Bayesian inference to characterize Josephson oscillations in a double-well trap

Abstract

We use quantum trajectories to simulate Josephson oscillations of atomic condensates between the two sides of a double-well potential. In the simulations the atoms in both wells are monitored using off-resonant light scattering, and the ultimate outcome of our thought experiment is a sequence of photon counts probing the numbers of the atoms in each potential well. We show how to reconstruct the Josephson oscillations from the observed photon counts using Bayesian inference, and study the oscillations quantitatively by averaging the inferred time dependent oscillation amplitude over a large number of realizations. Scaling behaviors that characterize the oscillations are uncovered and related to physics principles such as measurement back-action. It turns out that the scalings hold true for quite small atom numbers, so that in this sense four atoms in a potential well may already make a Bose-Einstein condensate.

Polaritonic Rabi and Josephson Oscillations

“…Notably, in the case of BECs, the first transposition of this physics was considering noninteracting particles [4] and the role of the phase difference as a drive for the superflow was the focus of attention. The question of the phase of macroscopically degenerate quantum states remained anchored in the phenomenon but also took a separate route of its own [7][8][9], that is still actively investigated to this day [10,11].…”

Experimentally detecting a quantum change point via the Bayesian inference

“…In particular, Bayesian inference as a classic technique in the ML domain has been discussed in Ref. [10,12,[23][24][25] and applied to quantum tasks in many cases, such as quantum Hamiltonian learning [10,12], phase estimation [24][25][26][27][28], and several others [29,30](spectral function reconstruction and Josephson oscillation characterization).…”