[Paper Review] A coherent beam splitter for electronic spin states

J. R. Petta, Hai‐Feng Lü+1 more|Oct 4, 2010

Quantum and electron transport phenomena3 citations

TL;DR

This paper demonstrates an all-electrical, nanosecond-scale coherent beam splitter for electron spin states in a double quantum dot using Landau-Zener transitions at a singlet-triplet anti-crossing. By tuning gate voltages to sweep through the anti-crossing, the system coherently oscillates between the spin singlet and triplet states (T+), achieving quantum control via hyperfine coupling with the nuclear spin bath, with observed Stückelberg interference confirming coherent dynamics on a 1.5–1.6 ns period.

ABSTRACT

Rapid coherent control of electron spin states is required for implementation of a spin-based quantum processor. We demonstrate coherent control of electronic spin states in a double quantum dot by sweeping an initially prepared spin singlet state through a singlet-triplet anti-crossing in the energy level spectrum. The anti-crossing serves as a beam splitter for the incoming spin singlet state. Consecutive crossings through the beam splitter, when performed within the spin dephasing time, result in coherent quantum oscillations between the singlet state and a triplet state. The all-electrical method for quantum control relies on electron-nuclear spin coupling and drives single electron spin rotations on nanosecond timescales.

Motivation & Objective

• To achieve fast, all-electrical coherent control of single electron spin states in a semiconductor double quantum dot.
• To overcome limitations of conventional electron spin resonance (ESR) and optical methods, which are difficult to localize and scale.
• To demonstrate that singlet-triplet anti-crossings can function as a beam splitter for quantum state manipulation.
• To achieve coherent oscillations between the singlet and T+ triplet states using only local gate voltage pulses.
• To enable scalable spin-based quantum computing by enabling fast, localized, and coherent single-spin rotations.

Proposed method

• The system uses a double quantum dot (DQD) in a triple quantum dot geometry, with gate voltages VL and VR tuning the detuning ε to control the energy levels.
• A singlet state is prepared at positive detuning and swept through the S-T+ anti-crossing using a rapid voltage pulse (~1.1 ns), inducing Landau-Zener transitions.
• The return sweep through the anti-crossing generates coherent quantum oscillations between the singlet and T+ states, with phase accumulation governed by the Zeeman energy and detuning.
• Spin-to-charge conversion via a quantum point contact (QPC) charge sensor measures the final singlet state probability PS.
• The system's dynamics are modeled using unitary operations: a 50:50 beam splitter (Hadamard-like gate) when PLZ = 1/2, and a Z-rotation from phase accumulation during the detuning pulse.
• Pulse shaping and sweep rate control are used to tune the Landau-Zener transition probability PLZ and minimize level velocity near the anti-crossing to improve visibility.

Experimental results

Research questions

• RQ1 Can a singlet-triplet anti-crossing in a double quantum dot serve as a coherent beam splitter for electron spin states?
• RQ2 What is the role of hyperfine interaction with the nuclear spin bath in enabling coherent oscillations between singlet and triplet states?
• RQ3 How does the Landau-Zener transition probability depend on sweep rate, and can it be tuned to achieve high-fidelity quantum operations?
• RQ4 Can consecutive sweeps through the anti-crossing produce observable Stückelberg interference patterns?
• RQ5 To what extent can pulse shaping improve the visibility and fidelity of coherent spin rotations?

Key findings

• Coherent oscillations between the singlet and T+ triplet states were observed with a period of ~1.5 ns, in good agreement with the Zeeman energy of 1.6 ns at 100 mT magnetic field.
• The measured singlet return probability PS exhibited clear Stückelberg interference fringes as a function of detuning and pulse length, confirming coherent dynamics.
• The oscillation visibility ranged from 15% to 30%, with higher visibility achieved at lower sweep rates, indicating that PLZ ≈ 0.96 in the measured conditions.
• The interference pattern shifted and slowed with decreasing external magnetic field (BE), consistent with theoretical predictions based on Zeeman splitting and anti-crossing energy shifts.
• Theoretical modeling of PS using unitary operations and phase accumulation matched the experimental data well, with visibility set by PLZ = 0.96.
• The observed decay of oscillations with increasing pulse length is attributed to fluctuations in the Overhauser field, indicating a dominant dephasing mechanism.