Atom-ion Feshbach resonances controlled by quantum statistics

Researchers at Albert-Ludwigs-Universität Freiburg and collaborating institutions have demonstrated a pronounced nonlinear dependence between ion loss rate and spin polarization in a unique hybrid system. The work centers on a single trapped ion immersed in a two-component Fermi gas of lithium atoms near an atom-ion Feshbach resonance, allowing isolation of quantum statistics in atom-atom-ion collisions. The observations reveal that antisymmetrization restricts available pathways during recombination, leading to interference between indistinguishable processes. This establishes atom-ion systems as a platform for controlling three-body collisions via quantum statistics.

Atom-Ion Feshbach Resonance Setup and Trapping

This arrangement allows precise control over the spin composition of the lithium gas, a key parameter in isolating the influence of quantum statistics on collision dynamics. Calculated density profiles for both fully polarized and mixed lithium atom clouds reveal a significant difference in central density, with the mixed cloud exhibiting a higher concentration for a total atom count of 40,000, though this difference remains unresolved by current experimental resolution.

Establishing a spin-independent density calibration was a necessary step before investigating the polarization dependence of atom-atom-ion interactions, performed s-wave Feshbach resonance at a specific magnetic field. By preparing the ion in the electronic ground state S_1/2, the team measured the resulting ion loss rate, denoted as, as a function of the central spin polarization, P.

The measured ion loss rate demonstrates a pronounced nonlinear dependence on spin polarization, indicating that the recombination process is not simply proportional to the spin alignment. This observation suggests a more complex interplay of quantum effects influencing the collision dynamics, with the recombination rate changing in a non-intuitive manner as the spin is adjusted. “With the broad spectrum of atom-ion Feshbach resonances already identified in this system, the dependence of the recombination ratio on the underlying scattering parameters can be explored systematically,” the paper states, highlighting the potential for detailed investigation of these interactions.

The work reveals that quantum statistics leads to a symmetry-dependent modification of recombination dynamics, with the collision temperatures cold enough to ensure these effects are prominent. This suppression of recombination pathways involving identical fermions is already apparent at the level of experimental observables, even under thermal averaging that would typically obscure such threshold-law behavior.

Further exploration aims to transition from this quantum-statistical suppression to the enhancement of identical-fermion recombination predicted by the hyperspherical model, a theoretical framework describing atomic and molecular collisions. Increasing the collision energy within the current platform will introduce additional contributing partial waves, redistributing quantum scattering weights while maintaining the underlying symmetry constraints.

This provides a direct benchmark for microscopic three-body descriptions beyond the threshold-law regime, offering the possibility of disentangling the roles of intermediate-state formation and subsequent relaxation. Looking ahead, the team proposes circumventing radio frequency-induced heating through all-optical trapping of both ions and atoms, a technique that promises access to lower and more precisely controlled collision energies.

This advancement would enable tunable few-body collisions at the single-particle level. “More generally, the observed suppression identifies regimes in which strong atom-ion interactions persist while dominant loss channels are reduced, offering the prospect of resolving microscopic collision pathways that are currently hidden by thermal averaging,” the study concludes.

Spin-Selective Atom Removal Controls Polarization

The ability to manipulate the polarization of a lithium atom cloud surrounding a single trapped ion demonstrates a level of control over three-body collisions previously unseen in hybrid atom-ion systems. By individually addressing each lithium hyperfine level with a near-resonant laser, scientists established a method to remove atoms in a controlled manner, effectively tuning the bath polarization and total atom number.

This preparation allows for the investigation of spin-dependent recombination processes, revealing that the ion experiences a local polarization varying across the trap, a factor accounted for in quantitative mapping of total atom number to local density. Experiments revealed a pronounced nonlinear dependence of the ion loss rate on spin polarization, with the rate increasing significantly towards balanced mixtures before saturating when dominated by the resonant spin component.

Maintaining a constant local density while varying polarization over its full range, from -1 to 1, confirmed that resonant loss is negligible when only one atomic spin state is present, highlighting the necessity of at least two distinct states for recombination to occur. The observed suppression of recombination pathways is consistent with a two-step process where the ion initially forms a weakly bound dimer with a lithium atom at a rate denoted as ${\Gamma }_{dimer}$.

This dimer formation is then followed by a second recombination step. The team’s analysis suggests that the observed suppression reflects the underlying dynamics of an intrinsic three-body process, rather than an artifact of the phenomenological description used.

This consistency reinforces the role of the second atom in the recombination dynamics, demonstrating that quantum statistics become decisive in the presence of the ion, governing the relative contributions of different recombination channels even though atom-atom interactions remain negligible in the isolated Fermi gas. The work establishes a quantitative link between the total atom number and the local density at the ion position, which is important for distinguishing spin-dependent three-body processes from density-profile effects. By controlling the bath polarization via spin-selective atom removal, researchers were able to isolate the role of quantum statistics in atom-atom-ion collisions, demonstrating that exchange-symmetry effects remain robust even under thermal averaging.

Three-Body Recombination Measures Ion Loss Rate

The observed behavior indicates that the rate of recombination varies significantly as the spin composition of the surrounding atomic gas changes, a finding that moves beyond simple linear models of atom-ion interactions. This complexity arises from the quantum statistics governing the collisions, specifically the differing behavior of identical and distinguishable fermions during the recombination process. Calculations of three-body recombination rates incorporated exchange-symmetry constraints and centrifugal barriers, revealing a ratio between recombination pathways involving identical and distinguishable fermions.

The team’s analysis defines this ratio as ${\xi }_F$ = $L_3^{FFX}/L_3^{\text{FF^′X}}$, a metric that quantifies the influence of fermionic exchange symmetry on the observed loss ratio across a range of experimentally realistic parameters. This agreement between theoretical modeling and experimental data provides a quantitative constraint on microscopic three-body descriptions, identifying fermionic exchange symmetry as a dominant mechanism governing the observed loss ratio.

The work establishes that even with thermal averaging obscuring finer details, these quantum statistical effects remain experimentally observable. For P = -1, minimal resonant loss was observed, indicating that recombination requires the presence of at least one atom with a different spin state. This behavior is best described by a rate equation of the form, where effective three-body recombination rate constants for the FFX and $F{F}^{\text{′}}X$ entrance channels are considered. Fitting the data to a functional form ${\Gamma }_{\text{S\_(1/2)}}(P)$ = $a{P}^2$ + bP + c, the researchers found strong agreement with a two-step recombination model.

This model posits an initial dimer formation followed by a second recombination step, with the analysis suggesting that the second atom is important in the recombination dynamics. “More generally, our results show that Pauli-imposed constraints on the accessible Hilbert space can remain experimentally observable even when signatures of centrifugal-barrier suppression are obscured by thermal averaging,” the researchers write. The observed suppression of recombination involving identical fermions is an intrinsic feature of the recombination process, not an artifact of the experimental setup.

The team observed that the three-body atom-atom-ion recombination rate is lower for identical fermions than for distinguishable ones, a finding that emphasises the importance of quantum statistics in these interactions. This observation confirms that the recombination process is sensitive to the indistinguishability of fermionic atoms, providing further evidence for the role of exchange symmetry in governing the observed loss ratio. The results demonstrate that the system is capable of resolving subtle differences in recombination pathways based on the quantum properties of the colliding particles.

Quantum Statistics Reduce Fermion Recombination

This precise control revealed a diminished contribution from recombination pathways involving identical fermions, a result observable directly in the experimental data. This system’s unique characteristics alter few-body dynamics, yet thermal averaging typically obscures underlying quantum behavior, presenting a challenge to observing these effects. The team’s findings demonstrate that even with thermal averaging, Pauli exclusion principle constraints on accessible quantum states remain experimentally detectable, a result that validates the underlying theoretical framework.

The observations align with a two-step recombination model and an adiabatic hyperspherical approach, where the act of antisymmetrization, a requirement of quantum mechanics for identical fermions, restricts the available pathways for recombination. The restriction of entrance channels during recombination leads to interference between indistinguishable pathways, a direct consequence of the atoms’ quantum nature.

This interference manifests as a suppression of recombination involving identical fermions, a phenomenon confirmed by the experimental data. The team’s findings extend beyond the realm of ultracold atomic gases, with potential implications for understanding and controlling chemical reactions at low energies, where quantum effects are significant.

Hyperspherical Approach Explains Collision Dynamics

The measured rate at which ions are lost during recombination exhibits a pronounced nonlinear dependence on the spin polarization of the surrounding lithium atoms, a finding that reveals how quantum statistics directly influences collision dynamics. This deviation from a simple proportional relationship indicates that the recombination process isn’t uniform across all atomic spin states, and that the contribution of pathways involving identical fermions is demonstrably reduced even within the experimental measurements.

Researchers verified this by isolating the role of quantum statistics through careful tuning of the spin composition while maintaining constant density and temperature within the atom-ion system. This restriction, in turn, creates interference between indistinguishable recombination pathways, a phenomenon that further suppresses recombination events involving identical fermions.

The team’s analysis of the ion loss ratio, comparing recombination rates for different fermionic configurations, provides quantitative support for this interference effect and confirms that the observed suppression isn’t a result of data analysis artifacts. The team’s evaluation of four configurations, FFX, FF’X, BBX and BB’X, demonstrated that the observed loss ratio is consistent with the dominance of fermionic symmetry, confirming that exchange symmetry is a key factor governing the observed recombination process.

The derived effective atom-ion scattering length of approximately 2. 7(1) R*, where R* is the characteristic atom-ion length scale, falls within a physically realistic range predicted by the adiabatic hyperspherical approach, further validating the theoretical framework. The consistency between the experimental data and the hyperspherical calculations indicates that the experiment is operating near the threshold where quantum statistical effects become particularly pronounced.

Although conceptually distinct, the two-step and hyperspherical models both accurately describe the observed phenomena, providing independent confirmation of the underlying microscopic dynamics. This convergence of theoretical and experimental results strengthens the conclusion that a Pauli-induced restriction of the accessible three-body Hilbert space is the dominant mechanism responsible for the observed suppression of recombination.

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