Dynamics and transport of Bose-Einstein condensates in bent potentials

TL;DR

The paper addresses curvature-induced quantum transport of weakly interacting bosons in a two-dimensional bent trap. It employs mean-field theory, the multiconfigurational time-dependent Hartree method for bosons (MCTDHB), and exact diagonalization to connect ground-state localization with dynamical transport through curvature-controlled barriers. Key findings show that increasing bend width B transforms the ground state into two localized lobes and induces fragmentation, while the bend acts as a tunable barrier that modulates coherent tunneling; the tunneling rate can be precisely controlled by geometric parameters, though higher-energy modes contribute beyond a simple two-mode description. The work demonstrates geometry as a versatile tool for designing geometry-controlled quantum transport and lays groundwork for future curved-lattice or long-range interaction studies in engineered quantum systems.

Abstract

The dynamics of bosons in curved geometries have recently attracted significant interest in quantum many-body physics. Leveraging recent experimental advances in tailored trapping landscapes, we investigate the quantum transport of weakly interacting bosons in two-dimensional bent trapping potentials, showing that geometry alone can serve as a precise control knob for tunneling dynamics. Using time-adaptive many-body simulations, complemented by mean-field analysis and exact diagonalization, we analyze both static and dynamical properties of bosons confined in the bent potential. We reveal how bending an initially straight channel induces a transition from density localization to delocalization and drives the buildup of correlations in the ground state. In the dynamics, the bent acts as a tunable barrier that enables controllable tunneling: weak curvature allows coherent tunnelling across the bend, while stronger bent suppresses transport and enhances self-trapping. The tunneling rate can be precisely tuned by geometric parameters, establishing bent traps as versatile platforms for geometry-controlled quantum transport.

Figures (7)

• Figure 1: Schematic diagram of the bent potential $V(x,y)$. The potential has the total width $2B$ and extends a distance $2D$ along the x-direction, which sets the sharpness of the bent. The central flat region spans $-L < y < L$. Boundaries are smoothly closed along the x-direction to prevent bosons from escaping. See text for more details. The quantities shown are dimensionless.
• Figure 2: ($a-d$) One-body density of the ground state in the bent potential for different values of the half-width $B$. As $B$ increases, the density gradually splits into two distinct, localized lobes. The effect becomes more pronounced at larger $B$: (a) $B=0$, (b) $B=2.0$, (c) $B=4.0$, and (d) $B=6.0$. While the results shown are from the many-body calculations, the mean-field densies exhibit similar structures. ($e$) Occupation in the first two natural orbitals as a function of $B$, showing loss of coherence with increase in the width of the bent. For sufficiently large $B$, the system exhibits 50% fragmentation. See text for further discussion. All quantities are dimensionless.
• Figure 3: (a) Position variance in the x-direction, $\frac{1}{N} \Delta_{\hat{X}}^2$, and (b) position variance in the y-direction, $\frac{1}{N} \Delta_{\hat{Y}}^2$, as functions of the half-width of the bent. As $B$ increases, the mean-field variances grow, while the many-body variances initially rise, then begin to decline beyond a certain threshold of $B$. This contrasting behaviour reflects the onset of fragmentation within the system. See the text for more details. All quantities are dimensionless.
• Figure 4: Position expectation values along the x- and y-directions are presented. Panels ($a$) and ($b$) display the mean-field and many-body $\langle x \rangle$, respectively, while panels ($c$) and ($d$) show the corresponding values for $\langle y \rangle$. The transport dynamics are investigated by analyzing the particle flow through the bent structure. The results reveal back-and-forth motion of the bosons between the upper-left and lower-right sides of the bent. As the width of the bent increases, the oscillations become more regular and the oscillations' period increases. Additionally, the many-body expectation values exhibit a reduction in oscillations' amplitude due to the onset of fragmentation. All quantities are dimensionless. Further details are discussed in the text.
• Figure 5: Time evolution of the variances in the x-direction (panels $a_1, b_1, c_1,d_1$) and y-direction (panels $a_2, b_2, c_2, d_2$) for four values of the half-width of the bent $B$: ($a_1,a_2$) $B=0.5$, ($b_1,b_2$) $B=1.5$, ($c_1,c_2$) $B=2.5$, and ($d_1,d_2$) $B=3.0$. In all cases, the mean-field variances exhibit a smooth, bound-like oscillatory dynamics, while the many-body variances increase with time in an oscillatory manner. The growing difference between the mean-field and many-body variances over time reflects the emergence of fragmentation in the system and its deviation from mean-field behavior. Note that the vertical scales differ in each panel to better visualize the differences between mean-field and many-body variances. See text for further details. All quantities are dimensionless.