# Measurement Back-Action in Quantum Point-Contact Charge Sensing

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## Abstract

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## 1. Introduction

## 2. Charge Detection with a Quantum Point Contact

**Figure 1.**(a) Generic measurement setup used in a charge detection measurement. A quantum dot is connected to source and drain electrodes via tunneling barriers. A QPC, placed nearby, serves as a single tunneling barrier in a separate electric circuit. Its transmission D can be tuned continuously from 0 to 1 using a gate voltage capacitively coupled to the QPC. Electrons tunneling on and off the QD have an effect completely analogous to that of the gate voltage because of the capacitive coupling between QPC and QD. This is used to determine the QD charge state using the QPC current. (b) Typical experimental time-dependence of a QPC current. Whenever an electron tunnels onto the dot, the QPC current drops and vice versa.

## 3. Photonic Back-Action in an InAs Double Dot

#### 3.1. Back-action in quantum-dot systems

**Figure 2.**Back-action of a QPC on a DQD. The QPC as a non-equilibrium system dissipates energy quanta $\Delta E$ which can be absorbed by the DQD and excite an electron from the energetically lower-lying dot to the neighboring dot if $\Delta E$ matches the interdot detuning δ. The spectrum of the dissipated energy $\Delta E$ depends on the QPC bias voltage ${V}_{\mathrm{qpc}}$.

#### 3.2. Sample and measurement description

**Figure 3.**(a) Scanning-electron micrograph of the sample used in the first experiment. An InAs nanowire (horizontal) lies on top of a GaAs/AlGaAs heterostructure containing a 2DEG under the surface. By chemical etching, two coupled dots (red disks) and two QPCs are defined. The left QPC serves both as a counter of the electron tunneling events between the dots, and as an energy source influencing those tunneling events. (b) Interdot tunneling rate measured as a function of DQD detuning δ and QPC source-drain voltage ${V}_{\mathrm{qpc}}$. The right panel is based on a model treating the QPC as a noise source with a ${V}_{\mathrm{qpc}}$-dependent spectrum known from QPC shot-noise theory. It takes into account the data measured close to ${V}_{\mathrm{qpc}}=0\phantom{\rule{0.166667em}{0ex}}\mathrm{mV}$ (i.e., in the “absence” of the QPC) in order to calculate the data expected at finite ${V}_{\mathrm{qpc}}$.

#### 3.3. Model based on QPC shot-noise

## 4. Charge Readout with Cross-Correlation Techniques

#### 4.1. Noise limitation of charge readout

**Figure 4.**(a) Atomic-force micrograph of the sample used for the cross-correlation experiment. The white ridges are oxidized parts of the surface of a GaAs/AlGaAs heterostructure containing a 2DEG. They form insulating barriers and pattern the 2DEG to form a DQD and two QPCs (yellow arrows). (b) Electron tunneling events between one of the dots and the adjacent lead as indicated in panel (a), measured simultaneously with both QPCs. The comparison of the traces shows perfect correlation of the readout signals.

#### 4.2. Cross-correlation analysis

**Figure 5.**Dot-lead tunneling rate (cf. Figure 4[a]) as a function of QPC bias voltages and one gate voltage tuning the energy level of the dot from above to below the potential of the leads. From the same raw time-trace data, the rate is once determined using a counting algorithm (left colorplot), and once using cross-correlation (right colorplot). The ${I}_{2}\left(t\right)$-time traces to the right for three different bias voltages demonstrate the decrease in signal quality for decreasing QPC bias.

## 5. Conclusions

## Acknowledgments

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**MDPI and ACS Style**

Küng, B.; Gustavsson, S.; Choi, T.; Shorubalko, I.; Pfäffli, O.; Hassler, F.; Blatter, G.; Reinwald, M.; Wegscheider, W.; Schön, S.; Ihn, T.; Ensslin, K. Measurement Back-Action in Quantum Point-Contact Charge Sensing. *Entropy* **2010**, *12*, 1721-1732.
https://doi.org/10.3390/e12071721

**AMA Style**

Küng B, Gustavsson S, Choi T, Shorubalko I, Pfäffli O, Hassler F, Blatter G, Reinwald M, Wegscheider W, Schön S, Ihn T, Ensslin K. Measurement Back-Action in Quantum Point-Contact Charge Sensing. *Entropy*. 2010; 12(7):1721-1732.
https://doi.org/10.3390/e12071721

**Chicago/Turabian Style**

Küng, Bruno, Simon Gustavsson, Theodore Choi, Ivan Shorubalko, Oliver Pfäffli, Fabian Hassler, Gianni Blatter, Matthias Reinwald, Werner Wegscheider, Silke Schön, Thomas Ihn, and Klaus Ensslin. 2010. "Measurement Back-Action in Quantum Point-Contact Charge Sensing" *Entropy* 12, no. 7: 1721-1732.
https://doi.org/10.3390/e12071721