Spectral tuning of single T centres by the Stark effect

This paper demonstrates that integrating single silicon T centres into nanophotonic cavities with p-i-n diodes enables Stark-effect spectral tuning up to 30 GHz, which significantly increases the yield of mutually resonant emitters and enhances entanglement rates for scalable quantum technologies.

The Gist

The Big Picture: Tuning a Quantum Orchestra

Imagine you are trying to build a quantum computer using silicon chips. To make this work, you need tiny light sources (called T centres) that act like musical instruments. For these instruments to play together in harmony (a process called entanglement), they must all sing the exact same note (frequency).

The problem is that when you manufacture these instruments on a chip, they are never perfectly identical. Some are slightly sharp, some are slightly flat, and they are all scattered across a wide range of notes. This is like having an orchestra where every violinist is playing a slightly different pitch; they can't make music together.

This paper shows how the researchers built a "volume knob" for these quantum instruments. By applying electricity, they can physically shift the pitch of individual T centres up or down, allowing them to tune out-of-tune instruments until they match each other perfectly.

The Device: A Quantum Piano with Electric Keys

The researchers created a special device that combines three things:

1. The Instrument: A single T centre (a defect in the silicon crystal that emits light).
2. The Amplifier: A tiny optical cavity (a mirror box) that makes the light brighter and faster.
3. The Tuner: A p-i-n diode (a type of electrical switch) built right next to the instrument.

Think of the diode as a tuning fork you can press with your finger. When you apply a reverse voltage (a specific type of electrical pressure), it creates an electric field. This field pushes on the T centre, stretching its energy levels and changing the color (frequency) of the light it emits. This is known as the Stark effect.

What They Discovered

1. The "Super-Tuner" Range
The researchers found they could shift the pitch of these T centres by a massive amount—up to 30 Gigahertz.

• The Analogy: Imagine a piano where the keys are stuck. Usually, you can only wiggle a key a tiny bit. Here, they found a way to slide the entire key up and down the keyboard.
• The Result: Because they can slide the pitch so far, they calculated that they can tune 55% of the randomly manufactured T centres on a single chip to match each other. Before this, most of them would have been useless because they couldn't be made to match.

2. The "Fuzzy Note" Problem
While they could tune the pitch, they noticed a side effect: as they turned the "volume knob" (voltage) higher, the note became "fuzzier" (the light spectrum got wider).

• The Analogy: It's like tuning a guitar string. As you tighten it, the string starts to vibrate a little more chaotically, making the sound slightly less pure.
• The Cause: The electric field makes the T centre very sensitive to tiny, invisible electrical "noise" from the surrounding silicon, causing the note to wobble.

3. The "On/Off" Switch (Dark State)
When they pushed the voltage too high, the light didn't just get fuzzier; it disappeared completely.

• The Analogy: Imagine a lightbulb that, when you twist the dimmer too far, doesn't just get dimmer—it changes color into a "dark" state where it stops glowing entirely.
• The Science: The high voltage forces the T centre to change its electrical charge, turning it into a "dark" version that doesn't emit light. They observed this as a sudden drop in brightness.

4. The "Spin" Twist
The T centre has a property called "spin" (like a tiny internal magnet). The researchers found that by applying an electric field, they could slightly twist the way this spin interacts with magnetic fields.

• The Analogy: It's like using electricity to slightly bend a compass needle. This suggests that in the future, they might be able to use electricity (instead of just magnetic fields) to control the spin of the qubit, which is a crucial step for building quantum computers.

Why This Matters (According to the Paper)

The paper concludes that this ability to tune individual emitters is a game-changer for scaling up quantum technology.

• Before: You had to hope that by pure luck, two T centres on a chip happened to be the same pitch.
• After: You can actively tune them to match.
• The Payoff: By tuning two different T centres to the same pitch, the researchers modeled that the chance of them successfully "entangling" (linking their quantum states) increases by five orders of magnitude (100,000 times more likely).

In short, they built a tool that turns a chaotic, out-of-tune quantum orchestra into a synchronized ensemble, making it much easier to build large-scale quantum networks using silicon chips.

Technical Summary

1. Problem Statement

Silicon T centres are promising candidates for scalable quantum technologies due to their long-lived spin qubits, telecommunications-band emission (O-band), and compatibility with silicon manufacturing. However, a major bottleneck for large-scale integration is spectral inhomogeneity.

• Fabrication Variations: Integrating T centres into nanophotonic cavities introduces local strain and charge variations, leading to an inhomogeneous spectral distribution (typically ~30 GHz wide).
• Resonance Requirement: High-fidelity quantum entanglement protocols (e.g., Hong-Ou-Mandel interference) require separate emitters to be spectrally resonant with each other and with optical cavities.
• Previous Limitations: While DC Stark tuning has been demonstrated in diamond and SiC, previous attempts to tune T centre ensembles in p-i-n diodes showed no observable Stark shift below breakdown voltages. Furthermore, the impact of Stark tuning on single emitters within integrated photonic circuits was unexplored.

2. Methodology

The authors developed a hybrid device architecture combining single T centres, 1D nanophotonic cavities, and integrated p-i-n diodes on Silicon-on-Insulator (SOI) substrates.

• Device Fabrication:
  • Devices were fabricated on 220 nm SOI with high-resistivity silicon.
  • p-i-n Diodes: Formed by doping regions on either side of the cavity (intrinsic region widths of 12.5 µm or 15.0 µm).
  • T Centre Creation: Achieved via masked carbon and hydrogen implantation, confining T centre formation to $\pm 1$ µm of the cavity center.
  • Electrical Control: A grating coupler allows optical access, while the p-i-n diode structure enables independent electrical control of the electric field across the cavity for each device on a chip.
• Experimental Setup:
  • Measurements were conducted in a closed-cycle cryostat at $T \approx 1.6 - 2.5$ K.
  • Stark Tuning: Reverse bias voltages (up to -120 V) were applied to modulate the electric field, inducing DC Stark shifts in the T centre's zero-phonon line (ZPL).
  • Characterization: Photoluminescence Excitation (PLE) spectroscopy, time-resolved lifetime measurements, and Hanbury-Brown-Twiss (HBT) correlation measurements were used to analyze frequency shifts, linewidths, and photon statistics.
  • Modeling: Theoretical models were developed to predict the joint excitation probability and Hong-Ou-Mandel (HOM) visibility under varying detuning and linewidth conditions.

3. Key Contributions

• First Demonstration of Single-Emitters Tuning: Successfully demonstrated DC Stark tuning of single T centres in integrated nanophotonic cavities, overcoming the lack of observable shifts in previous ensemble studies.
• Quantification of Tuning Range: Established a tuning range of up to 30 GHz, sufficient to bring a significant fraction of inhomogeneously distributed emitters into mutual resonance.
• Trade-off Analysis: Characterized the trade-off between spectral tuning and linewidth broadening (spectral diffusion), attributing the broadening to increased sensitivity to charge noise in non-depleted regions.
• Charge State Dynamics: Identified a mechanism for reversible luminescence quenching at high reverse biases, linked to the conversion of the T centre from a bright neutral state to a dark charge state via Fermi level crossing or field ionization.
• Spin-Orbit Coupling Discovery: Observed electric-field-induced modulation of the spin-dependent optical transition splitting (C-B splitting), suggesting a mechanism for electrically driven excited-state spin mixing.

4. Key Results

• Spectral Tuning Performance:
  • Single T centres exhibited linear Stark shifts with rates up to 2.99 GHz/V.
  • A maximum red-shift of 30 GHz was achieved at -14 V for specific centres.
  • Based on the measured inhomogeneous distribution, 55(2)% of on-chip T centres can be tuned into mutual resonance using this 30 GHz range.
• Linewidth and Broadening:
  • Tuning was accompanied by linear linewidth broadening (up to ~1 GHz increase).
  • This broadening is attributed to enhanced spectral diffusion caused by fluctuating charge traps near the emitter, which become more sensitive under high electric fields.
  • Despite broadening, modeling shows that the gain in resonance probability outweighs the loss in indistinguishability.
• Purcell Effect and Lifetime:
  • Tuning emitters into the cavity resonance resulted in a 2.18x reduction in excited-state lifetime, confirming Purcell enhancement.
• Entanglement Probability:
  • Modeling of the joint excitation probability revealed that tuning distinct emitters into mutual resonance can increase the success rate of remote entanglement by over five orders of magnitude (e.g., from $10^{-5}$ to $10^{-1}$).
• Intensity Modulation & Charge States:
  • At high reverse biases (> -120 V), luminescence was fully quenched.
  • This is attributed to the T centre transitioning to a dark charge state (likely $T^-$) when the hole quasi-Fermi level crosses the (0/−) charge transition level ($E_C - 200$ meV).
• Spin-Orbit Coupling:
  • Applied bias modulated the Zeeman splitting of the C and B transitions.
  • The sign of the modulation varied between emitters, likely due to different defect orientations relative to the electric field vector. This implies that electric fields can drive spin mixing via spin-orbit coupling, offering a pathway for Electric Dipole Spin Resonance (EDSR).
• Response Time:
  • The Stark shift response time was measured at 160 ns (limited by RC constants), enabling modulation rates > 5 MHz.

5. Significance and Impact

This work represents a critical step toward scalable silicon quantum networks:

1. Yield Improvement: By enabling local spectral compensation, the technique significantly increases the yield of functional spin-photon interfaces on a single chip, moving from a "lucky emitter" scenario to a deterministic one.
2. Scalable Entanglement: The ability to tune distinct emitters into resonance is a prerequisite for generating remote entanglement between arbitrary nodes in a quantum network. The demonstrated 5-order-of-magnitude increase in joint excitation probability makes large-scale entanglement feasible.
3. New Control Paradigms: The discovery of electric-field-mediated spin mixing and charge-state control expands the operational toolkit for T centres, potentially enabling all-electrical qubit manipulation and storage (shelving) without magnetic fields.
4. Device Optimization: The study highlights that while linewidth broadening is a current limitation, it is likely a consequence of specific fabrication-induced charge traps rather than an intrinsic limit, suggesting that future device optimization (e.g., better passivation) could retain wide tuning ranges while minimizing broadening.

In summary, the paper demonstrates that integrating T centres with p-i-n diodes provides a robust, electrically controllable platform for overcoming fabrication inhomogeneity, thereby unlocking the potential of silicon T centres for large-scale quantum computing and networking.