Sr-SrOH Atom-Molecule Complex

• Sr-SrOH is an atom-molecule system where a ground-state Sr atom interacts with an SrOH molecule, forming a complex with rich rotational structure and strong anisotropy.
• The system exhibits a dense spectrum of near-threshold resonances driven by anisotropic coupling and precise scattering dynamics under ultracold conditions.
• Experimental and theoretical studies suggest routes to coherent assembly of Sr2OH via STIRAP, integrating ultracold collision control with precision molecular engineering.

The Sr-SrOH system denotes the atom-molecule complex formed by a ground-state strontium atom, $\mathrm{Sr}(^1S)$, and ground-state strontium monohydroxide, $\mathrm{SrOH}(X^2\Sigma^+)$). It is studied as a route to forming $\mathrm{Sr_2OH}$, described as a near prolate symmetric top / asymmetric top with rich rotational structure. Current theory characterizes the system as strongly anisotropic and effectively non-reactive under ultracold conditions, with a dense spectrum of near-threshold resonances and candidate optical pathways for coherent transfer from weakly bound atom-molecule states to the rovibrational ground state (Kosicki et al., 20 Aug 2025).

1. Physical definition and thermochemical character

In the ultracold-matter literature, the Sr-SrOH system consists of a Sr atom in its ${}^1S$ ground state colliding with an SrOH molecule in its $X^2\Sigma^+$ ground state. The target bound product is $\mathrm{Sr_2OH}$, which the paper describes as a near prolate symmetric top / asymmetric top. The proposed attraction of this platform is that it would extend ultracold assembly from diatomics and linear radicals to an asymmetric-top species while retaining an alkaline-earth-centered optical and electronic structure (Kosicki et al., 20 Aug 2025).

A central result is that the entrance channel is non-reactive in the thermochemical sense relevant to ultracold collisions. The reported reference energies are

$\Delta E(\mathrm{Sr}+\mathrm{SrOH}) = 0,$

$$\Delta E(\mathrm{Sr_2}+\mathrm{OH}) = 54993.2\ \mathrm{cm^{-1}},$$

$$\Delta E(\mathrm{SrO}+\mathrm{SrH}) = 59864.7\ \mathrm{cm^{-1}}.$$

Accordingly, spontaneous rearrangement into $\mathrm{Sr_2}+\mathrm{OH}$ or $\mathrm{SrOH}(X^2\Sigma^+)$0 is not energetically accessible under ultracold conditions. The paper notes one important nuance: isotope exchange may still be possible in principle because its energetic cost is of order $\mathrm{SrOH}(X^2\Sigma^+)$1 (Kosicki et al., 20 Aug 2025).

This non-reactive character is significant because strong anisotropy in atom-molecule systems is often associated with complex short-range dynamics. Here, however, the primary issue is not an open chemical-loss channel but the structure of the interaction potential and the near-threshold bound-state spectrum. A common misconception is therefore that strong anisotropy in Sr-SrOH implies barrierless chemistry; the published thermochemistry indicates instead that the dominant ultracold phenomena should be resonance-rich scattering and bound-state control rather than energetically allowed rearrangement (Kosicki et al., 20 Aug 2025).

2. SrOH and Sr as experimentally prepared constituents

The feasibility of Sr-SrOH studies depends on the unusually advanced state control already achieved for SrOH. SrOH is a triatomic, linear free radical in its vibronic ground state and a polyatomic analog of laser-cooled diatomics. In a cryogenic buffer-gas beam, SrOH was produced by laser ablation of a pressed $\mathrm{SrOH}(X^2\Sigma^+)$2 target inside a $\mathrm{SrOH}(X^2\Sigma^+)$3 helium cryogenic buffer-gas cell, yielding roughly $\mathrm{SrOH}(X^2\Sigma^+)$4 molecules per pulse with pulse duration $\mathrm{SrOH}(X^2\Sigma^+)$5, forward speed $\mathrm{SrOH}(X^2\Sigma^+)$6, and transverse velocity spread $\mathrm{SrOH}(X^2\Sigma^+)$7. Optical cycling on the rotationally closed $\mathrm{SrOH}(X^2\Sigma^+)$8 transition at $\mathrm{SrOH}(X^2\Sigma^+)$9, together with a single $\mathrm{Sr_2OH}$0 repumper for $\mathrm{Sr_2OH}$1, produced a beam deflection of $\mathrm{Sr_2OH}$2 via scattering of $\mathrm{Sr_2OH}$3 photons per molecule (Kozyryev et al., 2016).

The optical-cycling closure of SrOH was subsequently quantified much more deeply. Vibronic branching ratios from the first two electronically excited states were measured experimentally at the $\mathrm{Sr_2OH}$4 level, and a Markov-chain analysis using the measured branching network predicted more than $\mathrm{Sr_2OH}$5 photon scatters on average before decay into an unaddressed vibrational state. The corresponding practical cooling scheme used 8–10 lasers, depending on rotational handling in manifolds such as $\mathrm{Sr_2OH}$6 and $\mathrm{Sr_2OH}$7, and supported the claim of $\mathrm{Sr_2OH}$8 photon scatters per molecule (Lasner et al., 2022).

That level of closure enabled trapping-based spectroscopy and optical trapping. MOT-assisted spectroscopy identified two new repumping transitions, $\mathrm{Sr_2OH}$9 at ${}^1S$0 and ${}^1S$1 at ${}^1S$2, and their addition increased the trapped molecule number to ${}^1S$3, a 4.5-fold increase over the previous shallower cycle, with MOT lifetime reaching ${}^1S$4 in the best reported conditions (Lunstad et al., 11 Sep 2025). An optical dipole trap at ${}^1S$5 then trapped ${}^1S$6 SrOH molecules, with measured lifetimes of ${}^1S$7 for ${}^1S$8, ${}^1S$9 for $X^2\Sigma^+$0, and $X^2\Sigma^+$1 for $X^2\Sigma^+$2 (Sawaoka et al., 1 Sep 2025).

Cold atomic Sr can also be generated in the same general cryogenic-source framework. Direct thermal emission from a pressed HfC/SrO target in a $X^2\Sigma^+$3 cryogenic buffer-gas beam source released $X^2\Sigma^+$4 Sr atoms per pulse, and adding water vapor to the cell yielded $X^2\Sigma^+$5 SrOH molecules with peak SrOH density $X^2\Sigma^+$6 (Winnicki et al., 2024). Taken together, these results establish that both constituents of the Sr-SrOH system are not merely spectroscopic abstractions but experimentally producible, laser-addressable, and, for SrOH, trappable.

3. Ground-state interaction potential and structure of $X^2\Sigma^+$7

The ground-state interaction in Sr-SrOH was computed with high-level electronic-structure theory. For Sr-SrOH, the potential was represented as

$X^2\Sigma^+$8

with fitted long-range coefficients $X^2\Sigma^+$9 a.u. and $\mathrm{Sr_2OH}$0 a.u. The same study reported the first computed static polarizability of SrOH, with permanent dipole moment $\mathrm{Sr_2OH}$1 at RCCSD(T), compared with an experimental value of $\mathrm{Sr_2OH}$2, average polarizability $\mathrm{Sr_2OH}$3 a.u., and polarizability anisotropy $\mathrm{Sr_2OH}$4 a.u. (Kosicki et al., 20 Aug 2025).

The fully relaxed bound complex $\mathrm{Sr_2OH}$5 has the following reported equilibrium properties:

Property	Reported value
$\mathrm{Sr_2OH}$6	$\mathrm{Sr_2OH}$7
$\mathrm{Sr_2OH}$8	$\mathrm{Sr_2OH}$9
$\Delta E(\mathrm{Sr}+\mathrm{SrOH}) = 0,$0	$\Delta E(\mathrm{Sr}+\mathrm{SrOH}) = 0,$1
$\Delta E(\mathrm{Sr}+\mathrm{SrOH}) = 0,$2	$\Delta E(\mathrm{Sr}+\mathrm{SrOH}) = 0,$3
$\Delta E(\mathrm{Sr}+\mathrm{SrOH}) = 0,$4	$\Delta E(\mathrm{Sr}+\mathrm{SrOH}) = 0,$5
$\Delta E(\mathrm{Sr}+\mathrm{SrOH}) = 0,$6	$\Delta E(\mathrm{Sr}+\mathrm{SrOH}) = 0,$7
$\Delta E(\mathrm{Sr}+\mathrm{SrOH}) = 0,$8	$\Delta E(\mathrm{Sr}+\mathrm{SrOH}) = 0,$9
$$\Delta E(\mathrm{Sr_2}+\mathrm{OH}) = 54993.2\ \mathrm{cm^{-1}},$$0	$$\Delta E(\mathrm{Sr_2}+\mathrm{OH}) = 54993.2\ \mathrm{cm^{-1}},$$1
$$\Delta E(\mathrm{Sr_2}+\mathrm{OH}) = 54993.2\ \mathrm{cm^{-1}},$$2	$$\Delta E(\mathrm{Sr_2}+\mathrm{OH}) = 54993.2\ \mathrm{cm^{-1}},$$3
$$\Delta E(\mathrm{Sr_2}+\mathrm{OH}) = 54993.2\ \mathrm{cm^{-1}},$$4	$$\Delta E(\mathrm{Sr_2}+\mathrm{OH}) = 54993.2\ \mathrm{cm^{-1}},$$5

In the reduced Jacobi representation used for scattering, where the SrOH fragment is kept linear, the potential minimum is shallower and occurs at

$$\Delta E(\mathrm{Sr_2}+\mathrm{OH}) = 54993.2\ \mathrm{cm^{-1}},$$6

The paper also reports a secondary minimum at

$$\Delta E(\mathrm{Sr_2}+\mathrm{OH}) = 54993.2\ \mathrm{cm^{-1}},$$7

and saddle points in the linear geometries at $$\Delta E(\mathrm{Sr_2}+\mathrm{OH}) = 54993.2\ \mathrm{cm^{-1}},$$8 and $$\Delta E(\mathrm{Sr_2}+\mathrm{OH}) = 54993.2\ \mathrm{cm^{-1}},$$9 (Kosicki et al., 20 Aug 2025).

The anisotropy is unusually strong. The isotropic term $$\Delta E(\mathrm{SrO}+\mathrm{SrH}) = 59864.7\ \mathrm{cm^{-1}}.$$0 alone has a minimum

$$\Delta E(\mathrm{SrO}+\mathrm{SrH}) = 59864.7\ \mathrm{cm^{-1}}.$$1

whereas the full short-range interaction is dominated by a large, structureless $$\Delta E(\mathrm{SrO}+\mathrm{SrH}) = 59864.7\ \mathrm{cm^{-1}}.$$2 term, with higher $$\Delta E(\mathrm{SrO}+\mathrm{SrH}) = 59864.7\ \mathrm{cm^{-1}}.$$3 components still non-negligible. The paper attributes this to the directional ionic/metal-ligand bonding character of SrOH, the presence of two metal centers competing to interact with the OH ligand, and strong orientation dependence of the electron-density redistribution (Kosicki et al., 20 Aug 2025).

4. Ultracold scattering and the near-threshold resonance spectrum

Quantum scattering calculations for Sr-SrOH were carried out at collision energy $$\Delta E(\mathrm{SrO}+\mathrm{SrH}) = 59864.7\ \mathrm{cm^{-1}}.$$4 using reduced mass $$\Delta E(\mathrm{SrO}+\mathrm{SrH}) = 59864.7\ \mathrm{cm^{-1}}.$$5 u, SrOH rotational constant $$\Delta E(\mathrm{SrO}+\mathrm{SrH}) = 59864.7\ \mathrm{cm^{-1}}.$$6, rotational basis up to $$\Delta E(\mathrm{SrO}+\mathrm{SrH}) = 59864.7\ \mathrm{cm^{-1}}.$$7, and radial propagation from $$\Delta E(\mathrm{SrO}+\mathrm{SrH}) = 59864.7\ \mathrm{cm^{-1}}.$$8 to $$\Delta E(\mathrm{SrO}+\mathrm{SrH}) = 59864.7\ \mathrm{cm^{-1}}.$$9. Scattering lengths were extracted with molscat using the hybrid log-derivative Airy propagator. To assess sensitivity to short-range uncertainty, the full PES was scaled as

$\mathrm{Sr_2}+\mathrm{OH}$0

with $\mathrm{Sr_2}+\mathrm{OH}$1 varied over roughly $\mathrm{Sr_2}+\mathrm{OH}$2 (Kosicki et al., 20 Aug 2025).

The resulting scattering-length landscape is dominated by a dense forest of narrow resonances. Over the full $\mathrm{Sr_2}+\mathrm{OH}$3 scaling scan, the calculation identified

$\mathrm{Sr_2}+\mathrm{OH}$4

equivalent to about

$\mathrm{Sr_2}+\mathrm{OH}$5

The physical origin is the coupling of the entrance channel to a large number of near-threshold bound states involving rotationally excited SrOH states, end-over-end angular momentum $\mathrm{Sr_2}+\mathrm{OH}$6, and strong anisotropic couplings (Kosicki et al., 20 Aug 2025).

A particularly instructive comparison is between isotropic and anisotropic dynamics. If only the isotropic term $\mathrm{Sr_2}+\mathrm{OH}$7 is retained, the scattering length shows a single broad resonance. Restoring the full anisotropic potential splits that behavior into the dense resonance spectrum. This shows that the resonance proliferation is not a generic feature of a deep potential alone; it is specifically driven by the anisotropic structure of the Sr-SrOH interaction (Kosicki et al., 20 Aug 2025).

This distinction addresses another common misconception. Dense resonances do not imply that the system is chemically reactive. For Sr-SrOH, the calculations instead indicate a non-reactive but strongly coupled ultracold complex in which short-range sensitivity, rotational channel mixing, and near-threshold level density are the controlling features. The paper further suggests that magnetically tunable Feshbach resonances may exist, and it also highlights a mergoassociation route in which two optical tweezers are merged and a trap-induced avoided crossing is followed adiabatically to convert separated atom and molecule into a weakly bound molecule (Kosicki et al., 20 Aug 2025).

5. Excited states, transition dipoles, and coherent formation of ground-state $\mathrm{Sr_2}+\mathrm{OH}$8

To examine optical assembly beyond scattering resonances, the Sr-SrOH study computed low-lying excited states in a reduced one-dimensional model. The targeted electronic manifolds were three $\mathrm{Sr_2}+\mathrm{OH}$9 states and two $\mathrm{SrOH}(X^2\Sigma^+)$00 states, correlating asymptotically as follows:

• $\mathrm{SrOH}(X^2\Sigma^+)$01,
• $\mathrm{SrOH}(X^2\Sigma^+)$02,
• $\mathrm{SrOH}(X^2\Sigma^+)$03 (Kosicki et al., 20 Aug 2025).

The excited-state curves are reported to be mostly smooth and nearly parallel to the ground-state curve. The same calculations found a conical intersection between $\mathrm{SrOH}(X^2\Sigma^+)$04 and $\mathrm{SrOH}(X^2\Sigma^+)$05 near $\mathrm{SrOH}(X^2\Sigma^+)$06–$\mathrm{SrOH}(X^2\Sigma^+)$07, depending on geometry, and strong short-range state mixing in some channels. Transition dipole moments were evaluated through

$\mathrm{SrOH}(X^2\Sigma^+)$08

For states correlating to $\mathrm{SrOH}(X^2\Sigma^+)$09, the transition dipole moment decays strongly at large $\mathrm{SrOH}(X^2\Sigma^+)$10. By contrast, for states correlating to $\mathrm{SrOH}(X^2\Sigma^+)$11, the transition dipole moment remains above $\mathrm{SrOH}(X^2\Sigma^+)$12 even at long range (Kosicki et al., 20 Aug 2025).

These properties motivate a STIRAP-based route to coherent molecule formation. The analysis used a Tang-Toennies form,

$\mathrm{SrOH}(X^2\Sigma^+)$13

with fixed $\mathrm{SrOH}(X^2\Sigma^+)$14 and $\mathrm{SrOH}(X^2\Sigma^+)$15 a.u., estimated by scaling from $\mathrm{SrOH}(X^2\Sigma^+)$16. The basic idea is to connect an initial weakly bound atom-molecule state to the rovibrational ground state through an excited bound state. Because the ground and excited potentials are very similar, the Franck-Condon factors are nearly diagonal, which makes simple three-level two-photon STIRAP difficult. The paper therefore suggests multi-step transfer, for example weakly bound state $\mathrm{SrOH}(X^2\Sigma^+)$17 via $\mathrm{SrOH}(X^2\Sigma^+)$18, and then $\mathrm{SrOH}(X^2\Sigma^+)$19 via $\mathrm{SrOH}(X^2\Sigma^+)$20. Among the candidate intermediate states, $\mathrm{SrOH}(X^2\Sigma^+)$21 is identified as the best because it maintains nonzero transition-dipole coupling across the full range (Kosicki et al., 20 Aug 2025).

The importance of this section is methodological as much as spectroscopic. The published result is not an experimental demonstration of coherent $\mathrm{SrOH}(X^2\Sigma^+)$22 formation. It is a one-dimensional STIRAP model supported by ab initio excited states and transition dipoles, and the paper explicitly treats the route as plausible but experimentally demanding (Kosicki et al., 20 Aug 2025).

6. Relation to the broader SrOH platform

The interest in the Sr-SrOH system is amplified by the fact that isolated SrOH is already an advanced ultracold and precision-measurement platform. SrOH was identified as the first and, so far, the only polyatomic molecule to be directly laser cooled to sub-millikelvin temperatures, and its nearly degenerate $\mathrm{SrOH}(X^2\Sigma^+)$23 rovibrational transitions were analyzed as probes of ultralight bosonic dark matter. For the branches discussed in that work, the reported enhancement factors include $\mathrm{SrOH}(X^2\Sigma^+)$24 at $\mathrm{SrOH}(X^2\Sigma^+)$25 and $\mathrm{SrOH}(X^2\Sigma^+)$26 at $\mathrm{SrOH}(X^2\Sigma^+)$27–$\mathrm{SrOH}(X^2\Sigma^+)$28, with estimates that $\mathrm{SrOH}(X^2\Sigma^+)$29 is achievable and that a one-day measurement could reach $\mathrm{SrOH}(X^2\Sigma^+)$30 (Kozyryev et al., 2018).

Later MOT-assisted spectroscopy directly measured the $\mathrm{SrOH}(X^2\Sigma^+)$31–$\mathrm{SrOH}(X^2\Sigma^+)$32 structure, reporting that the observed $\mathrm{SrOH}(X^2\Sigma^+)$33 level lies about $\mathrm{SrOH}(X^2\Sigma^+)$34 above $\mathrm{SrOH}(X^2\Sigma^+)$35 and that many spacings in the $\mathrm{SrOH}(X^2\Sigma^+)$36–$\mathrm{SrOH}(X^2\Sigma^+)$37 band fall in the $\mathrm{SrOH}(X^2\Sigma^+)$38–$\mathrm{SrOH}(X^2\Sigma^+)$39 range (Lunstad et al., 11 Sep 2025). Optical trapping then established that the relevant internal states are long-lived on the few-hundred-millisecond scale, with measured lifetimes $\mathrm{SrOH}(X^2\Sigma^+)$40 for $\mathrm{SrOH}(X^2\Sigma^+)$41 and $\mathrm{SrOH}(X^2\Sigma^+)$42 for $\mathrm{SrOH}(X^2\Sigma^+)$43, consistent with spontaneous radiative decay and black-body excitation limits (Sawaoka et al., 1 Sep 2025).

A separate line of work on fully spin-polarized $\mathrm{SrOH}(X^2\Sigma^+)$44 showed ratios of elastic to inelastic collision rates well in excess of $\mathrm{SrOH}(X^2\Sigma^+)$45 over magnetic fields $\mathrm{SrOH}(X^2\Sigma^+)$46–$\mathrm{SrOH}(X^2\Sigma^+)$47 and collision energies $\mathrm{SrOH}(X^2\Sigma^+)$48–$\mathrm{SrOH}(X^2\Sigma^+)$49, with spin relaxation dominated by the direct magnetic dipole-dipole mechanism and the indirect spin-rotation mechanism strongly suppressed (Morita et al., 2017). That study does not establish analogous cooling behavior for Sr-SrOH, but it does show that a heavy $\mathrm{SrOH}(X^2\Sigma^+)$50 radical such as SrOH can participate in favorable ultracold collisions.

Within this wider context, the Sr-SrOH system occupies a specific niche. Isolated SrOH already supplies optical cycling, MOT loading, optical trapping, and precision-sensitive internal structure; Sr-SrOH adds a non-reactive atom-molecule entrance channel, a strongly anisotropic PES, an exceptionally dense near-threshold resonance spectrum, and a theoretically motivated route to coherent assembly of $\mathrm{SrOH}(X^2\Sigma^+)$51 (Kosicki et al., 20 Aug 2025). A plausible implication is that successful control of Sr-SrOH would connect two strands of current research that are often treated separately: ultracold atom-molecule association and precision-ready polyatomic-state engineering.