Coherent Microwave Control of Optically Addressable Donor Qubits in ZnO

This paper demonstrates coherent microwave control of optically addressable $^{115}\mathrm{In}$ donor qubits in ZnO, achieving nanosecond-scale Rabi oscillations and characterizing spin coherence while revealing an unexpected reduction in coherence time at low magnetic fields compared to previous optical studies.

The Gist

Imagine you have a tiny, invisible switch inside a piece of crystal called Zinc Oxide (ZnO). This switch is made of an atom of Indium that has been "implanted" into the crystal. Scientists call this a "qubit," which is the basic unit of information for future quantum computers.

For a long time, scientists could only "poke" these switches with light (lasers) to turn them on or off. But light is a bit like a gentle tap; it can only make the switch wobble a little bit. To build a real computer, you need to be able to flip the switch all the way over (a 180-degree turn) quickly and precisely. This paper reports that the team has finally figured out how to use microwaves—the same kind of energy used in your kitchen, but much more controlled—to flip these switches completely.

Here is how they did it and what they found, explained simply:

1. The Setup: A Crystal with a "Viewing Hole"

To control these switches, the team needed to hit them with microwaves while also shining a laser on them to see what happened.

• The Problem: Usually, microwaves and lasers don't like to play nice together in this specific type of crystal. The microwaves need to hit the crystal from the side, but the lasers need to look straight down through it.
• The Solution: They built a special "tuning fork" (a microwave resonator) with a tiny hole in the middle. They put the crystal inside this fork. The microwaves buzzed around the crystal from the side, while the laser shone straight down through the hole. This allowed them to both control and watch the switches at the same time.

2. The Control: Spinning the Switch

Once they had the setup, they tested if they could actually control the switches.

• The "Spin": Think of the electron in the Indium atom like a spinning top. The team used the laser to set the top spinning in a specific direction (initialization).
• The Flip: Then, they hit it with a microwave pulse. They successfully made the top spin all the way around and flip to the opposite direction.
• The Speed: They did this incredibly fast. The time it took to flip the switch was about 14 nanoseconds. To put that in perspective, a nanosecond is to a second what a second is to about 32 years. They did this faster than the switch could naturally get "confused" and lose its direction.

3. The "Radio Station" Effect

The Indium atom has a special feature: it has a "nuclear spin" (a tiny internal compass) that talks to the electron. This interaction creates 10 different radio stations (called hyperfine transitions).

• By tuning their microwaves to specific frequencies, they could pick exactly which "station" they wanted to control.
• They also discovered that shining the laser on the atom didn't just set the electron spinning; it also helped align the internal compass (the nucleus), effectively "polarizing" the whole system.

4. The Surprise: The Switch is Noisier Than Expected

This is the most interesting part of the paper.

• The Expectation: In previous studies using only lasers, these switches in Zinc Oxide were reported to stay stable for a long time (about 50 microseconds).
• The Reality: When the team used microwaves to control them, the switches only stayed stable for about 200 nanoseconds. That is roughly 250 times shorter than expected.
• The Investigation: They played detective to find out why.
  • Was it heat? No. They cooled the system down even more, and the problem didn't go away.
  • Was it the microwave pulse flipping too many neighbors? No. They changed the strength of the pulse, and the problem remained.
  • Was it the Indium atoms themselves? No. They tested Aluminum atoms in the same crystal, and they had the same short lifespan.
• The Conclusion: The team suspects the problem is "magnetic noise" from the surrounding environment. Imagine trying to hear a whisper in a room where everyone else is quietly shuffling their feet. Even if you aren't the one shuffling, the collective noise of the room (other electrons nearby) is messing up the signal. The high magnetic fields used in the old laser studies might have silenced this noise, but the lower fields used here let the noise back in.

Summary

The paper proves that scientists can now use microwaves to flip Indium switches in Zinc Oxide crystals with extreme speed and precision, opening the door to more complex quantum operations. However, they also discovered that these switches are much more sensitive to "background noise" from their neighbors than previously thought. Before these switches can be used in a real computer, scientists will need to figure out how to quiet down that noisy neighborhood.

Technical Summary

Technical Summary: Coherent Microwave Control of Optically Addressable Donor Qubits in ZnO

Problem Statement
Optically addressable shallow donors in Zinc Oxide (ZnO) represent a promising platform for spin-photon quantum technologies due to their efficient optical transitions and potential for long spin coherence in an isotopically purifiable host. However, a critical limitation has been the lack of coherent control beyond small-angle rotations. Previous attempts using ultrafast optical pulses were restricted to small rotations (saturating near 40% population transfer) due to laser-induced dephasing. Furthermore, achieving full coherent control (e.g., $\pi$-pulses) requires resonant microwave fields at the millitesla scale to operate within the short inhomogeneous dephasing time ($T_2^* \approx 17$ ns) of natural-abundance ZnO. A significant technical hurdle is the Faraday optical geometry required for spin-selective initialization and readout, which necessitates microwave magnetic fields parallel to the crystal surface—a configuration difficult to achieve with high field strength while maintaining optical access.

Methodology
The authors utilized a 300 $\mu$m-thick ZnO crystal with a 3 $\mu$m-thick molecular-beam epitaxy (MBE) epilayer. Indium (In) ions were implanted at a concentration of $10^{11}$ ions/cm$^2$ with an energy of 380 keV, followed by annealing at 700°C. The implantation profile yielded a peak donor density of $\sim 10^{16}$ ions/cm$^3$ at a depth of 90 nm.

To overcome the geometric constraints of microwave delivery, the team embedded the ZnO sample within a microstrip resonator featuring a central 0.8 mm aperture. This design allowed for optical access through the center while generating strong in-plane microwave magnetic fields perpendicular to the external static magnetic field (Faraday geometry). The resonator was designed for high-power pulsed operation (up to 100 W).

Experiments were conducted in a helium immersion cryostat at 1.7–5.5 K with an external magnetic field ($B_{ext}$) of approximately 300 mT. The spin system was manipulated using:

1. Resonant Optical Pumping: 369 nm laser pulses to initialize and read out the electron spin via donor-bound exciton transitions, utilizing polarization selectivity ($\sigma^+$ and $\sigma^-$).
2. Pulsed Optically Detected Magnetic Resonance (PODMR): Microwave pulses applied while sweeping the magnetic field to resolve hyperfine transitions.
3. Coherent Control Sequences: Rabi oscillations, Ramsey interferometry, Hahn-echo, and Carr-Purcell-Meiboom-Gill (CPMG) dynamical decoupling sequences to characterize coherence.

Key Contributions and Results

• Demonstration of Coherent Microwave Control: The study successfully demonstrated coherent microwave control of implanted $^{115}$In donors in ZnO. The system resolved ten distinct hyperfine transitions corresponding to the $I=9/2$ nuclear spin of Indium, with a splitting of $\sim 104$ MHz.
• Nuclear Spin Polarization: The researchers observed optical-pumping-induced nuclear spin polarization. By analyzing the asymmetry in the ODMR spectra under different optical pumping polarizations, they extracted a nuclear spin polarization of $P_N \approx -0.19$.
• Rabi Oscillations: The team achieved full coherent rotations of the donor electron spin. They observed Rabi oscillations with a maximum frequency of $\Omega/2\pi = 36.2 \pm 0.7$ MHz, corresponding to a $\pi$-pulse time of $13.8 \pm 0.3$ ns. This duration is shorter than the inhomogeneous dephasing time ($T_2^* \approx 17$ ns), enabling coherent manipulation despite rapid ensemble dephasing.
• Spin Coherence Characterization:
  • Inhomogeneous Dephasing: Ramsey interferometry confirmed $T_2^* = 17 \pm 1$ ns, consistent with the PODMR linewidth and Rabi decay modeling.
  • Homogeneous Coherence: Hahn-echo measurements yielded a coherence time of $T_2 = 200 \pm 20$ ns. While CPMG sequences extended this time, the measurements were limited by sample heating at higher pulse numbers.
• Decoherence Source Analysis: A critical finding was that the measured $T_2$ (200 ns) is more than two orders of magnitude shorter than values ($\sim 50$ $\mu$s) reported in previous all-optical studies of ZnO donors at high magnetic fields. Through a series of control experiments, the authors ruled out microwave heating and instantaneous diffusion as the primary causes.
  • Heating was ruled out by comparing measurements at 1.8 K and 5.5 K, which showed no difference in $T_2$.
  • Instantaneous diffusion was ruled out by varying the refocusing pulse angle and comparing In-doped regions with Al-doped regions (which showed similar short coherence times).
  • The authors conclude that the shortened coherence is likely due to spectral diffusion arising from magnetic noise in the broader local electronic spin environment, rather than the nuclear spin bath or the specific donor species.

Significance and Claims
The paper establishes that coherent microwave control can be achieved in optically addressable spin systems even with nanosecond-scale inhomogeneous dephasing. This capability bridges the gap between optical initialization/readout and full spin manipulation, a prerequisite for donor-based quantum technologies.

The authors claim that their results demonstrate the feasibility of creating optically interfaced electron-nuclear spin registers in ZnO. However, they modestly note that the unexpectedly short coherence times at low magnetic fields reveal that suppressing the nuclear-spin bath alone (via isotopic purification) may be insufficient to realize long-lived qubits. Instead, the work highlights the necessity of identifying and mitigating residual paramagnetic defects and impurities that contribute to spectral diffusion. The demonstrated techniques provide a direct route to systematically investigate coherence-limiting mechanisms as a function of magnetic field, temperature, and material processing, which was previously inaccessible to all-optical control methods.