🔬 atomic physics

Production and stabilization of a spin mixture of ultracold dipolar Bose gases

This paper reports the successful production and stabilization of an ultracold dipolar Bose gas mixture of $^{162}$ Dy atoms in two Zeeman states, demonstrating that a light-induced quadratic Zeeman effect creates dark states where an interference phenomenon dramatically suppresses dipolar relaxation rates, while also determining the scattering lengths necessary to predict the mixture's miscibility.

Original authors: Maxime Lecomte, Alexandre Journeaux, Julie Veschambre, Jean Dalibard, Raphael Lopes

Published 2026-08-04

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Maxime Lecomte, Alexandre Journeaux, Julie Veschambre, Jean Dalibard, Raphael Lopes

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 a world where atoms don't just bump into each other like tiny billiard balls, but act more like tiny, invisible magnets that can feel each other from far away. This is the realm of ultracold quantum gases, a playground for scientists where matter behaves in strange, magical ways. To understand the story in this paper, you need to know three things. First, atoms have "spins," which you can think of as tiny internal compass needles pointing in different directions. Second, when these atoms get super cold, they can clump together into a single, giant wave called a Bose-Einstein Condensate (BEC), acting like a super-atom. Third, some atoms, like Dysprosium, are incredibly magnetic. When they get close, their magnetic fields interact strongly, which can be a double-edged sword: it creates exciting new physics, but it can also cause the atoms to crash and fly apart, destroying the delicate experiment. Scientists have long wanted to mix different "spins" of these magnetic atoms to see what happens, but the magnets usually make the mixture explode too quickly to study.

This paper is about a team of physicists who figured out how to stop that explosion. They created a stable mixture of two specific types of Dysprosium atoms (labeled as state |-8> and state |-7>) and discovered a special "sweet spot" where the atoms stop destroying each other. By carefully tuning a magnetic field and using laser tricks, they found a way to make the atoms coexist peacefully, allowing them to measure how strongly the atoms interact with each other. This is a big deal because it opens the door to studying new, exotic states of matter that were previously impossible to observe, essentially turning a chaotic, short-lived mess into a long-lived, stable laboratory for quantum physics.

The Magnetic Dance Floor

Think of these ultracold Dysprosium atoms as dancers on a very crowded, magnetic dance floor. Usually, if you mix two different types of dancers (let's call them Team Blue and Team Red), they get so excited by their magnetic attraction that they trip over each other, spin out of control, and fly off the floor. In the world of atoms, this is called "dipolar relaxation." It's like a chaotic mosh pit where the energy of the crash is so high that the dancers are instantly ejected from the room. For a long time, scientists thought this was just the nature of the game: if you wanted to mix these magnetic atoms, you had to accept that they would disappear in a flash.

But the researchers in this paper, working at the Kastler Brossel Laboratory in Paris, decided to try a different choreography. They focused on two specific "spins" of Dysprosium-162 atoms. Imagine these as two specific dance moves that, under normal circumstances, would lead to a disaster. The team used a clever combination of lasers and magnetic fields to create a special environment. They shone a laser beam that acted like a spotlight, changing the energy levels of the atoms just enough to make two specific moves (the |-7> and |-8> states) "dark." In this context, "dark" doesn't mean invisible; it means these states are safe from the usual light-induced chaos that would normally knock the dancers off the floor.

The Magic "Sweet Spot"

The real magic happened when they adjusted the magnetic field. The paper reports that at a specific magnetic field strength of about 2.5 Gauss (a unit of magnetic strength), something spectacular occurred. The rate at which the atoms crashed and disappeared dropped by a factor of 100 compared to what scientists expected based on standard physics laws (known as the Wigner threshold law).

Why did this happen? The authors explain it using the concept of "interference." Imagine two waves of sound meeting; if the peak of one wave hits the trough of the other, they cancel each other out, creating silence. Something similar happened here. The atoms have a probability of crashing and flipping their spins, but this probability depends on how their internal "waves" overlap. At that specific 2.5 Gauss field, the waves from the different possible paths of the crash interfered destructively. It was as if the universe hit the "cancel" button on the explosion. The atoms could still bump into each other, but the specific process that usually kicked them out of the trap was suppressed by two orders of magnitude. This turned a fleeting moment into a stable, long-lived mixture.

Measuring the Invisible Handshake

Once the atoms were safe and stable, the team could finally ask the big question: How do these two types of atoms actually interact? In the quantum world, this interaction is described by something called a "scattering length," which you can think of as a measure of how "bouncy" or "sticky" the atoms are when they meet.

To find this out, the researchers did two things. First, they watched how fast the atoms disappeared when they were mixed. By analyzing the rate of loss at different magnetic fields, they could back-calculate the interaction strength between a |-7> atom and a |-8> atom. They found this value to be roughly 40 to 60 times the size of a hydrogen atom (measured in units of Bohr radii, $a_0$ ).

Second, they looked at a pure group of just |-7> atoms. They let this group expand and fly apart after being released from their trap. By watching how the cloud of atoms spread out, they could measure how strongly the |-7> atoms pushed against each other. This gave them a scattering length of about 110 $a_0$ . They also double-checked their work with |-8> atoms, confirming a value of 136 $a_0$ , which matched what other scientists had found before.

The Future of Quantum Mixtures

With these numbers in hand, the team could predict what would happen if they mixed these atoms in different ways. They found that in a 3D space, the magnetic forces would likely push the two types of atoms apart, making them "immiscible" (like oil and water). However, if they squeezed the atoms into a flat, pancake-like shape (a 2D system), the rules change, and the atoms might happily mix together.

The paper also points out that near this magical 2.5 Gauss field, there are other "resonances"—special magnetic settings where the atoms can be tuned to be even more or less sticky. This gives scientists a dial to turn, allowing them to explore different phases of matter, from mixtures that stay together to those that separate.

In short, this paper didn't just find a way to stop the atoms from exploding; it built a stable platform where scientists can now tune the interactions between magnetic atoms with precision. It turns out that by finding the right magnetic "sweet spot," you can silence the chaos and let the quantum dance begin. This paves the way for discovering new, exotic states of matter, like "supersolids" that flow without friction while holding a rigid shape, all thanks to a little bit of interference and a lot of careful tuning.

Technical Summary: Production and Stabilization of a Spin Mixture of Ultracold Dipolar Bose Gases

Problem Statement
The study of quantum matter using ultracold gases with long-range interactions is a central focus of modern quantum simulation. While mixtures of dipolar gases (such as those involving Erbium and Dysprosium) offer a rich phase diagram including self-bound droplets and spin-textured supersolids, their experimental realization is hindered by intrinsic instability. Specifically, spin mixtures of atoms with large magnetic moments suffer from rapid dipolar relaxation. In these processes, spin-flip collisions release Zeeman energy that exceeds the trap depth, leading to immediate particle loss. Furthermore, the chaotic nature of pairwise interactions in highly magnetic atoms complicates the prediction of "sweet spots" where interactions might be controlled or suppressed. Consequently, only the lowest-energy Zeeman sublevels of these species have been previously characterized, limiting the exploration of binary dipolar mixtures.

Methodology
The authors present an experimental protocol to create and stabilize a binary dipolar quantum gas using $^{162}\text{Dy}$ atoms in the two lowest Zeeman sublevels, $|J=8, m_J=-8\rangle$ (labeled $|-8\rangle$ ) and $|J=8, m_J=-7\rangle$ (labeled $|-7\rangle$ ).

State Preparation and Control:
- Samples are initially prepared in the $|-8\rangle$ state within a crossed dipole trap.
- A spin-dependent light shift is induced using a blue-detuned ( $\Delta = 2\pi \times 2.5$ GHz) laser beam with $\sigma^-$ polarization propagating along the $z$ -axis. This creates a quadratic Zeeman-like energy shift, $E(m_J) = \alpha m_J + \gamma(m_J+7)(m_J+8)$ , which renders $|-7\rangle$ and $|-8\rangle$ "dark states" uncoupled to the excited manifold.
- Two-photon Raman transitions, facilitated by co-propagating laser beams detuned from the 626.1 nm transition, are used to transfer population between $|-8\rangle$ and $|-7\rangle$ , allowing the preparation of quasi-pure samples or tunable spin mixtures.
Loss Rate Characterization:
- The team measures the two-body loss rate ( $L_2$ ) by monitoring the time evolution of atom numbers in minority and pure samples of $|-7\rangle$ across a magnetic field range of 0.4 to 6 G.
- They compare experimental data against theoretical predictions based on the Fermi Golden Rule (FGR), incorporating dipolar interaction potentials and van der Waals forces. The model accounts for the interference between incoming $s$ -wave and outgoing $d$ -wave scattering channels.
Scattering Length Determination:
- Inter-species ( $a_{78}$ ): Determined by fitting the non-monotonic evolution of the loss rate in minority samples to the theoretical model.
- Intra-species ( $a_{77}$ ): Determined via two methods: (i) fitting the loss rate of pure $|-7\rangle$ samples, and (ii) analyzing the time-of-flight (TOF) expansion of a pure BEC in $|-7\rangle$ . The expansion data is compared against numerical simulations based on generalized Castin-Dum scaling equations that include dipolar interactions.
- Validation: The method is validated by reproducing known scattering lengths for $|-8\rangle$ ( $a_{88}$ ) and $|-6\rangle$ ( $a_{66}$ ).
Feshbach Resonance Mapping:
- The authors scan magnetic fields near the loss minimum to identify spin-dependent Feshbach resonances, distinguishing between intra-species and inter-species loss features using pure and 50-50 mixtures.

Key Results

Suppression of Dipolar Relaxation: The authors identify a "sweet spot" at a magnetic field of $B \approx 2.5$ G. At this field, the two-body loss rate for the spin mixture is reduced by approximately two orders of magnitude compared to the Wigner threshold law prediction ( $\propto \sqrt{B}$ ). This suppression is attributed to a destructive interference phenomenon where the overlap integral of the initial and final scattering wavefunctions vanishes.
Scattering Lengths:
- Inter-species scattering length: $a_{78} = 40(20) a_0$ .
- Intra-species scattering length for $|-7\rangle$ : $a_{77} = 110(10) a_0$ .
- These values, combined with the known $a_{88} = 140 a_0$ , allow for the prediction of the mixture's stability and miscibility.
Miscibility: Based on the measured scattering lengths and the anisotropy of dipolar interactions, the authors predict that the mixture is miscible under their specific trap confinement conditions, despite being non-miscible in a homogeneous 3D gas.
Feshbach Resonances: The study identifies multiple spin-dependent Feshbach resonances near 2.5 G. Notably, inter-species resonances are observed in 50-50 mixtures, characterized by three-body recombination processes involving particles in different spin states.

Significance and Claims
The paper claims that this work represents a significant advancement in the preparation and stabilization of binary dipolar gases. By identifying a magnetic field region where dipolar relaxation is suppressed by two orders of magnitude, the authors demonstrate that such spin mixtures can be long-lived, comparable to their fermionic counterparts.

The determination of the scattering lengths ( $a_{77}, a_{88}, a_{78}$ ) provides the necessary parameters to predict the miscibility regime of the mixture, which is crucial for exploring new quantum phases such as self-bound droplets and supersolids. The combination of low loss rates and the presence of tunable Feshbach resonances near the stabilization point opens a pathway to explore miscible-immiscible transitions and other novel phases within binary dipolar condensates. The authors note that while their current single-channel scattering model provides good agreement, a multi-channel approach could further improve the accuracy of these scattering length determinations.

The Magnetic Dance Floor

The Magic "Sweet Spot"

Measuring the Invisible Handshake

The Future of Quantum Mixtures

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