Electric-Field Control of Josephson Oscillations in Dipolar Bose-Einstein Condensates

TL;DR

This paper investigates how external electric fields can control Josephson oscillations in dipolar BECs, enabling tunable macroscopic quantum tunneling between spatially separated condensates. The authors formulate a three-component dipolar GP model with pumping between a ground-state condensate $\Psi_1$ and two excited states $\Psi_2,\Psi_3$, then adiabatically eliminate the upper states to yield an effective single-component GP equation for $\Psi_1$ with an electric-field–dependent potential $V_{1\mathrm{eff}}$ and interaction strength $\gamma_{1\mathrm{eff}}$. A central barrier creates a Josephson junction, and the applied field tunes the effective dipole moment $p_{\text{eff}}$, progressively enhancing dipolar interactions and increasing the Josephson frequency from about $f_J \approx 26\,\mathrm{Hz}$ to about $f_J \approx 46\,\mathrm{Hz}$. Roton-like features emerge at intermediate to high fields, indicating richer phases and the potential for field-controlled dipolar quantum simulations and sensors, with experimental viability supported by lifetimes under microwave stabilization.

Abstract

We study the dynamic behavior of a Bose-Einstein condensate (BEC) with dipolar interactions when the influence of external electric fields affects the coherent tunneling properties. Here, we propose a tunable platform based on BECs where Josephson oscillations can be engineered and modulated through external electric fields. We develop a theoretical and numerical frame-work that reveals how electric fields affect intercondensate tunneling, phase dynamics, and collective excitations. By employing a coupled set of Gross-Pitaevskii equations with adiabatic elimination of excited states, we demonstrate field-induced tuning of Josephson frequencies and a transition from contact to dipole-dominated regimes. These findings corroborate theoretical predictions about the sensitivity of dipolar BECs to external fields and deepen our understanding of quantum coherence and tunneling in long-range interacting quantum systems.

Figures (5)

• Figure 1: Stationary wave function for dipolar Bose-Einstein condensates. Population distribution in the $xy$ plane for the states (a) $\Psi_1$, (b) $\Psi_2$, and (c) $\Psi_3$. (d) Logarithm of the probability density of each condensate as a function of $x$.
• Figure 2: (a) Dispersion relation of the three condensates. (b) Population deviation from the mean as a function of time. $n_1$, $n_2$, and $n_3$ denote the populations of $\Psi_1$, $\Psi_2$, and $\Psi_3$, respectively, while $\langle n_1 \rangle$, $\langle n_2 \rangle$, and $\langle n_3 \rangle$ represent their corresponding mean values.
• Figure 3: Josephson effect in dipolar condensates. (a) Fractional population imbalance $z$ and (b) sine of the relative phase $\delta \theta$ as functions of time under different electric field conditions. The red line corresponds to the case with no electric field, while the other curve displays the behavior under an electric field of $1.08 E_o$, with $E_o = 1.0\text{kV/cm}$.
• Figure 4: Josephson frequency as a function of the external electric field applied. $E_o = 1.0 \text{kV/cm}$. The inset shows the effective dipole moment as a function of the applied electric field.
• Figure 5: Dispersion relation of the system for the untrapped case at different electric field applied. The dashed line represent the system without electric field, the continous line represent $E=0.46 E_o$, the plus-line $E=1.08 E_o$ and the star-line $E = 37.0E_o$ with $E_o = 1.0 \text{kV/cm}$