Dynamics of the central-depleted-well regime in the open Bose-Hubbard trimer

Dynamical properties of two coupled quantum cavities with single-mode amplification

Coupled optical cavities provide one of the simplest possible schemes to engineer the interaction of bosonic modes. This paper investigates a two-mode model where, in addition to the usual mode coupling, the presence of an amplification term associated to one of the modes triggers an unexpectedly rich dynamical scenario. The resulting nontrivial model is diagonalized by implementing the dynamical-algebra method, a group-theoretic approach which allows one to determine the stability diagram of the model Hamiltonian in terms of the two mode frequencies for given values of the interaction and amplification parameters. The mode interaction significantly modifies the simple amplification effect of the noninteracting model causing the separation of the unstable domain (where the amplification takes place) into two subdomains, one of which is stable, features no amplification effect, and exhibits an extension controlled by the interaction parameter. The analysis of stability properties is corroborated by the fully analytic study of the energy spectrum which exhibits the transition from a discrete to a continuous structure whenever the system undergoes the transition from a stable region to an unstable region where the amplification effect occurs. This scenario is further confirmed by the calculation of the time evolution of the mode populations.

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.

Continuous-variable approach to the spectral properties and quantum states of the two-component Bose-Hubbard dimer

A bosonic gas formed by two interacting species trapped in a double-well potential features macroscopic localization effects when the interspecies interaction becomes sufficiently strong. A repulsive interaction spatially separates the species into different wells while an attractive interaction confines both species in the same well. We perform a fully analytic study of the transitions from the weak- to the strong-interaction regime by exploiting the semiclassical method in which boson populations are represented in terms of continuous variables. We find an explicit description of low-energy eigenstates and spectrum in terms of the model parameters which includes the neighborhood of the transition point. To test the effectiveness of the continuous-variable method we compare its predictions with the exact results found numerically. Numerical calculations confirm the spectral collapse evidenced by this method when the space localization takes place.

Tunneling dynamics and band structures of three weakly coupled Bose-Einstein condensates

We study the tunneling dynamics and energy bands of three Bose-Einstein condensates which are coupled weakly with each other. The study is carried out with both the mean-filed model and the second-quantized model. The results from these two models are compared and found to agree with each other when the particle number is large. Without interaction, this system possesses a Dirac point in its energy band. This Dirac point is immediately destroyed and develops into a loop structure with arbitrary small interaction. This loop structure has a strong effect on the tunneling dynamics. We find that the tunneling dynamics in this system is very sensitive to the system parameter, e.g., the interaction strength. This sensitivity is found to be caused by the chaos in the mean-field model and the avoided energy crossings with tiny gaps in the second-quantized model. This result gives a certain indication on how the classical dynamics and quantum dynamics are connected in the semi-classical limit. Our mean-field results are also valid for three mutually coupled optical nonlinear waveguides.