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Abstract
We report an experimental approach to produce spatially localized photoinduced superconducting state in a cuprate superconductor using optical vortices with ultrafast pulses. The measurements were carried out using coaxially aligned three-pulse time-resolved spectroscopy, in which an intense vortex pulse was used for coherent quenching of superconductivity and the resulting spatially modulated metastable states were analyzed by the pump-probe spectroscopy. The transient response after quenching shows a spatially localized superconducting state that remains unquenched at the dark core of the vortex beam for a few picoseconds. Because the quenching is instantaneously driven by photoexcited quasiparticles, the vortex beam profile can be transferred directly to the electron system. By using the optical vortex-induced superconductor, we demonstrate spatially resolved imaging of the superconducting response and show that the spatial resolution can be improved using the same principle as that of super-resolution microscopy for fluorescent molecules. The demonstration of spatially controlled photoinduced superconductivity is significant for establishing a new method for exploring novel photoinduced phenomena and applications in ultrafast optical devices.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent years, novel photoinduced phase transitions using structured pulse beams have been proposed to explore new collectively ordered electronic states and their functionalities inaccessible by conventional laser beams [1,2]. Optical vortices (OVs) characterized by phase singularities are among the most recent advancements in light-field shaping technology [3] that have led to a whole new range of applications in many fields, such as telecommunications [4], super-resolution microscopy [5,6], and materials science [7–9]. In the field of photoinduced phase transition spectroscopy, theoretical proposals for optical excitation of electric currents [10], magnetic defects [11,12], and superconducting (SC) vortices [13,14], which take advantage of the characteristics of structured light waves, have attracted particular attention. Spatially modulated photoinduced phase transitions are also expected to be applied to ultrafast devices with complex patterns using highly controllable beam-shaping techniques [15,16]. In particular, the realization of transient localized SC is important because of its strong potential for future applications in optimizing various SC devices. However, their experimental realizations have been, thus far, limited mainly because of the spatial mismatch between the electron system and the optical field [17,18]. Earlier studies using spatially inhomogeneous ultrashort photoexcitation (transient grating experiments) in cuprates have been used to measure macroscopic diffusion properties [19]. Near-field methods including the use of metamaterials are promising solutions [20,21], but they reduce the spatio-temporal degrees of freedom inherent in structured light and their controllability.
In this study, spatially modulated SC was produced by quenching the SC (instantaneous SC to normal conducting (NC) state transition) with OV pulses with an intensity dark core. The resulting transient NC reflects the ring-shaped beam profile and produces a spatially-localized SC state in the dark core of the OV beam for a time range from 0.5 to 5 ps after the OV pulse excitation. Because the NC is driven by photoexcited quasiparticles (QPs), the OV beam profile can be transferred to the electron system without any constraints of spatial matching. The localized SC remaining around the dark core was identified using coaxially aligned three-pulse time-resolved spectroscopy and manifested by moving the position of the dark core of the OV beam. By using the OV-induced SC, we performed spatially resolved imaging of transient SC response on a high-$T_{\rm c}$ cuprate. Because the SC is produced by the non-saturation region reflecting the ring-shaped OV, one would expect the OV-SC region to shrink with the increasing excitation fluence of OV pulses. We compared the spatial distribution of the SC response with various OV fluences and showed that the spatial resolution is improved in a manner similar to super-resolution microscopy [5].
2. Experimental
We use coherent quench (CQ) spectroscopy to generate spatio-temporally modulated SCs and analyze their properties. CQ spectroscopy is a time-resolved spectroscopy that extends standard two-pulse pump-probe (Ppr) spectroscopy to three pulses by adding an intense destruction (D) pulse. This technique has revealed new photoinduced collective excitations in various types of ordered electron systems [22–25]. In Fig. 1(a), we used a wavelength of 800 nm (1.55 eV) for the pr-pulse and its second harmonic of 400 nm (3.1 eV) for the D- and P-pulses, all of which were derived from a cavity-dumped mode-locked Ti:sapphire laser with a pulse duration of approximately 120 fs and a pulse repetition rate of 270 kHz. Each of the three pulses passed through an independent optical delay system, and the measurement was performed using the delay time difference between the D- and P-pulses ($t_{\rm DP}$) and between the P- and pr-pulses ($t_{\rm Ppr}$), as shown in Fig. 1(b). All pulses were coaxially combined and focused onto the sample using an objective lens. The transient reflectivity change $\Delta R/R$ in the pr-pulse was measured using a standard lock-in technique synchronized with the chopping frequency of the P-pulse. The sample was mounted in a He-flow cryostat with optical windows, which could be scanned for imaging using a three-axis translational stage.
Fig. 1. (a) Schematic of CQ spectroscopy realized by combining time-resolved pump (P) and probe (pr) with destruction (D) pulse. These three pulses are coaxially aligned and focused by objective lens on the cuprate sample mounted in the He-flow cryostat. (b) Pulse sequence with beam profiles and delay notation. (c) Schematics of transient normal conducting (NC) states on the sample using D-pulse with and without vortex core (left and right). Spatially distributed NC and/or superconducting (SC) states are generated depending on time and spatial distribution and elapsed time ($t_{\rm DP}$) of the D-pulse. Because the NC is driven by QPs induced by the intense D-pulse, the intensity profile of the D-pulse can be directly transferred to the electron system. (d) Beam profiles of the D-pulse with and without dark core focused on the sample surface (left and right) observed by CCD (charge-coupled device) camera. The profiles are generated by varying the lateral position of the spiral phase plate in (a). $\Delta x$ indicates the position of the dark core with respect to the beam center. (e) Cross-sectional intensity profile of the D-pulse with a centered dark core corresponding to a symmetric OV.
In standard Ppr experiments, the SC state is characterized by the QP response excited by the P-pulse [26], which is detected by reflectivity changes $\Delta R/R$ of the weak pr-pulse with a delay time $t_{\rm Ppr}$. A simple expression of $\Delta R/R$ is given by
In CQ spectroscopy, we add an intense D-pulse that excites all Cooper pairs in the photoexcited region to introduce SC quenching in the corresponding region [23,24]. The resulting metastable states are analyzed by Ppr spectroscopy and their time evolution is measured as a function of $t_{\rm DP}$ (see Fig. 1(b)). Because the spatial region of the photoinduced quench is determined by the intensity distribution of the D-pulse for SC saturation, spatially localized SC that is not limited by the spatial matching between the electron system and the optical field is expected when OV pulses are used as D-pulses (see Fig. 1(c)).
The OV for the D-pulse was obtained by converting a fundamental Gaussian laser using a spiral phase plate (SPP), as shown in Fig. 1(a). The topological charge of 4 was selected to obtain a distinct dark core showing almost zero intensity. The OV generated when the phase singularity of the SPP coincides with the D-pulse center can be regarded as a point vortex, which in principle forms an infinitely small dark core [28]. The SPP can be moved transversely in a plane perpendicular to the D-pulse propagation direction, and the position of the dark core of the OV beam can be changed without changing the optical path length. The half-power beam widths of the focused pulses were estimated to be $w_{\rm P,\ D} =$ 18 $\mu$m for P- and D-pulses and $w_{\rm pr} =$ 22 $\mu$m for pr-pulse, respectively. Figure 1(d) shows the intensity distribution of the D-pulse detected in the reflection configuration when the D-pulse was focused on the sample surface, which confirms the absence/presence of the dark core corresponding to the position of the SPP. The cross-sectional intensity distribution of the ring-shaped OV obtained at the focal plane shows a dark core of nearly zero intensity, as shown in Fig. 1(e).
3. Results and discussion
3.1 Fundamental properties
The SC sample used was a slightly over-doped cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta }$ (Bi2212, $T_{\rm c}$ = 82 K) grown by the traveling solvent floating zone method. Bi2212 is a widely studied cuprate superconductor and is suitable for optical measurements because of its well-flattened surface. Although we selected the slightly over-doped sample that exhibits a distinct SC response, the observations in this study are not specific to this hole doping concentration. In this subsection, we show the results of conventional Ppr spectroscopy without D-pulse excitation. The photoinduced QP characteristics of the sample obtained using Ppr spectroscopy are summarized in Figs. 2(a) and (b).
Fig. 2. (a)Typical transient $\Delta R/R$ obtained by Ppr spectroscopy at selected temperatures. A large SC response is dominant at $T = 20$ K $<~T_{\rm c}$ (82 K), while a negatively peaked PG response is visible above $T_{\rm c}$, which disappears at $T = 280$ K. The P-pulse fluence is set to be $\mathcal {F}_{\rm P} = 21~\mu$J/cm$^2$. (b) Plot of the amplitude of SC response as a function of P-pulse fluence at $T = 20$ K. The solid line shows the fit obtained using a saturation function [31]. (c1) Transient $\Delta R/R$ obtained by CQ spectroscopy with a fundamental Gaussian D-pulse at selected $t_{\rm DP}$ at $T = 8$ K. The D-pulse and P-pulse fluences are set to be $\mathcal {F}_{\rm D} = 240~\mu$J/cm$^2$, and $\mathcal {F}_{\rm P} = 15~\mu$J/cm$^2$, respectively. (c2) Density plot of the transient $\Delta R/R$ of CQ using fundamental Gaussian D-pulse. (d1) and (d2) are the same as (c1) and (c2), respectively, but with a symmetric OV D-pulse. The inset shows difference spectrum obtained by subtracting (c2) from (d2)
Figure 2(a) shows the transient reflectivity changes $\Delta R/R$ as a function of $t_{\rm Ppr}$ at representative temperatures, where the intrinsic response appears to reflect the electronic state at thermal equilibrium for each temperature [29]. Below $T_{\rm c}$, an intense and gradual SC response reflecting QP relaxation across the SC gap $\Delta _{\rm SC}(T)$ is dominant, and its time evolution is determined by the excitation and relaxation of high-energy phonons with energies above $\Delta _{\rm SC}(T)$ [26]. At temperatures above $T_{\rm c}$, a pseudogap (PG), which characteristically appears above $T_{\rm c}$ in cuprates, contributes to the QP response. A distinct difference from the SC response is observed ($\Delta R/R$ of negative sign with fast relaxation < 1 ps) [30]. The amplitude of this component gradually decreases with increasing temperature, and a fast response associated with electron-phonon relaxation in the metallic state becomes visible. These characteristic $\Delta R/R$ transients as a function of $t_{\rm Ppr}$ are used to identify the electronic states of the CQ dynamics and spatial distribution.
Figure 2(b) shows the excitation-fluence dependence of the SC response amplitude at $T = 20$ K$\ll T_{\rm c}$. The SC response under weak excitation shows a linear fluence dependence reflecting an increase in photoinduced QPs, whereas the response under strong excitation conditions shows a saturation property corresponding to SC quenching. All Cooper pairs in the region determined by the beam diameter and penetration depth of the excitation pulse are excited as QPs. The observed saturation property can be reproduced using an analytical function, as shown by the solid line in Fig. 2(b) [31]. This approximation yields a saturation threshold of fluence $\mathcal {F}_{\rm th} = 5\, \mu$J/cm$^2$, which is consistent with previously reported results [32].
3.2 Coherent quench with fundamental Gaussian beam
Figures 2(c1) and (c2) show the results of CQ spectroscopy with a fundamental Gaussian (vortex-free beam) D-pulse at $T = 8$ K. We set the D-pulse fluence as $\mathcal {F}_{\rm D} = 240\,\mu$J/cm$^2$, which is approximately 50 times higher than $\mathcal {F}_{\rm th}$, and the P-pulse fluence as $\mathcal {F}_{\rm P} = 15\,\mu$J/cm$^2$. It is important to note that the high $\mathcal {F}_{\rm D}$ for SC destruction is accompanied by an instantaneous temperature rise in the electronic system, while the steady-state temperature rise is small (<5 K) owing to the low repetition rate of the laser pulse (270 kHz) [32]. Figure 2(c1) shows the transient $\Delta R/R$ as a function of $t_{\rm Ppr}$ observed at typical $t_{\rm DP}$. The variation in the transient response depending on $t_{\rm DP}$ (elapsed time after the D pulse) can be observed. For comparison, the transient $\Delta R/R$ without a D-pulse (red), where the SC dynamics dominate, is also shown. Hereafter, we focus on the $t_{\rm DP}$ time region, where the transient NC is dominant, and we can realize spatially modulated SC by spatially controlling the saturation characteristics of the photoinduced phase transition. To identify the $t_{\rm DP}$ time region of transient NC (quenched SC), a density plot of $\Delta R/R$ as a function of $t_{\rm DP}$ (vertical axis) and $t_{\rm Ppr}$ (horizontal axis) is shown in Fig. 2(c2). The warm colors (yellow to red) roughly correspond to the SC response. The SC response completely disappears (SC in the photoexcited volume is quenched) at $t_{\rm DP}\approx 0.5$ ps, indicating that the photoinduced SC destruction is complete. $\Delta R/R$ at $t_{\rm DP} = 1$ ps reflects the NC state consisting of PG and metallic responses, followed by a recovery of SC dynamics (Cooper pair reformation) at $t_{\rm DP}\approx$5 ps. $\Delta R/R$ at $t_{\rm DP} = 100$ ps is nearly identical to the SC response without a D-pulse, indicating that SC recovery is complete. The recovery dynamics are consistent with the previous results of CQ spectroscopy of Bi2212 and can be assigned to SC order parameter dynamics [24].
3.3 Coherent quench with optical vortex beam
The CQ dynamics of transient $\Delta R/R$ using ring-shaped OV D-pulse are shown in Figs. 2(d1) and (d2), where the fluence conditions are the same as those in Figs. 2(c1) and (c2). A comparison of the results between the two data sets (Figs. 2(c) and (d)) shows that the OV-induced SC is manifested in the period between post-quench and the start of SC recovery ($t_{\rm DP} =$ 0.5–5 ps). The difference spectrum shown in the inset of Fig. 2(d2) is obtained by subtracting Fig. 2(c2) from Fig. 2(d2), highlighting the SC response induced by the OV D-pulse excitation. Note that the OV-induced SC shows a $t_{\rm DP}$ dependence due to the difference in recovery dynamics with the surrounding NC region.
To show that the observed SC response is derived from the intensity dark core of the OV D-pulse, results of CQ spectroscopy using an OV D-pulse with different core positions are summarized in Fig. 3, where $t_{\rm DP}$ is fixed at 2 ps. The $\Delta R/R$ values measured by moving the SPP in the horizontal direction perpendicular to the D-pulse beam are shown in Fig. 3(a). The vertical axis shows the relative position $\Delta x$ of the dark core with respect to the D-pulse beam center on the sample surface. In other words, at $\Delta x = 0$, the dark core is coincident with the beam center, forming a symmetric ring-shaped OV. A comparison of the Ppr responses averaged over the selected $\Delta x$ is shown in Fig. 3(b). A strong SC response appears for a symmetric OV, whereas the SC response disappears, and the PG response is visible when the dark core is outside the D-pulse. Therefore, the observed SC response was attributed to the residual SC in the dark core of the OV, i.e., photoinduced SC localized within the NC saturated with an OV pulse was realized.
Fig. 3. Spatial properties of OV-induced SC response. (a) Density plot of the transient $\Delta R/R$ of CQ using OV with various dark core positions ($\Delta x$) at $T = 8$ K. The elapsed time after the D-pulse is fixed at $t_{\rm DP} = 2$ ps. The destruction and pump fluences are $\mathcal {F}_{\rm D} = 240~\mu$J/cm$^2$ and $\mathcal {F}_{\rm P} = 15~\mu$J/cm$^2$, respectively. (b) Transient $\Delta R/R$ averaged over the inner $\Delta x$ (red; $\Delta x = -5$ to $+5~\mu$m) and the outer $\Delta x$ (blue; $\Delta x = -65$ to $-40~\mu$m and $+40$ to $+65~\mu$m) regions. (c) Transient $\Delta R/R$ averaged over $t_{\rm Ppr} =$ 1–2 ps. The solid line shows the best fit to a Gaussian distribution with FWHM of 27 $\mu$m.
The spatially localized SC response at the vortex is further evidenced by the spatial distribution of $\Delta R/R$ shown in Fig. 3(c). Here, the amplitude is $\Delta R/R$, averaged over the time domain of $t_{\rm Ppr} =$ 1–2 ps, where the SC response is dominant. Recall that $\Delta R/R$ reflects the spatial overlap of P-pr pulses. Since the beam width $w_{\rm pr} =$ 22 $\mu$m for pr-pulses is larger than $w_{\rm P} =$ 18 $\mu$m for P-pulses in our experiment, the result corresponds to the spatial distribution of the P-pulse traced by the OV-induced SC. The full width at half maximum (FWHM) of the SC response obtained by assuming a Gaussian distribution (solid line) was 27 $\mu$m. We roughly estimate the OV induced SC region to be 20 $\mu$m by deconvolution between the $w_{\rm P}$ and the SC response distribution (27 $\mu$m). Note that this value has a large error because the beam profile changes with the position of the SPP. A more accurate size estimation is achieved by the sample-scanning imaging in the next subsection. We will also show the OV-SC region can be reduced according to the fluence of the OV D-pulse.
3.4 Spatially resolved imaging of superconducting response
Because the size of the OV-induced SC is determined by the non-saturation region reflecting the intensity distribution of the OV, one would expect the region to shrink indefinitely with increasing excitation fluence of the OV. This relationship is equivalent to the spatial resolution enhancement of stimulated emission depletion (STED) microscopy [5]. Using ring-shaped STED pulses with intensity $I$ above the saturation intensity $I_s$, the diameter ($d$) of the emission region of the fluorescent molecules is reduced well below the focused beam size and is given by the modified Abbe diffraction limit
where the wavelength $\lambda$ divided by a lens of the numerical aperture $n \sin {\alpha }$ is the normal diffraction limit. Based on a similar principle, the OV-induced SC is expected to yield a reduced spatial distribution with increasing D-pulse fluence, as approximated byAs a proof-of-principle experiment, we performed imaging measurements of the transient response in the region with a defect structure spontaneously formed in the cleaved Bi2212 (see the optical microscope image shown in Fig. 4(d)). Spatially resolved images of $\Delta R/R$ obtained by CQ spectroscopy are shown in Figs. 4(a1)–(c1), where the imaging region is indicated by the white box in Fig. 4(d). The OV D-pulse fluence was set to $\mathcal {F}_{\rm D} = 0\,\mu$J/cm$^2$ for (a1), 150 $\mu$J/cm$^2$ for (b1) and 370 $\mu$J/cm$^2$ for (c1), respectively. In all cases, we set $t_{\rm Ppr} = 2$ ps, where the SC response is dominant. The elapsed time after the arrival of the D pulse was fixed at $t_{\rm DP} = 1$ ps, shorter than the $t_{\rm DP}$ (2 ps) used in Fig. 3 to minimize the non-saturated SC region. The comparison of Figs. 4(a1)–(c1) shows that the spatial variation in the SC response of CQ spectroscopy observed in the defect structure is abrupt compared to that of Ppr spectroscopy.
Fig. 4. Spatially resolved imaging of the transient $\Delta R/R$ obtained by (a1) Ppr ($t_{\rm Ppr} = 2$ ps, $\mathcal {F}_{\rm P} = 25~\mu$J/cm$^2$) and (b1, c1) CQ ($t_{\rm DP} = 1$ ps, $t_{\rm Ppr} = 2$ ps, $\mathcal {F}_{\rm P} = 25~\mu$J/cm$^2$) using OV D-pulse with (b1) $\mathcal {F}_{\rm D} = 150~\mu$J/cm$^2$ and (c1) $\mathcal {F}_{\rm D} = 370~\mu$J/cm$^2$ at $T = 10$ K. The result of (a1) corresponds to $\mathcal {F}_{\rm D} = 0~\mu$J/cm$^2$. (a2)–(c2) The corresponding horizontal distributions of $\Delta R/R$ at the vertical position of 1.5 $\mu$m in (a1)–(c1). The solid curve in each graph is a least-squares approximation obtained using the sum of a third-order polynomial and a Gaussian distribution. (d) Optical microscope image of the sample, where the white box indicates the scanning area of (a1)–(c1). (e) Plot of the FWHM of the Gaussian distribution estimated from the horizontal distributions of $\Delta R/R$ at the same vertical position of 1.5 $\mu$m at different $\mathcal {F}_{\rm D}$ (3 of 4 data sets are shown in (a2)–(c2)). The solid curve shows the best fit from Eq. (3) to the data.
To quantitatively estimate the improvement in the spatial resolution in CQ spectroscopy, we focus on the $\Delta R/R$ distribution along the defect where the minimum response appears. Figures 4(a2)–(c2) show the cross-sectional distributions of $\Delta R/R$ at a vertical position of 1.5 $\mu$m in Figs. 4(a1)–(c1), respectively. The solid curve in each figure is a least-squares approximation based on the sum of a third-order polynomial and Gaussian distribution. The FWHM of the dip estimated from the Gaussian distribution in Fig. 4(a2) is 24 $\mu$m, which is approximately equal to the half-power beam width (18 $\mu$m) of the P-pulse. By contrast, the dip width derived from Fig. 4(c2) is 11 $\mu$m, indicating that the spatial resolution is well below the beam size. We also compared the dip widths for different fluences of the OV D-pulse in Fig. 4(e). The dip width systematically decreases with increasing OV D-pulse fluence, indicating that the increase in the saturated NC region (i.e., the decrease in the size of the OV-SC) is responsible for the improvement in the spatial resolution. The solid line in Fig. 4(e) is an approximate curve obtained using the modified Abbe diffraction-limit formula in Eq. (3) and reproduces the OV fluence dependence of the dip width well.
4. Conclusion
We realized a spatially modulated photoinduced SC state in a high-$T_{\rm c}$ cuprate Bi2212 using OV ultrafast pulses. The spatio-temporal properties of the OV-induced SC were investigated by CQ spectroscopy with the spiral phase plate. The CQ dynamics of transient $\Delta R/R$ using OV D-pulse shows the SC unquenched around the dark core for a time range from 0.5 to 5 ps after the D-pulse excitation. The SC localization is evidenced by the spatial distribution of the SC response traced by shifting the position of the dark core within the D-pulse beam. Spatially resolved imaging of transient SC using OV-SC was also demonstrated by scanning the Bi2212 sample. The technique allows the measurement of mesoscopic properties of SC dynamics without any sample processing. The enhanced spatial resolution of the SC response with increasing D-pulse fluence indicates that spatially resolved imaging based on the same principle as STED microscopy can be realized for correlated electron systems. The demonstration of spatially controlled transient SC is also significant for establishing a new method for exploring novel device applications. More complex circuit structures can be generated using advanced pulse beam shaping techniques [33–35]. Potential applications include the optimization of various superconducting devices, such as single-photon detectors [36,37] and quantum circuits [38–42]. The use of the topological properties of structured light, such as orbital angular momentum and spatially distributed polarization, holds promise for new collective excitations of charge and spin.
Funding
Japan Society for the Promotion of Science (19H05826, 22H01978).
Disclosures
The authors declare no conflicts of interest.
Data availability
The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.
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