Spin SWAP operation in double quantum dots at the LaAlO3/SrTiO3 interface

Abstract: Progress in the fabrication of nanoscale transition-metal-oxide heterostructures makes these platforms promising candidates for the realization of spin qubits, mainly due to the $d$-character of their electronic structures, which could potentially result in a reduction of hyperfine interactions and spin decoherence. Here, we present a systematic study of spin control within the SWAP operation in double quantum dots embedded in a two-dimensional electron gas at the LaAlO$3$/SrTiO$_3$ interface. Our analysis starts with a study of single-electron spin dynamics, focusing on the influence of spin-orbit and interorbital coupling on the spin evolution. In this case, our findings are supported by semiclassical calculations based on the Bloch equations, which show good agreement with full quantum mechanical simulations. We then simulate the SWAP operation by analyzing the crossover between two regimes: (i) large quantum dots, where the electronic structure is dominated by the $d{xy}$ orbitals and the spin dynamics is affected primarily by Rashba-type spin-orbit interaction; and (ii) small quantum dots, where higher-energy orbitals $d_{xz/yz}$ contribute to the electronic structure, leading to a significant reduction in the SWAP fidelity. In the first regime, particularly relevant from the application point of view, we analyze in detail the anisotropy of the SWAP operation induced by the spin-orbit coupling.

• The paper demonstrates that tuning quantum dot size to achieve a dominant d_xy orbital character minimizes spin–orbit induced errors, enhancing SWAP fidelity.
• It employs a real-space tight-binding model with full multiorbital structure and configuration interaction to reveal complex spin dynamics and anisotropy in SWAP operations.
• The study introduces a scaled computational approach that preserves critical singlet–triplet energy splitting, offering practical guidelines for high-fidelity oxide-based qubit design.

Spin SWAP Operation in Double Quantum Dots at the LaAlO$_3$/SrTiO$_3$ Interface

Introduction and Motivation

The realization of scalable quantum information processing devices critically depends on platforms that support robust spin qubits with enhanced coherence properties and fast gate operations. Transition-metal oxide heterostructures, particularly the LaAlO$_3$/SrTiO$_3$ (LAO/STO) interface, have emerged as promising materials due to their $d$-electron character, potentially suppressing hyperfine-induced decoherence. However, the inherent multiorbital band structure and pronounced spin–orbit (SO) interaction introduce nontrivial complexities for quantum dot (QD) spin qubits, especially considering the absence of significant hyperfine coupling.

This work provides a comprehensive theoretical investigation of spin dynamics and the SWAP operation in double quantum dots (DQDs) formed within the two-dimensional electron gas (2DEG) at the LAO/STO interface. The analysis is based on a real-space tight-binding model, incorporating the full multiorbital structure and SO coupling. The central focus is quantifying the influence of orbital character, SO interaction, and dot size on the fidelity and anisotropy of spin SWAP operations—a crucial primitive for universal quantum computation and error correction.

Model Overview

The LAO/STO 2DEG is described using a tight-binding Hamiltonian on the Ti $t_{2g}$ ($d_{xy}$, $d_{xz}$, $d_{yz}$) orbital manifold, incorporating kinetic energy, atomic SO interaction, interface-induced Rashba SO coupling, and coupling to an external magnetic field. The model is discretized on a square lattice, and the quantum dot confinement is defined via tunable external potentials.

For a single electron, quantum evolution is treated exactly; for the two-electron case, a configuration interaction (CI) method is employed, with Slater determinants constructed from single-particle orbitals. Full Coulomb matrix elements—including realistic dielectric screening—are used.

Figure 1: The confining potential in the double LAO/STO QD for typical parameters, showing tunable interdot coupling and dot size.

Single-Electron Spin Dynamics

Single-electron spin dynamics are governed by the interplay between SO interaction and orbital composition. For large QDs, the electronic spectrum is dominated by the $d_{xy}$ orbital, and the SO coupling takes an effective Rashba form. In this regime, spin precession follows the semiclassical Bloch equations with a Rashba effective field, and agreement between semiclassical and full quantum evolution is quantitatively demonstrated.

Figure 2: Single-electron spectrum as a function of dot size, with RGB decomposition showing $_3$0, $_3$1, and $_3$2 content.

For small QDs, confinement-induced mixing with $_3$3 orbitals becomes significant, yielding irregular, multi-frequency spin dynamics (beating). Here, Bloch-equation-based descriptions break down, and complex multiorbital quantum evolution is essential.

Figure 3: Time evolution of spin components in left/right QD; notable precession and coherent tunneling for $_3$4 nm.

Figure 4: Analogous spin-component time evolution for larger dot size $_3$5 nm, with enhanced amplitude and regularity due to dominant $_3$6 character.

Two-Electron SWAP Dynamics: Regimes and Mechanisms

SWAP dynamics are critically tied to two competing energy scales: the SO energy and the confinement/kinetic energy dictating orbital composition.

• Small QDs ($_3$7 nm): Multiple excited states contribute, with $_3$8 admixture producing irregular spin oscillations and reducing SWAP fidelity. Multiple Fourier components are evident in the spin dynamics.
• Intermediate QDs ($_3$9 nm): The system reaches an optimal "sweet spot" where spin SWAP is coherent, primarily involving only the lowest singlet and (unpolarized) triplet. Here, SO-induced fidelity loss is minimal due to enhanced level spacing and nearly pure $_3$0 character.
• Large QDs ($_3$1 nm): Electronic states are $_3$2-like and SWAP oscillations become regular, but the increasing relative strength of Rashba SO interaction induces significant precession in the transverse spin components ($_3$3, $_3$4), limiting maximum SWAP fidelity due to leakage outside the computational spin subspace.

Numerically, SWAP times span from $_3$5 ps for $_3$6 nm to $_3$7 ns for $_3$8 nm, primarily set by the exchange energy $_3$9.

Figure 5: Two-electron energy spectrum as a function of dot size; the admixture of $_3$0 orbitals in small dots is evident.

Figure 6: Exchange energy $_3$1 versus barrier height $_3$2 for various $_3$3; pronounced dependence on confinement and SO interaction. Insets highlight singlet–triplet crossings and SO-induced corrections.

Figure 7: Time evolution of $_3$4 for different $_3$5; contrast between SO-including and SO-free cases reveals SO-driven fidelity loss in large dots and spectral complexity in small dots.

Figure 8: Fourier analysis of $_3$6 reveals dominant energy transitions responsible for SWAP for each dot size regime.

Anisotropy of SWAP Operation

A key result is the clear demonstration of SWAP operation anisotropy induced by SO coupling. In the $_3$7-dominated regime, the effective SO field is oriented along $_3$8 (Rashba field). When the initial spin polarization aligns with this direction, SWAP operation fidelity is maximized, as there is minimal SO-induced leakage into transverse spin subspaces. For spins initialized along the $_3$9 or mixed orientations, SO-induced precession generates nontrivial oscillations in $d$0 and $d$1, reducing SWAP fidelity.

Figure 9: Time evolution of $d$2 for different initialization axes; the $d$3-aligned polarization realizes near-perfect SWAP.

Figure 10: Polarization dependence of key transition coefficients $d$4, quantifying anisotropy in the SWAP process for $d$5 nm.

Notably, for strong SO interaction and/or large quantum dots, these anisotropies become pronounced and must be considered in gate design and error correction.

Computational Acceleration: Scaled Tight-Binding Approach

Because the tight-binding lattice for realistic LAO/STO-based DQDs is computationally demanding, a scaling procedure is validated. By scaling the lattice spacing and appropriately renormalizing TB parameters, the essential singlet–triplet energy splitting and SWAP dynamics are preserved down to scaling factors $d$6–$d$7. This enables tractable simulation of larger device geometries without significant fidelity loss, as validated by direct comparison of spin dynamics.

Figure 11: Comparison of spin evolution calculated in the full and scaled TB models; scaling maintains dynamical fidelity of SWAP essential for device design.

Implications and Future Directions

Practically, this work identifies operational regimes in LAO/STO-based spin qubits where high-fidelity SWAPs are feasible. In particular, the interplay of dot size, orbital composition, and SO coupling is mapped in detail, establishing experimental design rules. The quantification of SO-induced anisotropy suggests protocols for optimal qubit initialization and axis choices.

Theoretically, these results underscore the inadequacy of single-orbital effective models to capture fidelity-critical phenomena in oxide 2DEG qubits, especially for realistic device sizes and couplings. Extension beyond Rashba-only or effective single-band models is required.

For future AI-driven quantum control, these findings indicate that automated approaches must embed explicit models of orbital composition and SO-induced anisotropies, particularly in oxide qubit platforms. As experiment advances towards the first demonstration of electrically driven spin control and two-qubit gates in LAO/STO, these insights will inform device design, optimal operation points, and error mitigation protocols.

Conclusion

This study establishes the microscopic limits of SWAP operation fidelity in LAO/STO DQDs by accounting for the full multiorbital band structure and SO interaction. The identification of a robust operational window with suppressed SO-induced errors, and the demonstration of computationally efficient scaled-tight-binding methods, directly supports ongoing experimental and theoretical work in transition-metal-oxide quantum devices. The framework and results presented here offer a reference for the practical implementation and simulation of high-fidelity quantum gates in emerging oxide-based qubit platforms (2606.06948).