Terahertz field control of interlayer transport modes in cuprate superconductors

We theoretically show that terahertz pulses with controlled amplitude and frequency can be used to switch between stable transport modes in layered superconductors, modeled as stacks of Josephson junctions. We find pulse shapes that deterministically switch the transport mode between superconducting, resistive, and solitonic states. We develop a simple model that explains the switching mechanism as a destabilization of the center-of-mass excitation of the Josephson phase, made possible by the highly nonlinear nature of the light-matter coupling.

Figure 1

(a) A short, layered superconductor is driven by a short laser pulse and a dc current $j_{\text{ext}}$. (b) The interplay between the current, the nonlinearity of the crystal, and the light field $E_{\text{ext}}$ allows for the switching between the superconducting state, where the current flows as a supercurrent (red), the resistive state, where the current is supported by quasiparticles (gray), causing oscillatory supercurrents, and solitonic states, where quasiparticle and supercurrents coexist. Numerical results of simulations of these transitions are shown in Figs. 2, 3, and 4, respectively.

Figure 2

Linear response and light-induced switching between sc and resistive state. (a) Electric field evolution (red) at the left boundary after excitation by a weak pulse (gray, dashed) at the plasma resonance, i.e., ${\omega }_{dr}=1$. The residual signal at large times stems from thermal fluctuations. (b) Excitation from an initial sc state by a strong pulse with ${\omega }_{dr}=2$ and amplitude $A=1.8$ that drives the system into the resistive state, signified by a constant electric field, i.e., the emergence of a voltage drop across the junctions. (c) Destabilization of the resistive state by another strong pulse (with ${\omega }_{dr}=0.5$), which disturbs the voltage drop and thus stops the quasiparticle current. (d) Supercurrent evolution $sin(\varphi (\xi ,\tau ))$ in the junction during the excitation process shown in panel (b). (e) Supercurrent evolution $sin(\varphi (\xi ,\tau ))$ during the destabilization process shown in panel (c). We fix the values ${\nu }_c={\nu }_{ab}=0.1$ and $j_{\text{ext}}=0.25$, $L=3.3$, as well as the pulse parameters ${\tau }_0=60$ and $\gamma =0$ in the simulations.

Figure 3

Light-induced switching between sc and solitonic state. (a) Electric field evolution (red) at the left boundary during the excitation by a pulse with $A=2$ and ${\omega }_{dr}=1$ that drives the system from the sc into the solitonic state. (b) The inverse transition from the solitonic to the sc state is induced by a pulse with amplitude $A=1.5$ and frequency ${\omega }_{dr}=0.4$. (c) Supercurrent evolution during the optical excitation of a traveling soliton by the same pulse as in panel (a). (d) Supercurrent evolution during the destruction of the soliton by the same pulse as in panel (b). The remaining parameters are identical to Fig. 2.

Figure 4

(a) Electric field evolution (red) at the left boundary after excitation by a pulse with $A=2$ and ${\omega }_{dr}=2$ (i.e., with the same parameters as the pulse in Fig. 2 that switches the sc to the resistive state) that drives the system from the solitonic into the resistive state, signified by a constant electric field, i.e., the emergence of a voltage drop across the junctions. (b) The inverse transition from the resistive to the solitonic state is induced by a pulse with amplitude $A=1.5$ and frequency ${\omega }_{dr}=1$ (like a pulse that creates a soliton from the sc state). (c) Supercurrent evolution $sin(\varphi (\xi ,\tau ))$ in the junction during the excitation process shown in panel (a). (d) Supercurrent evolution $sin(\varphi (\xi ,\tau ))$ during the destabilization shown in panel (b). The remaining parameters are identical to Fig. 2.

Figure 5

(a) Final macroscopic quantum state after excitation by a pulse with inverse bandwidth $\sigma =10$, amplitude $A$, and carrier frequency ${\omega }_{dr}$. The system is initialized in the sc state. The parameters of Figs. 2 and 3 are indicated by red diamonds. Blue regions indicate parameters in which the system remains in the sc state, and the pulse merely induces transient plasma waves. Dark (bright) ochre regions indicate parameters in which traveling solitons (resistive states) are excited. (b) Destabilization of the COM mode according to Eq. (9).

Figure 6

(a) Final macroscopic quantum state after excitation by a pulse with inverse bandwidth $\sigma =10$, amplitude $A$, and carrier frequency ${\omega }_{dr}$. The system is initialized in the resistive state. (b) Destabilization of the COM mode according to Eqs. (B19, B20, B21).

Figure 7

Final macroscopic quantum state after excitation by a pulse with inverse bandwidth $\sigma =10$, amplitude $A$, and carrier frequency ${\omega }_{dr}$. The system is initialized in the soliton state.

Figure 8

Final macroscopic quantum state after excitation by a single cycle pulse with bandwidth $\sigma =2/{\omega }_{dr}$ and CEP (a) $\gamma =0$, (b) $\pi /2$, (c) $\pi$, and (d) $3\pi /2$. The system is initialized in the soliton state (same as Fig. 7). The panels on the left indicate the pulse form for the given CEP, which is identical for any frequency.

Figure 9

Optical signals and noise. (a) Time evolution (left) and reflectance ${\left|r\left(\omega \right)\right|}^2$ (right) of a weak excitation in a short junction without noise. The blue, dashed line in the reflectance plot shows the theoretical expectation for the bulk system according to Eq. (C3). (b) The same including the noise level used in the paper. (c) Time evolution and reflectance in a long junction. The simulations and theoretical expectation coincide and cannot be distinguished.