Photorefractive tuning seeded by third-harmonic light in a diamond photonic crystal cavity

This paper demonstrates deterministic, in situ resonance tuning of a diamond nanocavity via a photorefractive effect seeded by third-harmonic light, which induces a significant blue-shift and reveals a non-zero second-order nonlinearity arising from electric fields generated by charged crystal defects.

The Gist

Imagine a tiny, perfect diamond shaped like a microscopic trampoline. This isn't just any diamond; it's a "photonic crystal cavity," a device designed to trap light so tightly that it bounces around millions of times before escaping. Think of it as a very high-quality echo chamber for light.

In this study, scientists from the University of Calgary and other institutions discovered a way to "tune" this diamond trampoline using light itself, specifically by creating a new color of light inside it. Here is how they did it, broken down into simple steps:

1. The Setup: A Diamond Trampoline

The researchers built a tiny diamond structure with a pattern of holes in it. They shone a beam of invisible infrared light (the kind used for fiber-optic internet) into this diamond. Because the diamond is so good at trapping light, the energy builds up inside, like water filling a bucket with a tiny hole.

2. The Magic Trick: Turning Invisible Light into Green Light

When the light gets strong enough inside the diamond, something cool happens. Three invisible infrared photons (particles of light) crash together and merge into one single photon of green light. This is called "Third-Harmonic Generation."

• The Analogy: Imagine three people pushing a swing gently at the same time. If they push perfectly in sync, the swing goes so high it suddenly launches a fourth person into the air. In this case, the "fourth person" is a flash of green light that you can actually see with a camera.

3. The Surprise: The Diamond "Remembers" the Light

While they were making this green light, the scientists noticed something unexpected. The diamond wasn't just making green light; it was also changing its own shape in a way that shifted the color of the light it was trapping.

• The Shift: The "pitch" of the light trapped inside the diamond got higher (a "blue shift"). It shifted so much that it moved past the entire range of the light it was originally holding.
• The Analogy: Imagine a guitar string. Usually, to change the note, you have to tighten the string with a key. Here, the light itself acted like a magical tuner, tightening the string just by being there.

4. Why Did This Happen? (The "Space Charge" Story)

Diamond is usually a very stubborn material that doesn't like to change its properties easily. However, this diamond had tiny "defects" inside it—missing atoms or extra nitrogen atoms, like small potholes in a road.

• The Mechanism: When the bright green light (created in step 2) hit these potholes, it knocked electrons (tiny charged particles) loose. These electrons ran away to different spots, leaving behind a static electric field.
• The Result: This electric field acted like a magnet, pulling on the diamond's structure and changing how light moves through it. This is called the photorefractive effect.
• The Catch: The paper notes that this effect is very slow. It took about 4.5 hours of shining the light to reach the maximum shift, and once they turned the light off, it took 36 hours for the diamond to slowly relax back to its original state. It's like stretching a piece of very stiff gum; it takes a long time to stretch, and a long time to snap back.

5. The "Green Light" Requirement

The scientists tested if the green light was actually necessary. They found that if they shone the infrared light without the green light being present, the tuning effect happened much slower or not at all.

• The Analogy: The green light acts like a catalyst or a spark. It's the key that unlocks the ability for the diamond's internal "potholes" to move the electrons around. Without the green light, the diamond stays stubborn.

6. Why This Matters (According to the Paper)

The paper highlights a few specific reasons this is useful, based strictly on their findings:

• Precise Tuning: They can now tune the diamond's resonance frequency (the note it sings) by a large amount (20.2 GHz) just by shining a laser on it.
• Individual Control: Unlike heating the whole chip (which changes everything at once), this method allows them to tune one specific diamond device without messing up its neighbors on the same chip.
• Non-Volatile: Once tuned, the change stays for a long time (tens of hours) without needing constant power, which is great for setting up experiments.
• New Tools: This proves that diamond, which was thought to be too symmetrical to do certain things, can actually be used for second-order nonlinear effects (like electro-optic modulation) if you use these defect centers and light to break the symmetry.

In Summary:
The team used a diamond cavity to turn invisible infrared light into visible green light. This green light then triggered a slow-motion rearrangement of electric charges inside the diamond, which acted like a remote control to permanently (for a while) shift the diamond's resonant frequency. It's a way of using light to tune a diamond, one photon at a time.

Technical Summary

Technical Summary: Photorefractive Tuning Seeded by Third-Harmonic Light in a Diamond Photonic Crystal Cavity

Problem and Motivation
Single-crystal diamond nanocavities are promising platforms for quantum and nonlinear optical technologies due to their wide bandgap, high thermal conductivity, and large third-order nonlinearity ($\chi^{(3)}$). However, precise control of their resonant frequencies is essential for applications such as coupling to embedded single-photon emitters (e.g., nitrogen-vacancy centers) and realizing doubly-resonant nonlinear processes. Existing tuning methods, such as thermal heating or gas condensation, typically induce red-shifts and often affect all devices on a chip simultaneously, lacking the ability to independently tune individual cavities. Furthermore, while diamond is centrosymmetric and theoretically lacks a second-order nonlinearity ($\chi^{(2)} = 0$), recent observations of second-harmonic generation suggest that local electric fields from charged defects can induce an effective $\chi^{(2)}$. The authors investigate whether these defect-mediated effects can be harnessed for deterministic, non-volatile resonance tuning in diamond nanocavities.

Methodology
The study utilizes a photonic crystal cavity (PCC) fabricated from "optical grade" single-crystal diamond (Element Six) containing substitutional nitrogen ($N_s \approx 1$ ppm) and nitrogen-vacancy (NV) centers ($\approx 0.01$ ppm). The device is a suspended nanobeam with a periodic array of holes, evanescently coupled to a fibre-taper waveguide.

The experimental approach involves:

1. Cavity Characterization: Measuring the transmission spectrum of the PCC to determine quality factors ($Q \approx 1.07 \times 10^4$) and mode volumes ($V_{eff} \approx 0.13 (\lambda_0/n_0)^3$).
2. Third-Harmonic Generation (THG): Driving the cavity with a continuous-wave (CW) infrared laser (1566 nm) at moderate powers (up to 75 mW) to generate green light (522 nm) via $\chi^{(3)}$ processes.
3. Tuning Observation: Monitoring the cavity resonance frequency over extended periods (hours) while maintaining high intracavity power. The authors distinguish between fast thermo-optic effects (red-shifting) and slower photorefractive effects (blue-shifting).
4. Control Experiments:
   • Varying input power to observe relaxation dynamics.
   • Simultaneously injecting a green laser (520 nm) to test the role of visible light in the tuning mechanism.
   • Alternating between high and low power to demonstrate deterministic, reversible tuning.

Key Contributions and Results

• Cavity-Enhanced THG: The authors demonstrated efficient third-harmonic generation, converting telecom-wavelength IR photons to visible green light. The end-to-end conversion efficiency was measured at $\tilde{\eta}_{THG} = 6 \times 10^{-7} \text{ W}^{-2}$. The intracavity peak field intensity reached $56 \text{ GW/cm}^2$, facilitated by the high $Q/V_{eff}$ ratio.
• Photorefractive Blue-Shifting: While high-power IR pumping initially caused a thermo-optic red-shift ($\sim -9.1$ GHz), prolonged exposure led to a dominant blue-shift of the cavity resonance. Over approximately 4 hours, the resonance shifted by $\Delta\omega/2\pi = 20.2(2)$ GHz, exceeding the cold-cavity linewidth. This corresponds to a fractional refractive index change of $\Delta n/n_0 = -1.05(1) \times 10^{-4}$.
• Mechanism Identification: The blue-shift is attributed to the photorefractive effect. The authors propose that the strong intracavity field and the internally generated green light (THG) photoionize crystal defects (primarily substitutional nitrogen $N_s$ and NV centers). This creates a space-charge distribution, generating a static electric field ($E_{sp}$). This field modulates the refractive index via an induced electro-optic effect. Although diamond is centrosymmetric, the authors argue that charged defects create local fields that couple with the bulk $\chi^{(3)}$ to induce an effective $\chi^{(2)}_{eff} = 3\chi^{(3)}E_{DC}$, enabling the electro-optic response.
• Green Light Dependence: A critical control experiment showed that the rate of blue-shifting accelerates significantly when an external green laser is injected alongside the IR pump. This confirms that the photorefractive process is seeded by the green light (either generated internally via THG or externally), which provides the necessary photon energy to ionize defects and redistribute charges.
• Relaxation and Reproducibility: The blue-shifted state is non-volatile, with relaxation occurring over tens of hours (characterized by fast and slow time constants). The authors demonstrated deterministic control by toggling the laser power: high power induces blue-shifting, while low power allows for red-shifting (relaxation), enabling reproducible in situ tuning of individual cavities without degrading the $Q$-factor.

Significance and Claims
The paper claims that this work demonstrates the first observation of photorefractive tuning in a diamond nanocavity. The significance lies in several areas:

1. Novel Tuning Mechanism: It offers a robust, non-volatile method for blue-tuning diamond cavities, complementing existing red-shifting techniques. Crucially, it allows for the independent tuning of individual devices on the same chip, a capability not afforded by global thermal or gas-based methods.
2. Second-Order Nonlinearity in Diamond: The observation supports the hypothesis that electric fields from charged defects can induce a measurable $\chi^{(2)}$ in centrosymmetric diamond, potentially enabling future diamond-based electro-optic modulators and frequency converters.
3. Quantum Applications: The ability to align cavity resonances with the electronic transitions of embedded color centers (like NV centers) without permanent damage or $Q$-factor degradation is valuable for quantum photonics, including Purcell-enhanced coupling and on-chip magnetometry.
4. Green Light Generation: The work represents the first demonstration of integrated nonlinear optics in the visible regime within a diamond nanocavity, highlighting diamond's potential for high-intensity green light generation despite its moderate nonlinearity.

The authors maintain a modest stance, noting that the conversion efficiency is currently limited by the $Q$-factor compared to other platforms and that the underlying charge dynamics require further investigation. They suggest that future work could focus on improving THG efficiency through device engineering and exploring surface passivation to better control the photorefractive parameters.