Factor of 1000 suppression of the depolarization rate in ultracold thulium collisions

This paper demonstrates that applying a carefully tuned magnetic field can suppress depolarization collisions in ultracold thulium atoms by a factor of 1000, thereby enabling the efficient utilization of their Zeeman manifold for quantum simulations.

The Gist

Imagine you have a room full of tiny, spinning tops (atoms). These tops are special because they are made of a rare earth metal called Thulium, and they are incredibly magnetic. Scientists love these tops because they can be used to build "quantum computers" or simulate complex physics problems, but there's a big problem: they are messy.

The Problem: The "Spin-Off" Party

Normally, when two of these magnetic tops bump into each other, they get excited and start spinning wildly.

• The "Depolarization" Crash: Imagine two tops spinning in perfect sync. When they collide, they might knock each other out of sync. They don't fly away, but they lose their special "team alignment." In the quantum world, this is called depolarization. It ruins the experiment because the tops are no longer doing what you told them to do.
• The "Relaxation" Crash: Sometimes, the collision is so violent that the tops gain so much speed they fly right out of the room (the trap). This is called loss.

For a long time, scientists thought the only way to stop this chaos was to force every single top to spin in the exact same direction (the "stretched state"). If they all spin the same way, they can't knock each other out of sync. But this is like having a room full of people all wearing the same red shirt; you can't tell them apart or use their different colors to do complex calculations. You need a mix of colors (different spin states) to do interesting quantum magic.

The Discovery: The "Silent Zone"

The researchers in this paper found a magical trick. They discovered that if they apply a very specific, weak magnetic field (about 0.9 Gauss, which is roughly the strength of a fridge magnet), something amazing happens.

Think of the magnetic field as a conductor directing traffic. Usually, when the tops collide, it's like a busy intersection where cars crash and spin out of control. But at this specific magnetic field setting, the traffic lights turn green for a "silent lane."

The Result:

• 1,000x Quieter: The rate at which the tops lose their alignment (depolarization) drops by a factor of 1,000. It's like turning a loud rock concert into a library whisper.
• 50x Safer: The rate at which tops fly out of the room drops by a factor of 50.

How They Did It (The Analogy)

The scientists used a technique like a microwave remote control.

1. They cooled the atoms down to almost absolute zero (colder than outer space) so they moved very slowly.
2. They used microwave pulses (like a remote control for the atoms) to flip the spins of the tops into specific, messy configurations.
3. They watched what happened over time. Usually, the tops would quickly lose their order.
4. But when they tuned the magnetic field to that "sweet spot" (0.9 G), the tops stayed in their messy, mixed-up states for a long time without crashing or flying away.

Why This Matters

Before this discovery, scientists were forced to keep their quantum tops perfectly aligned (all red shirts) to avoid the crashes. This limited what they could study.

Now, thanks to this "silent zone," scientists can:

• Mix and Match: They can use a variety of different spin states (different colored shirts) without the system falling apart.
• Build Better Simulators: They can use these atoms to simulate complex materials, like superconductors or exotic magnets, with much higher precision.
• Unlock New Physics: It opens the door to studying "strongly correlated matter," which is basically a fancy way of saying "how huge groups of particles behave when they are all deeply connected to each other."

The Bottom Line

The researchers found a "magic setting" on the magnetic field dial that acts like a quantum noise-canceling headphone. It silences the chaotic collisions that usually ruin experiments, allowing scientists to finally use the full, colorful potential of Thulium atoms for the next generation of quantum technology.

Technical Summary

1. Problem Statement

Ultracold lanthanide atoms, such as thulium (Tm), are valuable for quantum simulation due to their large magnetic moments, which introduce strong dipole-dipole interactions (DDI), and their dense spectra of Feshbach resonances. These properties allow for the exploration of strongly correlated matter, quantum magnetism, and exotic topological phases.

However, a major obstacle in utilizing the full Zeeman manifold of lanthanide ground states is depolarization. When magnetic atoms collide, they can undergo:

• Relaxation collisions: Where the total magnetic quantum number ($m_F$) decreases, converting Zeeman energy into kinetic energy, often leading to atom loss from the trap.
• Depolarization collisions: Where $m_F$ is conserved but redistributed among sublevels. While these do not cause immediate loss, they destroy the spin purity required for quantum simulations.

While preparing atoms in the "stretched state" ($m_F = \pm F$) eliminates depolarization, it restricts the system to a single spin state, preventing the study of rich spin dynamics. The challenge is to access non-stretched states (e.g., $m_F = F-1$) without suffering rapid depolarization. Previous methods to mitigate this (optical lattices, RF fields) have limitations, and no magnetic field-dependent suppression of depolarization had been predicted or observed prior to this work.

2. Methodology

The researchers utilized an ultracold gas of $^{169}\text{Tm}$ atoms (the only stable isotope of thulium) to investigate spin dynamics under varying magnetic fields.

• Experimental Setup:

  • Cooling: Atoms were cooled via a Zeeman slower and 2D optical molasses (410.6 nm transition), then loaded into a magneto-optical trap (MOT) at 530.7 nm.
  • Trapping: Atoms were transferred to a 1064 nm optical dipole trap (ODT) and evaporatively cooled to $\approx 2.5 \, \mu\text{K}$, resulting in $\approx 2.0 \times 10^5$ atoms.
  • State Preparation: Using a microwave (MW) protocol, the team manipulated the spin mixture. They prepared atoms in the $|F=4, m_F=-3\rangle$ state (a non-stretched state where depolarization is normally allowed) and monitored the population transfer to other sublevels (specifically $|4, -4\rangle$ and $|4, -2\rangle$) over time.
  • Detection: Absorption imaging was used to measure the total atom number ($N_{tot}$) and specific sublevel populations ($N_3$, $N_4$) after varying time delays ($\tau$).

• Data Analysis:

  • The evolution of populations was modeled using a system of rate equations describing two-body collisions (depolarization and relaxation).
  • The team extracted the depolarization rate ($\beta_{depol}$) and loss rate ($\beta_{loss}$) by fitting the experimental decay curves.
  • Experiments were conducted across a range of magnetic fields to identify resonances.
  • Theoretical models, including the Born approximation and Fermi's Golden Rule with coupled scattering lengths, were compared against experimental data.

3. Key Contributions

• Discovery of a Suppression Resonance: The authors identified a specific magnetic field ($B \approx 0.90 \, \text{G}$) where the depolarization rate is suppressed by a factor of 1000 compared to the baseline.
• First Observation of this Phenomenon: This is the first time such a magnetic-field-dependent suppression of depolarization has been observed in lanthanides, a phenomenon not previously predicted by standard perturbative theories.
• Validation of Two-Body Dynamics: The study confirmed that the observed spin dynamics are dominated by two-body collisions, as the rates remained constant regardless of the initial atom number.
• Demonstration of Extended Lifetimes: By tuning the magnetic field to the resonance, the lifetime of the non-stretched $|4, -3\rangle$ state was extended significantly, making it viable for long-duration quantum simulations.

4. Results

• Depolarization Suppression: At $B = 0.90 \, \text{G}$, the depolarization rate $\beta_{depol}$ dropped from a baseline of $\approx 2 \times 10^{-11} \, \text{cm}^3/\text{s}$ to values more than 1000 times lower.
• Correlated Loss Suppression: The loss rate ($\beta_{loss}$) also exhibited a resonance at the same magnetic field, showing a suppression factor of approximately 50.
• Non-Monotonic Behavior: Both rates displayed complex, non-monotonic behavior with multiple resonances, contradicting the Born approximation which predicts a monotonic or constant dependence on the magnetic field.
• Theoretical Discrepancy: Standard perturbative approaches (Born approximation) failed to reproduce the magnitude and shape of the experimental data. The authors attribute the non-monotonic behavior to the coupling of different scattering channels and the proximity of Feshbach resonances, which are dense in lanthanides due to their complex angular momentum structure.
• State Lifetimes: At the optimal field (0.90 G), the lifetime of the $|4, -3\rangle$ state was measured to be approximately 2.3 seconds, only 3 times shorter than the stretched $|4, -4\rangle$ state (6.8 s).

5. Significance

This work represents a breakthrough in the control of ultracold lanthanide gases. By demonstrating that depolarization can be suppressed by three orders of magnitude via magnetic field tuning, the authors have:

1. Opened the Zeeman Manifold: Enabled the use of non-stretched spin states, which are essential for simulating complex quantum magnetism, exotic topological phases, and long-range interacting spin-lattice models.
2. Provided a New Control Knob: Established magnetic field tuning as a powerful tool to engineer collisional properties in dipolar quantum gases, beyond just Feshbach resonance tuning for scattering lengths.
3. Highlighted Theoretical Gaps: The failure of perturbative models suggests that future theoretical work on lanthanides must employ full coupled-channels calculations to account for the complex interatomic potentials and dense Feshbach resonance spectra.

In conclusion, the ability to suppress depolarization in thulium by a factor of 1000 paves the way for robust, long-lived quantum simulations using the rich internal degrees of freedom of lanthanide atoms.