Reconfigurable photothermal doping filament for selective spin manipulation and addressing

Significance

The modulation of electromagnetic field–matter interaction at micro/nanoscale is crucial for a variety of studies ranging from nanophotonics to quantum information science. Traditionally, subwavelength structures are fabricated to modify the local electromagnetic field. However, the fixed shape lacks the capability of programmable modulation. This work reports a solution by controlling the reversible insulator-to-metal transition in vanadium dioxide through a “photothermal doping” method. Conductive filament with reconfigurable shape is realized to produce near-field electromagnetic signal, the distribution of which can be modulated without changing the structure of the nanodevice. The technique is applied for the manipulation and selective addressing of solid-state spins in diamond and will enable new approaches for developing quantum devices.

Abstract

The room temperature manipulation of solid-state spins provides an opportunity to develop quantum applications under ambient conditions. Local electromagnetic fields, that usually produced by current in micro/nanoscale metal wires, have been employed for the coherent driving and addressing of spin qubit. However, the fixed distribution limits the spatial selectivity and efficiency of qubit manipulation, which is of central importance in a scaled-up quantum system. Here, we report a solution by demonstrating a reconfigurable current with arbitrary shape to engineer microwave and DC magnetic field at microscale. A “photothermal doping” method was proposed to optically control local insulator-to-metal transition in vanadium dioxide. It generates a conducting filament with adjustable position, direction, and width. Universal manipulation and selective addressing of spins at arbitrary sites are realized, by freely changing the filament and electromagnetic field on demand. Our work paves the way for developing quantum devices with large-scale spin qubits.

Quantum technologies hold the potential to revolutionize information science (1–6). Among various platforms (7–9), solid-state spin defects are one of the most promising candidates for quantum computing (10–14) and sensing (15– 19). The spin qubits show long coherence time and stable fluorescence emission, even at elevated temperature (20–23). At the core of applications with this atomic-sized quantum system is the high-fidelity qubit control. While the visible light excitation is used for spin qubit initialization and detection, the resonant microwave driving is required for coherent spin manipulation. This highlights the critical importance of precise and adaptable local electromagnetic field modulation for quantum information devices. Reconfigurable optical excitation at the nanoscale can be easily achieved by modulating free-space light beams with optical components, such as acousto-optic deflectors, galvo mirrors, and spatial light modulators, and then focusing laser beams with a high NA objective (24–27).

However, the versatility of microwave driving from far-field is constrained by the much longer wavelengths in comparison with visible light, due to the diffraction limit. Instead, various micro- and nanodevices, including microcircuits (28–34) and magnetic materials (35–38), have been used to confine microwave magnetic field at nanoscale. Though the local microwave driving strength is enhanced, the near-field distribution cannot be freely modulated, as it is determined by the fixed structure of devices. Therefore, realizing high efficiency and spatial selectivity in coherent manipulation and addressing of spin qubits remains an open challenge. It hinders the development of scaled-up quantum devices.

Here, we overcome this challenge by realizing a reconfigurable current path for the coherent manipulation and selective addressing of spin qubits. A conductive filament, even with curved shapes, is generated in vanadium dioxide (VO₂) film via a “photothermal doping” method, which modifies the local insulator-to-metal transition (IMT) by scanning a focused laser beam. We show that the position, direction, and width of the current in VO₂ can be accurately controlled. Rabi oscillation and Ramsey fringes of spins in diamond are performed, confirming the coherence of microwave signal transmitted through the reconfigurable filament. The spatial selectivity is subsequently investigated with freely modulated microwave and DC magnetic field gradients. It enables the addressing of spin qubits at arbitrary positions. The results will help to develop large scale quantum information devices. And the method can be extended to other quantum systems beyond solid-state spins.

Results

Generation of Reconfigurable Current Path.

VO₂ is a strongly correlated material that shows reversible IMT at the critical temperature around 68 °C (39). The transition substantially changes electrical conductivity, making VO₂ a promising candidate for various applications, including sensors (40, 41) and memristor (42, 43). In this work, a 100-nm epitaxial VO₂ film was grown on a c-Al₂O₃ substrate by the oxide molecular beam epitaxy technique (See SI Appendix, Fig. S1 and previous works (44, 45) for detail). Two metallic electrodes (Au/Cr 100/10 nm) with a width of W and a gap of L, were fabricated on the VO₂ film, as illustrated in Fig. 1A. DC and microwave current sources were then connected to the electrodes.

Fig. 1.

Principle of the experiments. (A) Schematic illustration of the reconfigurable current path for spin manipulation. (B) The change of VO₂ resistance is recorded to show the Joule heating induced phase transition, which is modified by a scanning laser beam. $I_{\text{c,up}}$ ($I_{\text{c,up}}^{\prime }$) and $I_{\text{c,down}}$ ($I_{\text{c,down}}^{\prime }$) denote the critical current during processes of increasing (solid red and pink lines) and decreasing (dashed blue lines) current amplitude, respectively. (C) The generation of a “S”-shape curved filament is imaged by detecting the VO₂ scattering signal (wavelength longer than 637 nm) under the illumination of a 532-nm laser. The signal is higher with metal phase.

In the experiments, the device was placed on a hot stage with a constant temperature of about 58 °C, which was slightly lower than the critical temperature of the prepared VO₂ film. When electrical current higher than $I_{\text{c,up}}$ is applied through the electrodes on VO₂ film, the two-terminal device would undergo a sharp phase transition due to Joule heating. A current path is subsequently formed (46, 47), as shown in Fig. 1B. However, the current triggered conductive filament will show a random route due to the homogeneous property of defect-free VO₂ film (47–49). Selective ion doping can break the homogeneity of VO₂ film, and subsequently lead to a preferred conductive filament. But the price is losing the capability of adjusting current path after the sample is fabricated.

In pursuit of flexible spin manipulation and selective addressing, we proposed a laser-written strategy to control the conductive filament in VO₂ film. A 532-nm laser is focused on the VO₂ film surface to create a reconfigurable path on demand (SI Appendix, Fig. S2 for details of experimental setup). The sample’s position is controlled by a piezo stage, thus leading to the movement of laser spot on VO₂ film surface. Due to the photothermal effect, the electrical conductivity in the laser scanned area will increase. When current is applied to the device, it concentrates in this laser scanning area, further raising the local temperature. Consequently, the IMT and formation of a conductive filament in the scanned area is triggered by a threshold current $I_{\text{c,up}}^{\prime }$, which is much lower than $I_{\text{c,up}}$ without the laser beam. The absence of hysteresis-loop with scanning laser is possibly due to the phase transition in a limited area. An example of laser-written phase transition pattern is illustrated in Fig. 1C, which shows a curved shape.

After the establishment of laser-defined current path, the laser can be turned off, as the current’s Joule heating maintains the conductive filament. To erase the path, we simply turn off the current source, showing distinctive advantage superior to the counterparts of metallic wires and ion doped VO₂. More details about current path control can be found in SI Appendix, Fig. S3. Since the formation of local conductive filament is modulated by photothermal effect, we name our method as “photothermal doping,” to distinguish from the traditional ion doping.

To directly monitor the current in reconfigurable filament for the selective manipulation of spin qubit, a single-crystal diamond plate was placed on the top of VO₂ film. High density (approximately 6,100/μm²) Nitrogen-Vacancy (NV) color centers in diamond were created through nitrogen ion implanting with a dose of $2\times {10}^{13}$/cm² and an energy of 40 keV, followed by annealing (SI Appendix, Device and Experimental Setup). The side of diamond with doped NV centers faced toward the VO₂ film. The resonant frequency of NV center spin state transition ($m_{\text{s}}=0$ to $m_{\text{s}}=\pm 1$) in ground state varies with an external magnetic field along symmetry axis $B_{\text{z}}$, as $f_{\pm }=D\pm \gamma B_{\text{z}}$, where $D\approx$ 2.87 GHz is the zero field splitting and $\gamma$ is gyromagnetic ratio.

As shown in Fig. 2, current paths with varied shapes were generated with the assistance of a 30 mW, 532 nm focused laser. Without external magnetic field, microwave signal with a frequency of 2.87 GHz is injected into the current path, along with a DC current of 2.5 mA. After the laser-writing process, the green laser power is reduced to 0.7 mW for NV center spin initialization and detection. The optically detected magnetic resonance (ODMR) measurement of the NV center was performed to reveal the current path. The ODMR contrast, defined as $(I_0-I_{\text{mw}})/I_{\text{0}}$, where $I_{\text{mw}}$ ($I_0$) presents the spin-dependent NV fluorescence with (without) microwave, is recorded to illustrate the distribution of local microwave driving. The temperature induced shift of $D$, approximately 74 kHz/K (50), during phase transition is expected to be much smaller than the linewidth (approximately 10 MHz, SI Appendix, Fig. S8) of NV ensemble ODMR spectrum. Therefore, the ODMR image can be used to present the generation of current path. In Fig. 2A–C, straight-line microwave driving areas are obtained by scanning the laser beam along the y-axis direction. The position is adjusted by changing the x-axis coordinate of the laser beam.

Fig. 2.

NV center ODMR imaging reveals the spin driving with reconfigurable current of varied shapes. (A–C) The laser beam is scanned along y axis, with x $=$$-$20 $\mathrm{\mu }$m, 0, and 20 $\mathrm{\mu }$m, respectively. (D–F) The laser beam is scanned along y $=$ tan$\theta ·$x, with $\theta ={125}^{°},{110}^{°}$, and 55°, respectively. The dashed lines indicate the trajectories of scanning laser beams. The power of microwave signal is 10 dBm here for imaging the current path through ODMR measurement. The samples were fabricated as $L=40$ μm and $W=50$ μm here. (Scale bars are 10 μm in length.)

For spin qubit manipulation and addressing, the vector of the electromagnetic field determines the interaction with spins. The angle of magnetic components should be carefully controlled (51, 52), in addition to the magnitude. It can be realized by changing the direction of current flow that produces the electromagnetic field. In Fig. 2D–E, we adjusted the scanning direction of laser beam. The ODMR images confirm that the achieved current paths match well with the laser beam scanning traces, demonstrating the capability of building a current path with arbitrary shape in VO₂ film.

As mentioned before, electrical DC current is applied to maintain the conductive filament after turning off the laser beam. It can also be adjusted to modify the current path shape. In Fig. 3, the conducting filament is written in the center of gap between electrodes. Then, electrical current with varied amplitude is applied. Examples of NV center ODMR images under the microwave driving through the current path are presented in Fig. 3A–D. The results show that the width of current path changes with the current amplitude, which determines the Joule heating power. The full width at half-maximum (FWHM) of ODMR distribution in the x direction is plotted as a function of DC current in Fig. 3E. While the central position of current path is almost unchanged, the width varies from 6.8 $\mathrm{\mu }$m to 21 $\mathrm{\mu }$m by increasing the current from 2.3 mA to 6 mA. This rough estimation of microwave driving area agrees with the trends in other experimental observations and theoretical results (53–55).

Fig. 3.

Adjusting the width of current path and spin driving area. (A–D) ODMR images of NV centers illustrate the current paths with different DC current. (E) The width of current path changes with the current amplitude. [Scale bars in (A–D) are 10$\mathrm{\mu }$m in length.]

The amplitude dependence of the current path width provides a feasible approach to adjust the area for qubit driving. A strong current could be used for the qubit manipulation in a large area. And it should be avoided for the generating of complicated current path. For the selective qubit manipulation with current path in VO₂, we set the DC current to approximately 2.5 mA in the rest of the experiments.

Selective Manipulation and Addressing of Solid-State Spins.

The “photothermal doping” protocol enables us to generate, erase, and reproduce current path at designed positions within VO₂ film. Both DC and microwave signals can be transmitted through the current path, enabling a confined and adjustable electromagnetic field distribution for qubit addressing. As illustrated in Fig. 4A–F, the current path is optically switched by a focused laser beam. Frequency-scan ODMR measurements are conducted to evaluate the selectively driving of NV centers at two distinct locations, each contains approximately six NV centers. When the current path is generated at position A (Fig. 4A), we see that a high ODMR contrast is achieved for NV-A, while the spin transition of NV-B can hardly be driven (Fig. 4 B and C). Conversely, shifting the current path to site B (Fig. 4D), enable the selectively microwave pumping of NV-B (Fig. 4 E and F).

Fig. 4.

Spin manipulation with VO₂ current path. (A) Fluorescence image indicates the generation of current path at position A. (B and C) The ODMR measurement of NV A and NV B, respectively. (D–F) show the results after moving the current path to position B. (G) Rabi oscillation of NV center under microwave driving through VO₂ current path. (H) Ramsey fringes of NV center. Error bars are the SE of measurements. (I) The position-dependent resonance frequency shift of NV center. Inset shows the example of ODMR measurement with current path at different positions. Error bars represent 68% CI of ODMR spectrum fitting.

Coherent spin qubit manipulation is of utmost importance for applications in quantum information science. Rabi oscillation of NV centers is subsequently performed in Fig. 4G. With a microwave power of 12 dbm, a Rabi oscillation rate of approximately 1.4 MHz is reached. This result indicates that the efficiency of microwave driving through conducting VO₂ is comparable to that with metallic wire (32, 56). More importantly, the reconfigurable current path can be adjusted to optimize the spin manipulation for NV centers at different locations. The coherent spin manipulation is further applied for the Ramsey fringes measurement in Fig. 4H. It shows a spin dephasing time of $T_2^{\ast }\approx 0.7\mathrm{\mu }$s with NV center ensemble in this diamond sample. It confirms that the universal spin manipulation can be realized with the reconfigurable current path. The microwave driving shows a high-level temporal stability (SI Appendix, Fig. S9). It helps to realize high fidelity spin manipulation. To further improve the stability in future applications, another scanning laser beam, which does not excite NV centers, could be applied to actively compensate the local temperature fluctuation during spin manipulation.

Selective spin manipulation is further investigated by utilizing the gradient of magnetic field vector from a DC current (32, 33). Due to the Zeeman effect, the electronic spin resonance frequencies of NV center will be determined by the relative distances between spin defects and current path. In Fig. 4I, we changed the current path position from −5 μm to 5 μm using the focused laser beam and measured the frequency-scanning ODMR spectrum. The resonant frequency of NV centers was extracted and plotted as the function of the current path’s position. With a DC current of 2.5 mA, we see that a maximum gradient of approximately 2.6 MHz/$\mathrm{\mu }$m is obtained for the spatially dependent resonant frequency of NV center. Meanwhile, a linewidth of approximately 200 kHz is usually observed with single NV center spin resonance spectrum (57). And it can be reduced to 55 kHz with isotopically purified sample (21). Therefore, NV centers with a distance shorter than 100 nm are expected to be distinguished by simply recording ODMR spectrum. Other methods, such as Fourier magnetic imaging (30, 58), can be applied to further improve the spatial selectivity. Since the position of current can be freely moved, the resonant frequency of target NV center will be modulated with high flexibility, in contrast to the qubit addressing with a fixed magnetic gradient (30, 32, 58).

To show the distinctive flexibility of our method, we further performed the parallel driving of NV centers at multiple sites, which is crucial for building scalable quantum architectures (8, 12). NV center ensembles were created via ion implantation and subsequently etched into an array of pillars, as shown in Fig. 5A. Each pillar contains several hundred NV centers. The NV centers were denoted as NVi,j according to the coordinates (Fig. 5B). Without the external magnetic field, microwave signal with a fixed frequency of 2.87 GHz was applied through the current path. The differential fluorescence counts $I_0-I_{\text{mw}}$ are plotted in Fig. 5C–H. For example, with a straight line-shaped current path in Fig. 5C, NV centers at positions where i = −j, were simultaneously driven by microwave. And by changing the current path to that in Fig. 5D, NVi,j centers with i = j were driven.

Fig. 5.

Parallel driving using custom-shaped filament. (A) Fluorescence image of an array of NV center ensembles. (B) The NV centers were numbered in rows i and columns j. (C–H) Driving result by using the curved filament. Nonzero ODMR contrast means that the NV center is driven. The dashed lines indicate the design of laser-written conducting filament. (The scale bars are 5 μm in length.)

In further step, conducting filaments with curved profiles, such as “C” and “S” shapes, were generated in Fig. 5E–H. The ODMR results confirm that these complex current paths can effectively drive spins at arbitrary sites, demonstrating the high flexibility of “photothermal doping” filament for qubit manipulation and addressing.

Discussion

In summary, leveraging the phase transition of VO₂ film, conductive filament with reconfigurable position and shape has been realized through “photothermal doping.” With freely modulated local electromagnetic field, this technique shows the capability for manipulation and addressing of spin qubits with high flexibility. Recently, optically addressable coherent manipulation of diamond spins has also been demonstrated based on local optical Stark shift (11). But it requires a cryogenic environment for operation, in contrast to the robustness of our method. Though only demonstrated with diamond NV centers in this experiment, our method can be used for a variety of solid-state spin defects, as well as other quantum systems. For example, near-field microwave and magnetic gradient are also used for trapped ion manipulation and addressing (59–61).

In this work, a green laser is used for both NV spin initialization and conducting filament writing. It is turned off during the spin manipulation process. For future application, we can use laser beams with different wavelengths and powers to separately pump NV centers and generate the conducting filament. In this way, the current path-writing light beam can be applied with higher flexibility. Further enhancing the spatial selectivity of spin manipulation requires a higher magnetic gradient, which is determined by the balance between current amplitude and filament width. A lower stage temperature and a thicker VO₂ film would increase the amplitude of current, while maintaining a small width of conductive filament (53–55) (SI Appendix, Current Path Generation Process and Fig. S5). And the temporally modulating of current pulse may improve the current peak amplitude without increasing the average heating power. Using a nonresonant microwave to maintain the conductive filament, the AC stark shift (62, 63) with microwave gradient could also be explored for realizing individual NV manipulation. Material engineering, such as W or Mo doping, can be used to lower the critical temperature of phase transition (64, 65). It will further increase the feasibility of our method.

Supplementary Material

Appendix 01 (PDF)

Movie S1.

The illustration of addressing NV center arrays with the reconfigurable conductive filament in a single device.

Data, Materials, and Software Availability

All study data are included in the article and/or supporting information.