Hyperfine lifting of parity degeneracy and the question of inversion in a rigid molecule

Butcher, R.J.; Chardonnet, Ch.; Bordé, Ch. J.

doi:10.1103/physrevlett.70.2698

Cited by 14 publications

(16 citation statements)

References 18 publications

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“…For isolated E lines no such splitting is observed, e.g., R͑17͒E 0 . This is comparable to what was observed for the u-g splittings in SF 6 [2,3,9,10] but different from the PH 3 case for which an E splitting was observed for an isolated line [11]. To understand these differences, we analyze below the structure of the wave functions in these various cases.…”

Section: Hyperfine-induced Lifting Of Parity Degeneracy In Noninvertisupporting

confidence: 75%

Hyperfine-Induced Lifting of Parity Degeneracy in Noninverting Molecules

1996

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We report experimental evidence for the splitting of E levels in 28 SiF 4 , which are degenerate in parity as far as the rovibrational Hamiltonian solely is concerned. The parity degeneracy of rovibrational levels is in fact lifted by hyperfine interactions, even though the associated total spin is I 0. We compare this situation with that in other molecules (SF 6 and PH 3 ) for which similar effects have already been reported. We also predict the splitting of the P͑7͒ E 0 ͑6͒ line of 12 CH 4 , a resonance used currently as a frequency standard, assumed up to now to be perfectly degenerate. [S0031-9007(96)00392-4] PACS numbers: 33.20. Ea, 33.25.+k Inversion of all space coordinates of every particle belonging to a given physical system is a relevant symmetry as long as weak interactions are not taken into account. Two stationary states completely identical, but for parity, in a semirigid (i.e., noninverting) molecule, should be perfectly degenerate. Such parity degenerate molecular states thus represent excellent candidates to detect a parity violating interaction, which should result in their splitting.We have observed such a splitting of parity degenerate E states of the molecule 28 SiF 4 . Although the total spin of the fluorines is zero, we show that hyperfine couplings with neighboring states are responsible for this splitting. A similar lifting of parity degeneracy has already been observed in the spectrum of SF 6 and PH 3 . We analyze in detail the different mechanisms involved. We point out that, in all cases, the Pauli principle forbids the existence of identical states but for parity in such molecules, and, thus, any degeneracy may be removed by mechanisms different from inversion and weak interactions.Extensive saturation spectra of the n 3 vibration-rotation band of 28 SiF 4 have been recorded in our laboratory with our ultrahigh resolution saturation spectrometer [1][2][3][4][5]. The current linewidth for these spectra was 1.5 kHz. We have used various isotopic species of CO 2 and a microwave electrooptic modulation technique [5] in order to increase the spectral coverage. In previous studies of SiF 4 [6], the hyperfine structure of the lines could not be resolved. Figures 1 and 2 display, respectively, the hyperfine structures of the R͑34͒F 0 1͑2͒ E 0 F 0 1͑1͒ and P͑22͒A 1 2͑1͒ F 5 1͑2͒ E 3 superfine clusters. It is well known that the Pauli principle limits drastically the number of existing states: The F 1 and A 2 rovibrational states are associated with total nuclear spins I respectively equal to 1 and 2 and give rise to partly resolved triplets and quintuplets in these spectra; moreover, only one of the two parity states is allowed. On the other hand, E states are associated with I 0 and may have both parities [7,8]. The observed splitting of the E lines correspond necessarily to the two parity labels. As we shall see, this degeneracy removal is related to the neighbor hyperfine states (with a symmetric neighborhood for Fig. 1 and an asymmetric one for Fig. 2). For isolated E lines no such ...

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Section: Hyperfine-induced Lifting Of Parity Degeneracy In Noninvertisupporting

confidence: 75%

Hyperfine-Induced Lifting of Parity Degeneracy in Noninverting Molecules

1996

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“…However, because these hyperfine matrix elements conserve l, they do not appear on the diagonal of the Hamiltonian matrix, contrary to the argument presented in Ref. [12]. The nature of the parity doubling mechanism in this PH 3 spectrum seems to be an open question at this point.…”

Section: Introductioncontrasting

confidence: 65%

“…1 of Ref. [12], the upper state was made up primarily of the basis function |v 4 = 1, J = 9, kl = 3 , but had a significant admixture of |v 4 = 1, J = 9, kl = −1 . The energy doubling was attributed to the ( k = ±2) hyperfine matrix elements acting through the (K = 1) component.…”

Section: Introductionmentioning

confidence: 97%

“…The splitting was explained by the ( k = ±2) matrix elements of the chlorine quadrupole interaction and strong l-type resonance effects between basis functions with G = 1. In 1993, the ν 4 band of PH 3 in the 10 µm region was studied with a linewidth of 3 kHz using saturation spectroscopy [12]. In this case, there was no quadrupole interaction, but still the hyperfine structure was completely resolved.…”

Section: Introductionmentioning

confidence: 99%

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Anomalous hyperfine structure of NSF3in the degenerate vibrational statev5=1: Lifting of the parity degeneracy by the

et al. 2010

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For the principal isotopologue 14 N 32 S 19 F 3 of thiazyl trifluoride in the degenerate fundamental state (v 5 = 1), the hyperfine structure has been investigated in the Q-branch spectrum between 8 and 26.5 GHz using microwave Fourier transform waveguide spectrometers with a resolution limit of ≈30 kHz. In addition to l-type doubling spectra and l-type resonance transitions with ( k = l = ±2), perturbation-allowed spectra were measured with (k − l) = ±3, ±6. The range in J was from 13 to 61; for the lower states, kl = −3, −2, −1, 0, +1. For all the transitions, the hyperfine patterns observed are predicted to be doublets when only the nitrogen quadrupole Hamiltonian H N Q is taken into account. Doublets were indeed measured for transitions with RV = A 1 ↔ A 2 , where RV is the rovibrational symmetry. However, when RV = E ↔ E, triplets and quartets were observed in addition to doublets. These anomalous hyperfine patterns are shown to be due to the ( k = ±1) and ( k = ±2) matrix elements of the fluorine spin-rotation Hamiltonian H F SR characterized by the fluorine spin-rotation constants c(1) = 1 2 (c xz + c * zx ) and c(2) = 1 2 (c xx − c yy ), respectively. These terms in H F SR lift the parity degeneracy for RV = E. The rovibrational Hamiltonian H RV was adopted from an earlier partner study [S. Macholl et al., J. Phys. Chem. A 113, 668 (2009)]. A good fit to the hyperfine data was obtained with a standard deviation of 3.1 kHz. In the fitting process, 12 rovibrational parameters were varied, while the remaining constants in H RV were left at the values of Macholl et al. In addition, six hyperfine parameters were determined: four in H N Q , and two in H F SR . It was found that |c(1)| = 7.48(24) kHz and |c(2)| = 2.423 (22) kHz. This determination of c(1) is the first to be reported based on frequency measurements. In all the previous detections of parity doubling where the splittings were accounted for quantitatively, the levels involved had K = |k| = 1 in studies of the ground vibrational state or G ≡ |k − l| = 1 in investigations of degenerate vibrational states. In the current work, several different values of G were involved, thus demonstrating experimentally for the first time that this splitting process is a general phenomenon. The key to the observation of the parity doubling lies in the regional resonances discovered by Macholl et al. The clustering of rovibrational levels at low K leads to severe mixing. For each eigenstate involved in a regional resonance, the eigenstate consists of a linear superposition of basis vectors with several different values of kl having sizable expansion coefficients. As a result, the ( k = ±1, ±2) matrix elements of H F SR that typically connect levels widely separated in energy occur here effectively on the diagonal, thereby greatly enhancing the effects of c(1) and c(2). These spin-rotation matrix elements are derived here for RV = E in the low-field representation.

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“…The current standard at 30THz is provided by the CO 2 laser locked onto a saturated absorption resonance of OsO 4 in a cell, the reference signal having full width half maximum (FWHM) of 20 kHz [1,2]. The same area is particularly rich in molecular spectra and many problems in this area, together with questions of fundamental physics, have been investigated using the related saturation spectroscopy [3,4]. Typical linewidths are 1-100 kHz.…”

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confidence: 99%

Two-photon Ramsey fringes at 30 THz referenced to an H maser/Cs fountain via an optical-frequency comb at the 1-Hz level

Shelkovnikov

Grain

Butcher

et al. 2004

IEEE J. Quantum Electron.

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Index Terms--Carbon dioxide lasers, Frequency stability, SF 6 , Optical frequency standard. I. INTRODUCTIONThe carbon dioxide laser has given to the 30 THz spectral region particular significance in frequency metrology. The current standard at 30THz is provided by the CO 2 laser locked onto a saturated absorption resonance of OsO 4 in a cell, the reference signal having full width half maximum (FWHM) of 20 kHz [1,2]. The same area is particularly rich in molecular spectra and many problems in this area, together with questions of fundamental physics, have been investigated using the related saturation spectroscopy [3,4]. Typical linewidths are 1-100 kHz. This paper presents continuing work on a two-photon Ramsey fringe experiment on a supersonic beam of SF 6 with the objectives, now essentially realized, of resolving the entire complex hyperfine structure over some 50 kHz and establishing absolute frequencies at the 1Hz level. Both aspects represent huge advances over cell saturation techniques. Two experimental developments have led to the recent advances. First, the distance between the absorption zones has been increased to 1m, so that the fringe periodicity is now 200 Hz for pure SF 6 . Data is routinely recorded with a signal-to-noise ratio (SNR) of 20 in a bandwidth of 1 Hz. The implied limit on the resolution of two components within the hyperfine structure of the SF 6 spectrum is only 10Hz. This is indeed found when fringe patterns are fitted. Second the entire system can now be directly related to the frequency comb of a femtosecond laser, itself referenced to a Hydrogen maser. The maser is compared to a Caesium fountain and to the GPS system. This gives a long-term stability and frequency reproducibility limited by the performance of the current electronics, various optical links and, possibly, the reference maser. The fs technology is necessarily operated in a new area of precision, comparable with the best currently in use [5,6]. Figure 1 gives a block outline of the entire experiment.Two related series of experiments are presented. First the central Ramsey fringe is employed as the reference point for a molecular clock; the clock frequency is measured, and its performance established, relative to the H maser. Second, and separately, Ramsey fringes are measured on an absolute frequency scale provided by the H maser. This gives a second measurement of the central fringe and the entire spectrum of Ramsey fringes over 50 kHz is put onto an absolute frequency scale.This work is partly directed at a new frequency standard. Since a two-photon transition is used the absolute frequency depends on the optical power. Given the absolute scale, this small effect can be investigated and results are reported.

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Hyperfine lifting of parity degeneracy and the question of inversion in a rigid molecule

Cited by 14 publications

References 18 publications

Hyperfine-Induced Lifting of Parity Degeneracy in Noninverting Molecules

Hyperfine-Induced Lifting of Parity Degeneracy in Noninverting Molecules

Anomalous hyperfine structure of NSF3in the degenerate vibrational statev5=1: Lifting of the parity degeneracy by the

Two-photon Ramsey fringes at 30 THz referenced to an H maser/Cs fountain via an optical-frequency comb at the 1-Hz level

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