Statistics of orbital entanglement production in a chaotic quantum dot with nonideal contacts

We investigate the statistics of orbital entanglement production between electrons in a chaotic quantum dot with two-channel leads. Through a random-matrix simulation, we obtain the probability density of two entanglement measures, concurrence and entanglement formation, by varying the transparency of the contacts in the presence and absence of time-reversal invariance of the electron dynamics inside the cavity. The results suggest that orbital entanglement production is optimized by increasing the asymmetry between the transparency of the contacts, especially when time-reversal invariance is broken.

Figure 1

Schematic view of a chaotic quantum dot with two double-channel leads. The solid line inside each lead represents an illustrative separation between the two open scattering channels. The transparency of the contact between lead $\nu$ and the chaotic cavity is ${\Gamma }_{\nu }$. The physical symmetry of electron dynamics inside the cavity is indexed by $\beta$.

Figure 2

Concurrence distribution for a quantum dot with symmetric contacts in the presence $\left(\beta =1\right)$ and absence $\left(\beta =2\right)$ of TRI. The transparency of the contacts is represented by the numbers labeling the symbols which are simulated data. The dotted lines are merely for guidance and the solid line is the exact result for ideal contacts (Ref. 17).

Figure 3

Entanglement formation distribution for a quantum dot with symmetric contacts in the presence $\left(\beta =1\right)$ and absence $\left(\beta =2\right)$ of TRI. The transparency of the contacts is represented by the numbers labeling the symbols which are the simulated data. The dotted lines are merely for guidance.

Figure 4

Average of concurrence versus contact transparencies for a quantum dot in the presence $\left(\beta =1\right)$ and absence $\left(\beta =2\right)$ of TRI.

Figure 5

Average of entanglement formation versus contact transparencies for a quantum dot in the presence $\left(\beta =1\right)$ and absence $\left(\beta =2\right)$ of TRI.

Figure 6

Concurrence distribution for a quantum dot in the presence $\left(\beta =1\right)$ and absence $\left(\beta =2\right)$ of TRI. One of the contacts is ideal $\left({\Gamma }_1=1\right)$ while the other has a transparency $\left({\Gamma }_2\right)$ represented by the numbers labeling the symbols which are simulated data. The dotted lines are merely for guidance and the solid line is the exact result for ideal contacts (Ref. 17).

Figure 7

Entanglement formation distribution for a quantum dot in the presence $\left(\beta =1\right)$ and absence $\left(\beta =2\right)$ of TRI. One of the contacts is ideal $\left({\Gamma }_1=1\right)$ while the other has a transparency $\left({\Gamma }_2\right)$ represented by the numbers labeling the symbols which are simulated data. The dotted lines are merely for guidance.