Theory of dynamic nuclear polarization and feedback in quantum dots

Abstract

An electron confined in a quantum dot interacts with its local nuclear spin environment through the hyperfine contact interaction. This interaction combined with external control and relaxation or measurement of the electron spin allows for the generation of dynamic nuclear polarization. The quantum nature of the nuclear bath, along with the interplay of coherent external fields and incoherent dynamics in these systems renders a wealth of intriguing phenomena seen in recent experiments such as electron Zeeman frequency focusing, hysteresis, and line dragging. We develop in detail a fully quantum, self-consistent theory that can be applied to such experiments and that moreover has predictive power. Our theory uses the operator sum representation formalism in order to incorporate the incoherent dynamics caused by the additional, Markovian bath, which in self-assembled dots is the vacuum field responsible for electron-hole optical recombination. The beauty of this formalism is that it reduces the complexity of the problem by encoding the joint dynamics of the external coherent and incoherent driving in an effective dynamical map that only acts on the electron spin subspace. This together with the separation of timescales in the problem allows for a tractable and analytically solvable formalism. The key role of entanglement between the electron spin and the nuclear spins in the formation of dynamic nuclear polarization naturally follows from our solution. We demonstrate the theory in detail for an optical pulsed experiment and present an in-depth discussion and physical explanation of our results.

23 pages, 13 figures; published PRB version

References in corpus (13)

• Driven coherent oscillations of a single electron spin in a quantum dot
• Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics
• Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization
• Nuclear spin physics in quantum dots: an optical investigation
• Theory of electron spin decoherence by interacting nuclear spins in a quantum dot
• Stimulated and spontaneous optical generation of electron spin coherence in charged GaAs quantum dots
• Enhancing the Coherence of a Spin Qubit by Operating it as a Feedback Loop That Controls its Nuclear Spin Bath
• Pure quantum dephasing of a solid state electron spin qubit in a large nuclear spin bath coupled by long-range hyperfine-mediated interactions
• Large nuclear Overhauser fields detected in vertically-coupled double quantum dots
• Integrability-based analysis of the hyperfine-interaction -nduced decoherence in quantum dots
• Nonperturbative master equation solution of central spin dephasing dynamics
• Electron-nuclear dynamics in a quantum dot under non-unitary electron control
• Different types of integrability and their relation to decoherence in central spin models

Cited by in corpus (25)

• Relaxation to Negative Temperatures in Double Domain Systems
• Filter function formalism beyond pure dephasing and non-Markovian noise in singlet-triplet qubits
• Quantum model for mode locking in pulsed semiconductor quantum dots
• Nuclear magnetic resonance inverse spectra of InGaAs quantum dots: Atomistic level structural information
• Nuclear Spin Dynamics in Double Quantum Dots: Multi-Stability, Dynamical Polarization, Criticality and Entanglement
• Influence of the nuclear Zeeman effect on mode locking in pulsed semiconductor quantum dots
• Nuclear frequency focusing in periodically pulsed semiconductor quantum dots described by infinite classical central spin models
• Efficient algorithms for the dynamics of large and infinite classical central spin models
• Interplay of valley polarization and dynamic nuclear polarization in 2D transition metal dichalcogenides
• Spin inertia and polarization recovery in quantum dots: Role of pumping strength and resonant spin amplification
• Equilibration in closed quantum systems: Application to spin qubits
• Interplay of spin mode locking and nuclei-induced frequency focusing in quantum dots
• Narrowing of the Overhauser field distribution by feedback-enhanced dynamic nuclear polarization
• Two-laser dynamic nuclear polarization with semiconductor electrons: feedback, suppressed fluctuations, and bistability near two-photon resonance
• Increased coherence time in narrowed bath states in quantum dots
• Quantum Coherence from Periodic Driving with Laser Pulses and Decay
• Driven dynamics of a quantum dot electron spin coupled to bath of higher-spin nuclei
• A solvable quantum model of dynamic nuclear polarization in quantum dots
• Dynamic Nuclear Polarization from Topological Insulator Helical Edge States
• Stabilisation of an optical transition energy via nuclear Zeno dynamics in quantum dot-cavity systems
• Resonant spin amplification in Faraday geometry
• Real-time monitoring of Lévy flights in a single quantum system
• Demonstration of Open Quantum System Optimal Control in Dynamic Nuclear Polarization
• Entangling nuclear spins in distant quantum dots via an electron bus
• Quantifying electron-nuclear spin entanglement dynamics in central-spin systems using one-tangles