Front. Phys.Frontiers in PhysicsFront. Phys.2296-424XFrontiers Media S.A.152706210.3389/fphy.2025.1527062PhysicsOpinionThe cooling prospect of hydrogenated nitrogen ions for quantum defect integrationIizawa and Narita10.3389/fphy.2025.1527062IizawaMasatomi1*NaritaYasuhito121Institut für Theoretische Physik, Technische Universität Braunschweig, Braunschweig, Germany2Max Planck Institute for Solar System Research, Göttingen, Germany
Edited by:Mario Siciliani de Cumis, Italian Space Agency (ASI), Italy
Reviewed by:Somnath Bhowmick, The Cyprus Institute, Cyprus
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synthesizing quantum materialqubit integrationNV color centerlaser coolingPaul trapion micro beamdissociationautodetachmentsection-at-acceptanceAtomic and Molecular Physics1 Introduction
Diamond nitrogen-vacancy (NV) color centers and other point defects are promising candidates for solid-state qubits, but there are problems with their integration [1, 2]. Recently, a one-by-one irradiation device with the positional accuracy of dopant atoms on the Ångström order has been developed [3–5] or is under development [6–9]. However, the dopant atom Xn+/− is limited to be laser-coolable, and even the alternative method of sympathetic cooling has various problems as an irradiation device. Therefore, the hydrogenated molecules XHmn+/− could be focused on as irradiation ions because the hydrogenated ions have long attracted attention as laser-coolable molecules [10, 11], and proton irradiation does not have a negative effect on the substrate.
In this paper, we review the cooling prospects of hydrogenated nitrogen NHmn+/− to achieve the integration of the most studied quantum defect, the NV center. We summarize the chemical stability of each hydrogenated nitrogen, both the electronic ground state and the optically transitive excited states from the ground state. The term chemical stability here refers to no dissociation and, for anions, no autodetachment. Transitions excited by other than visible or near light, such as vibrational transitions that do not involve electronic transitions, are excluded.
We do not pursue the validity of the transition cycle for cooling, including Rosa’s three fundamental requirements for cooling molecules [10], because the electronic structure of most of the molecules listed here is not sufficiently investigated. We discuss which hydrogenated nitrogen should be the focus of future cooling research to develop precision irradiation.
2 Chemical stability of hydrogenated nitrogens
Hydrogenated nitrogen, namely, hydronitrogen NlHmn+/−, has a variety with l, m, and n as variables. For a one-by-one irradiation of nitrogen, the molecules must be composed of single nitrogens, so we will only consider l=1. The molecule of m>5 has not been found, and there is a density functional theory (DFT) calculation that m=5 is stable above 55 GPa [12]. Therefore, only m≤4 should be considered.
The following is a comprehensive description of previous research. It makes it clear that knowledge of the electronic structures of hydronitrogens is still insufficient to propose Doppler cooling schemes. The following section gives a concise summary of Tables 1 and 2.
Investigation status of the stability of the hydrogenated nitrogen cations NHmn+. Good candidates: the ions for which cooling proposals can be found. Unstable: the ions for which the ground state or the lowest excited state that can be optically transitive from the ground state are known to be unstable. Poorly documented: the others.
NHmn+
Ionization
1H
2H
3H
4H
+
Good candidate
Unstable
Poorly documented
Poorly documented
++
Unstable
Poorly documented
Poorly documented
Unstable
Higher
Poorly documented
Poorly documented
Unstable
Unstable
Investigation status of the stability of the hydrogenated nitrogen anions NHmn−. The legend is the same as Table 1.
The monovalent cations or monocations (n=1), such as NH+, NH2+, NH3+, and NH4+, are all stable at low temperatures and pressures [13]. A cooling proposal has already been published for NH+, one of the most promising candidates. The transition for cooling cycle is 12Π(v″=0)↔12Σ+(v′=0) with the light of 438.5 nm (see Figure 1), and the temperature estimated to be achieved to 6.63 µK [14].
Energy levels of NH+ cited from [14]. fij is a Franck–Condon factor from v′=i to v″=j. In the case of Sisyphus cooling, three lasers, 438.5 nm, 502.5 nm, and 517.3 nm, are required, but in our case of Doppler cooling of translational motion, only the 438.5 nm laser is needed.
The amidogen cation NH2+ has the electronic states X̃3B1, ã1A1, b̃1B1, and c̃1Σg+ in order from the ground state [15]. However, X̃3B1→ã1A1 is spin-forbidden. In addition, transitions between ã1A1, b̃1B1, and c̃1Σg+ are allowed transitions, but the potential energy curve for b̃1B1 already has no local minima [16]. Therefore, NH2+ is not laser-coolable.
The electronic structure of NH3+ on the ground state X̃2A2″ and the first excited state Ã2E are investigated both experimentally and theoretically. The transition X̃2A2″→Ã2E is optically allowable; however, Ã2E have rapid radiationless relaxation processes of 30 fs [17], which means that a simple cooling process that excites and de-excites between two levels cannot be constructed.
We could not find any studies on the electronic excited states of the ammonium ion NH4+. However, the rotational spectrum ν3 band with vibrational transitions is well studied [18–25]. Such vibrational transitions could be used for cooling using near-ultraviolet lasers. Future research is desired.
2.2 Divalent cations
The cooling feasibility of high-valence ions is rarely noticed. However, high-valence ions are more appropriate for precision irradiation applications because irradiating them can lower the acceleration voltage to achieve the same beam energy.
The stability of the dication of the diatomic molecule XY2+ can be briefly evaluated by the large value of the Δ in Equation 1:Δ:=IX−IY+,where I is the ionization energy; that is, I(X) is the first ionization energy of X, and I(Y+) is the second ionization energy of Y [26, 27]. This means that the energy potential curve of A2++B is placed at a position well below the curve of A++B+. Because the first ionization energy of hydrogen is 13.6 eV [28], the atoms with a second ionization energy sufficiently higher than 13.6 eV can form stable dications. The second ionization energy of nitrogen is 29.6 eV [28]. There is still a possibility that NH2+ is stable. However, NH2+ is predicted to dissociate spontaneously, according to the calculation of ab initio molecular orbital (MO) theory [29]. The dissociation study from NH32+ [30] also pointed out that NH2+ is unstable. There have been reports of observing a long-lived state [31], but NH2+ is not a candidate for cooling because even the ground state is metastable.
NH22+ was observed by charge stripping using neutral gas [32] and by electron impact [30, 33, 34]. There are some theoretical reports on the calculation regarding the electronic ground state [29, 35–37] and excited states [38]. There is also an experimental report that an excited state of NH22+ has been observed [34]. This excited state was caused by a collision with helium, resulting in a transition of X2A1(Πu2)→2A1(Σg+2). 2Σg+ was thought to be the first electronic excited state, but later theoretical research has suggested that there is a lower excited state than 2Σg+ [38]. NH22+ can take chemically (quasi-)stable excited states. Research on these excited states is inadequate, and there has been no progress for more than 30 years. Further research is desired in the future.
NH32+ is the most well-investigated dication of hydronitrogen. NH32+ was experimentally found through electron impact ionization [30, 33, 39–43], photoionization by synchrotron radiation [44–49], and by the other photon sources [50–52]. Auger electron spectroscopy (AES) [53–55] and doubly charged transfer spectroscopy (DCT spectroscopy, DCS) [56–58] were also carried out, and there are several theoretical works [29, 47–49, 59–67]. The dissociation studies from highly excited rovibrational states or excited electronic states of NH32+ [30, 41, 43, 44, 46, 48, 49, 68] are useful for considering the stability of the cooling cycle. The excited states of NH32+ have been well studied both experimentally and theoretically. However, their studies have been mainly motivated by the dissociation process through coincidence measurement. We could not find any studies on the existence of low-lying excited states, which are difficult to dissociate, or on the transitions between states of NH32+. Because divalent ions are convenient for high energy irradiation, NH32+ should be thoroughly investigated in the future.
NH42+ is predicted to be unstable as a MO calculation [29], multireference configuration interaction (MRCI) calculation [35, 36], and coupled cluster (CC) calculation [69]. There is a report to possibly generate NH42+ by the charge stripping with neutral gas and instantly dissociate to NH3++H+ [32]. NH42+ is chemically unstable and therefore not a cooling target.
2.3 Trivalent and higher valence cations
For NH23+, no reports were found for either experiments or calculations. There is a dissociation study of NH3n+(n=3,4,5) obtained by polyvalent argon irradiation [70], and NH33+ was obtained by ionization by proton irradiation [68]. These reports show that NH33+ should be dissociated, which means unstable. As CC calculation [69], there is no local minimum on the potential energy curve of NH43+; therefore, NH43+ does not even have a metastable state. This result is not surprising, as even NH42+ was unstable.
2.4 Anions
The polyvalence anion is first discussed. The reports of dianions, that is, divalent anions, are mostly related to large organic molecules, and the relatively small ones are AX32−(A=Li,Na,KandX=F,Cl), which is a compound of alkali metals and halogens [71, 72], EX42−(E=Be,MgandX=F,Cl), which is a compound of alkaline earth metals and halogens [73, 74], and a compound of metals and pseudohalogens CN [75]. Only molecules with strong correlations, such as metal-halide, may allow stable dianions. Therefore, we will only consider monovalent anions (n=1).
NH− is experimentally well investigated, and the ground states are chemically stable [76]. NH− realizes the similar transition as the prominent cooling candidate NH+, but NH− of the excited state is theoretically estimated to be neutralized by autodetachment [14]. Therefore, NH− should not be a cooling candidate.
The ground state of NH2− is known as stable [77]. NH2− is autodetached through photoelectron spectroscopy of the X̃1A1→1B1 transition excited by a 3.408 eV photon [77]. It is not known whether 1B1 is the lowest excited state.
The stability report of NH3− cannot be found because all of the p subshells in N are half-filled, so it is difficult for four more electrons to form a stable system with sufficient separation from each other. The possibility remains that there are states with finite lifetimes due to vibrational rotational degrees of freedom, but in any case, NH3− cannot be used for cooling.
While NH3− is unstable, NH4− is stabilized in two forms: H−(NH3)1, which is stabilized by the ion–dipole interaction [78–82], and NH4− as a double Rydberg anion (DBA), which is stabilized by the two Rydberg-like electrons attached to NH4+ [80–90]. The dissociation studies of H−(NH3)1 and NH4− have been well investigated. However, we could not find any research focusing on the electronic excited states that can be reached through optical transitions. Further research is needed.
3 Discussion and outlook
The above discussion is summarized in Table 1 for the cations and Table 2 for the anions. The electronic structures of the hydrogenated nitrogens have hardly been investigated. Although there have been previous studies on the cooling potential of NH+ and NH−, this does not mean that NH+ is the only promising candidate. The electronic structures of the ions listed here, namely, NHm+(m=1,3,4), NHm2+(m=2,3), NH23+, NHm−(m=2,4), and H−(NH3)1, have not yet begun to be studied other than NH+.
In order to investigate the cooling capability of hydrogenated nitrogens, the energy potential curves of the ground state and the optically transitive excited states should be derived by ab initio calculations. The study of some hydrogenated molecules stagnated for about 30 years, but more recently, calculations using large basis sets have become practically feasible. Ab initio calculations are the first step in the study of Doppler cooling. We strongly emphasize the importance of ab initio calculations of hydrogenated nitrides for integrating solid-state qubits. We encourage quantum chemistry theorists to conduct intensive research on hydrogenated nitrides.
As a next step, absorption, photoelectron, and various active spectra should be obtained over a wide range of wavenumbers for each hydrogenated nitrogen ion. In particular, because the energy levels of the excited state are difficult to match with the calculation results, the spectra must be scanned over a wide range. Obtaining such comprehensive data is less likely to produce immediate scientific results than the effort required for the experiment. Therefore, a cooling investigation driven by engineering and social demands to develop solid-state quantum devices is necessary. As with semiconductor research in the past, research based on engineering and social demands will lead to the development of science.
In addition, a method for analyzing the obtained large-scale spectral data should be developed. Currently, the rovibrational spectra of small molecules are assigned semi-manually using software such as pgopher [91–94]. For extensive data sets, semi-manual assignments are unrealistic. Modern pattern recognition techniques should be applied based on physical understanding. Furthermore, scientific software packages are often developed by individual researchers, and the development is sometimes not stable. pgopher also stopped being updated in 2022 because the author passed away. Standard assignment tools should be systematically developed to analyze large data sets.
The science of molecular cooling must assist in achieving the integration of the NV color centers. As we have discussed, the science of molecular cooling, at least of hydrogenated nitrogen, is not sufficiently advanced. We hope this will be a case where pure science evolves dramatically due to engineering needs.
Author contributions
MI: writing–original draft and writing–review and editing. YN: writing–review and editing.
Funding
The author(s) declare that financial support was received for the research and/or publication of this article. We acknowledge support by the Open Access Publication Funds of Technische Universität Braunschweig.
MI would like to thank K. Chartkunchand for insightful discussions.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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The author(s) declare that no Generative AI was used in the creation of this manuscript.
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