Strong Correlations in the Dynamical Evolution of Lowest Landau Level Bosons

TL;DR

The paper addresses non-mean-field dynamics of a strip-like Bose condensate in the lowest Landau level at low filling, where Gross–Pitaevskii theory fails. It develops a cluster-based framework in which the many-body spectrum and dynamics are governed by repulsively bound few-body clusters, with fast oscillations at cluster-energy scales and a long-time spreading that grows as a power of the logarithm, signaling quantum many-body scars. A semiclassical treatment of inter-cluster interactions predicts exponential convergence of cluster energies with center-of-mass angular momentum and a logarithmic growth of the cloud width, while exact diagonalisation supports the cluster picture and exposes selection rules in spectroscopic observables. The results bridge few-body cluster physics and many-body dynamics in the LLL, offering experimentally accessible signatures via density-density correlations and higher-order moments, and revealing a pathway to observe logarithmic thermalisation and scar-like behavior in ultracold gases. These insights have implications for understanding non-ergodic dynamics and the crossover from cluster-dominated to mean-field behavior in rapidly rotating quantum gases.

Abstract

Recent experiments with rotating Bose gases have demonstrated the interaction-driven hydrodynamic instability of an initial extended strip-like state in the lowest Landau level. We investigate this phenomenon in the low density limit, where the mean-field Gross--Pitaevskii theory becomes inadequate, using exact diagonalisation studies and analytic arguments. We show that the behaviour can be understood in terms of weakly-interacting repulsively-bound few-body clusters. Signatures of cluster behaviour are observed in the expectation values of observables which oscillate at frequencies characterised by the energies of few-body boundstates. Using a semiclassical theory for interacting clusters, we predict the long-time growth of the cloud width to be a power law in the logarithm of time. This slow thermalisation of bound clusters represents a form of quantum many-body scars.

Figures (9)

• Figure 1: A schematic of the system in question. The initial state is the condensate (dark blue) in the zero momentum state in the Landau gauge in the LLL. Interactions cause the condensate to deplete, producing pairs of atoms in opposite momentum states (red). These give rise to the dynamic instabilities. The inset shows the initial state in real space on a torus of size $L_x\times L_y$.
• Figure 2: The squared cloud width in (a) $N=3, \nu_\text{1D}=0.24$ and (b) $N=4, \nu_\text{1D}=0.16$ systems. The blue is the raw squared width, showing fast oscillations. The dashed orange curve is the time-averaged width, showing a long term growth that is consistent with our $(\ln t)^{1.5}$ prediction (dash-dotted green curve) described in section \ref{['sec:growth']}. The scaling is obtained from numerical fits. In $N=3$ we have direct calculations based on equation \ref{['eq:sinc']} yielding the dashed red curves.
• Figure 3: The power spectra of $\langle\hat{\rho}_0 \rangle$ and $\langle\hat{\rho}_0^2 \rangle$ in the $N=3, \nu_\text{1D}=0.12$ system. Peaks corresponding to transitions between different cluster states can be seen, including the $3V_0\to V_0$ transition. The $3V_0\to 0$ transition is missing in $\langle\hat{\rho}_0 \rangle$ but is present in the $\langle\hat{\rho}_0^2 \rangle$ spectrum.
• Figure 4: The density of states and the normalized eigenvalues of the Hamiltonian and $\hat{C}_E(0)$ in $N=4, \nu_\text{1D}=0.32$. In (a), the solid blue shows the density of states, while the hollow orange shows the density of states weighted by the their overlaps with the initial state $|\braket{n|\Psi(t=0)}|^2$. In (b), the $\hat{C}_E(0)$ eigenvalues correspond well to the energy eigenvalues in the manner of equation \ref{['eq:decomp']}: energy eigenstates $\ket{i}$ are nearly eigenstates of $\hat{C}_E(0)$ as $\braket{i|\hat{C}_E(0)|i}$ closely reproduces the $\hat{C}_E(0)$ eigenvalues. In particular, the $2V_0$ states are precisely the $2V_0^{(2)}$ states. The $25V_0^{(2)}$ states are present but not shown.
• Figure 5: The series of states as functions of CoM angular momenta $l$ converging to $3V_0$ and $2V_0$ with $N=4$ in an infinite system. Their energies approach the asymptotic values exponentially (linearly on a log plot). The black lines are straight lines to guide the eye.