🔬 atomic physics

Microsecond-Scale Coherent Control of a Forbidden Clock Transition with Doppler-Free Multiphoton Excitations

This paper demonstrates two Doppler-free multiphoton excitation schemes that enable microsecond-scale coherent control of the forbidden clock transition in thermal strontium-88 ensembles, achieving significant Doppler dephasing suppression and relaxing the requirements for ultra-cold temperatures or tight confinement.

Original authors: Guglielmo Panelli, Erik J. Porter, V. Rose Knight, Shaun C. Burd, Mark Kasevich

Published 2026-07-09

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CC BY 4.0

Original authors: Guglielmo Panelli, Erik J. Porter, V. Rose Knight, Shaun C. Burd, Mark Kasevich

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to teach a massive crowd of people (atoms) to dance in perfect unison. The specific dance move you want them to do is very difficult and rare; in the world of physics, this is called a "forbidden clock transition." Usually, to get these atoms to dance together, you have to freeze them until they are almost motionless and trap them in a tiny, invisible cage. If they move even a little bit, the dance falls apart because of the Doppler effect—think of it like trying to hear a siren clearly while driving past it at high speed; the pitch changes, and the signal gets messy.

This paper describes a new way to get a huge crowd of warm, moving atoms to perform this difficult dance perfectly, without needing to freeze them or trap them. The researchers achieved this in just a few millionths of a second (microseconds).

Here is how they did it, using two different "choreography" methods:

The Problem: The Moving Crowd

Normally, if you shine a light on a moving atom to make it dance, the atom's speed changes how it "sees" the light. Some atoms see the light as too fast, others too slow. This causes the crowd to lose sync immediately. To fix this, scientists usually have to slow the atoms down to near absolute zero.

The Solution: Canceling the Speed

The researchers used a clever trick with laser beams. Imagine three laser beams hitting the atoms from different angles. They carefully adjusted the angles so that the "push" from one beam canceled out the "push" from the others.

The Analogy: Imagine three people pushing a car. If two people push forward and one pushes backward with just the right force, the car doesn't move forward or backward relative to the ground, even if the people are running.
The Result: Because the "pushes" canceled out, the atoms didn't "feel" their own speed. The Doppler effect was silenced. This allowed the researchers to use a hot, moving cloud of atoms (about 3 million of them) and still get them to dance in perfect sync.

Method 1: The Three-Beat Rhythm (Simultaneous)

In the first method, they used three lasers hitting the atoms all at once.

How it works: Instead of one big step, the atoms take three tiny steps at the same time to get from the "ground" state to the "clock" state.
The Analogy: It's like a drummer playing three different drums at once. Even if the drummer is slightly off-beat, the combination of the three sounds creates a perfect rhythm that the crowd can follow.
The Result: They got 76% of the atoms to do the dance move perfectly.

Method 2: The Relay Race (Sequential)

The second method was even faster. They used a two-step relay race.

How it works: First, they used one laser to get the atoms to a "waiting room" state. Then, immediately after, they used two other lasers to push them from the waiting room to the final "clock" state.
The Analogy: Imagine a relay race where the first runner hands the baton to a second runner who sprints to the finish line. Because the handoff is so fast and the runners are so coordinated, the whole team finishes in record time.
The Result: This method was incredibly fast, completing the dance in less than a microsecond (about 600 nanoseconds), with over 90% of the atoms doing it correctly.

Why This Matters (According to the Paper)

The researchers tested these methods by trying to keep the atoms in sync for a long time (a technique called Ramsey spectroscopy).

The Old Way: With normal lasers, the atoms would lose sync in about 4.5 microseconds (millionths of a second) because of their movement.
The New Way: With their new laser tricks, the atoms stayed in sync for over 4 milliseconds. That is 1,000 times longer.

The Big Picture

The paper claims that by using these "Doppler-free" laser tricks, scientists can now:

Use more atoms: They don't need tiny, cold traps; they can use huge clouds of atoms.
Go faster: They can manipulate the atoms in microseconds instead of milliseconds.
Simplify the setup: They don't need to cool the atoms to ultra-low temperatures or trap them tightly.

The authors suggest these techniques could be used to build better atomic clocks, improve sensors that measure gravity or time, and help with quantum computing, but they emphasize that the core achievement is simply mastering this fast, precise control over moving atoms without the usual heavy equipment.

Technical Summary: Microsecond-Scale Coherent Control of a Forbidden Clock Transition with Doppler-Free Multiphoton Excitations

Problem Statement
The coherent manipulation of optical clock transitions, specifically the strongly forbidden $^1S_0 - ^3P_0$ transition in alkaline-earth-like atoms such as $^{88}\text{Sr}$ , is fundamental to atomic sensors, quantum computing, and precision metrology. However, achieving high-contrast excitation of these ultra-narrow transitions typically imposes stringent technical requirements: systems must be ultracold or confined within Lamb-Dicke regimes (e.g., optical lattices, tweezers, or ion traps) to mitigate Doppler dephasing and recoil. In thermal ensembles without confinement, single-photon excitation is limited by the Doppler width and low Rabi frequencies (typically kilohertz range), necessitating long excitation times that are incompatible with fast quantum operations or large-atom-number sensing in free space.

Methodology
The authors demonstrate two distinct Doppler-free (DF) multiphoton excitation schemes designed to manipulate the $^1S_0 - ^3P_0$ clock transition in thermal ensembles of $3 \times 10^6$ $^{88}\text{Sr}$ atoms in free space. Both methods utilize a specific wavevector configuration where three coplanar lasers interact with the atoms such that the net wavevector sum is zero ( $k_1 + k_2 - k_3 = 0$ ). This geometry ensures the first-order Doppler shift $(k_1 + k_2 - k_3) \cdot v$ vanishes regardless of atomic velocity.

Simultaneous Three-Photon Excitation (Method 1): Three lasers simultaneously drive a coherent three-photon transition from the ground state $|g\rangle$ ( $^1S_0$ ) to the clock state $|e\rangle$ ( $^3P_0$ ) via intermediate states. The lasers are phase-synchronized via beatnote locks to a frequency comb. The net wavevector is nulled to suppress the Doppler effect, allowing for a three-photon Rabi frequency of 192 kHz.
Sequential Doppler-Free Excitation (Method 2): This protocol combines a single-photon excitation from $|g\rangle$ to an intermediate state $|s\rangle$ ( $^3P_1$ ) followed immediately by a two-photon Raman excitation from $|s\rangle$ to $|e\rangle$ . The lasers remain in the DF configuration ( $k_1 + k_R = 0$ , where $k_R = k_2 - k_3$ ). This sequential approach achieves an effective Rabi frequency of 820 kHz.

Both methods employ state-selective imaging to resolve populations in the ground, intermediate, and clock states. The experiments are conducted with a bias magnetic field to induce Zeeman splitting, enabling specific laser couplings.

Key Results

Microsecond-Scale Excitation: The sequential method (Method 2) achieves a $\pi$ -pulse (complete population transfer) in 610 ns with over 90% efficiency. The simultaneous method (Method 1) achieves a $\pi$ -pulse with 76% efficiency.
Doppler Suppression: Both schemes demonstrate a suppression of Doppler dephasing by three orders of magnitude compared to single-photon excitation. In Ramsey spectroscopy, the coherence time (1/e contrast decay time) for a 9 $\mu$ K thermal sample was extended from 4.5 $\mu$ s (single-photon) to 4.5 ms (sequential) and 4.1 ms (simultaneous).
Fourier-Limited Linewidths: Method 1 achieved resonance features with a full-width-at-half-maximum (FWHM) below 300 Hz, limited primarily by residual wavevector misalignment and atomic free-fall, rather than the Doppler width.
High-Contrast Ramsey Spectroscopy: The authors successfully performed high-contrast Ramsey spectroscopy on thermal ensembles, observing Ramsey fringes with dark times up to 3 ms. The techniques maintained high contrast at short interrogation times comparable to single-photon schemes but with vastly extended coherence times.
Systematic Effects: The authors analyzed AC Stark shifts and recoil. While multi-spectral excitation introduces AC Stark shifts, these are static and can be nulled or calibrated. The net photon recoil is zero in the DF configuration, eliminating recoil-induced dephasing during the excitation.

Significance and Claims
The paper claims that these techniques enable fast, coherent manipulation of narrow-line transitions without the need for tight confinement or ultra-low temperatures. By relaxing the requirements for atomic cooling and trapping, the methods allow for the use of large thermal ensembles ( $N \approx 10^6$ ), which offers a potential atom-number advantage for quantum-enhanced metrology scaling as $\sqrt{N}$ .

The authors identify several specific applications enabled by these results:

Quantum-Enhanced Sensing: Facilitating the generation of spin-squeezed states in large, free-space ensembles, potentially improving sensitivity beyond the standard quantum limit.
Precision Metrology: Supporting atom-interferometric gravitational wave detection proposals that rely on large-momentum-transfer techniques using optical clock transitions.
Optical Tweezer Arrays and Rydberg Physics: The reduction of net photon recoil allows for shallower trapping potentials in optical tweezer arrays and may accelerate the preparation of Rydberg states from the clock state.

The work is presented as a generalizable approach applicable to various atomic species and optical clock transitions, including both bosonic and fermionic isotopes, providing a pathway to faster and more scalable quantum devices.