Nuclear Dynamics During Landau-Zener Singlet-Triplet Transitions in Double Quantum Dots

Abstract

We consider nuclear spin dynamics in a two-electron double dot system near the intersection of the electron spin singlet $S$ and the lower energy component $T_{+}$ of the spin triplet. The electron spin interacts with nuclear spins and is influenced by the spin-orbit coupling. Our approach is based on a quantum description of the electron spin in combination with the coherent semiclassical dynamics of nuclear spins. We consider single and double Landau-Zener passages across the $S$-$T_{+}$ anticrossings. For linear sweeps, the electron dynamics is expressed in terms of parabolic cylinder functions. The dynamical nuclear polarization is described by two complex conjugate functions ${\Lambda }^{\pm }$ related to the integrals of the products of the singlet and triplet amplitudes ${\tilde{c}}_S^{\ast }{\tilde{c}}_{T_{+}}$ along the sweep. The real part $P$ of ${\Lambda }^{\pm }$ is related to the $S$-$T_{+}$ spin-transition probability, accumulates in the vicinity of the anticrossing, and for long linear passages coincides with the Landau-Zener probability $P_{LZ}=1-e^{-2\pi \gamma }$, where $\gamma$ is the Landau-Zener parameter. The imaginary part $Q$ of ${\Lambda }^{+}$ is specific for the nuclear spin dynamics, accumulates during the whole sweep, and for $\gamma \gtrsim 1$ is typically an order of magnitude larger than $P$. $Q$ has a profound effect on the nuclear spin dynamics, by (i) causing intensive shake-up processes among the nuclear spins and (ii) producing a high nuclear spin generation rate when the hyperfine and spin-orbit interactions are comparable in magnitude. We find analytical expressions for the back-action of the nuclear reservoir represented via the change in the Overhauser fields the electron subsystem experiences.

19 pages, 5 figures

References in corpus (17)

• Single-shot read-out of an individual electron spin in a quantum dot
• Coherent control of a single electron spin with electric fields
• Spin-orbit qubit in a semiconductor nanowire
• Electrically driven single electron spin resonance in a slanting Zeeman field
• Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization
• Theory of electron spin decoherence by interacting nuclear spins in a quantum dot
• Enhancing the Coherence of a Spin Qubit by Operating it as a Feedback Loop That Controls its Nuclear Spin Bath
• A coherent beam splitter for electronic spin states
• Electron Spin Dephasing due to Hyperfine Interactions with a Nuclear Spin Bath
• Hyperfine-mediated gate-driven electron spin resonance
• Spin relaxation and anticrossing in quantum dots: Rashba versus Dresselhaus spin-orbit coupling
• Interlaced Dynamical Decoupling and Coherent Operation of a Singlet-Triplet Qubit
• Dynamic Nuclear Polarization with Single Electron Spins
• Nuclear State Preparation via Landau-Zener-Stueckelberg transitions in Double Quantum Dots
• Spin state mixing in InAs double quantum dots
• Non-destructive measurement of electron spins in a quantum dot
• Phase Transitions in Dissipative Quantum Transport and Mesoscopic Nuclear Spin Pumping

Cited by in corpus (21)

• Semiconductor Spin Qubits
• Coherent control of three-spin states in a triple quantum dot
• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Singlet-triplet splitting in double quantum dots due to spin orbit and hyperfine interactions
• Quenching of dynamic nuclear polarization by spin-orbit coupling in GaAs quantum dots
• Trap-free manipulation in the Landau-Zener system
• Effects of colored noise on Landau-Zener Transitions: Two and Three-Level Systems
• Measurement-assisted Landau-Zener transitions
• Multiphoton transitions in Josephson-junction qubits (Review Article)
• Spin-orbit-coupled quantum memory of a double quantum dot
• High Fidelity Singlet-Triplet $S$-$T_{-}$ Qubits in Inhomogeneous Magnetic Fields
• Preparation of Non-equilibrium Nuclear Spin States in Double Quantum Dots
• The theory of coherent dynamic nuclear polarization in quantum dots
• Interplay of spin-orbit and hyperfine interactions in dynamical nuclear polarization in semiconductor quantum dots
• Narrowing of the Overhauser field distribution by feedback-enhanced dynamic nuclear polarization
• Dynamical Self-Quenching of Spin Pumping into Double Quantum Dots
• Characterization of S-T${}_{+}$ Transition Dynamics via Correlation Measurements
• Electron spin-flip correlations due to nuclear dynamics in driven GaAs double dots
• The formation of a nuclear-spin dark state in silicon
• Self-Quenching of Nuclear Spin Dynamics in Central Spin Problem
• Quantum dynamics intervened by repeated nonselective measurements