Optical probing of phononic properties of a tin-vacancy color center in diamond

This paper investigates the phononic properties and coherence characteristics of tin-vacancy color centers in diamond by combining temperature-dependent linewidth measurements to determine phononic coupling coefficients with coherent population trapping experiments to reveal picosecond-scale orbital depolarization and estimate thermally limited spin dephasing times.

The Gist

Imagine a diamond not just as a shiny gem, but as a microscopic city where tiny "defects" act like special citizens. One of these citizens is the Tin-Vacancy (SnV) center. Think of it as a tiny atom-sized machine made of a tin atom missing a spot in the diamond's crystal grid. Scientists love these machines because they are incredibly stable and could one day help build quantum computers.

However, for these machines to work perfectly, they need to stay calm and quiet. If they get too jiggly or confused by their surroundings, they lose their "coherence" (their ability to hold information). This paper is like a detective story where the researchers try to figure out exactly how much the SnV machine gets jiggled by the heat and vibrations (phonons) inside the diamond.

Here is a breakdown of what they found, using simple analogies:

1. The Problem: The "Jiggly" Ground

The SnV machine has two main "floors" (energy levels) where it can sit. Usually, it likes to sit on the lower floor. But the diamond is never perfectly still; it vibrates like a jelly. These vibrations are called phonons.

• The Challenge: When the diamond vibrates, it can kick the SnV machine from the lower floor to the upper floor, or make it wobble so much that it forgets what it was doing.
• The Difficulty: These kicks happen incredibly fast—faster than a blink of an eye (in just picoseconds, which is a trillionth of a second). Trying to film this with a camera is impossible because the camera (detectors) is too slow. It's like trying to take a photo of a hummingbird's wings with a camera that only takes one picture every hour.

2. The First Clue: Measuring the "Blur" (Linewidth Broadening)

Since they couldn't film the fast movement directly, the scientists looked at the "blur" of the light the SnV emits.

• The Analogy: Imagine a singer holding a perfect note. If the singer is in a quiet room, the note is pure and sharp. If the singer is in a windy, noisy room, the note gets "fuzzy" or broad.
• The Experiment: The researchers heated the diamond up and watched how the "note" (the light color) got fuzzier.
  • At low temperatures (very cold, around 4 Kelvin), the fuzziness was caused by single "kicks" from the vibrations (single-phonon events).
  • At higher temperatures (around 24 Kelvin and up), the fuzziness grew much faster. This told them that now, the SnV was getting hit by two vibrations at once (two-phonon events).
• The Discovery: They found a "tipping point" at 24 Kelvin. Below this, the machine is mostly safe from double-kicks. Above it, the chaos increases rapidly. They also measured a very hard-to-see part of the machine (the "D transition") for the first time, confirming how the vibrations affect it.

3. The Second Clue: The "Traffic Jam" Trick (Coherent Population Trapping)

To measure the speed of the vibrations without a super-fast camera, they used a clever trick called Coherent Population Trapping (CPT).

• The Analogy: Imagine a busy intersection with two roads leading to a parking garage (the excited state).
  • If you send cars down Road A only, they all go to the garage.
  • If you send cars down Road B only, they all go to the garage.
  • But, if you send cars down both roads at the exact same time with perfect timing, the cars get "stuck" in a traffic jam at the entrance. They can't enter the garage anymore, so the garage stays empty (no light is emitted).
• The Experiment: The scientists shined two lasers (Road A and Road B) on the SnV. They watched how deep the "traffic jam" (the dip in light) was.
  • If the vibrations were slow, the traffic jam would be deep and stable.
  • If the vibrations were fast, the cars would get kicked out of the jam before they could get stuck, and the jam would be shallow.
• The Result: By analyzing how "shallow" the jam was, they calculated that the SnV gets kicked out of its state in about 30 picoseconds. This is incredibly fast—so fast that standard cameras can't see it, but this "traffic jam" trick allowed them to measure it indirectly.

4. What This Means for the Future (According to the Paper)

The paper concludes with a few key takeaways about how "safe" this quantum machine is:

• The Upper Floor is Unsafe: The upper floor of the SnV machine is very short-lived (it falls back down in 30 picoseconds). This means you can't use that specific floor to store information (a qubit) because it's too unstable.
• The Lower Floor is Safe (at Cold Temps): However, the time it takes to get kicked up to that unstable floor is much longer (about 958 nanoseconds at 4 Kelvin).
• The Verdict: Because the "kick up" time is so much longer than the "kick down" time, the SnV is actually quite good at holding information at very cold temperatures (like 1.8 Kelvin). The vibrations aren't the main problem at these low temperatures; the machine is stable enough to be a useful building block for quantum technology.

In summary: The scientists used the "fuzziness" of light and a "traffic jam" laser trick to figure out how fast a diamond defect gets jiggled by heat. They found that while it gets jiggled incredibly fast, it stays stable enough at very cold temperatures to be a promising candidate for future quantum computers.

Technical Summary

Technical Summary: Optical Probing of Phononic Properties of a Tin-Vacancy Color Center in Diamond

Problem Statement
Group-IV color centers in diamond (G4Vs), particularly the silicon-vacancy (SiV), are promising candidates for quantum technologies due to their inversion-symmetric structure, which offers resistance to charge noise. However, their utility is limited by decoherence arising from phononic interactions between the split orbital ground states. While the negatively charged tin-vacancy (SnV) center exhibits superior coherence properties at temperatures around 1 K compared to SiV and germanium-vacancy (GeV) centers—attributed to a large ground-state spin-orbit splitting (~850 GHz)—a quantitative understanding of its phononic coupling dynamics remains incomplete.

Directly measuring the ultrafast phononic processes (occurring on picosecond timescales) in the time domain is challenging due to limitations in pulse synchronization and photon detection jitter. Furthermore, the "D" optical transition of the SnV, which originates from the upper orbital ground state, has historically been difficult to measure spectroscopically because the thermal population of this state is negligible at cryogenic temperatures. Consequently, key phononic coupling coefficients and relaxation rates for the SnV have not been fully characterized.

Methodology
The authors employed a dual-approach strategy combining temperature-dependent spectroscopy and Coherent Population Trapping (CPT) to investigate a high-quality SnV emitter (E1) with a lifetime-limited linewidth and a second emitter (E2) embedded in a nanopillar.

1. Temperature-Dependent Linewidth Broadening:

   • The team performed Photoluminescence Excitation (PLE) spectroscopy on the "C" transition (lower ground state to excited state) and the "D" transition (upper ground state to excited state) at temperatures ranging from 4 K to 40 K.
   • At higher temperatures, where linewidths exceeded the laser scan range, Photoluminescence (PL) spectra were utilized.
   • The data was analyzed to separate single-phonon and two-phonon broadening regimes. The single-phonon regime was modeled using Boltzmann-distribution-based equations, while the two-phonon regime was fitted using a cubic temperature dependence ($T^3$).
   • Spectral shifts of the zero-phonon lines were also analyzed to distinguish between thermal expansion effects and phononic interactions.

2. Coherent Population Trapping (CPT):

   • To access ultrafast relaxation rates in the time domain via the frequency domain, CPT experiments were conducted at 4 K.
   • A lambda-type energy configuration was driven using two lasers: the "C" laser kept resonant with the C transition and the "D" laser scanned across the D transition.
   • The resulting fluorescence dips (dark states) were analyzed by numerically integrating a Lindblad master equation. This allowed the extraction of the orbital phononic relaxation rate ($\gamma_-$) and the excitation rate ($\gamma_+$) without requiring direct picosecond time-resolved detection.

Key Results

• Phononic Regimes and Coupling Coefficients: The study identified a transition temperature of approximately 24 K. Below this threshold, single-phonon processes dominate the linewidth broadening; above it, two-phonon processes (scaling as $T^3$) become dominant. The authors extracted electron-phonon coupling parameters $\alpha_-$ and $\alpha_+$, with $\alpha_-$ matching previously reported values for similar systems.
• Spectral Shifts: Analysis of the temperature-dependent spectral shift revealed that thermal expansion models failed to explain the observed trends. Instead, the shifts were accurately described by a model of SnV coupling to E-symmetric phonons, confirming the prevalence of these phonon modes below 110 K.
• Ultrafast Relaxation Times: The CPT experiments yielded an orbital depolarization time ($T_-$) of approximately 31 (5) ps and an orbital excitation time ($T_+$) of 958 (138) ns at 4 K. These measurements were achieved with picosecond resolution by transforming spectral information into its conjugate time variable.
• Spin Coherence Implications: Using the extracted rates, the authors estimated the spin dephasing time ($T^*_2$) limited by thermal effects. At 1.8 K, the calculated orbital excitation time is ~91 ms, which is an order of magnitude longer than the currently recorded spin coherence times (10 ms).

Significance and Claims
The paper claims to provide the first experimental quantification of phonon coupling rates for SnV centers at 4 K, a standard operating temperature for helium cryostats. By successfully measuring the previously inaccessible D transition and utilizing CPT to resolve picosecond dynamics, the work establishes that:

1. Phonons are not the limiting factor for SnV spin coherence at temperatures of 1.8 K and below, as the phonon-mediated relaxation timescales are significantly longer than current spin coherence records.
2. CPT is a superior method for characterizing ultrafast decoherence in solid-state emitters, offering resolution beyond the jitter limits of standard avalanche photodiodes and the complexity of direct time-domain pump-probe measurements.
3. The upper branch of the SnV orbital ground state is short-lived (~30 ps), preventing it from serving as a practical qubit, similar to observations in SiV centers. However, the lower branch remains robust for quantum information processing applications.

The authors conclude that these findings provide a necessary benchmark for the performance of G4V qubits and support the SnV as a favorable platform for integrated photonic quantum information processing.