Engineering Ponderomotive Potential for Realizing $π$ and $π/2$ Bosonic Josephson Junctions

TL;DR

The paper addresses how to engineer relative-phase dynamics in a bosonic Josephson junction subject to fast periodic modulation. By applying a ponderomotive potential through time-scale separation, it derives an effective static potential that governs slow dynamics and analyzes transitions between self-trapping and $π$-phase oscillations, supported by numerical simulations. A key finding is that a Kapitza-like stabilization yields a robust $π$-phase mode under high-frequency drive, and when the small-population-difference regime breaks down, a momentum-shortening effect can stabilize a $π/2$-phase mode under specific conditions; both phenomena are interpreted via a pendulum mapping. These results demonstrate a route to Floquet-engineered BJJ dynamics with potential applications in matter-wave interferometry and quantum simulation, while outlining limitations and avenues for exploring nonperturbative regimes and asymmetries.

Abstract

We study the ponderomotive potential of a bosonic Josephson junction periodically modulated by a high-frequency electromagnetic field. Within the small population difference approximation, the ponderomotive drive induces the well-known Kapitza pendulum effect, stabilizing a $π$-phase mode. We discuss the parameter dependence of the dynamical transition from macroscopic quantum self-trapping to $π$-Josephson oscillations. Furthermore, we examine the situation where the small population difference approximation fails. In this case, an essential momentum-shortening effect emerges, leading to a stabilized $π/2$-phase mode under certain conditions. By mapping this to a classical pendulum scenario, we highlight the uniqueness and limitations of the $π/2$-phase mode in bosonic Josephson junctions.

Figures (6)

• Figure 1: A bosonic Josephson junction. Cold atoms are constrained in the two traps by a double-well potential. The high barrier potential between two condensates leads to weak coupling as well as the tunneling effect.
• Figure 2: Lines with different colors show effective potential with respect to $\phi$ at different oscillation strength $\lambda$. The dimensionless oscillation frequency is $\omega=12$. The dimensionless interatomic energy is $\Lambda=11$.
• Figure 3: Particle number difference $n$ and phase difference $\phi$ as a function of dimensionless time. The left two figures (a) and (c) show the numerical result of equations of motion without the driving field. Meanwhile, the right two figures (b) and (d) show the motion with the driving field. For both the two situations we have $\Lambda=11$ and the same initial conditions: $n(0)=0.01, \phi (0)=\pi$. And the parameters of the driving field are $\lambda = 6, \omega=12$.
• Figure 4: The illustration of two different types of pendulum with the same vertical driving force. The left figure shows a momentum-shortened pendulum vibrates around $\pi/2$ point in a counter-intuitive way: the length of the rod shrinks and recovers according to its motion, which stabilizes the $\pi/2$ modes. While the classical pendulum with a rigid rod will just go through the $\pi/2$ point, as shown in the right figure.
• Figure 5: With high-frequency modulation and the condition $K_0=0$, numerical results of equations of motion corresponding to the BJJ (a) and classical rigid pendulum (b) are presented. Initial conditions are $n(0)=0, \theta (0)=0.1$ for both (a) and (b), parameters are $\Lambda' =1\times 10^{-3}, \omega'=8$ for both (a) and (b). In the context of classical pendulum, $1/\Lambda'$ is the moment of inertia of the rigid rod. The rapid dynamic behaviors are displayed in detail.