Tune-out wavelength for the thulium atom near 576 nm

This paper reports the theoretical prediction and experimental measurement of a tune-out wavelength at approximately 575.646 nm for the ground state of thulium atoms, demonstrating that Bose-Einstein condensation can be achieved near this wavelength by optimizing trap polarization to manage polarizability components.

The Gist

Imagine you are trying to build a delicate house of cards, but you have a very strong, invisible wind blowing through the room. If the wind is too strong, it knocks the cards over. If it's too weak, the cards don't stand up straight. But what if you could find a specific "sweet spot" where the wind stops blowing entirely, allowing you to arrange your cards perfectly without any interference?

This is essentially what the scientists in this paper achieved, but instead of cards, they are working with Thulium atoms (a rare, heavy metal element), and instead of wind, they are using laser light.

Here is the breakdown of their discovery in simple terms:

1. The Invisible "Wind" (Light Pressure)

Usually, when you shine a laser on an atom, the light pushes on the atom. Physicists call this "polarizability." Think of it like a fan blowing on a feather.

• Strong push: The atom gets trapped in the light beam (like a fan holding a feather in place).
• No push: The atom ignores the light and floats away.
• Reverse push: The atom is pushed away from the light.

Scientists often want to trap atoms to study them or build quantum computers. To do this, they use "Optical Dipole Traps" (ODTs)—basically, invisible bowls made of laser light that hold atoms in place.

2. The Problem: The "Tune-Out" Wavelength

The tricky part is that the strength of this "wind" depends on the color (wavelength) of the laser.

• If you use a red laser, the wind might be strong.
• If you use a blue laser, it might be weak.
• Somewhere in between, there is a specific color where the wind completely stops. The atom becomes "invisible" to that specific color of light.

This specific color is called the "Tune-Out Wavelength." Finding this is like finding the exact frequency where a radio station goes silent.

3. Why Thulium?

Thulium is a special atom. It's not a simple ball; it's more like a spinning top with a complex shape. Because of this shape, the "wind" from the laser doesn't just push it; it can also twist it or push it differently depending on how the laser is oriented. This makes calculating the "silent spot" (the tune-out wavelength) very difficult.

4. The Experiment: Finding the Silence

The team of Russian scientists wanted to find this silent spot for Thulium near a yellow-green color (576 nm). They didn't just guess; they built a sophisticated test:

• The Setup: They trapped thousands of Thulium atoms in a "bowl" made of two crossing laser beams (one red, one yellow-green).
• The Shake Test: To measure how strong the "wind" was, they shook the bowl and watched how fast the atoms wiggled.
  • If the atoms wiggled fast, the wind was strong.
  • If they wiggled slowly, the wind was weak.
  • If the atoms stopped being trapped and flew away, the wind had reversed (pushing them out).
• The Radio Tuner: They also used a radio-frequency signal to "tune" the atoms, helping them separate the different types of "wind" (pushing vs. twisting).

5. The Big Discovery

They found the exact color where the Thulium atoms stopped feeling the laser's push.

• The Result: The "silent spot" is at 575.646 nanometers.
• The Proof: When they set the laser to this exact color, the atoms in the trap vanished because the laser stopped holding them. When they tweaked the color just a tiny bit, the atoms came back. This confirmed they had found the zero point.

6. The "Magic" Bonus: Bose-Einstein Condensation (BEC)

Here is the coolest part. Usually, when you shine light on atoms, it heats them up (like sunlight warming your skin). This heat ruins delicate quantum experiments.

However, the scientists proved that even at this "silent" wavelength, the light wasn't heating the atoms up enough to destroy them. They successfully cooled the atoms down until they formed a Bose-Einstein Condensate (BEC).

• What is a BEC? Imagine a crowd of people all marching in perfect lockstep, acting as a single giant "super-atom." It's a state of matter that only exists at near-absolute zero.
• Why it matters: They managed to create this super-atom while the laser was tuned to the exact color where the atoms should be "invisible." This proves they can manipulate these atoms with extreme precision without accidentally cooking them.

Summary Analogy

Imagine you are trying to balance a spinning top on a table.

1. The Laser: A fan blowing on the top.
2. The Tune-Out Wavelength: A specific fan speed where the air pressure perfectly cancels out, and the top doesn't move or spin faster.
3. The Experiment: The scientists found the exact fan speed (color of light) where the Thulium top ignores the air.
4. The Achievement: They proved they could make the top spin in a perfect, synchronized dance (BEC) even while the fan was set to that "magic" speed, showing that the fan wasn't blowing hot air that would melt the top.

Why does this matter?
This discovery gives scientists a new, precise tool to control Thulium atoms. This is a huge step forward for building quantum computers and ultra-precise sensors, where controlling atoms without disturbing them is the ultimate goal.

Technical Summary

1. Problem Statement

Optical dipole traps (ODTs) and optical lattices are essential tools for quantum simulation, precision measurement, and sensing. The interaction strength between an atom and a laser field is governed by its dynamic polarizability, which varies with wavelength.

• Tune-out wavelengths are specific wavelengths where the total polarizability of an atomic state vanishes. At these points, the light shift disappears, allowing researchers to selectively trap or manipulate specific atomic states while leaving others unaffected.
• While tune-out wavelengths have been measured for alkali and some rare-earth atoms, the tune-out wavelength for the ground state of Thulium (Tm) had not been experimentally determined prior to this work.
• Thulium is a lanthanide with a non-zero orbital angular momentum in its ground state, leading to significant scalar, tensor, and vector contributions to its polarizability. Accurately determining the tune-out wavelength requires separating these components, which is challenging, particularly when the total polarizability becomes negative (repulsive potential), making standard frequency measurements impossible.

2. Methodology

The authors employed a combination of theoretical modeling and advanced experimental spectroscopy to measure the polarizability components and locate the tune-out wavelength.

Theoretical Framework

• The total dynamic polarizability $\alpha_{total}(\lambda)$ was modeled using second-order perturbation theory, summing contributions from 59 known atomic transitions.
• The model accounts for the scalar ($\alpha_{sc}$), tensor ($\alpha_{ten}$), and vector ($\alpha_{vec}$) parts, which depend on the angle between the laser polarization, the magnetic field, and the wave vector.
• Theoretical predictions were generated to guide the experimental search for the zero-crossing point.

Experimental Setup

• Atomic Source: An ultracold ensemble of $^{169}\text{Tm}$ atoms was prepared using a Zeeman slower, 2D optical molasses, and a magneto-optical trap (MOT). Atoms were polarized into the $|F=4, m_F=-4\rangle$ ground state.
• Trap Configuration: A Crossed Optical Dipole Trap (cODT) was used, formed by the intersection of:
  1. A transport beam (1064 nm).
  2. A tunable "yellow" beam (yODT) near 576 nm.
• Measurement Techniques:
  1. Trap Frequency Spectroscopy: By measuring the oscillation frequency of the atomic cloud in the cODT, the total polarizability was derived. This was performed at various polarization angles ($\theta_p$) to separate scalar and tensor components.
  2. RF-Assisted Trap Loss Spectroscopy: To isolate the tensor polarizability directly, Radio Frequency (RF) fields were applied to drive transitions between hyperfine levels. The differential Stark shift was measured, allowing the extraction of the tensor component without needing to measure negative total polarizability regions.
  3. Vector Polarizability Measurement: By varying the polarization ellipticity of the yODT using a quarter-wave plate, the vector component was isolated.
  4. Direct Observation of Zero Crossing: The number of trapped atoms was monitored as the yODT wavelength was scanned. A loss of atoms indicated a transition to a repulsive (negative) potential, bracketing the tune-out wavelength.
  5. Bose-Einstein Condensation (BEC) Verification: BEC was successfully achieved at various wavelengths within the range to confirm that photon scattering (heating/imaginary part of polarizability) was negligible.

3. Key Contributions

• First Measurement: This is the first experimental determination of the tune-out wavelength for the Thulium ground state.
• Component Separation: The study successfully separated scalar, tensor, and vector polarizabilities without relying on measurements in the negative polarizability regime, utilizing a novel combination of trap frequency and RF loss spectroscopy.
• Refinement of Tune-out Wavelength: The authors refined the tune-out wavelength from a theoretical prediction to a highly precise experimental value by observing the transition from trapping to anti-trapping (atom loss).
• Demonstration of BEC across Tune-out: The authors demonstrated that Bose-Einstein condensation is achievable even when the trap wavelength is tuned across the tune-out point, proving that the imaginary part of the polarizability (heating) is negligible in this spectral region.

4. Key Results

• Tune-out Wavelength:
  • Initial measurement via fitting: $575.646 \pm 0.016$ nm.
  • Refined measurement via direct atom loss observation: $575.646 \pm 0.004$ nm.
  • Theoretical prediction: $575.568 \pm 0.07$ nm (consistent with experimental data).
• Polarizability Components:
  • Measured values for scalar, tensor, and vector polarizabilities were obtained at five wavelengths (575.348 nm to 575.689 nm).
  • Scalar and Vector: Experimental results showed excellent agreement with the theoretical model.
  • Tensor: The measured tensor polarizability showed a slight deviation from the theoretical prediction, though the overall fit of the angular dependence remained consistent with RF spectroscopy results.
• Negative Polarizability: The experiment confirmed the existence of a wavelength region where the total polarizability is negative (repulsive), causing atoms to be ejected from the cODT while remaining in the 1064 nm transport trap.
• BEC Achievement: Thulium BECs were successfully created at all tested wavelengths, including those near the tune-out point, confirming the stability of the trap against heating.

5. Significance

• Quantum Simulation: The precise knowledge of the tune-out wavelength enables the creation of state-selective optical lattices. This allows for the manipulation of specific spin states of Thulium atoms without affecting others, a critical capability for simulating complex many-body physics and dipolar quantum gases.
• Precision Metrology: Understanding the polarizability components of lanthanides is vital for developing atomic clocks and precision sensors where systematic shifts must be minimized.
• Methodological Advancement: The technique of combining RF spectroscopy with trap frequency measurements to extract tensor polarizabilities offers a robust method for studying other complex atoms where direct frequency measurements in negative potential regions are difficult.
• Thulium Physics: This work solidifies Thulium as a versatile platform for quantum research, demonstrating its controllability across a wide spectral range including the critical tune-out region.