[Paper Review] Quantum dots investigated with charge detection techniques

Thomas Ihn, Simon Gustavsson+8 more|ArXiv.org|May 20, 2009

Quantum and electron transport phenomena3 citations

TL;DR

This paper reviews the use of quantum point contact (QPC) charge detectors to measure individual electron charges in semiconductor quantum dots with sub-femtoampere sensitivity. The technique enables time-resolved detection of shot noise and full counting statistics, revealing electron interference and back-action effects, and provides a non-invasive method for probing few-electron states and spin dynamics in quantum dot systems.

ABSTRACT

The detection of the quantum dot charge state using a quantum point contact charge detector has opened a new exciting route for the investigation of quantum dot devices in recent years. In particular, time-resolved charge detection allowed the precise measurement of quantum dot shot noise at sub-femtoampere current levels, and the full counting statistics of the current. The technique can be applied to different material systems and holds promise for the future application in quantum dot based quantum information processing implementations. We review recent experiments employing this charge detection technique, including the self-interference of individual electrons and back-action phenomena.

Motivation & Objective

• To investigate the charge state of quantum dots with single-electron sensitivity using a quantum point contact (QPC) as a charge detector.
• To enable time-resolved measurements of quantum dot shot noise and full counting statistics at extremely low current levels.
• To explore electron interference and back-action phenomena in quantum dots via charge detection.
• To demonstrate the applicability of QPC charge detection across different material systems, including Ga[Al]As heterostructures and InAs nanowires.
• To establish QPC charge detection as a non-invasive, chip-integrable tool for quantum dot-based quantum information processing research.

Proposed method

• A Ga[Al]As heterostructure with a two-dimensional electron gas (2DEG) is patterned using local anodic oxidation to form a quantum dot and a nearby quantum point contact (QPC).
• The QPC acts as a charge detector by sensing changes in conductance due to Coulombic coupling from electron addition to the quantum dot.
• The conductance of the QPC is measured as a function of gate voltage (V_G2), with changes in G_QPC indicating individual electron additions to the quantum dot.
• The system is operated at low temperatures (liquid helium range), with source–drain bias voltages below 1 mV to avoid exciting transverse quantization energy levels.
• Time-averaged and time-resolved charge detection are used to extract tunneling coupling strengths (Γ_S, Γ_D) and observe avoided level crossings due to inter-dot coupling.
• Theoretical modeling, including circuit models and Bose–Einstein phonon bath distributions, is used to interpret current signals not explainable by shot noise alone.

Experimental results

Research questions

• RQ1 How can individual electron charges in quantum dots be detected with sub-femtoampere sensitivity?
• RQ2 What insights into quantum dot transport can be gained from time-resolved charge detection of shot noise and full counting statistics?
• RQ3 How does the QPC charge detector influence the quantum dot system, and what are the observed back-action effects?
• RQ4 What mechanisms explain the observed current in a double quantum dot at zero source–drain bias, despite negligible direct tunneling?
• RQ5 To what extent can QPC charge detection be used to probe spin states and quantum coherence in semiconductor quantum dots?

Key findings

• The QPC charge detector enables precise measurement of quantum dot shot noise at sub-femtoampere current levels, revealing full counting statistics of electron transport.
• The technique allows extraction of tunneling coupling strengths (Γ_S and Γ_D) for both ground and excited states in single- and double-quantum-dot systems.
• Time-resolved charge detection revealed self-interference of individual electrons and avoided level crossings due to finite inter-dot tunneling coupling (Γ_c).
• A current was observed in a double quantum dot at zero source–drain bias, attributed to phonon-assisted tunneling driven by heating of the phonon bath via QPC current, with the phonon bath temperature as the sole fitting parameter.
• The observed current maximum at finite detuning Δ, and zero at Δ = 0, is explained by symmetric tunneling leading to cancellation, with sign reversal at large Δ due to preferential tunneling direction.
• The model assuming a Bose–Einstein-distributed phonon bath with temperature T_ph fitted to data successfully reproduces the high-energy cutoff in the measured current, confirming the role of phonon absorption in current generation.