Atomtronic routing of dipolar bosons in a four-well star potential

TL;DR

This work studies atomtronic routing of dipolar bosons in a star-shaped four-well potential, identifying an integrable regime with four conserved quantities that yields a harmonic resonant tunneling dynamics among outer wells. By employing an external field to control the gradient, symmetry breaking, and timing, the authors derive analytic expressions for edge-population dynamics and demonstrate three independent control modes: frequency tuning via field intensity, directional routing via field displacement, and amplitude modulation through staged field switching. The routing protocols realize atomic 2:1 multiplexing and 1:2 demultiplexing, enabling selective transfer of population between wells with high fidelity. The results offer a principled, analytically tractable platform for controllable quantum state transport in atomtronic devices with potential impact on quantum information processing and quantum networks.

Abstract

The ability to precisely control and predict the evolution of quantum states is a fundamental requirement for advancing quantum technologies. Here, we develop tunable atomic routing protocols based on an integrable model of dipolar bosons confined in a four-well potential with a star-shaped configuration. By adjusting the system parameters, we identify a harmonic dynamical regime of the atomic population that can be treated analytically, providing a complete description of the system's behaviour for precise manipulation. We demonstrate three independent modes of control over the atomic population dynamics under the action of an external field: frequency tuning via variation in the field intensity, directional switching via spatial displacement of the field, and amplitude modulation by varying its duration. These modes operate under two distinct configurations: one source and two drains, and, in reverse order, two sources and one drain. These cases emulate an atomic 1:2 demultiplexer and 2:1 multiplexer, respectively. Our results may contribute to the development of control mechanisms in the design of quantum devices.

Figures (9)

• Figure 1: Schematic representation. A central well, denoted by 4, is connected to three outer wells, denoted by 1, 2, and 3. The interactions between the atoms (blue spheres) can influence the population dynamics in the wells.
• Figure 2: Energy levels as a function of $UN/J$. Plot of $E/J$ versus $UN/J$ for the Hamiltonian \ref{['h']}, varying $U$ for $N=16$. The vertical dashed line indicates the value of $UN/J$, corresponding to $U/J = 0.51$ and $\sigma/J = 1.56$. The red dashed line indicates the expectation value $\langle \Psi_{\rm ini}|H|\Psi_{\rm ini}\rangle$ for the initial state $|\Psi_{\rm ini}\rangle = |14,2,0,0\rangle$. The circle marks a region within this band, which is magnified in the inset plot showing the uniform distribution of energy levels.
• Figure 3: Quantum dynamics. Expectation values of the fractional populations $\langle N_1\rangle/N$ (red), $\langle N_2\rangle/N$ (blue), $\langle N_3\rangle/N$ (green), and $\langle N_4\rangle/N$ (purple). Numerical results obtained using the Hamiltonian \ref{['h']} (markers) are compared with the analytical expression in Eq. \ref{['n_k']} (solid lines), for parameter values (a) $\sigma/J = 15.3$, (b) $\sigma/J = 1.57$, and (c) $\sigma/J = -10$. (d) Fidelity $\mathcal{F}$. The vertical dotted line represents the critical value $\sigma/J = \sigma_{\rm crit}/J = -15.3$, and the vertical dashed lines represent the values $\sigma/J = -10,\, 1.57$, and $15.3$. In all cases we consider $U/J = 0.51$ and the initial state $|\Psi_{\rm ini}\rangle = |14,2,0,0\rangle$.
• Figure 4: (a) Schematic representation of the external field displacement. An additional harmonic potential (gray disk) is displaced from well 4 toward well 3 by a distance $\Delta l$ and centered at the red cross. (b) Symmetry breaking. The displaced external field induces an energy offset $\nu$ between well 3 and the other two, which are kept at the same level. As a result, wells 1 and 2 form a resonant tunnel channel, denoted by $C_{1,2}$.
• Figure 5: Schematic representations of the directional control mechanism, (a) and (c). The symbol '$\times$' indicates the center of the external field $F_2 (F_3)$, which selects the tunneling channel through which the atomic flow (blue arrow) from the source - well 1 - toward the drain - well 3 (2) - occurs. Corresponding dynamics are shown in (b) and (d). Fractional populations: $\langle N_1\rangle_k/N$ (red), $\langle N_2\rangle_k/N$ (blue), $\langle N_3\rangle_k/N$ (green), and $\langle N_4\rangle_k/N$ (purple). Comparison between analytical expression \ref{['njk2']} (solid lines) and the numerical results using Hamiltonian \ref{['hi']} (markers), for $k=2$ (b) and $k=3$ (d). In both cases, the parameters are: $U/J = 0.51$, $\sigma/J = 1.56$, $\nu/J = 1.05$, and initial state $|\Psi_{\rm ini}\rangle = |16,0,0,0\rangle$. The transfer time $t=\tau$ of the atoms from the source to the drain is indicated by the dashed vertical line.