Aharonov-Bohm effect for confined matter in lattice gauge theories

Abstract

Gauge theories arise in physical systems displaying space-time local symmetries. They provide a powerful description of important realms of physics ranging from fundamental interactions, to statistical mechanics, condensed matter and more recently quantum computation. As such, a remarkably deep understanding has been achieved in the field. With the advent of quantum technology, lower energy analogs, capable to capture important features of the original quantum field theories through quantum simulation, have been intensively studied. Here, we propose a specific scheme implementing an analogic quantum simulation of lattice gauge theories constrained to mesoscopic spatial scales. To this end, we study the dynamics of mesons residing in a ring-shaped lattice of mesoscopic size pierced by an effective magnetic field. In particular, we find a new type of Aharonov-Bohm effect that goes beyond the particle-like effect and reflecting the the features of the confining gauge potential. The coherence properties of the meson are quantified by the persistent current and by specific features of the correlation functions. When the magnetic field is quenched, Aharonov-Bohm oscillations and correlations start a specific matter-wave current dynamics.

Figures (10)

• Figure 1: Lattice gauge theory on a ring of mesoscopic scale. Illustration of meson dynamics on a ring pierced by a magnetic flux $\Phi$. The screen captures the Aharonov-Bohm oscillations produced by clockwise and anti-clockwise components of the wave function.
• Figure 2: A single meson whose center of mass has been localized within a gaussian distribution of width $\Sigma$, as in Eq.(\ref{['eqn:initialstate']}), is quenched by applying the Hamiltonian (\ref{['Hamiltonian']}) as in Eq.\ref{['eq:quench']}. To this end, the flux is quenched to the value $\Phi/\Phi_0 = 0.8$. The average current (representing the center of mass velocity) and the probability to find the meson with string length $R$ (labelling the length of a string of spin ups connecting the two bound particles), $\mathcal{I}(t)$ and $P(R) = \sum_s |\braket{s,R}{\psi(t)}|^2$, are displayed in panels a),b) and c),d) respectively. The upper panels refer to $\Sigma = 2$, $\tau = 1$; the lower panels refer to $\Sigma = 10^{-6}$, $\tau = 1$. In all cases, we consider $L = 21$ sites.
• Figure 3: Analysis of the meson Aharonov-Bohm oscillations. A single meson wave function, whose center of mass is initialized in the site $s_0$, as specified in Eq.(\ref{['eqn:initialstate']}), evolves along the ring and is monitored at $s=s_0 + L/2$. Here $L = 20$. The upper and the lower panels are respectively for $\tau = 0.1$ and $\tau = 10$. The panels (a),(c) display $P_{mid}(t) = \sum_r |\braket{s_0 + L/2,r}{\psi(t)}|^2$. Panels (b),(d) display the Fourier transform of $\left(P_{mid}(t) - \overline{P_{mid}}\right) = \tilde{P}_{mid}(w)$ at $\Phi/\Phi_0 = 0$, where $\overline{P_{mid}}$ is the time average of $P_{mid}(t)$. The figure in panel (c) is plot for $t$ up to $1000$: indeed, for large $\tau$, the relevant time scale is set by $t/\tau$ - see also text.
• Figure 4: Two particle states. Here, the admissible two particle configurations are shown. The positive direction along the ring is taken to be clockwise. Outgoing and ingoing arrows represent up and down spins respectively. Blue arrows highlight the spins between the ordered fermion positions.(a) $\ket{j_1,j_2}_\uparrow$. (b) $\ket{j_1,j_2}_\downarrow$.
• Figure 5: Current and string length fluctuations. In panel (a) we plot the fluctuations of the single meson current; in panel (b), the fluctuations of the meson extent. For visualization purposes, all the curves in panel (b) have been shifted to zero minimum. The fluctuations are plot for $\tau = 0.5,1,2,3$, respectively in yellow, green, red and blue. All the data are shown for $L=21$.