Quantum entanglement response to pulsed gate modulation

TL;DR

This work addresses how time-dependent gate pulses can initialize and control entanglement between two capacitively coupled charge qubits in a four-quantum-dot system. A theoretical framework combining a four-dot Hamiltonian with gate-tunable tunneling, a fermion-to-qubit mapping, and a Lindblad master equation models open-system dynamics under on-demand electron injection. Results show that pulse shape and timing critically determine entanglement, with square pulses achieving fidelity near 0.9 and negativity near 0.9 under optimized conditions, whereas Gaussian pulses yield markedly lower entanglement. The study highlights the importance of pulse engineering and noise mitigation for realizing robust entanglement in mesoscopic electronic devices based on charge qubits.

Abstract

We examine the impact of time-dependent gate voltages on entanglement generation in two capacitively coupled charge qubits, with single-electron injection triggered on demand. The gate voltage modulates the tunnel coupling between the qubits and electronic reservoirs, initiating charge transport into the system. The formation of entangled states arises from the competition between inter-qubit Coulomb interactions and electron hopping processes. Particular attention is paid to the temporal structure of the gate pulse, which plays a pivotal role in shaping the entanglement dynamics. By exploring a variety of pulse profiles, we uncover regimes of enhanced entanglement and identify optimal driving conditions. Additionally, we investigate how environmental dephasing deteriorates entanglement formation. Within the framework of the density matrix formalism, we calculate fidelity, linear entropy, and negativity to identify robust operational windows. These results provide insights into controlling quantum correlations in mesoscopic systems and underscore the importance of error mitigation strategies in realizing high-performance electronic quantum devices.

Figures (7)

• Figure 1: Illustration of the system of interest. Four quantum dots labeled as 1, 2, 3, 4 are arranged in an array that forms a bipartite two-qubit structure. The upper dots 1 and 2 hybridizes their orbitals thus forming a molecular structure that provides one charge qubit. Similarly, the lower dots 3 and 4 constitutes a second qubit. No charge can flow between the qubits, however they are capacitivelly coupled to each other via Coulomb interactions with strength $J$ and $J'$. Left and right leads can inject charge into the qubits.
• Figure 2: The maximum fidelity for the initial target state $\ket{0110}$ as a function of the electronic pulse parameters: intensity ($\Gamma_0$) and width ($\sigma_\theta$). Small values of $\sigma_\theta$ combined with large values of $\Gamma_0$ provide optimal initialization conditions. The fidelity does not reach 100%, as additional states may also be populated during the initialization pulse. In the figure, three specific points are highlighted with the letters H, M, and P, corresponding to high, medium, and poor-quality initialization conditions, respectively.
• Figure 3: Maximum value of negativity, $\mathcal{N}$, after pulse initialization as a function of $\Gamma_0$ and $\sigma_\theta$. The negativity behavior shows a strong correlation with the fidelity in Fig. \ref{['fig2']}, indicating that achieving high-quality initialization is essential for forming a highly entangled state. The same points H, M and P, from Fig. \ref{['fig2']}, are highlighted here.
• Figure 4: (Color online) Panel (a): Fidelity (black lines) and linear entropy (blue lines) as a function of $\theta/2\pi$ for the three points in Figs. \ref{['fig2']}-\ref{['fig3']}, corresponding to high (H) (solid line), medium (M) (dashed line), and poor (P) (dotted line) initialization quality. The rectangular pulse (red lines) is illustrated for the three cases. The fidelity $\mathcal{F}$ is calculated for $\sigma_{tar}=\ket{\phi}\bra{\phi}$, with $\phi=\pi/2$. Panel (b): Negativity $\mathcal{N}$ against $\theta$ for the three cases H, M, and P. Note that both fidelity $\mathcal{F}$ and negativity $\mathcal{N}$ attain higher values in the H case and become more suppressed in the M and P cases. Observe that $\mathcal{N}$ also peaks at the fidelity dips, indicating that the evolved state reaches highly entangled states twice within a fidelity period.
• Figure 5: Maximum value of negativity, $\mathcal{N}$, after pulse initialization as a function of $\Gamma_0$ and $\sigma_\theta$ for a Gaussian pulse. Compared to Fig. (\ref{['fig3']}), which employed a square pulse yielding $\mathcal{N} \approx 0.9$, the Gaussian pulse here results in markedly lower entanglement, peaking near $0.4$. This highlights the decisive influence of pulse shape on entanglement generation.