[Paper Review] Semiconductor quantum ring as a solid-state spin qubit

E. Zipper, Marcin Kurpas+2 more|arXiv (Cornell University)|Nov 11, 2010

Diamond and Carbon-based Materials Research1 references18 citations

TL;DR

This paper proposes a semiconductor quantum ring as a solid-state spin qubit using Zeeman sublevels of the highest occupied orbital in a single or few-electron system. The qubit is initialized, manipulated, and read out via electrical or optical control, with relaxation times exceeding seconds in thin rings (r₀ ≤ 10 nm), making them viable for scalable quantum information processing due to suppressed spin-flip mechanisms and tunable confinement.

ABSTRACT

The implementation of a spin qubit in a quantum ring occupied by one or a few electrons is proposed. Quantum bit involves the Zeeman sublevels of the highest occupied orbital. Such a qubit can be initialized, addressed, manipulated, read out and coherently coupled to other quantum rings. An extensive discussion of relaxation and decoherence is presented. By analogy with quantum dots, the spin relaxation times due to spin-orbit interaction for experimentally accessible quantum ring architectures are calculated. The conditions are formulated under which qubits build on quantum rings can have long relaxation times of the order of seconds. Rapidly improving nanofabrication technology have made such ring devices experimentally feasible and thus promising for quantum state engineering.

Motivation & Objective

• To demonstrate that semiconductor quantum rings can serve as robust solid-state spin qubits with long coherence times.
• To analyze the feasibility of initializing, manipulating, and reading out spin qubits in quantum rings using Zeeman sublevels.
• To evaluate relaxation and decoherence mechanisms in quantum rings, especially due to spin-orbit coupling.
• To compare relaxation times in quantum rings with those in quantum dots, identifying conditions for superior performance.
• To assess experimental viability of quantum ring qubits using current and emerging nanofabrication techniques.

Proposed method

• The study uses a 2D ring Hamiltonian with electron effective mass, vector potential, and Zeeman coupling to model spin-orbit interaction and magnetic field effects.
• Numerical solutions are employed to calculate energy levels and wavefunctions for finite-thickness quantum rings under axial magnetic fields.
• Relaxation times are estimated using spin-orbit interaction mechanisms, with focus on the dominant spin-flip processes in ring geometries.
• The analysis assumes a single electron in the highest occupied orbital (l) and applies the condition ΔZ ≪ Δl to isolate a two-level system.
• The model considers both electrostatically defined and self-assembled quantum rings, with parameter sets matching recent InGaAs and GaAs ring experiments.
• Feasibility is evaluated using realistic nanofabrication constraints, including ring radii <12 nm and gate-defined quantum ring architectures.

Experimental results

Research questions

• RQ1 Can a single or few-electron quantum ring support a stable two-level spin qubit system under Zeeman splitting?
• RQ2 What are the dominant relaxation mechanisms in quantum rings, and can they yield relaxation times exceeding seconds?
• RQ3 How do relaxation times in quantum rings compare to those in quantum dots under similar conditions?
• RQ4 What nanoscale dimensions and material parameters are required to achieve long coherence times in quantum rings?
• RQ5 Can current or emerging nanofabrication techniques realize quantum rings with sub-10 nm radii and sufficient quality for qubit operation?

Key findings

• Quantum rings with radii ≤10 nm can achieve electron spin relaxation times exceeding one second, even for single-electron occupation.
• For thin rings with higher electron occupation (|l| > 0), relaxation times can surpass those of quantum dots due to enhanced orbital symmetry and reduced spin-orbit coupling.
• The Zeeman sublevels of the highest occupied orbital form a well-isolated two-level system when kBT ≪ ΔZ ≪ Δl, satisfying the qubit condition.
• Relaxation times are strongly dependent on ring radius and electron confinement, with sub-10 nm rings showing optimal suppression of spin-flip processes.
• Electrostatically defined quantum rings with radii <12 nm are experimentally feasible and compatible with existing nanofabrication, including gate-defined heterostructures in nanowires.
• The combination of nanowire-based axial heterostructures and gate-defined potentials offers a promising path to realizing ultra-thin, high-quality quantum rings for qubit applications.