Assessing small accelerations using a bosonic Josephson junction

Bosonic Josephson junctions provide a versatile platform for exploring quantum tunneling and coherence phenomena in ultracold atomic systems. While extensive research has examined the Josephson-junction dynamics in various double-well configurations, most studies have been limited to inertial reference frames. In the present work we pose the question how placing a Josephson junction in a noninertial reference frame would impact the quantum tunneling. Our findings demonstrate that accelerating a Josephson junction alters the tunneling dynamics. Conversely, tunneling behavior can be used to assess the acceleration of the system. By analyzing the changes in physical properties, we can assess the acceleration of the double well. We begin with the most simple noninertial frame: moving with constant acceleration. The tunneling time decreases exponentially as acceleration increases, making it effective for measuring larger accelerations. However, for smaller accelerations, accurate assessment requires accounting for many-body depletion, which decreases linearly as acceleration rises. Next we explore a more complex scenario where the acceleration is time dependent. In this case, the acceleration is mapped onto the tunneling time period and depletion, which again serve as predictors of acceleration. We also explore how the tunneling time and condensate depletion are affected by changes in the interparticle interaction. We go further by conducting a detailed analysis of the change in tunneling dynamics when the system deviates from constant or zero acceleration. The quantitative analysis shows that the depletion changes exponentially near constant acceleration, while around zero acceleration, the change follows a polynomial pattern. A comprehensive analysis of the effects of damped motion on the condensate depletion is performed as well. All in all, we quantify how the tunneling process and the mean-field and many-body properties evolve in a noninertial system of increasing complexity.