Pump Frequency Resonances for Light-Induced Incipient Superconductivity in YBa2Cu3O6.5

Optical excitation in the cuprates has been shown to induce transient superconducting correlations above the thermodynamic transition temperature TC, as evidenced by the terahertz-frequency optical properties in the nonequilibrium state. In YBa2Cu3O6þx, this phenomenon has so far been associated with the nonlinear excitation of certain lattice modes and the creation of new crystal structures. In other compounds, like La2−xBaxCuO4, similar effects were reported also for excitation at near-infrared frequencies, and were interpreted as a signature of the melting of competing orders. However, to date, it has not been possible to systematically tune the pump frequency widely in any one compound, to comprehensively compare the frequency-dependent photosusceptibility for this phenomenon. Here, we make use of a newly developed nonlinear optical device, which generates widely tunable high-intensity femtosecond pulses, to excite YBa2Cu3O6.5 throughout the entire optical spectrum (3–750 THz). In the far-infrared region (3–24 THz), signatures of nonequilibrium superconductivity are induced only for excitation of the 16.4and 19.2-THz vibrational modes that drive c-axis apical oxygen atomic positions. For higher driving frequencies (25–750 THz), a second resonance is observed around the charge transfer band edge at approximately 350 THz. These findings highlight the importance of coupling to the electronic structure of the CuO2 planes, mediated either by a phonon or by charge transfer.

The equilibrium superconducting state of high-T C cuprates manifests itself in a number of characteristic features in the terahertz-frequency optical response. In Fig. 1, we report selected optical properties measured in YBa 2 Cu 3 O 6.5 above and below the superconducting transition temperature T C .
As the temperature is lowered from 100 (black curve, T ≫ T C ≃ 52 K) to 10 K (red curve, T ≪ T C ), the real part of the c-axis optical conductivity, σ 1 ðωÞ, evolves from that of a semiconductor with thermally activated carriers to a gapped spectrum [see Fig. 1(b)1]. Simultaneously, a zerofrequency δ peak emerges, indicative of dissipationless dc transport. This peak is not seen directly in σ 1 ðωÞ but is reflected in an 1=ω divergence in the imaginary conductivity, σ 2 ðωÞ [ Fig. 1(b)2]. Correspondingly, a sharp edge in the optical reflectivity of the superconducting state develops at the Josephson plasma resonance (JPR) ω JPR ≃ 30 cm −1 [4][5][6] [ Fig. 1(b) 3].
A number of recent pump-probe experiments have shown that these same optical signatures [red curves in Fig. 1(b)] can be recreated transiently in YBa 2 Cu 3 O 6þx for base temperatures T ≫ T C by optical excitation made resonant with the 20-THz lattice vibrations that modulate the position of the apical oxygen atoms along the c axis [1][2][3]. Measurements of the transient atomic structure with femtoscond x-ray diffraction revealed an average structural deformation in YBa 2 Cu 3 O 6.5 [7], associated with nonlinear lattice dynamics [8,9]. It was reasoned that such a transient structure may favor higher-temperature superconductivity [7].
However, the response of YBa 2 Cu 3 O 6þx or that of any other material has never been systematically checked for excitation of different lattice modes, as no optical device existed that could generate high-intensity pulses with sufficient spectral selectivity and tunability throughout the terahertz spectrum.
Furthermore, recent work in single-layer cuprates of the type La 2−x Ba x CuO 4 [10][11][12][13][14] has evidenced transient optical properties similar to those observed for mid-infrared driving in YBa 2 Cu 3 O 6þx , for excitation in the near-infrared and visible part of the spectrum, a phenomenon that has been assigned to melting of a competing charge order [15,16] (as already discussed for La 1.675 Eu 0.2 Sr 0125 CuO 4 [17]).
Here, we report a comprehensive study of the response of YBa 2 Cu 3 O 6.5 (the same compound investigated in Refs. [1][2][3]7]) to excitation at all frequencies throughout the terahertz electromagnetic spectrum (3-24 THz; 100-800 cm −1 ), as well as in the near-infrared and visible range (up to 750 THz). To this end, we make use of a newly developed nonlinear optical device [18] based on difference frequency mixing of chirped near-infrared pulses [19] in organic crystals (see Supplemental Material [20]).
In a first set of experiments, we studied the response to excitation of all phonons in the far infrared (3-24 THz; 100-800 cm −1 ). The relevant pump frequency range is displayed in Fig. 2(b), which reports the equilibrium broadband c-axis optical conductivity σ 1 ðωÞ at T ¼ 100 K [5,6].
Here, we show data taken under the same conditions as those reported in Refs. [1][2][3], to be used as a reference point for all the experiments that follow. The excitation pulses were centered at 19.2 THz (640 cm −1 ), which correspond to apical oxygen distortions at the oxygendeficient chains. These experiments were performed with the same broadband 4-THz-wide pulses used in Refs. [1][2][3] and then, for comparison, with the newly available 1-THz spectral bandwidth (narrow band). These pump pulses, polarized along the c axis of a YBa 2 Cu 3 O 6.5 single crystal [20], were focused onto the sample at a fluence of approximately 8 mJ=cm 2 . Note that in the narrow-band experiments the pulses were 4 times longer than in the broadband experiments (600 fs vs 150 fs). As these two measurements used the same pump fluence, the peak electric fields were of 3 and 6 MV=cm for narrow-band (long pulse) and broadband (short pulse) excitation, respectively.
As already discussed in Refs. [1][2][3], the transient c-axis optical properties were interrogated between 15 and 80 cm −1 by reflecting a second terahertz probe pulse generated by optical rectification in a nonlinear crystal. The electric field of these pulses, after reflection from the sample surface, was electro-optically sampled [ Fig. 2(b), gray spectrum] for different pump-probe time delays (see Supplemental Material [20] for further details).
Figures 2(c) and 2(d) report the photoinduced changes in the complex optical conductivity at T ¼ 100 K ≫ T C , as a function of the frequency and pump-probe time delay (color plots). Both excitation schemes induced qualitatively similar optical properties, with a significant increase in the imaginary conductivity σ 2 ðωÞ, which became positive and exhibited a superconductinglike 1=ω divergence for ω → 0.
This increase is particularly evident in the frequency spectra measured at the peak of the signal, displayed above the color plots in Figs. 2(c) and 2(d) (right). In these line cuts, the transient σ 2 ðωÞ measured at τ ≃ 0.5 ps after excitation (blue dots) is superimposed with the equilibrium σ 2 ðωÞ at T < T C (red line) for comparison.
Note that in both these experiments, for which the excitation fluence was a factor of 2 higher than that reported in Refs. [1][2][3], the response was that of a homogeneous medium. The effective medium model, introduced to reproduce the partial changes in the optical properties in Refs. [1,2], was no longer necessary to explain the data. We interpret this observation by positing that the excitation range achieved with the new setup may have overcome a dynamical "percolation threshold." Strikingly, for narrow-band excitation at T ¼ 100 K, we observed exactly the same σ 2 ðωÞ spectrum measured in the equilibrium superconducting state ( The photoinduced dynamics at longer time delays (τ ≳ 1 ps) evidenced decoherence and increased dissipation, as observed in the real part of the optical conductivity, σ 1 ðωÞ [Figs. 2(c) and 2(d), left]. On the left-hand side of each panel, we plot two frequency-integrated quantities as a function of the time delay: ωσ 2 ðωÞj ω→0 , which in an equilibrium superconductor is proportional to the superfluid density, and R Δσ 1 ðωÞdω, which is a reporter of dissipation and quasiparticle heating [21]. For both broadband and narrow-band excitation, it is evident that the dissipative part of the optical response [ . Figure 3 reports a more comprehensive set of experiments, obtained by tuning the pump pulse frequency widely throughout the far-infrared spectrum. Four selected results are displayed, corresponding to resonant narrow-band excitation of four different phonon modes (see Supplemental Material [20] for additional datasets). The data reported in Fig. 2 all driven by maintaining constant 3 MV=cm peak electric field strength.
The atomic displacements of these vibrational modes are displayed in Fig. 3(a). conductors (see Supplemental Material [20] for details on the fitting procedure).
The same experiments as those reported in Fig. 3 were systematically repeated for 42 pump frequencies throughout the far-infrared spectrum (3-24 THz), for which we report in Fig. 4 the results of the analysis of the transient optical properties at the time delay corresponding to the peak of the coherent response.
In Fig. 4(a), we show the total, spectrally integrated probe signal, that is, the modulus of the complex optical conductivity. In Fig. 4(b), we display only the dissipative component of the signal [ R Δσ 1 ðωÞdω] and in Fig. 4(c) only the superconducting contribution ωσ 2 ðωÞj ω→0 (see Supplemental Material [20] for extended datasets).
For comparison, we have also included horizontal dashed lines indicating the thermally induced increase in R σ 1 ðωÞdω when heating the sample from 100 to 200 K [ Fig. 4(b)] and the equilibrium superfluid density ωσ 2 ðωÞj ω→0 , measured at T ¼ 10 K [Fig. 4(c)].
For excitation at 19.2 and 16.4 THz, the nonequilibrium state includes a dissipative R Δσ 1 ðωÞdω response (analogous to that observed upon heating) that coexists with a superconductinglike imaginary conductivity [ωσ 2 ðωÞj ω→0 ] identical to that measured in the same material in the equilibrium superconducting state. On the other hand, when the pump frequency is tuned below 15 THz (500 cm −1 ), no superconductinglike component is observed, whereas the dissipative response is approximately the same as that observed for ω pump > 15 THz.
The different nature of the dissipative and the superconductinglike signal is underscored by the data reported in Fig. 5. Here, we show the dependence of R Δσ 1 ðωÞdω and ωσ 2 ðωÞj ω→0 on the base temperature (T > T C ), for two different pump frequencies.
The dissipative term [ Fig. 5(a)] is temperature independent and persists all the way up to 325 K, which suggests that its origin may be related to heating of quasiparticles. On the other hand, the superconductinglike response [ Fig. 5(b)], which is observed only for highfrequency pumping (blue circles), displays a strong reduction with increasing temperature, almost disappearing for T > 300 K. This result is consistent with the observation reported in Refs. [2,3].
Additional datasets taken in the superconducting state at T < T C are reported in the Supplemental Material [20]. There, we show that the preexisting, equilibrium superfluid density can be transiently enhanced (in agreement with Refs. [1,2]) only by photoexcitation at 19.2 THz, provided that a sufficiently high pump fluence is employed. For weaker driving fields [22], or when the pump is detuned to lower frequencies, only a transient depletion of the superconducting condensate is observed.
In a second set of experiments, we studied the response of the material to excitation at higher frequencies, above the  [20] for more details on the fitting procedure). (c) Pump frequency dependence of the superconducting response, represented by the low-frequency limit ωσ 2 ðωÞj ω→0 (red circles). The equilibrium optical conductivity σ equil 1 ðω pump Þ is shown as a blue line. (d) Normalized response ωσ 2 ðωÞj ω→0 =σ equil 1 ðω pump Þ (red circles). The gray line is a multi-Lorentzian fit. All data for ω pump < 300 THz were taken with constant pump fluence (8 mJ=cm 2 ) and peak electric field (3 MV=cm) at a fixed pulse duration of 600 fs. At λ pump ¼ 800 nm and λ pump ¼ 400 nm, for which the pump pulses were 100 fs long, we report data points taken at both 8 mJ=cm 2 (approximately 7 MV=cm, red circles) and 1.5 mJ=cm 2 (approximately 3 MV=cm, empty circles), keeping either the excitation fluence or peak electric field at the same values. phonon resonances and up to the region where electronic bands are found.
Similar to what is reported in Fig. 4 for frequencies immediately above 19 THz, the response at 29 THz (λ pump ¼ 10.4 μm) displays no superconductinglike component.
Note that, for these higher frequencies, the reconstruction procedure is less reliable than for the experiments reported in Figs. 2-5, as the penetration depth mismatch of pump and probe pulses becomes larger. Indeed, at all times, the raw response (optically induced change of the reflected terahertz probe electric field) is largest at the two phonon resonances displayed in Figs. 3 and 4 [20]. The error bars for high excitation frequencies [see Fig. 6(c)] reflect this uncertainty. Nevertheless, an error analysis indicates that the appearance of a divergent imaginary conductivity is robust.
A complete pump frequency dependence for the superconducting component ωσ 2 ðωÞj ω→0 is displayed in Fig. 6(c) (see Supplemental Material [20] for extended datasets). A negligible response of the imaginary conductivity is found for all driving frequencies between the apical oxygen phonon (approximately 21 THz) and 42 THz, whereas for higher pump frequencies a second resonance emerges, with a strength that follows the increase in pump absorption on the charge transfer resonance [visualized in this figure by the equilibrium optical conductivity σ equil 1 ðω pump Þ]. Figure 6(d) displays the same data after normalization against the oscillator strength of the material at each pump frequency. The normalized quantity ω probe σ 2 ðω probe Þj ω→0 = σ equil 1 ðω pump Þ is the frequency-dependent "photosusceptibility" for the transient state and, therefore, to be taken as an alternative way of visualizing the efficiency of the effect.
In the aggregate, the body of work reported above prompts the following considerations. First, from the data in Figs. 3-5, it is clear that some form of mode-specific lattice excitation must underpin optically induced superconductivity in the terahertz frequency range. In previous studies [7,9], it was conjectured that the lowest-order nonlinear lattice anharmonicity, of the type Q 2 IR Q R (where Q IR and Q R are the normal coordinates of the directly driven infrared-active mode and any anharmonically coupled Raman mode, respectively [8]), may explain the observed phenomenology. Indeed, this lattice term leads to a transient, average structural deformation that may be beneficial to superconductivity [7].
Hence, in addition to the nonlinear phononic mechanism, which is validated by x-ray experiments and certainly present, other phenomena are likely to come into play. As documented in the Supplemental Material [20], when considering the calculated average lattice deformations induced by an anharmonic Q 2 IR Q R coupling for driving each of the IR phonons in Fig. 3, one does not find a defining feature for the two modes at 16.4 and 19.2 THz.
Note also that the two high-frequency vibrations drive large-amplitude motions of the apical oxygen atoms, which are then expected to couple directly to the in-plane electronic and magnetic structure. This coupling is supposed to be much weaker for the other modes at a lower frequency [23,24]. We also note that the frequency of the two apical oxygen phonons matches approximately the sum of the inter-and intrabilayer Josephson plasma frequencies in YBa 2 Cu 3 O 6.5 (ω JPR;1 ≃ 1 − 2 THz and ω JPR;2 ≃ 14 THz, respectively). Hence, a mechanism in which driven lattice excitations couple directly to the inplane electronic structure may become resonantly enhanced at these frequencies [25][26][27][28][29].
The second resonance found at the charge transfer band appears to reinforce the notion that changes in the electronic properties of the planes are key in the observed phenomenon [30,31]. At the doping level studied here, charge-order melting is not expected to play an important role, as for YBa 2 Cu 3 O 6.6 [32] and La 1.875 Ba 0.125 CuO 4 [15]. At these frequencies, for the excitation polarized along the c axis, we expect a rearrangement of the electronic structure with some qualitative analogy to the direct action of the apical oxygen modes. It is, therefore, possible that a similar mechanism to that responsible for the resonances at 19.2 and 16.4 THz is at play. We have noted that for the two apical oxygen modes parametric excitation of interlayer fluctuations would be resonant with the sum frequency of the intra-and interbilayer modes [29]. Here, a similar parametric coupling may be at play, without the frequency resonance and, hence, less efficient.
Clearly, further studies that make use of the new pump device available here are needed, with special attention to measurements of time-dependent lattice dynamics [7] and inelastic excitations [33][34][35]. More generally, the tunable, spectrally selective nonlinear pump source, applied for the first time in the present study, is expected to strongly impact the investigation of nonequilibrium phenomena in solids.