Coherent matter wave emission from an atomtronic transistor

TL;DR

This study investigates coherent matter-wave emission from an atomtronic triple-well transistor using the one-dimensional Gross-Pitaevskii equation. By varying the source bias $V_{SS}$ and the interatomic interaction strength $a_s$, the authors identify resonant tunneling when the source chemical potential $ ext{mu}_{ ext{source}}$ aligns with discrete gate energies, leading to coherent emission into the drain at a frequency near the gate oscillation $rac{E_{ ext{Gate}}}{ ilde{h}}$ or $oxed{ ilde{ u}_{ ext{Gate}}}$. Across simulations, coherence peaks in the drain correlate with these resonances, while increasing $a_s$ degrades both coherence and drain population, arguing against a mean-field realization of interaction-driven current gain. These results challenge prior many-body predictions that rely on gate-mode coupling for gain and emphasize single-particle resonances as the primary coherence mechanism within the mean-field regime; they also highlight the need to consider finite-temperature effects and beyond-mean-field theories for comprehensive comparison with experiments. The work thus reframes the mechanism of coherent emission in atomtronic transistors and suggests that optimal coherence occurs in the weakly interacting limit, with extensions like ZNG or projected GP offering avenues for future refinement.

Abstract

The atomtronic matter-wave triple-well transistor is theoretically predicted to exhibit current gain and act as a coherent matter-wave emitter. In this work, we investigate the dynamics of an atomtronic transistor composed of a triple-well potential -- source, gate, and drain -- modeled by the time-dependent Gross-Pitaevskii equation. We systematically explore the dependence of the drain population and the current on the source bias potential and the strength of the interatomic interaction. Our simulations reveal signatures of resonant tunneling when the source chemical potential aligns with discrete energy levels in the gate well, leading to coherent matter-wave emission in the drain. Contrary to previous many-body studies that predicted interaction-induced current gain via coupling to gate well modes, our results suggest that coherence in the drain is primarily governed by single-particle resonances, with no evident broadening from nonlinear coupling.

Figures (5)

• Figure 1: (a) A 3-D schematic of the experimental realization of the atomtronic transistor used in experiments. An elongated, cigar-shaped Bose-Einstein Condensate (BEC) is held in a highly anisotropic trap, with its longest dimension along the $x-$axis. Two repulsive optical barriers partition the condensate into the source, gate, and drain regions. Due to high confinement along the radial direction ($y$ and $z$ axes), the dynamics effectively take place only along the $x$-axis. (b) The one-dimensional, triple-well potential landscape of the atomtronic transistor with the "source" well that supplies the atoms, the nearly harmonic "gate" well in the middle, and the flat "drain" well. The drain well extends far enough to prevent atoms from reflecting. The barrier heights are $V_{\mathrm{SG}} = 31$ kHz (between source and the gate) and $V_{\mathrm{GD}} = 33$ kHz (between gate and the drain), respectively. The gate well spans from $x_{\mathrm{SG}}=0$ to $x_{\mathrm{GD}}=4.8\;\mu$m, which we choose to be consistent with the experiments Caliga_2016_principleCaliga_2016. These structural parameters of the potential are held constant throughout all simulations.
• Figure 2: (a) Number of atoms in the gate and the drain well after $t=200$ ms for $a_{s}=5.186\times10^{-10}$m. The gray vertical dotted lines show the single particle energy levels in the gate well. The green vertical dotted line indicates the value of the source bias potential at which the chemical potential of the atoms in the source well at $t=0$ exceeds the source gate barrier $V_{\mathrm{SG}}$, after which the dynamics is no longer only tunneling. (b) Drain atom population and signal coherence versus source bias potential. The power spectrum is calculated for the signal $|\psi(x =40 \; \mu m, t)|^{2}$ from $t= 0$ to $t= 300$ ms for $a_{s} = 5.186 \times 10^{-10}$ m. The peaks in both quantities are strongly correlated, indicating that maximum coherence occurs at resonant tunneling peak. The vertical blue dotted line marks the threshold where the initial source chemical potential exceeds the source-gate barrier, $V_{\mathrm{SG}}$.
• Figure 3: (Top) Raw power spectrum of the atom density $n(t) = |\psi(x=40\mu m, t)|^{2}$ from $t=0$ to $t=300$ ms for $a_{s} = 0.5\times 10^{-9}$m and $V_{\mathrm{SS}} = 26.4$ kHz. (Bottom) The same power spectrum with Savitzky-Golay filter (window width $51 (1068.14$ rad/s), and polynomial order $2$), showing a Gaussian fit to the peak at $\omega=\omega_{\mathrm{Gate}}$.
• Figure 4: Maximum FFT power in the frequency window $\omega=(\omega_{\mathrm{Gate}}/2, 3\omega_{\mathrm{Gate}}/2)$ for all $V_{\mathrm{SS}} < \mu_{\mathrm{source}}$ values plotted as a function of the scattering length $a_{s}$.
• Figure 5: Atom populations as a function of scattering length $a_{s}$ calculated at the source bias values that give the maximum coherence. The number of atoms in the source, gate, and drain wells is recorded at $t=300$ ms. For each $a_{s}$, the data corresponds to the source bias $V_{\mathrm{SS}}$ that yields the maximum FFT power of the drain signal.