Detecting superconductivity out of equilibrium

Recent pump-probe experiments on underdoped cuprates and similar systems suggest the existence of a transient superconducting state above $T_c$. This poses the question of how to reliably identify the emergence of long-range order, in particular superconductivity, out of equilibrium. We investigate this point by studying a quantum quench in an extended Hubbard model and by computing various observables, which are used to identify (quasi-)long-range order in equilibrium. Our findings imply that, in contrast to current experimental studies, it does not suffice to study the time evolution of the optical conductivity to identify superconductivity. In turn, we suggest to utilize time-resolved angle-resolved photoemission spectroscopy experiments to probe for the formation of a condensate in the two-particle channel.

Figure 1

(a) Real and (b) imaginary part of the optical conductivity ${\sigma }_{1,2}(\omega ,\mathrm{\Delta }t)$ with probe pulses applied at different time delays $\mathrm{\Delta }t$ and the corresponding quantities in the CDW ground state (violet) and the SC ground state (orange). The bottom panel (c) shows the real-time evolution of the response current $j(t-\mathrm{\Delta }t,\mathrm{\Delta }t)$ after application of a probe pulse at time delay $\mathrm{\Delta }t$ following the quench (green) and in the SC ground state (orange). The charge flow after applying the probe pulse in the SC ground state at $\mathrm{\Delta }t=0$ is shown in the inset.

Figure 2

Spectral functions of two-particle excitations in (a) equilibrium SC phase, (b) CDW phase, and (c) in nonequilibrium after quenching from the CDW ground state into the SC phase evaluated at time $t=15$. Note that only regions with significant spectral weight are displayed.

Figure 3

Spectral functions of single-particle excitations in (a) equilibrium SC phase, (b) CDW phase, and in (c) nonequilibrium after quenching from the CDW ground state into the SC phase evaluated at time $t=15$. Note that only regions with significant spectral weight are displayed.

Figure 4

Separation of largest natural orbital occupation $\mathrm{\Delta }\lambda /L=\frac{{\lambda }_L-{\lambda }_{L-1}}{L}$ during time evolution after quench for various system sizes. The inset shows the scaling behavior of the normalized dominating eigenvalue $\overline{\lambda }{}_L/L$ with system size $L$.