the anticrossing point, the transition rates show intriguing features. We also investigate the electric-field dependence of the transition rates and find that the transition rates are almost independent of the electric field. This is of great importance in the spin manipulation, since the lifetime remains almost the same during the change of the qubit configuration from (1,1) to (2,0) by the electric field.
While bulk silicon has long been understood to exhibit relatively weak spin-orbit coupling (SOC), confinement of electrons to quantum dots (QDs) at a silicon heterointerface results in significantly larger SOC. This is a concern for electron spin qubit performance, as intravalley and intervalley SOC can significantly perturb the operation of electron spin qubits. While these interactions can be harnessed to drive coherent rotations in a singlet-triplet qubit, coupling to low-lying excited valley states can lead to undesirable spin relaxation when valley splitting is on resonance with the Zeeman energy. In this work, we measure the angular dependence of the interfacial spin-orbit interaction as a function of the direction and magnitude of an applied external magnetic field in SiMOS and Si/SiGe heterostructures, two common material platforms for silicon spin qubits. We construct a physical model that accurately infers intra- and inter-valley SOC physics from fits to the data, allowing for a direct comparison between these two material systems. For the devices measured we find that, while the ggg-factor differences are comparable, the SiMOS QDs exhibit an order of magnitude larger spin-valley coupling than for Si/SiGe. Moreover, we find that the angular dependence of the spin-valley coupling is similar for both devices, with similar magnetic field orientations minimizing the spin-valley coupling. Our work points towards operational schemes for optimizing spin-valley coupling to avoid or exploit this mechanism for qubit operation.
Valley excitations are considered one of the biggest challenges for a coherent spin shuttling in Si/SiGe heterostructures. In this work we theoretically investigate the valley dynamics during spin shuttling in a Si/SiGe heterostructure by considering a two-level system given by the two low-lying valley states of the mobile quantum dot. We assume that the electron is initially in the valley ground state and analyze the evolution of this state during shuttling. We find that, depending on the shuttling velocity, the system can be in three distinct regimes. In one of these regimes, the quantum information is preserved even in the presence of the valley excitations, allowing for coherent spin shuttling independently of the shuttling distance. This regime is obtained for a shuttling velocity of tens of m/s, a desired regime where dephasing mechanisms, such as spin-valley hotspots and spatially varying spin splitting, can be suppressed. This result is in accordance with recent experimental work that obtained a high spin shuttling fidelity after a fast and long shuttling. We also propose strategies based on the Partial Landau-Zener model to enhance the valley shuttling fidelity, which was found to be much more efficient than previously proposed strategies based on the standard Landau-Zener model.
We study theoretically the phonon-induced relaxation and decoherence of spin states of two electrons in a lateral double quantum dot in a SiGe/Si/SiGe heterostructure. We consider two types of singlet-triplet spin qubits and calculate their relaxation and decoherence times, in particular as a function of level hybridization, temperature, magnetic field, spin orbit interaction, and detuning between the quantum dots, using Bloch-Redfield theory. We show that the magnetic field gradient, which is usually applied to operate the spin qubit, may reduce the relaxation time by more than an order of magnitude. Using this insight, we identify an optimal regime where the magnetic field gradient does not affect the relaxation time significantly, and we propose regimes of longest decay times. We take into account the effects of one-phonon and two-phonon processes and suggest how our theory can be tested experimentally. The spin lifetimes we find here for Si-based quantum dots are significantly longer than the ones reported for their GaAs counterparts.
Abstract Quantum dots in silicon are a promising architecture for semiconductor quantum computing due to a high degree of electric control and compatibility with existing silicon fabrication processes. Although electron charge and spin are prominent methods for encoding the qubit state, valley states in silicon can also store quantum information via valley-orbit coupling with protection against charge noise. By observing coherent oscillations between valley states in a Si/SiGe double quantum dot device tuned to the two-electron charge configuration, we measure the valley energy splitting in both quantum dots individually. We further demonstrate two-axis quantum control of the valley qubit using gated pulse sequences with X and Z rotations occurring within a fast operation time of 300 ps. This control is used to completely map out the surface of the Bloch sphere in a single phase-space plot that is subsequently used for state and process tomography.
We report a successful measurement of the magnetic field-induced spin singlet-triplet transition in silicon-based coupled dot systems. Our specific experimental scheme incorporates a lateral gate-controlled Coulomb-blockaded structure in Si to meet the proposed scheme of Loss and DiVincenzo [1], and a non-equilibrium single-electron tunneling technique to probe the fine energy splitting between the spin singlet and triplet, which varies as a function of applying magnetic fields and interdot coupling constant. Our results, exhibiting the singlet-triplet crossing at a magnetic field for various interdot coupling constants, are in agreement with the theoretical predictions, and give the first experimental demonstration of the possible spin swapping occurring in the coupled double dot systems with magnetic field. *Electronic address: jungchoi@chungbuk.ac.kr [1] D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120 (1998).