Pith. sign in

REVIEW 3 major objections 6 minor 51 references

Diatomic and Polyatomic Heteronuclear Ultralong-Range Rydberg Molecules

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper predicts that ultracold Rb–Cs mixtures form heteronuclear diatomic and polyatomic ultralong-range Rydberg molecules, with binding energies that add up from dimer values.

desk verdict A workmanlike extension of the Fermi pseudopotential model to Rb-Cs ULRMs; the polyatomic prediction rests on an additivity rule that is almost certainly fine for 55S but should be defended explicitly. read the letter →

arxiv 2501.09282 v1 pith:3E3AEASM submitted 2025-01-16 quant-ph

Qing Li , Shi-Yao Shao , Li-Hua Zhang , Bang Liu , Zheng-Yuan Zhang , Jun Zhang , Qi-Feng Wang , Han-Chao Chen
show 4 more authors
Yu Ma Tian-Yu Han Dong-Sheng Ding Bao-Sen Shi
This is my paper · ORCID
classification quant-ph
keywords ultralong-rangeRydbergmoleculesheteronuclearpolyatomicRb-Csultracoldmixturespotentialenergycurvespermanentelectricdipolemomentsmolecularspectra
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper predicts that an ultracold mixture of rubidium and cesium can host heteronuclear ultralong-range Rydberg molecules, in which a Rydberg electron's scattering off ground-state atoms binds additional atoms into the molecule. For diatomic molecules, it calculates potential energy curves, vibrational levels, and electric dipole moments, and finds that all four nuclear combinations—RbRb, RbCs, CsRb, CsCs—should form simultaneously near a Rydberg resonance with species-dependent spectra. For polyatomic molecules made of a 55S Rydberg atom plus several Rb and Cs ground-state atoms, it predicts that the total binding energy is the sum of the individual dimer binding energies, producing a discrete spectral ladder. These predictions give experimentalists concrete line positions to search for heteronuclear polyatomic Rydberg molecules and suggest pathways for quantum simulation and precision measurements.

What carries the argument

The calculations rest on a Fermi zero-range pseudopotential for the electron–ground-state-atom interaction, including both s-wave scattering with an effective-range correction and p-wave scattering that can produce a shape resonance. Near the nearly degenerate high-angular-momentum Rydberg states, degenerate perturbation theory is used to build and diagonalize the interaction Hamiltonian, giving potential energy curves whose wells support vibrational states. For polyatomic molecules, the load-bearing mechanism is a linear additivity rule imported from homonuclear S-state studies: the total binding energy is the sum of dimer binding energies, with no explicit correction for ground-state–ground-state interactions.

What would settle it

Measure the 55S photoassociation spectrum of an ultracold Rb–Cs mixture and compare line positions with the predicted comb $i a + j b$ for a Rb Rydberg atom and $i c + j d$ for a Cs Rydberg atom; if the observed positions show nonlinear spacing with the number of captured atoms, density-dependent shifts, or a strong departure from the dimer-sum values, the additivity rule fails.

Watch

Extended reading notes

Core claim

The paper's central claim is that heteronuclear ultralong-range Rydberg molecules can be formed in two-species ultracold Rb–Cs gases, both as diatomic molecules and as polyatomic complexes where one Rydberg atom captures multiple ground-state atoms of either species. For the diatomic case, the authors compute potential energy curves and vibrational levels for nD states and show that the outer potential well is deeper when the ground-state atom is cesium, while the well positions are set by the Rydberg species. They further predict that in a Rb–Cs mixture, excitation near the atomic Rydberg line should simultaneously produce four types of molecules whose vibrational binding energies scale as $n^{-6}$. For polyatomic molecules, the energy shift relative to the isolated Rydberg atom is claimed to be $\Delta E_{\mathrm{Rb}} = i a + j b$ when a Rb Rydberg atom binds $i$ Rb and $j$ Cs ground-state atoms, and $\Delta E_{\mathrm{Cs}} = i c + j d$ for a Cs Rydberg atom, with the dimer values $a = -1.3012$ MHz, $b = -1.8470$ MHz, $c = -3.0934$ MHz, and $d = -5.6164$ MHz. The resulting theoretical spectra in Fig. 6 are offered as a guide for future experiments.

Load-bearing premise

The total binding energy of a polyatomic heteronuclear molecule is assumed to be exactly the sum of individual dimer binding energies, with no correction for interactions between the captured ground-state atoms or for the mixed-species environment; this rule is carried over from homonuclear S-state experiments and is not derived or numerically validated for Rb–Cs systems.

Editorial extensions

If this is right

  • In an ultracold Rb–Cs mixture, scanning the excitation laser near the Rydberg resonance should reveal four distinct ULRM spectra corresponding to RbRb, RbCs, CsRb, and CsCs, with the relative depths of the wells set by which atom is the ground-state perturber.
  • The D-state vibrational binding energies of all four molecular types scale as $n^{-6}$ and the level curves do not cross, so spectral assignments remain stable over a broad range of principal quantum numbers.
  • Cs–Rb S-state ULRMs should carry permanent electric dipole moments around 1670 Debye—smaller than the 2081 Debye of Cs–Cs but still large enough to be seen as Stark broadening in a weak electric field.
  • Polyatomic heteronuclear ULRMs built on a 55S Rydberg atom should produce discrete spectra at integer-combination shifts $ia+jb$ (Rb Rydberg) or $ic+jd$ (Cs Rydberg), giving predictable lines for molecules with up to several captured atoms.
  • These predicted line positions can serve as a direct experimental signature that heteronuclear polyatomic Rydberg molecules have formed in a two-species gas.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper does not state this, but if the additivity rule holds, the spectrum of a mixed gas acts as a composition counter: the spacing pattern between lines directly reveals the numbers of Rb and Cs atoms in each molecular complex, in analogy with homonuclear few-body series.
  • The paper leaves implicit that the same additive construction should be testable at other principal quantum numbers by rescaling the dimer energies; systematic deviations at higher gas densities would expose ground-state–ground-state interactions among the captured atoms, an effect the current model neglects.
  • The authors' comparison of dipole moments suggests a route the paper does not develop: tuning the ratio of Rb to Cs atoms in a polyatomic molecule could be used to engineer the net permanent dipole moment and hence the dipolar interaction strength in a many-body setting.
  • The approach should extend in principle to other alkali mixtures, but the p-wave shape-resonance positions and quantum defects would need to be recomputed for each new pair of species.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper presents a theoretical study of heteronuclear ultralong-range Rydberg molecules (ULRMs) in Rb-Cs mixtures. For diatomic molecules, it computes potential energy curves (PECs), vibrational energy levels, and permanent electric dipole moments (PEDMs) for nD states (and nS states for PEDMs), comparing homonuclear and heteronuclear combinations. The central new claim is the prediction of polyatomic heteronuclear ULRM spectra in Section III.B: for a 55S Rydberg atom, the binding energy of a molecule with i Rb and j Cs ground-state atoms is taken as the sum of the corresponding dimer binding energies, ΔE_Rb = i a + j b and ΔE_Cs = i c + j d, with a, b, c, d given in MHz. The paper also discusses potential applications in quantum technologies.

Significance. The diatomic calculations use standard methods (Fermi pseudopotential, quantum-defect theory, and the ARC package) and appear technically sound; they provide a useful comparison of heteronuclear vs homonuclear D-state ULRM vibrational levels and PEDMs. The polyatomic additivity prediction, if validated, is a simple and falsifiable result that could guide two-species photoassociation experiments and would extend the homonuclear findings of Gaj et al. The paper gives concrete numerical values for the energy shifts, which is a strength. However, the novelty of the diatomic part is incremental given existing heteronuclear ULRM studies (e.g., Peper & Deiglmayr, Whalen et al.), and the headline polyatomic prediction rests on an unverified additivity assumption. The manuscript also lacks experimental benchmarks and uncertainty estimates, which limits the strength of the quantitative predictions.

major comments (3)
  1. [Section III.B] The additivity rule ΔE_Rb = i a + j b and ΔE_Cs = i c + j d is the load-bearing assumption for the paper's central claim. It is imported from homonuclear S-state experiments (Gaj et al.) without a derivation or numerical validation for mixed Rb-Cs systems. The authors should either (i) derive the rule from first-order perturbation theory explicitly, showing that the isotropic 55S electron density, the small perturber shifts (1.3–5.6 MHz), and the large separation of coupled channels justify additivity to the stated precision, or (ii) perform a direct two-perturber calculation (e.g., solving the two-perturber electronic problem or computing the second-order correction) to confirm that the total shift equals the sum of dimer shifts. Without this, Fig. 6 is a restatement of the dimer energies rather than an independent prediction.
  2. [Section III.A and II.C] The PECs and vibrational levels for Cs-containing species (Rb-Cs, Cs-Cs, Cs-Rb) require the p-wave scattering phase shifts for electron-Cs scattering, but the paper only presents the e-Rb p-wave shift (Fig. 2(b)) and does not specify the e-Cs p-wave parameters used. Please state the Cs p-wave phase shift or scattering volume (or provide the reference and interpolated values) so that the results are reproducible. This is particularly important because the 35D PECs in Fig. 3 explicitly include p-wave interactions.
  3. [Section III.A, Fig. 4] The statement that the four ground-state and four first-excited-state energy level curves 'do not intersect, demonstrating that the relative depths of the potential wells ... remain unchanged over a wide range of n, which is a universal phenomenon' is a strong claim. As written it is an observation for n = 32–37, not a demonstration. Please temper the claim or provide a scaling argument (e.g., based on the n-dependence of the Rydberg wavefunction and the scattering lengths) to justify universality.
minor comments (6)
  1. [Fig. 3] The axis label 'Enegery' in Fig. 3 is a typo and should read 'Energy'.
  2. [Section III.B] The statement that 'the intensity of the molecular vibrational spectra is proportional to the square of the bond length' is incorrect; the line strength is determined by the Franck-Condon factor (the squared overlap of the initial continuum wavefunction and the final vibrational wavefunction), not by the bond length. Please correct this and, if relative intensities are intended to be shown, describe how they are computed.
  3. [Sections II.B and II.C] The quantum defects used for Rb and Cs are not listed, and the basis-set notation '32(l>2)' and '31(l>2)' is ambiguous. Please specify the quantum defects explicitly and clarify that the notation means all states with l ≥ 3 for those principal quantum numbers.
  4. [Section III.A] The paper would benefit from a quantitative comparison of the computed diatomic PECs or binding energies with existing experimental data for heteronuclear ULRMs (e.g., Peper & Deiglmayr, Whalen et al.) to validate the input scattering parameters.
  5. [Section III.B] The phrase 'Ne atoms with positive scattering lengths' is confusing (it appears in the discussion of Liu et al.). Please clarify whether 'Ne' denotes a generic neutral atom or the element neon, and if the latter, define it properly.
  6. [Section IV] The summary is largely a restatement of the results. Consider adding a brief discussion of limitations and open questions, such as the validity of the additivity rule for mixed species and the role of three-body interactions in the polyatomic spectra.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found; the polyatomic spectra follow an explicitly stated external additivity rule applied to independently computed dimer energies.

full rationale

I walked the derivation chain. The diatomic heteronuclear PECs are obtained by standard perturbation theory with the Fermi pseudopotential (Eq. 2), using external scattering lengths, polarizabilities, and phase shifts; vibrational levels are then obtained by solving the nuclear Schrodinger equation in those PECs. No fitted parameter is relabeled as a prediction, and no target quantity enters as an input. The polyatomic heteronuclear spectra in Sec. III.B are not a self-referential derivation: the paper explicitly states that it is 'Following the approach of Gaj et al.' using a rule for isotropic nS states, and the dimer energies a, b, c, d are independently computed first-principles values from the same PEC formalism. Thus Delta E_Rb = i a + j b is an application of a stated external model, not a construction that assumes the spectrum it claims to predict. The cited prior work is external (Greene 2000, Gaj 2014, Fey 2019, etc.); the acknowledged code provider (W. Li) is not an author of this paper, and no uniqueness theorem or author-imported constraint is used. The physical validity of extending the additivity rule to mixed Rb-Cs systems is a robustness/correctness question, not a circularity, and the paper is transparent that this is an adopted approach rather than a derived result.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central calculations rest on the standard Fermi pseudopotential model with literature scattering lengths (four input numbers), on the Born-Oppenheimer and effective-range approximations, and on an unvalidated additivity rule for polyatomic heteronuclear molecules. No new entities are introduced.

free parameters (4)
  • Rb zero-energy s-wave scattering length a0(Rb) = -18.5 a.u.
    Taken from prior measurements (refs [4,9,39]); used in as(k) to compute PECs. Uncertainty not propagated.
  • Cs zero-energy s-wave scattering length a0(Cs) = -21.7 a.u.
    Taken from prior measurements; used in as(k). Uncertainty not propagated.
  • Rb polarizability alpha(Rb) = 319.2 a.u.
    Input to the effective-range formula for as(k); from refs [4,9,39].
  • Cs polarizability alpha(Cs) = 400.8 a.u.
    Input to the effective-range formula for as(k); from refs [4,9,39].
assumptions (5)
  • domain assumption Born-Oppenheimer approximation separates electronic and nuclear motion.
    Invoked in Section II.A to define PECs and the vibrational Hamiltonian.
  • domain assumption Electron-ground-state-atom interaction is a zero-range Fermi pseudopotential with s- and p-wave terms.
    Equation (2); standard in ULRM literature but an approximation.
  • domain assumption The core-ground-state atom interaction Vaa ~ 1/R^4 is neglected.
    Section II.A; justified at large internuclear distances.
  • domain assumption The effective range formula as(k) = a0 + alpha * pi * k / 3 holds.
    Section II.A, from O'Malley et al.; used to compute s-wave scattering lengths.
  • ad hoc to paper Vibrational binding energy of a polyatomic heteronuclear ULRM is the sum of dimer binding energies.
    Section III.B; assumed following Gaj et al. without derivation or numerical validation for heteronuclear systems.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Diatomic and Polyatomic Heteronuclear Ultralong-Range Rydberg Molecules." pith.science (2026). https://pith.science/paper/3E3AEASM

@misc{pith2026250109282,
  author       = {Pith},
  title        = {Pith review of: Diatomic and Polyatomic Heteronuclear Ultralong-Range Rydberg Molecules},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3E3AEASM}},
  note         = {Machine review of arXiv:2501.09282}
}
read the original abstract

Ultra-long-range Rydberg molecules (ULRMs) have attracted significant interest due to their unique electronic properties and potential applications in quantum technologies. We theoretically investigate the formation and characteristics of heteronuclear ULRMs, focusing on Rb-Cs systems. We explore the vibrational energy levels of heteronuclear nD ULRMs and compare them with homonuclear counterparts. We also predict the formation of polyatomic heteronuclear ULRMs, discussing how the binding energy and spectral features evolve as the number of ground-state atoms increases. Our theoretical predictions are presented in terms of molecular spectra and provide insight into the formation dynamics of these systems. The study further explores the potential applications of heteronuclear ULRMs in quantum information processing, quantum simulation, and precision measurements, offering new avenues for future research in many-body physics and quantum technologies.

Figures

Figures reproduced from arXiv: 2501.09282 by the authors.

Figure 1
Figure 1. Rb(n = 35) ULRMs are formed solely through s-wave scattering. (a) The green solid line shows the PECs of the Rb(35S) state, with the green dashed line representing the vibrational wave function. The horizontal lines near the dashed line represent the vibrational ground state and first excited state levels, shaded in light green. The shifts relative to the Rb(35S) Rydberg line are -23.18 MHz and -10.44 MHz, respectiv… view at source ↗
Figure 2
Figure 2. Rb(n = 35) ULRMs are formed by both s-wave scattering and p-wave interactions. (a) The blue solid line shows the PECs near the 35S state, with the zero-energy reference at the n = 32 hydrogen atom line. In the region marked by the thick blue line around 680 a.u., p-wave scatter￾ing induces shape resonance, causing the previously isolated 32(l > 2), 35S, 33D, and 34P to couple, forming the “but￾terfly” ULRMs at the r… view at source ↗
Figure 4
Figure 4. Vibrational energy levels of ULRMs. The plot il [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figures from the paper (3 more)
Figure 3
Figure 3. Figure 3: PECs of ULRMs (35 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png]
Figure 5
Figure 5. Figure 5: Cylindrical coordinate surface plots of the [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Theoretical spectra of polyatomic heteronuclear [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

51 extracted references · 49 canonical work pages

  1. [1]

    C. H. Greene, A. Dickinson, and H. Sadeghpour, Cre- ation of polar and nonpolar ultralong-range Rydberg molecules, Phys. Rev. Lett. 85, 2458 (2000)

    work page 2000

  2. [2]

    Lombardi and A

    M. Lombardi and A. Matzkin, Dynamical entanglement and chaos: The case of Rydberg molecules, Phys. Rev. A 73, 062335 (2006)

    work page 2006

  3. [3]

    C. H. Greene, E. L. Hamilton, H. Crowell, C. Vadla, and K. Niemax, Experimental verification of minima in ex- cited long-range Rydberg states of Rb 2, Phys. Rev. Lett. 97, 233002 (2006)

    work page 2006

  4. [4]

    Bendkowsky, B

    V. Bendkowsky, B. Butscher, J. Nipper, J. P. Shaffer, R. L¨ ow, and T. Pfau, Observation of ultralong-range Ry- dberg molecules, Nature 458, 1005 (2009)

    work page 2009

  5. [5]

    Kurz and P

    M. Kurz and P. Schmelcher, Electrically dressed ultralong-range polar Rydberg molecules, Phys. Rev. A 88, 022501 (2013)

    work page 2013

  6. [6]

    Matzkin and T

    A. Matzkin and T. Monteiro, Rydberg molecules in ex- ternal fields: a semiclassical analysis, Phys. Rev. Lett. 87, 143002 (2001)

    work page 2001

  7. [7]

    Wang and S

    D. Wang and S. Ding, Alternative model potential for the semiclassical calculation of the recurrence spectra of the Rydberg molecule in strong external fields, Phys. Rev. A 71, 013420 (2005)

    work page 2005

  8. [8]

    Lesanovsky, P

    I. Lesanovsky, P. Schmelcher, and H. Sadeghpour, Ultralong-range Rydberg molecules exposed to a mag- netic field, J. Phys. B: At., Mol. Opt. Phys. 39, L69 (2006)

    work page 2006

Show all 51 references
  1. [9]

    Booth, S

    D. Booth, S. Rittenhouse, J. Yang, H. Sadeghpour, and J. Shaffer, Production of trilobite Rydberg molecule dimers with kilo-Debye permanent electric dipole mo- ments, Science 348, 99 (2015)

    2015

  2. [10]

    W. Li, T. Pohl, J. Rost, S. T. Rittenhouse, H. R. Sadegh- pour, J. Nipper, B. Butscher, J. Balewski, V. Bend- kowsky, R. L¨ ow,et al., A homonuclear molecule with a permanent electric dipole moment, Science 334, 1110 (2011)

    2011

  3. [11]

    Alth¨ on, M

    M. Alth¨ on, M. Exner, R. Bl¨ attner, and H. Ott, Exploring the vibrational series of pure trilobite Rydberg molecules, Nat. Commun. 14, 8108 (2023)

    2023

  4. [12]

    Niederpr¨ um, O

    T. Niederpr¨ um, O. Thomas, T. Eichert, C. Lippe, J. P´ erez-R ´ ıos, C. H. Greene, and H. Ott, Observation of pendular butterfly Rydberg molecules, Nat. Commun. 7, 12820 (2016)

    2016

  5. [13]

    Hummel, C

    F. Hummel, C. Fey, and P. Schmelcher, Alignment of s- state Rydberg molecules in magnetic fields, Phys. Rev. A 99, 023401 (2019)

    2019

  6. [14]

    Gonz´ alez-F´ erez, H

    R. Gonz´ alez-F´ erez, H. Sadeghpour, and P. Schmelcher, Rotational hybridization, and control of alignment and orientation in triatomic ultralong-range Rydberg molecules, New J. Phys. 17, 013021 (2015)

    2015

  7. [15]

    A. T. Krupp, A. Gaj, J. B. Balewski, P. Ilzh¨ ofer, S. Hof- ferberth, R. L¨ ow, T. Pfau, M. Kurz, and P. Schmelcher, Alignment of D-state Rydberg molecules, Phys. Rev. Lett. 112, 143008 (2014)

    2014

  8. [16]

    S. T. Rittenhouse and H. Sadeghpour, Ultracold gi- ant polyatomic Rydberg molecules: coherent control of molecular orientation, Phys. Rev. Lett. 104, 243002 (2010)

    2010

  9. [17]

    S. T. Rittenhouse, M. Mayle, P. Schmelcher, and H. Sadeghpour, Ultralong-range polyatomic Rydberg molecules formed by a polar perturber, J. Phys. B: At., Mol. Opt. Phys. 44, 184005 (2011)

    2011

  10. [18]

    A. Gaj, A. T. Krupp, J. B. Balewski, R. L¨ ow, S. Hof- ferberth, and T. Pfau, From molecular spectra to a den- sity shift in dense Rydberg gases, Nat. Commun. 5, 4546 (2014)

    2014

  11. [19]

    C. Fey, J. Yang, S. T. Rittenhouse, F. Munkes, M. Baluk- tsian, P. Schmelcher, H. R. Sadeghpour, and J. P. Shaf- fer, Effective three-body interactions in Cs(6 s) − Cs(nd) Rydberg trimers, Phys. Rev. Lett. 122, 103001 (2019)

    2019

  12. [20]

    P. J. Luukko and J.-M. Rost, Polyatomic trilobite Ryd- berg molecules in a dense random gas, Phys. Rev. Lett. 119, 203001 (2017). 9

    2017

  13. [21]

    Butscher, V

    B. Butscher, V. Bendkowsky, J. Nipper, J. B. Balewski, L. Kukota, R. L¨ ow, T. Pfau, W. Li, T. Pohl, and J. M. Rost, Lifetimes of ultralong-range Rydberg molecules in vibrational ground and excited states, J. Phys. B: At., Mol. Opt. Phys. 44, 184004 (2011)

    2011

  14. [22]

    Junginger, J

    A. Junginger, J. Main, and G. Wunner, Quantum- classical lifetimes of Rydberg molecules, J. Phys. B: At., Mol. Opt. Phys. 46, 085201 (2013)

    2013

  15. [23]

    Camargo, J

    F. Camargo, J. Whalen, R. Ding, H. Sadeghpour, S. Yoshida, J. Burgd¨ orfer, F. Dunning, and T. Kil- lian, Lifetimes of ultralong-range strontium Rydberg molecules, Phys. Rev. A 93, 022702 (2016)

    2016

  16. [24]

    Whalen, S

    J. Whalen, S. Kanungo, Y. Lu, S. Yoshida, J. Burgd¨ orfer, F. Dunning, and T. Killian, Heteronuclear Rydberg molecules, Phys. Rev. A 101, 060701 (2020)

    2020

  17. [26]

    Peper and J

    M. Peper and J. Deiglmayr, Heteronuclear long-range Rydberg molecules, Phys. Rev. Lett. 126, 013001 (2021)

    2021

  18. [27]

    Wojciechowska, M

    A. Wojciechowska, M. Tomza, and M. T. Eiles, Ultralong-range Rydberg molecules of Hg atoms, arXiv preprint arXiv:2412.05025 (2024)

    2024 arXiv

  19. [28]

    Peper and J

    M. Peper and J. Deiglmayr, Formation of ultracold ion pairs through long-range rydberg molecules, J. Phys. B: At., Mol. Opt. Phys. 53, 064001 (2020)

    2020

  20. [29]

    Giannakeas, M

    P. Giannakeas, M. T. Eiles, F. Robicheaux, and J. M. Rost, Dressed ion-pair states of an ultralong-range ryd- berg molecule, Phys. Rev. Lett. 125, 123401 (2020)

    2020

  21. [30]

    M. T. Eiles, Trilobites, butterflies, and other exotic spec- imens of long-range Rydberg molecules, J. Phys. B: At., Mol. Opt. Phys. 52, 113001 (2019)

    2019

  22. [31]

    Fermi, Sopra lo spostamento per pressione delle righe elevate delle serie spettrali, Nuovo Cim 11, 157 (1934)

    E. Fermi, Sopra lo spostamento per pressione delle righe elevate delle serie spettrali, Nuovo Cim 11, 157 (1934)

    1934

  23. [32]

    Omont, On the theory of collisions of atoms in Ryd- berg states with neutral particles, J

    A. Omont, On the theory of collisions of atoms in Ryd- berg states with neutral particles, J. De. Phys. 38, 1343 (1977)

    1977

  24. [33]

    E. L. Hamilton, C. H. Greene, and H. Sadeghpour, Shape-resonance-induced long-range molecular Rydberg states, J. Phys. B: At., Mol. Opt. Phys. 35, L199 (2002)

    2002

  25. [34]

    M. T. Eiles, Formation of long-range Rydberg molecules in two-component ultracold gases, Phys. Rev. A 98, 042706 (2018)

    2018

  26. [35]

    Khuskivadze, M

    A. Khuskivadze, M. Chibisov, and I. Fabrikant, Adia- batic energy levels and electric dipole moments of Ry- dberg states of Rb 2 and Cs 2 dimers, Phys. Rev. A 66, 042709 (2002)

    2002

  27. [36]

    Bahrim, U

    C. Bahrim, U. Thumm, and I. Fabrikant, 3Se and 1Se scattering lengths for e −+ Rb, Cs and Fr collisions, J. Phys. B: At., Mol. Opt. Phys. 34, L195 (2001)

    2001

  28. [37]

    Bahrim, U

    C. Bahrim, U. Thumm, and I. Fabrikant, Negative- ion resonances in cross sections for slow-electron–heavy- alkali-metal-atom scattering, Phys. Rev. A 63, 042710 (2001)

    2001

  29. [38]

    T. F. O’Malley, L. Rosenberg, and L. Spruch, Low-energy scattering of a charged particle by a neutral polarizable system, Phys. Rev. 125, 1300 (1962)

    1962

  30. [39]

    M. D. Gregoire, I. Hromada, W. F. Holmgren, R. Trubko, and A. D. Cronin, Measurements of the ground-state po- larizabilities of Cs, Rb, and K using atom interferometry, Phys. Rev. A 92, 052513 (2015)

    2015

  31. [40]

    ˇSibali´ c, J

    N. ˇSibali´ c, J. D. Pritchard, C. S. Adams, and K. J. Weatherill, Arc: An open-source library for calculating properties of alkali Rydberg atoms, Computer Physics Communications 220, 319 (2017)

    2017

  32. [41]

    J. J. Sakurai, S. Fu Tuan, and R. G. Newton, Modern quantum mechanics (1986)

    1986

  33. [42]

    Tallant, S

    J. Tallant, S. Rittenhouse, D. Booth, H. Sadeghpour, and J. Shaffer, Observation of blueshifted ultralong-range Cs2 Rydberg molecules, Phys. Rev. Lett. 109, 173202 (2012)

    2012

  34. [43]

    Manthey, T

    T. Manthey, T. Niederpr¨ um, O. Thomas, and H. Ott, Dynamically probing ultracold lattice gases via Rydberg molecules, New J. Phys. 17, 103024 (2015)

    2015

  35. [44]

    Whalen, R

    J. Whalen, R. Ding, S. Kanungo, T. Killian, S. Yoshida, J. Burgd¨ orfer, and F. Dunning, Formation of ultralong- range fermionic Rydberg molecules in 87Sr: role of quan- tum statistics, Molecular Physics 117, 3088 (2019)

    2019

  36. [45]

    Whalen, S

    J. Whalen, S. Kanungo, R. Ding, M. Wagner, R. Schmidt, H. Sadeghpour, S. Yoshida, J. Burgd¨ orfer, F. Dunning, and T. Killian, Probing nonlocal spatial cor- relations in quantum gases with ultra-long-range Ryd- berg molecules, Phys. Rev. A 100, 011402 (2019)

    2019

  37. [46]

    D. A. Anderson, S. A. Miller, and G. Raithel, Photoasso- ciation of long-range nd Rydberg molecules, Phys. Rev. Lett. 112, 163201 (2014)

    2014

  38. [47]

    Saßmannshausen, F

    H. Saßmannshausen, F. Merkt, and J. Deiglmayr, Ex- perimental characterization of singlet scattering channels in long-range Rydberg molecules, Phys. Rev. Lett. 114, 133201 (2015)

    2015

  39. [48]

    B¨ ottcher, A

    F. B¨ ottcher, A. Gaj, K. M. Westphal, M. Schlagm¨ uller, K. S. Kleinbach, R. L¨ ow, T. C. Liebisch, T. Pfau, and S. Hofferberth, Observation of mixed singlet-triplet Rb 2 Rydberg molecules, Phys. Rev. A 93, 032512 (2016)

    2016

  40. [49]

    Exner, R

    M. Exner, R. Srikumar, R. Bl¨ attner, M. T. Eiles, P. Schmelcher, and H. Ott, High precision spec- troscopy of trilobite Rydberg molecules, arXiv preprint arXiv:2412.19710 (2024)

    2024 arXiv

  41. [50]

    I. C. Liu and J. M. Rost, Polyatomic molecules formed with a Rydberg atom in an ultracold environment, Eur. Phys. J. D.-At., Mol., Opt. Plasma Phys. 40, 65 (2006)

    2006

  42. [51]

    I. C. Liu, J. Stanojevic, and J. M. Rost, Ultra-long-range Rydberg trimers with a repulsive two-body interaction, Phys. Rev. Lett. 102, 173001 (2009)

    2009

  43. [52]

    C. Fey, F. Hummel, and P. Schmelcher, Building principle of triatomic trilobite Rydberg molecules, Phys. Rev. A 99, 022506 (2019)

    2019

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.