Statistical electron excitation in a double quantum dot induced by two independent quantum point contacts

We investigate experimentally the influence of current flow through two independent quantum point contacts to a nearby double quantum dot realized in a GaAs-AlGaAs heterostructure. The observed current through the double quantum dot can be explained in terms of coupling to a bosonic bath. The temperature of the bath depends on the power generated by the current flow through the quantum point contact. We identify the dominant absorption and emission mechanisms in a double quantum dot as an interaction with acoustic phonons. The experiment excludes coupling of a double quantum dot to shot noise generated by quantum point contact as the dominant mechanism.

Figure 1

(Color online) (a) SFM image of the sample. In-plane gates are defined by the thick white lines while titanium oxide lines are indicated by dashed lines. Top gates are labeled with black letters. The QDs are indicated with gray (red online) circles. The white (yellow online) arrows indicate the positive direction of the current in the QPCs. (b) Calculated electrostatic potential in the 2DEG generated by the oxide lines and the top gates. (c) Modulated current component proportional to the transconductance measured through QPC2 for $V_{\text{QPC}2}=0.5\text{mV}$. An ac voltage of 1.5 mV with a frequency of 34 Hz was applied to the in-plane gate ipg1 and detected in the QPC2 circuit using lock-in techniques. The honeycomb pattern and four pairs of triple points are visible. (d) Simultaneously measured double-dot dc current. The source-drain voltage was $V_{\text{SD}}=60\mu \text{V}$.

Figure 2

(Color online) (a) Double dot current as a function of the gate voltages $V_{\text{ipg}1}$ and $V_{\text{ipg}2}$. It represents the charge stability diagram of the DQD. The dashed lines outline the edges of the honeycomb cells (Ref. 2). $M$ and $N$ refer to the number of electrons in the left and the right dots, respectively. The dashed gray line (red online) denotes the detuning axis, with zero detuning occurring at the triple point. The gray crosses (red online) crosses correspond to the positions of the current maxima. The solid gray line (green online) depicts the calculated charge configuration diagram with the tunneling coupling $t=50\mu \text{eV}$. It was obtained by assuming the constant interaction model with a finite tunnel coupling (Ref. 2). The data was taken with $V_{\text{SD}}=100\mu \text{V}$ applied symmetrically across the DQD, lifting the chemical potential in the source lead ${\mu }_L$ up and lowering the energy of the drain lead ${\mu }_R$. The insets schematically show the level alignment at points indicated by the arrows. (b) The same region as in (a) but with a 1 mV dc bias voltage applied across QPC1 and $60\mu \text{V}$ applied symmetrically across the DQD. The triangle indicates the region with the induced DQD current. The insets show schematic diagrams of the electrochemical potentials in the left and the right quantum dots along the selected honeycomb boundaries. (c) Calculated current through a double dot as a function of gate voltages. The calculation refers to the measurement presented in panel (a), where no bias voltage was applied to the QPC. The details of the calculation are discussed in the text. (d) Calculated stability diagram corresponding to the situations in (b), where a voltage of 1 mV was applied across the QPC2. The dark blue color in (d) was used to mark the region with a negative current. The comparison between (b) and (d) is presented in the text.

Figure 3

(Color online) Current through the DQD along the detuning line: (a) for different QPC1 and (b) different QPC2 currents. Fits are plotted with solid lines (see text).

Figure 4

(Color online) (a) Current through the DQD at fixed detuning of $200\mu \text{eV}$ as a function of QPC1 and QPC2 currents. The open and closed symbols correspond to the “+” and “−” signs in the corresponding expression, respectively. (b) Temperature of the bosonic bath as a function of the QPC1 and QPC2 currents calculated from (a) (see text).

Figure 5

(Color online) (a) The DQD current as a function of the QPC1 and QPC2 currents. The data was taken at a fixed detuning $\delta =200\mu \text{eV}$. (b) Calculated temperature of the bosonic bath $T_b$.

Figure 6

(Color online) (a) Driving current through the QPC induces a current through the DQD. An electron absorbs an energy quantum $\Delta$ emitted from the left or the right QPC and is excited to the excited state. It leaves the dot via the left barrier and another electron can tunnel from the right into the right dot. (b) Schematic energy-level diagram for the DQD. The wave functions of the bonding $\left({\Phi }_B\right)$ and antibonding $\left({\Phi }_A\right)$ states are shown. The electrochemical potential of the left (right) lead is ${\mu }_L$ $\left({\mu }_R\right)$.

Figure 7

(Color online) Energy level diagrams presenting four possible charge states of the DQD in the vicinity of a pair of triple points. The state GS0 corresponds to the situation with no excess electron present in the double dot. The states GS1 and EX1 are the ground and excited states of the double dot in the case of one excess electron, respectively. The fourth state GS2 is a two-excess electron ground state. The occupation probabilities of these states are labeled as $p_{\text{GS}0}$, $p_{\text{GS}1}$, $p_{\text{EX}1}$, and $p_{\text{GS}2}$. The transitions between these states are determined by tunneling rates ${\Gamma }_{i,j}$ and Fermi function $f_{i,j}$. The index $i=\left(L,R\right)$ correspond to the transition occurring through the left $i=\left(L\right)$ and through the right $i=\left(R\right)$ leads. The second index $j=0,1,2,3$ labels the transition of the electron in the DQD.