Quantum Point Contact with Local Two-body Loss

TL;DR

The paper studies two-terminal mesoscopic transport through a 1D chain with localized two-body loss, modeled for ultracold atomic gases. It develops a Keldysh Green's function formalism with a noise-field representation of Lindblad dynamics and applies the self-consistent Born approximation in the weak-dissipation regime. A key finding is that the effective dissipation becomes occupation-dependent, $\gamma n_{0\bar{\\sigma}}$, which leads to weaker current suppression compared to one-body loss. The results yield analytic current formulas applicable to both single- and multi-site QPC geometries and offer pathways to experimentally probe dissipative transport in ultracold atomic setups and optical lattices.

Abstract

Motivated by recent advances in ultracold atomic gas experiments, we investigate a two-terminal mesoscopic system in which two-body loss occurs locally at the center of a one-dimensional chain. By means of the self-consistent Born approximation in the Keldysh formalism, we uncover mesoscopic current formulas that are experimentally relevant and applicable to the weak dissipation regime. Although these formulas are analogous to those for systems with one-body loss, it turns out that the channel transmittance and loss probability depend on the nonequilibrium occupation at the lossy site. We demonstrate that this occupation dependence leads to a weaker suppression of currents in the presence of two-body loss compared to one-body loss.

Figures (10)

• Figure 1: Schematic of the mesoscopic transport setup: two normal reservoirs are connected via a 1D chain representing a QPC. Particle, energy, and spin currents are induced by the difference in chemical potentials for each spin between the left and right reservoirs $\mu_{L/R, \uparrow/\downarrow}$. The local two-body loss, with rate $\gamma$, occurs at the central site when the spin-up and spin-down particles are simultaneously present.
• Figure 2: (a) Feynman diagram corresponding to the SCBA. (b) Crossing diagram neglected in the SCBA. (c) Diagram to be discarded for consistency with the Lindblad master equation. The thin line represents the unperturbed Green's function of the particle with spin $\sigma$, $g_{\sigma}^C$, the thick line the full Green's function of the particle with spin $\sigma$, $G_{\sigma}^C$, the double line in Fig. \ref{['SCBA']} the full Green function of the particle with opposite spin $\bar{\sigma}$, $G_{\bar{\sigma}}^C$, the double line in Fig. \ref{['diagram_cross_A']} and \ref{['diagram_cross_B']} the unperturbed Green function of the particle with opposite spin $\bar{\sigma}$, $g_{\bar{\sigma}}^C$, and the wavy line the Green's function for the noise field, $g_{\eta}^C$.
• Figure 3: The average number of particle at the central dot with two-body loss. The temperature is set to $T/\Gamma=0.1$. The blue, orange and red curves correspond to $\gamma/\Gamma=0.1, 0.5$ and $1.0$, respectively.
• Figure 4: Comparison between one- and two-body loss effects on the particle current. The temperature is set to $T/\Gamma=0.1$. The blue, orange and red curves correspond to $\gamma/\Gamma=0.1, 0.5$ and $1.0$, respectively. The solid ones represent results with two-body loss, while the dashed ones indicate those with one-body loss.
• Figure 5: Comparison of particle current and particle-loss rate in the cases of one-body and two-body loss. The temperature and chemical potential deference are set to $T/\Gamma=0.1$ and $\Delta\mu/\Gamma=0.4$, respectively. We vary $\gamma/\Gamma$ from $0$ to $10$. The solid line represents results with two-body loss, while the dashed one indicates those with one-body loss.