Dynamically generated correlations in a trapped bosonic gas via frequency quenches

Abstract

We study a system of $N$ noninteracting bosons in a harmonic trap subjected to repeated quantum quenches, where the trap frequency is switched from one value to another after a random time duration drawn from an exponential distribution. Each cycle contains two steps: (i) changing the trap frequency to enable unitary evolution under a Hamiltonian, and (ii) reapplying the original trap at stochastic times to cool the gas back to its initial state. This protocol effectively makes it an open quantum system and drives it into a unique nonequilibrium steady state (NESS). We analytically and numerically characterize the NESS, uncovering a conditionally independent and identically distributed (CIID) structure in the joint probability density function (JPDF) of the positions. The JPDF in the CIID structure is a product of Gaussians with a common random variance, which is then averaged with respect to its distribution, making the JPDF non-factorizable, giving rise to long-range emergent dynamical correlations. The average density profile of the gas shows significant deviations from the initial Gaussian shape. We further compute the order and the gap statistics, revealing universal scaling in both bulk and edge regimes. We also analyze the full counting statistics, exposing rich parameter-dependent structure. Our results demonstrate how stochastic quenches can generate nontrivial correlations in quantum many-body systems.

Figures (5)

• Figure 1: PDF of $V$ for various values of $f=\omega_1/\omega_2$ and $q= r/\omega_2$. The solid dashed lines indicate the analytical function $h(V)$ in Eq. \ref{['eq:h_V']}. The markers are obtained from direct numerical simulations (averaged over $10^7$ realizations) described at the end of Sec. \ref{['sec:setup']}.
• Figure 2: The top panel plots of the average density profile for various $f=\omega_1/\omega_2$ and $q=r/\omega_2$, with the solid lines indicating the analytical function in Eq. \ref{['eq:den']}. The markers are obtained numerically by the procedure described in Sec. \ref{['sec:setup']}, with $\sigma_1 =1$, and averaged over $10^7$ realizations. The bottom panel highlights the asymptotic tail of $\rho(x)$. The central cusp-like feature in analytics is an artifact of the approximate expression in Eq. \ref{['eq:den_tail']}, which is valid only far from the center (large $x$).
• Figure 3: Plot of the scaled collapsed distribution of $M_k/\theta_\alpha$ for $\alpha =$ 0.0001 (square), 0.1 (circle), 0.3 (diamond), 0.45 (hexagon), and various values of parameters $f=\omega_1/\omega_2$ and $q=r/\omega_2$. The markers indicate the numerical data (details in Sec. \ref{['sec:setup']}) for parameters $\sigma_1=1$, $N=10^6$, averaged over $10^6$ realizations. The solid dashed lines are the analytical plots of the scaling function $z \, h(z^2/2) \equiv |\theta_\alpha| \, \mathrm{Prob}.(M_k)$ [Eq. \ref{['eq:os']}].
• Figure 4: Plot of the scaled collapsed distribution of $d_k/\lambda$ for $\alpha =$ 0.0001 (square), 0.1 (circle), 0.3 (diamond), 0.45 (hexagon) and various values of parameters $f = \omega_1/\omega_2$ and $q = r/ \omega_2$. The markers indicates numerically obtained data (see Sec. \ref{['sec:setup']}), for $\sigma_1=1$, $N=10^6$, averaged over $10^6$ realizations. The solid dashed lines represent the scaling function $F(z)$ given in Eq. \ref{['eq:gap_scalfn']} with integral evaluated numerically.
• Figure 5: FCS plot for $L=1$, $q= r/\omega_2=1$ and various $f = \omega_1/\omega_2$. The markers indicate simulations (details in section \ref{['sec:setup']}) for $\sigma_1=1$, $N=10^5$, averaged over $10^5$ realizations. The solid dashed curves are analytical plots of the function $\mathrm{Prob}.(\kappa,L)$ in Eq. \ref{['eq:fcs']}.