Hilbert Space Black Hole Analog: Unidirectional Transport without Driving

Abstract

Black holes permit matter to cross their event horizon in only one direction. We show that interacting bosons in optical lattices with asymmetric barrier exhibit an analogous phenomenon, creating unidirectional quantum transport without external driving or dissipation. This directionality emerges purely from many-body interactions, which cause asymmetric projection of the initial state onto transport-enabled or transport-forbidden sectors. The resulting dynamics create an effective one-way boundary in Hilbert space, forming a quantum analog of a black-hole event horizon. Our results establish interactions as a fundamentally new route to directional transport, enabling coherent rectification in atomtronic circuits by the use of intrinsic properties of the system only.

Figures (5)

• Figure 1: Initial state preparation protocol. Starting from a random distribution of $N$ bosons across the $L$-site lattice (top), a strong localizing potential ($3h$, shown in blue) is applied to all sites except the leftmost $L/2-1$ sites to obtain the ground state (middle). The system is then evolved under the asymmetric triangular barrier configurations: (a) "vertical" orientation with barrier heights $h$ and $h/2$ at sites $L/2$ and $L/2+1$, respectively, or (b) "angled" orientation with the barrier heights reversed.
• Figure 1: Population imbalance $\Delta n$ as a function of time $t$ and interaction strength $U$ for varying particle numbers: (a) $N=3$, (b) $N=4$, (c) $N=5$, and (d) $N=6$. System parameters: $L=8$ sites, barrier height $h=10J$, open boundary conditions. Red (blue) regions indicate preferential tunneling from the vertical (angled) side.
• Figure 2: Directional transport in the asymmetric Bose-Hubbard model. (a) Heatmap showing the population imbalance $\Delta n$ as a function of interaction strength $U$ and time $t$ for $N=4$ bosons, $L=6$ sites, barrier height $h=10 J$, and open boundary conditions. Red (blue) regions indicate preferential tunneling from the vertical (angled) side. The strongest directional transport occurs at $U \approx 1.42J$ (dark red band). Time evolution of $n_{\rm after}$ for $U=1.42J$ in case of (b) Fock state and (c) coherent state initial conditions. Blue curve: tunneling from vertical side, indicating collective many-body transport. Orange curve: tunneling from angled side remains suppressed.
• Figure 2: Population imbalance $\Delta n$ as a function of time $t$ and interaction strength $U$ for: (a) $L=10$ and $N=4$, (b) $L=12$ and $N=5$; barrier height $h=10J$, open boundary conditions. Red (blue) regions indicate preferential tunneling from the vertical (angled) side.
• Figure 3: Eigenstate structure underlying directional transport at $U = 1.42J$ and $h = 10J$ for a system of size $L = 6$ with $N = 4$ bosons. Main panel: Overlap $|\langle\psi_i|\psi_0\rangle|^2$ between the prepared initial state (ground state of the system with cooling barrier) and eigenstates of $\mathcal{H}_a$ (blue) and $\mathcal{H}_b$ (orange). Initial localization from the angled side projects almost entirely onto a single eigenstate ($i=3$, overlap $\approx 0.9$), while localization from the vertical side creates a superposition of three eigenstates ($i=5,6,7$, maximum overlap $\approx 0.4$). Insets: Fock-state composition $|c_j|^2$ of the dominant eigenstates. The top five Fock-state contributions to these eigenstates are detailed in Table \ref{['tab:eigenstates']}.