Mesoscopic Dynamical Differences from Quantum State Preparation in a Bose-Hubbard Trimer

Conventional wisdom is that quantum effects will tend to disappear as the number of quanta in a system increases, and the evolution of a system will become closer to that described by mean-field classical equations. In this Letter we combine newly developed theoretical and experimental techniques to propose and analyze an experiment using a Bose-Hubbard trimer where the opposite is the case. We find that differences in the preparation of a centrally evacuated trimer can lead to readily observable differences in the subsequent dynamics which increase with system size. Importantly, these differences can be detected by the simple measurements of atomic number.

Figure 1

The number of atoms in the center well as a function of scaled time $Jt$, for $N_1(0)=N_3(0)=1000$ and $\chi ={10}^{-4}$. The lower line is for initial number states and the upper, indistinguishable lines are for initial coherent and squeezed ($r=0.5$) states. These results are the averaged solutions for $10^6$ trajectories of the positive-$P$ equations and have converged to less than the plotted linewidths. All quantities in this and subsequent plots are dimensionless.

Figure 2

Number distributions in the center well, from binning of truncated Wigner trajectories at the first time of maximum transfer, $Jt=1.11$, for initial conditions (a) $N_1(0)=N_3(0)=100$ and $\chi ={10}^{-3}$ and (b) $N_1(0)=N_3(0)=1000$ and $\chi ={10}^{-4}$. The squeezed states $|\alpha ,r⟩$ have $r=0.5$.

Figure 3

The number distributions from binning of truncated Wigner trajectories at the first time of maximum transfer, $Jt=1.11$, for $N_1(0)=N_3(0)=100$ and $\chi ={10}^{-3}$. The wide distribution comes from initial Fock states, while the narrow distribution comes from coherent states with a $\pi /2$ initial phase difference.