Photodynamic melting of phase-reversed charge stripes and enhanced condensation

Abstract

The interplay between charge stripes and pairing has long been a subject of scrutiny in a broad class of unconventional superconductors, as in some cases it is unclear whether this interplay benefits the ensuing superfluidity. Experiments that explore the out-of-equilibrium dynamics of these systems aim to tip the balance toward one phase or the other by selectively coupling to relevant modes. Leveraging the fact that competition between stripes and pairing is not exclusive to fermionic systems, we explore the photoirradiation dynamics of interacting hardcore bosons, in which density-wave phase-reversal melting leads to enhanced phase-coherent transport response, as quantified by the dynamic amplification of both the zero-momentum occupancy and the condensate fraction, as well as finite out-of-equilibrium charge stiffness and superfluid weight, for a given system size. Our results, obtained using unbiased methods for an interacting system on a ladder geometry, demonstrate how one can engineer time-dependent perturbations to release suppressed orders, potentially providing insight into the underlying mechanism in related experiments.

Figures (12)

• Figure 1: (a) Schematic illustration of Eq. \ref{['fig:fig1']} with relevant terms annotated, subjected to $x$-polarized photoirradiation. Here, the hardcore bosons are represented by a composite local fermion. Momentum distribution profiles $n_{\bf k}$ focusing on $k_y = 0$ (b) and $k_y = \pi$ (c), comparing the equilibrium (before pump) with the out-of-equilibrium (after pump, averaged results from $t \in [11t_d, 26t_d] = [72, 169]t_h^{-1}$; shading gives the standard deviation) response to the external field. We observe an average relative enhancement of about 37% for the zero-momentum condensation under the photoirradiation. (d) The $x$-direction charge stiffness resolved for the first 200 eigenstates $|m\rangle$ of $\hat{\cal H}$; marker colors are mapped by the overlap of the time evolved state at $t_1=5t_d$ and the corresponding $|m\rangle$. (e) The instantaneous energy $E(t) = \langle \psi(t)|\hat{\cal H}(t)|\psi(t)\rangle$ over the dynamics; the shaded region marks the probing for the dynamical charge stiffness starting at $t_1$, with a linear-in-time vector potential with slope $\delta A_x$ --- top panel depicts the total ${\bf A}(t)$. Inset shows the energy variation in the probe regime as a function of the effective flux $\Phi_x(t)=\delta A_x L_x(t-t_1)$ for $t>t_1$; $\delta A_x=0.01$. Dashed line displays an approximant at small fluxes that quantifies the dynamical charge stiffness at $t =t_1$, confirming a robust charge transport induced by the pump (see text). (f) The dynamics of the condensate fraction, highlighting a $\sim 34\%$ increase when considering the running average (darker curve). Pulse parameters are $\Omega = 1.713\ t_h$, $A_0 = 0.62$ and $t_d = 6.5 t_h^{-1}$.
• Figure 2: Dependence of the density-density correlations across a stripe for the ground state (a) and the second excited state (b) on the stripe potential. The solid vertical line indicates our selected parameter set for the dynamics, $V_0/t_h=5$, featuring a robust charge $\pi$-phase shift for the ground state, which is absent in the excited state. The right vertical axes display the zero-momentum occupancies.
• Figure 3: (a) Gaussian pump field with amplitude $A_0=0.62$, frequency $\Omega=\omega_{26}\simeq 1.713\ t_h$, and temporal width $t_d=6.5 t_h^{-1}$ --- the same as in Fig. \ref{['fig:fig1']}. Phase-averaged dynamics (solid curves) for a range of phases $\phi_t\in[0,2\pi)$ (shaded regions) are shown in (b)--(d). (b) Dynamics of the correlation functions $c_{{\bf i}_0}(2, 0)$ and $c_{{\bf i}_0}(2, 1)$, in respect to the reference site ${\bf i}_0$ marked in Fig. \ref{['fig:fig1']}(a), exhibiting $\pi$-phase shift reversal after the pulse --- the corresponding density dynamics is shown in Appendix \ref{['app:dens_dyn']}. (c) The zero-momentum occupation $n_{{\bf k}=0}$ exhibits a 37% enhancement in comparison to the equilibrium. (d) State projection coefficients for selected equilibrium eigenstates $|m\rangle$ (the ones showing significant weight over the dynamics), with state $|2\rangle$ gradually becoming dominant at long times, added by an enhanced overlap with state $|6\rangle$.
• Figure 4: Dependence on the pump width $t_d$ and amplitude $A_0$ of the long-time overlap at $t_{\rm max} = 9t_d$ with selected equilibrium eigenstates, $|m=2\rangle$ (a) and $|m=6\rangle$ (b). A finer mesh resolution is shown in the area with an enhanced overlap $|\langle \psi(t_{\rm max})|2\rangle|^2$ while the cross marker pinpoints the maximum value. Here, the pump frequency is set at $\Omega = \omega_{26} = 1.713\ t_h$. (c) The equilibrium $x$-direction current matrix in the low-lying spectrum; dashed lines highlight matrix elements with the target state $|2\rangle$. Other relevant matrix elements for the perturbative analysis are shown in Appendix \ref{['app:mat_elem']}.
• Figure 5: Dependence on the pump frequency $\Omega$ and amplitude $A_0$ of the long-time overlap at $t_{\rm max} = 9t_d = 27 t_h^{-1}$ with selected equilibrium eigenstates, $|m=2\rangle$ (a), $|m=3\rangle$ (b), and $|m=6\rangle$ (c). Horizontal lines indicate relevant gaps in the equilibrium spectrum; note the different ranges of the color bars, which are set to enhance visualization.