Double-weak-link interferometer of hard-core bosons in one dimension

Abstract

We study the dynamics of a lattice hard-core boson gas released from a domain wall initial state in the presence of two weak links (defects). When the two defects are separated by a finite distance, the resulting density profile exhibits clear deviations from the standard Euler-scale hydrodynamic description of the gas, due to genuine quantum interference effects between the two defects. By analyzing the exact fermionic propagators, we show that repeated reflections at the defects give rise to interference fringes and coherent patterns that are beyond the reach of the (generalized) hydrodynamic description. We derive a closed analytic expression for the density profile during the expansion, explicitly highlighting the role played by these interference processes.

Figures (8)

• Figure 1: Sketch of the nearest-neighbor hopping Hamiltonian $\hat{H}_\lambda$ of Ref. Capizzi_2023, given by Eq. \ref{['eq:singledefect']}, parameterised by the strength of the impurity $\lambda \in [0,1]$.
• Figure 2: Left: Schematic drawing of a particle propagating from $y$ to $x_\tau$ ($- x_\tau$) at time $\tau$ interpreted in the quasi particle picture. A particle initially at position $y < 0$ with quasimomentum $k$ and velocity $v(k) = \sin(k)$ arriving at the defect at $x = 0$ gets reflected (transmitted) with an amplitude given by $R(\lambda)$ ($T(\lambda)$). Right: the emerging hydrodynamic picture. Considering a domain wall \ref{['eq:DW_initstate']} and evolving it according to Eq. \ref{['eq:timev_unitary']} results in the phase-space picture given by hydrodynamic description.
• Figure 3: Sketch of the system with Hamiltonian $\hat{H}_{\lambda_1, \lambda_2}$ given by Eqs. \ref{['eq:hoppingH2']} and \ref{['eq:2defects']}, parametrised by the strength of the two impurities $\lambda_1,\lambda_2 \in \left[0,1\right]$, that introduce a staggered onsite potential on site $0,1$ and $N,N+1$ as well as a different hopping terms.
• Figure 4: Left: The two solutions $k_+$ (red) and $k_-$ (blue) of the quantisation condition \ref{['eq:quant_cond_2def_4']}. Horizontal dashed lines show the values in case of a clean system (without the defects). Right: The parameters $\delta_n^+$ (red) and $\delta_n^-$ (blue) introduced in Eq. \ref{['eq:2defect_density_hydrolimit']}. The values for the quasimomenta $k_\pm$ were obtained by exact diagonalization for a system of size $L = 20$, for defect parameters $\lambda_1 = 0.77$ and $\lambda_2 = 0.63$.
• Figure 5: Schematic drawing of the semiclassical picture of the propagators for different positions of x ($x \in L,C,R$ respectively) and $y \in L$, with time being the vertical axis and coordinate the horizontal, with defect strengths of $\lambda_1, \lambda_2 \in [0,1]$ at $x = 0,N$ repectively.