Observation of high partial-wave Feshbach resonances in $^{39}$K Bose-Einstein condensates

This paper reports the experimental observation and theoretical confirmation of several high partial-wave magnetic Feshbach resonances in $^{39}$K Bose-Einstein condensates, which are induced by dipolar spin-spin interactions and offer significant potential for studying many-body physics dominated by high partial-wave pairing.

The Gist

Imagine you have a giant dance floor filled with tiny, invisible dancers called Potassium atoms (specifically, the isotope 39K). These dancers are so cold they are almost frozen in time, forming a super-group called a Bose-Einstein Condensate (BEC), where they all move in perfect unison like a single giant wave.

Usually, these dancers either ignore each other or bump into each other gently. But physicists have a special "remote control" (a magnetic field) that can change how they interact. This is called a Feshbach Resonance. Think of it like tuning a radio: when you hit the right frequency (magnetic field strength), the dancers suddenly start grabbing hands, forming pairs, or even crashing into each other and disappearing.

The Big Discovery: Finding New "Dance Moves"

In the past, scientists mostly knew about the "easy" dance moves (called s-wave resonances). These are like simple, straight-line collisions. But in this paper, the researchers from Shanxi University discovered five new, complex dance moves that were hiding in plain sight.

They call these High Partial-Wave (HPW) Resonances.

• The Analogy: If the old moves were like two people walking straight into each other, these new moves are like dancers spinning, flipping, and orbiting each other before they interact. Some are "d-wave" (twisting like a figure skater) and some are "g-wave" (doing complex, multi-loop spins).

The Secret Ingredient: The "Spin-Spin" Handshake

How did they find these? They used a specific type of interaction called dipolar spin-spin interaction.

• The Old Way (Spin-Exchange): Imagine two dancers trying to hold hands. If they both have to be spinning the same way to hold hands, it's very picky. If they miss the spin, they don't connect. This creates a "split" effect where one resonance breaks into three or more tiny pieces.
• The New Way (Dipolar Spin-Spin): This is like a magnetic handshake. One dancer is spinning (s-wave), and the other is doing a complex spin (high partial-wave). Because of the magnetic nature of this handshake, they can connect even if their spins are different, as long as the total spin is conserved.
  • The Result: Instead of a messy split into three pieces, these new resonances appear as single, clean, symmetrical dips. It's like finding a secret door that leads to a single room, rather than a hallway with three confusing doors.

The Experiment: A Tale of Three Groups

The researchers tested these new "dance moves" on three different groups of atoms to see how they reacted:

1. The Super-Cold Group (BECs): When the atoms were super cold and dense, the new resonances caused the atoms to disappear (get lost) very quickly. It was like a dance floor where, at the right music, everyone suddenly vanished.
2. The Warm Group (Thermal Gas): When they warmed the atoms up, the behavior changed. Some resonances got weaker (the dancers didn't care as much), but one specific resonance got stronger. This told the scientists that this specific move is very sensitive to how fast the atoms are moving.
3. The Mixed Group (Potassium + Rubidium): They added a different type of atom (Rubidium) to the Potassium dance floor. The Rubidium atoms acted like bouncers or buffers.
   • For most of the new resonances, the bouncers got in the way, making the Potassium atoms collide less, so fewer disappeared.
   • However, for the strongest resonance (the "g-wave" one), the Potassium atoms were so eager to dance that the bouncers couldn't stop them. They kept disappearing even with the crowd.

Why Does This Matter?

Why should we care about Potassium atoms doing complex spins?

1. New Materials: In the real world, materials like high-temperature superconductors (which conduct electricity with zero resistance) rely on electrons pairing up in complex, spinning ways (d-wave pairing). By studying these atoms, scientists can simulate and understand how these materials work.
2. The "Toolbox" Expansion: Before this, scientists had a limited set of tools to control atoms. Now, they have a whole new set of "knobs" (these 5 new resonances) to tune how atoms interact. This allows them to create new states of matter, like "quantum droplets" or exotic superfluids, that were previously impossible to make.
3. Precision: Because these new resonances are clean and symmetrical (unlike the messy split ones), they are easier to measure and use for ultra-precise experiments.

The Bottom Line

The researchers found five hidden "secret doors" in the magnetic landscape of Potassium atoms. These doors lead to complex, spinning interactions that are different from anything seen before. By understanding how these doors work, we are one step closer to mastering the quantum world and potentially building the super-fast, super-efficient technologies of the future.

Technical Summary

1. Problem Statement

Feshbach resonances (FRs) are essential tools for tuning atomic interactions in ultracold gases, enabling the study of many-body physics, quantum droplets, and superfluidity. While $s$-wave FRs are well-understood and widely used, High Partial-Wave (HPW) FRs (involving $p, d, f, g...$ waves) offer unique opportunities to study pairing with non-zero orbital angular momentum, which is relevant to high-temperature superconductivity and exotic superfluid states.

However, HPW FRs are generally harder to observe and characterize than $s$-wave resonances. In the specific case of Potassium-39 ($^{39}$K), a system known for its tunable interactions and negative background scattering length, previous studies had identified only a few HPW resonances (mostly in thermal gases or with negative scattering lengths unsuitable for Bose-Einstein Condensates (BECs)). There was a lack of experimental data on HPW FRs within the positive scattering length regime of $^{39}$K BECs, which is crucial for stabilizing BECs and studying HPW superfluidity. Furthermore, distinguishing between HPW FRs induced by spin-exchange interactions (where both open and closed channels are HPW) and those induced by dipolar spin-spin interactions (open channel $s$-wave, closed channel HPW) requires precise characterization of line shapes and temperature dependencies.

2. Methodology

The researchers employed a combination of advanced experimental techniques and theoretical modeling:

• Experimental Setup:

  • Dual-Species BEC Production: They produced dual-species BECs of $^{39}$K and $^{87}$Rb. Atoms were cooled via a magneto-optical trap (MOT), transferred to an optical dipole trap, and sympathetically cooled.
  • State Preparation: Atoms were transferred to the $|F=1, m_F=-1\rangle$ hyperfine state. Crucially, the magnetic field was tuned to a region (near 120 G) where broad $s$-wave FRs provided a positive scattering length, allowing for the stable formation of $^{39}$K BECs despite the atom's naturally negative background scattering length.
  • Loss Spectroscopy: The team scanned the magnetic field from 20 G to 200 G. They measured the number of remaining $^{39}$K atoms after holding the gas at specific magnetic fields for varying durations ($T_h$). Loss dips in the atom number indicate the presence of a Feshbach resonance.
  • Comparative Measurements: Experiments were conducted on:
    1. Pure $^{39}$K BECs.
    2. Pure $^{39}$K thermal gases.
    3. $^{39}$K-$^{87}$Rb mixture BECs (to test interspecies collision effects).
  • Lifetime Analysis: Atomic loss curves were fitted with exponential functions to extract lifetimes and coupling strengths.

• Theoretical Modeling:

  • Multichannel Quantum Defect Theory (MQDT): The experimental data was analyzed using MQDT. The researchers calculated scattering hyper-volumes ($D_l$) and resonance positions by fitting quantum defect parameters ($K^c_{S,T}$ and $\beta_{S,T}$) to reproduce known resonances and predict new ones. This allowed them to assign partial-wave quantum numbers ($l, m_l$) to the observed resonances.

3. Key Contributions

• Discovery of Five New Resonances: The team experimentally observed five new magnetic Feshbach resonances in $^{39}$K BECs located between the two broad $s$-wave resonances (32.6 G and 162.8 G).
• Identification of Wave Types: Using MQDT, they confirmed:
  • Resonance (II) and (III): $g$-wave ($l=4$) resonances.
  • Resonance (V): $d$-wave ($l=2$) resonance.
  • Resonance (I) and (IV): Unidentified (likely HPW) resonances.
• Mechanism Clarification: They demonstrated that these resonances are induced by dipolar spin-spin interactions, characterized by an $s$-wave open channel and an HPW closed channel. This distinguishes them from HPW FRs driven by spin-exchange interactions (where both channels are HPW).
• Characterization of Unique Signatures: The study established distinct experimental signatures for this type of HPW FR:
  • Symmetric Line Shapes: Unlike spin-exchange induced HPW FRs which often show asymmetric dips, these resonances display symmetric loss dips.
  • No Multiplet Splitting: Due to the selection rules of dipolar interactions ($|\Delta l| = 0, 2, 4$), these resonances do not exhibit the $l+1$ splitting structure typical of spin-exchange induced HPW FRs.

4. Key Results

• Resonance Parameters:
  • $g$-wave (II): Located at 63.67 G, with a narrow width (1.67 G) and strong coupling (short holding time of 0.15 s for 50% loss).
  • $g$-wave (III): Located at 107.60 G, extremely narrow (0.11 G), but requires a long holding time (1 s) to observe significant loss, indicating a complex density/temperature dependence.
  • $d$-wave (V): Located at 138.00 G, with a width of 11.00 G.
  • Unknown (I & IV): Located at 53.62 G and 113.00 G respectively. Resonance (IV) showed a unique sensitivity to temperature and mixing.
• Temperature Dependence:
  • Resonances (I, III, V) became shallower as temperature increased (thermal gas), consistent with the lack of a centrifugal barrier in the $s$-wave open channel.
  • Resonance (II) remained largely unchanged, attributed to its strong coupling strength.
  • Resonance (IV) showed anomalous behavior, becoming deeper with temperature, suggesting a different underlying mechanism or sensitivity to collision energy.
• Effect of $^{87}$Rb Buffer Gas:
  • In the $^{39}$K-$^{87}$Rb mixture, most resonances (I, III, IV, V) showed reduced loss (shallower dips) because the $^{87}$Rb atoms acted as a buffer gas, reducing the $^{39}$K-$^{39}$K collision rate.
  • Resonance (II) remained strong even in the mixture, confirming its robust coupling.
  • Resonance (IV) was highly sensitive to the presence of $^{87}$Rb, further highlighting its unique nature.

5. Significance

• Expansion of the $^{39}$K Toolbox: This work significantly expands the magnetic field range and interaction types available for tuning $^{39}$K atoms. Crucially, these new resonances exist in the positive scattering length regime, which is essential for creating stable BECs and studying repulsive interactions.
• Insight into Interaction Mechanisms: The clear distinction between dipolar-induced HPW FRs (symmetric, no splitting) and spin-exchange induced HPW FRs provides a critical benchmark for theoretical models of ultracold collisions.
• Pathway to HPW Superfluidity: By providing accessible $d$-wave and $g$-wave resonances in a stable BEC environment, this research paves the way for creating and studying high-partial-wave superfluids and exotic pairing states in bosonic systems.
• Few-Body Physics: The unique temperature and density dependencies observed (especially for resonance IV) offer a new platform to investigate universal laws of two-body and three-body collision losses near HPW resonances.

In summary, this paper reports the first observation of multiple HPW Feshbach resonances in $^{39}$K BECs within the positive scattering length region, successfully identifying their wave character and distinguishing their physical mechanisms from previously known resonances, thereby opening new avenues for quantum simulation and many-body physics.