Control of emission interval and timing in triggered periodic superradiance

This study demonstrates that applying a trigger laser tuned to the superradiance transition wavelength in an Er:YSO crystal enables precise control over both the period and timing of triggered periodic superradiance by lowering the emission threshold and reducing variance, a phenomenon validated by Maxwell-Bloch simulations.

The Gist

Imagine a crowded room full of people (atoms) who are all holding flashlights. Normally, if you tell everyone to turn on their flashlights at once, they will do so at slightly different times because they are waiting for a signal from their neighbors. This results in a messy, chaotic flash of light that happens unpredictably. In physics, this chaotic flash is called Superradiance.

The scientists in this paper wanted to take control of this chaos. They wanted to make the flash happen at a specific time, with a specific rhythm, and with a specific amount of light. They did this using a special crystal (Er:YSO) and a "trigger" laser.

Here is the breakdown of their discovery using simple analogies:

1. The Problem: The Unpredictable Crowd

In a standard setup, the atoms are pumped with energy (like giving everyone a battery). Eventually, they all want to release that energy as light. However, without a leader, they start flashing based on random whispers (quantum fluctuations).

• The Result: The flash happens, but the timing is jittery. Sometimes it's fast, sometimes slow. It's like a crowd clapping after a joke; sometimes they clap immediately, sometimes they wait a second, and the rhythm is all over the place.

2. The Solution: The "Trigger" Laser

The researchers introduced a second laser, tuned to the exact color of the light the atoms want to emit. Think of this trigger laser as a conductor or a whistleblower.

• How it works: Instead of waiting for a random whisper, the atoms hear the conductor's whistle (the trigger laser). This gives them a clear signal to start flashing together.
• The Effect: The "flash" happens much faster and much more reliably. The randomness disappears.

3. Experiment A: The Metronome (Controlling the Rhythm)

The researchers found that this crystal naturally produces a repeating flash (a pulse every few milliseconds), like a heartbeat. They wanted to see if the trigger laser could control this heartbeat.

• The Discovery: When they turned on the trigger laser, the "heartbeat" sped up. The time between flashes got shorter.
• The Analogy: Imagine a drummer playing a beat. Without a metronome, they might speed up or slow down slightly. When you add a metronome (the trigger laser), the drummer locks into a tighter, faster, and more consistent rhythm.
• The Trade-off: As they turned up the volume of the trigger laser (the conductor's whistle), the flashes became more frequent, but each individual flash became dimmer.
  • Why? Because the trigger laser told the atoms to release their energy sooner. They didn't have time to build up a massive amount of energy before letting it go. It's like a crowd clapping faster; if they clap every second instead of every three seconds, each clap might be slightly less enthusiastic because they are rushing.

4. Experiment B: The "On-Demand" Light Switch

In a second experiment, they set up the conditions so that the crystal wouldn't flash at all on its own. The energy wasn't quite high enough to start the chain reaction.

• The Discovery: Even though the crystal was "asleep," a short burst of the trigger laser woke it up and forced a flash to happen.
• The Analogy: Imagine a campfire that is too wet to catch fire on its own. You can't just wait for it to light up. But if you throw a specific kind of spark (the trigger laser) onto it, it bursts into flames immediately.
• The Result: They created a device that acts like a light switch. They could decide exactly when the flash would happen by simply firing a short pulse of the trigger laser.

5. The Simulation: The Digital Twin

To make sure they understood why this was happening, they built a computer model (a digital twin) of the crystal.

• They programmed the model with the laws of physics (Maxwell-Bloch equations).
• The computer simulation perfectly matched the real-world experiment. It confirmed that the trigger laser lowers the "threshold" needed for the flash to happen, explaining why the flashes got faster and dimmer as the trigger got stronger.

Why Does This Matter?

This isn't just about making pretty lights. It's about control.

• Quantum Computing: In the future, we might need to send information using light pulses that are perfectly synchronized. This technology allows us to say, "Flash now, exactly at this microsecond," which is crucial for reading data from quantum memory.
• Precision: By controlling the timing, we can perform other delicate quantum operations right at the moment the light is brightest and most organized.

In Summary:
The scientists took a chaotic, unpredictable burst of light and turned it into a disciplined, rhythmic, and on-demand light source. They used a "trigger" laser to act as a conductor, speeding up the rhythm and allowing them to summon the light exactly when they wanted it, effectively turning a natural phenomenon into a controllable tool for future technology.

Technical Summary

1. Problem Statement

Superradiance (SR) is a collective quantum phenomenon where an ensemble of excited emitters releases energy coherently. While triggered SR (using an external laser seed) is well-known for controlling the timing of a single SR pulse in conventional systems, the control of periodic SR in solid-state systems remains challenging.

• Context: The authors previously observed "periodic superradiance" in an Erbium-doped Yttrium Orthosilicate (Er:YSO) crystal under continuous wave (CW) excitation. In this state, the system undergoes cycles of population inversion buildup followed by SR bursts.
• The Challenge: While the period of these bursts depends on excitation power, it exhibits significant fluctuations (variance) and lacks deterministic control. The goal was to determine if an external trigger laser could stabilize the periodicity, reduce timing jitter, and allow for on-demand generation of SR pulses in a solid-state system.

2. Methodology

The study employed a combination of experimental observation and numerical simulation based on the Maxwell-Bloch equations.

Experimental Setup:

• Medium: Er:YSO crystal doped with Er³⁺ ions (concentration 0.1%, density $5 \times 10^{18} \text{ cm}^{-3}$) at a cryogenic temperature of 4 K.
• Excitation: An 808 nm CW laser pumps the system, creating population inversion between the $^4I_{13/2}$ and $^4I_{15/2}$ states.
• Trigger: A 1545 nm CW laser (tuned to the SR transition wavelength) is injected as a seed.
• Protocol:
  • Scenario A (Power Dependence): Both excitation and trigger lasers are active. The trigger power is varied (10 µW to 9 mW) while measuring changes in the SR period, pulse height, and duration.
  • Scenario B (Timing Control): The excitation laser alone is insufficient to reach the SR threshold. A short trigger pulse (33 µs duration) is applied at specific intervals to induce SR.

Numerical Simulation:

• The authors extended their previous model [18] to include the trigger laser effect.
• Model: A reduced three-level system ($|1\rangle, |2\rangle, |3\rangle$) based on Maxwell-Bloch equations.
• Key Modification: A new term ($\alpha \kappa_0 \Omega_{\text{trig}}$) was added to the electric field evolution equation to represent the deterministic seed provided by the trigger laser.
• Dynamic Parameter: The field decay rate ($\kappa$) was modulated dynamically based on the electric field intensity to reproduce the periodic behavior observed experimentally.

3. Key Contributions

1. Demonstration of "Triggered Periodic SR": The first experimental realization of using an external trigger to control the periodicity and timing of SR in a solid-state crystal, moving beyond single-pulse control.
2. Quantitative Power Dependence: Established a proportional relationship between the SR period and the number of emitted photons as a function of trigger power, explained by a reduced SR threshold.
3. On-Demand Generation: Demonstrated a mechanism to generate SR pulses at desired timings even when the primary excitation is below the natural SR threshold.
4. Validation via Simulation: Successfully reproduced experimental trends (period reduction, pulse area scaling) using Maxwell-Bloch simulations, validating the theoretical model of threshold reduction via seeding.

4. Key Results

A. Control of Period and Variance

• Period Reduction: Applying the trigger laser significantly shortened the SR period. Without a trigger, the period was $350 \pm 40$ µs; with a 0.5 mW trigger, it dropped to $230 \pm 20$ µs.
• Variance Reduction: The standard deviation of the period decreased, indicating enhanced temporal stability and reduced shot-to-shot fluctuations.
• Pulse Characteristics: As the trigger power increased, the peak height of the SR pulse decreased, while the FWHM duration increased. This is consistent with a lower population inversion threshold being reached earlier in the cycle, resulting in fewer total photons per burst but a longer emission window.

B. Trigger Power Dependence

• Proportionality: A linear relationship was observed between the SR period and the pulse area (total photon number).
• Mechanism: The trigger laser lowers the effective population inversion threshold ($N_{th}$) required for SR. Since the excitation rate is constant, a lower threshold means the system reaches the burst condition sooner (shorter period) and with fewer accumulated ions (fewer photons).
• Saturation: At high trigger powers (>1 mW), SR emission ceased entirely, likely due to stimulated emission depleting the upper state population before the threshold for collective SR could be reached.

C. Timing Control (On-Demand Emission)

• Sub-Threshold Triggering: When the excitation laser alone could not induce SR, a short trigger pulse (33 µs) successfully initiated the emission.
• Timing Precision: The first SR pulse occurred, on average, 82 µs after the trigger pulse with a standard deviation of 15 µs.
• Device Capability: This establishes the system as a device capable of generating SR pulses at user-defined times with microsecond precision, effectively acting as a "SR switch."

D. Simulation Agreement

• The numerical simulations successfully reproduced the decrease in period and pulse area with increasing trigger power.
• The model confirmed that the trigger laser reduces the delay time ($T_D$) and the threshold population inversion ($N_{th}$).
• A discrepancy in absolute FWHM duration (experiment > simulation) was noted but attributed to potential frequency mode mismatches or spatial overlap limitations.

5. Significance and Implications

• Quantum Information Processing: The ability to generate narrow-linewidth optical pulses at precise, controllable intervals makes this system a candidate for quantum memory readout and synchronization in quantum networks.
• Stable Light Source: Triggered periodic SR offers a pathway to create solid-state light sources with stable nanosecond pulse trains, superior to spontaneous emission sources.
• Fundamental Physics: The study provides insights into the control of collective coherence dynamics in solids, bridging the gap between conventional triggered SR and complex periodic behaviors.
• Astrophysical Relevance: The findings contribute to understanding mechanisms behind Fast Radio Bursts (FRBs), where triggered SR has been proposed as a physical model.

In conclusion, Hara et al. have successfully demonstrated that an external trigger laser can deterministically control both the interval and timing of superradiance in a solid-state crystal, transforming a stochastic periodic phenomenon into a controllable device for advanced quantum applications.