The cooling prospect of the hydrogenated nitrogen ions for quantum defect integration

Masatomi Iizawa ^* Yasuhito Narita

• Technical University of Braunschweig, Braunschweig, Germany

Diamond nitrogen-vacancy (NV) color centers and other point defects are promising candidates for solidstate qubits, but there are problems with their integration [1,2]. Recently, a one-by-one irradiation device with positional accuracy of dopant atoms on the Ångström order has been developed [3,4,5] or is under development [6,7,8,9]. However, the dopant atom X n+/-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 XH n+/m 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 NH n+/m to achieve the integration of the most studied quantum defect, the NV center. We summarize the chemical stability of each hydrogenated nitrogen, both electronic ground state and 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 are excluded, e.g., vibrational transitions that do not involve electronic transitions.1 2 Π 1 2 Σ + v' = 0 v' = 1 v' ' = 0 v' ' = 1 v' ' = 3v' ' = 4 λ 00 = 438.5 nm λ 1 3 = 5 9 8 . 9 n m f 00 = 0.821 f 0 1 = 0 . 1 6 3f 0 3 + < × 1 0 -4 f 1 0 = 0 . 1 5 4 f 1 1 = 0 . 4 9 0 f 12 = 0.301 f 1 3 + < × 1 0 - 2 λ 12 = 517.3 nm λ 0 1 = 5 0 2 . 5 n m = 517.3 nm f 0 2 = 1 . 4 8 × 1 0 -2 Figure 1. Energy levels of NH + cited from [14]. f ij 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 438.5 nm is needed.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.The hydrogenated nitrogen, namely the hydronitrogenN l H n+/- m, 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 in Tables 1 and2.The monovalent cations or monocations (n = 1) such as NH + , NH + 2 , NH + 3 , and NH + 4 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 is1 2 Π (v ′′ = 0) ↔ 1 2 Σ + (v ′ = 0) with the light of 438.5 nm (see fig. 1) and the temperature estimated to be achieved to 6.63 µK [14].The amidogen cation NH + 2 has the electronic states X 3 B 1 , ã 1 A 1 , b 1 B 1 , and c 1 Σ + g in order from the ground state [15]. However, X 3 B 1 → ã 1 A 1 is spin-forbidden. In addition, transitions between ã 1 A 1 , b 1 B 1 , and c 1 Σ + g are allowed transitions, but the potential energy curve for b 1 B 1 already has no local minima [16]. Therefore, NH + 2 is not laser-coolable.The electronic structure of NH + 3 on the ground state X 2 A ′′ 2 and the first excited state à 2 E are investigated both experimentally and theoretically. The transitionX 2 A ′′ 2 → à 2 E is optical allowable, however à 2 Ehave 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 NH + 4 . However, the rotational spectrum ν 3 band with vibrational transitions is well studied [18,19,20,21,22,23,24,25]. Such vibrational transitions could be used for cooling using near-ultraviolet lasers. Future research is desired.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 XY 2+ can be briefly evaluated by the large value of∆ := I(X) -I(Y + ),(1)where I is the ionization energy i.e. 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 A 2+ + B is placed at a position well below the curve of A + + B + . Since 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], then there is still a possibility that NH 2+ is stable.However, NH 2+ is predicted to dissociate spontaneously, according to the calculation of ab initio molecular orbital (MO) theory [29]. The dissociation study from NH 2+ 3 [30] also pointed out NH 2+ is unstable. There have been reports of observing a long-lived state [31], but NH 2+ is not a candidate for cooling because even the ground state is metastable.▶ NH 2+ 2 (di-hydrogenation, divalence cation) NH 2+2 was observed by charge stripping using neutral gas [32] and by electron impact [33,30,34].There are some theoretical reports on the calculation regarding the electronic ground state [35,36,29,37] and excited states [38]. There is also an experimental report that an excited state of NH 2+ 2 has been observed [34]. This excited state was caused by a collision with helium, resulting in a transition ofX 2 A 1 ( 2 Π u ) → 2 A 1 ( 2 Σ + g ). 2 Σ +g was thought to be the first electronic excited state, but later theoretical research has suggested that there is a lower excited state than 2 Σ + g [38]. NH 2+ 2 can take chemically (quasi-)stable excited states. Research on these excited states is inadequate, and there has been no progress for over 30 years. Further research is desired in the future.▶ NH 2+ 3 (tri-hydrogenation, divalence cation)NH 2+3 is the most well-investigated dication of the hydronitrogen. NH 2+ 3 was experimentally found through electron impact ionization [39,40,33,30,41,42,43] and photoionization by synchrotron radiation [44,45,46,47,48,49] and by the other photon sources [50,51,52]. Auger electron spectroscopy (AES) [53,54,55] and doubly charged transfer spectroscopy (DCT spectroscopy, DCS) [56,57,58] were also carried out, and there are several theoretical works [59,60,61,62,29,63,64,65,66,67,47,48,49].The dissociation studies from highly excited rovibrational states or excited electronic states of NH 2+ 3 [30,44,41,46,48,49,68,43] are useful for considering the stability of the cooling cycle. The excited states of NH 2+ 3 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 NH 2+ 3 . Since divalent ions are convenient for high energy irradiation, NH 2+ 3 should be thoroughly investigated in the future.▶ NH 2+ 4 (tetra-hydrogenation, divalence cation)NH 2+4 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 NH 2+ 4 by the charge striping with neutral gas and instantly dissociate toNH + 3 + H + [32]. NH 2+ 4is chemically unstable and therefore not a cooling target.For NH 3+ 2 , no reports were found for both experiments and calculations. There is a dissociation study of NH n+ 3 (n = 3, 4, 5) obtained by polyvalent argon irradiation [70], and NH 3+ 3 was obtained by ionization by proton irradiation [68]. These reports show that NH 3+ 3 should be dissociated, which means unstable. As CC calculation [69], there is no local minimum on the potential energy curve of NH 3+ 4 , then NH 3+ 4 does not even have a metastable state. This result is not surprising, as even NH 2+ 4 was unstable.At first, the polyvalence anion is discussed. The reports of dianions, i.e. divalent anions, are mostly related to large organic molecules, and the relatively small ones are AX 2- 3 (A = Li, Na, K and X = F, Cl), which is a compound of alkali metals and halogens [71,72], EX 2- 4 (E = Be, Mg and X = 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], then NH -should not be a cooling candidate.The ground state of NH - 2 is known as stable [77]. NH - 2 is autodetached through photoelectron spectroscopy of the X 1 A 1 → 1 B 1 transition excited by 3.408 eV photon [77]. It is not known whether 1 B 1 is the lowest excited state.Table 1. Investigation status of the stability of the hydrogenated nitrogen cations NH n+ m . 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. The stability report of NH - 3 cannot be found because all of the p subshells in N are half-filled, so four more electrons are difficult 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, NH - 3 cannot be used for cooling.▶ NH - 4 (tetra-hydrogenation, monovalence anion)While NH - 3 is unstable, NH - 4 is stabilized in two forms: H -(NH 3 ) 1 , which is stabilized by the ion-dipole interaction [78,79,80,81,82], and NH - 4 as a double Rydberg anion (DBA), which is stabilized by the two Rydberg-like electrons attached to NH + 4 [83,84,85,86,80,87,88,89,90,81,82]. The dissociation studies of H -(NH 3 ) 1 and NH - 4 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.The above discussion can be summarized in Table 1 for the cations and Table 2 for the anions. The 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 in the last 30 years, calculations using large basis sets have become practically feasible. Ab initio calculations are the first step in the study of Doppler cooling. We then 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 [91,92,93,94]. 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 updating 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.