Assessing the time constancy of the proton-to-electron mass ratio by precision ro-vibrational spectroscopy of a cold molecular beam

TLDR: In this paper, the authors present an experiment that aims to constrain, over a few-year timescale, the fractional temporal variation of the proton-to-electron mass ratio, β = mp/me, at a level of 10 −15 /yr by means of a spectroscopic frequency measurement on a beam of cold CF3H molecules.

About: This article is published in Journal of Molecular Spectroscopy.The article was published on 2014-06-01 and is currently open access. It has received 21 citations till now. The article focuses on the topics: Proton-to-electron mass ratio & Molecular beam.

Figures

Figure 2: Buffer gas cooling apparatus.

Figure 1: CF3H two-photon transition selected for the Ramsey interrogation. The symbol ⊥ indicates that the vibrational transition moment is perpendicular to the top axis; accordingly, the following selection rules hold: ∆K ≡ Ki − Kf = ±1; ∆J = 0,±1. In addition, for (A1 → E)-type transitions, the following selection rules are valid for the quantum number l: ∆l = +1 for ∆K = −1; ∆l = −1 for ∆K = +1; the reverse is true for (E → A1)-type transitions.

Figure 3: Upper frame: electrostatic-hexapole-lens realization by means of six rod electrodes, with radius rrod, symmetrically arranged at distance r0 from the beam z axis. Lower frame: energy of the CF3H |J = 1,K = 1,ME = −1⟩ level in an external electric field, evidencing the linear behavior below 2.5 kV/mm and the lfs-to-hfs transition around 6 kV/mm.

Table 1: Relevant BGC parameters for a CF3H beam produced in the partially hydrodynamic regime. (⋆) 1 SCCM ≃ 4.5 · 1017 molec/s.

Figure 4: Schematic layout of whole experimental apparatus. The following legend holds: DC=dispersion compensation, SCG=supercontinuum generation, AOM=acoustooptic modulator, LO=local oscillator, MCT=HgCdTe detector, SLE=servo loop electronics, D=InGaAs detector, M=mixer.

Frequently asked questions

Q1. What have the authors contributed in "Assessing the time constancy of the proton-to-electron mass ratio by precision ro-vibrational spectroscopy of a cold molecular beam" ?

The authors report the design of an experiment that aims to constrain, over a-fewyear timescale, the fractional temporal variation of the proton-to-electron mass ratio, β = mp/me, at a level of 10 −15/yr by means of a spectroscopic frequency measurement on a beam of cold CF3H molecules. 

Q2. What is the prime target of the atomic/molecular transitions?

The prime target is the fine structure constant, α = e2/(4πε0~c), which defines the scale of quantum electrodynamics; the second prominent quantity is the proton-to-electron mass ratio, β = mp/me, which characterizes the strength of strong interaction in terms of the electro-weak one. 

Q3. What is the effect of a few collisions on the thermal speed?

While preserving the low temperature, these few collisions will have the effect of lowering the boosted forward velocity of the molecules closer to the thermal speed. 

Q4. What is the effect of a low-field seeking state?

for sufficiently intense electric fields, all rotational levels become high-field seeking (hfs); the corresponding states are deflected away from the z axis and will eventually be lost. 

Q5. What is the effect of the BGC on the molecule?

Since BGC operates with nearly all species, potentially any molecule with a relatively high electric dipole moment (EDM) and a favorable two-photon transition may be chosen for the experiment. 

Q6. What is the up-to-date constraint for /?

The most up-to-date constraint for ∆β/β is (0.0±1.0) ·10−7, deduced from the observation of radio-frequency transitions of methanol in the PKS1830-211 galaxy at redshift z = 0.89 (corresponding to a look-back time of 7 billion years). 

Q7. How many spectroscopic studies are planned for fluoroform?

In the meantime, after carrying out preliminary Fourier-Transform Infrared (FTIR) spectroscopy, high-resolution spectroscopic studies of fluoroform are planned in order to gain a deeper knowledge of the 8.63-µm spectrum. 

Q8. What is the way to measure the / of the beam?

Starting with the molecular sample, the beam emerging from the BGC source will be soon characterized either by Resonance-Enhanced Multi-Photon Ionization (REMPI) or Cavity RingDown (CRD) spectroscopy. 

Q9. What is the effect of an EHL on the beam?

For larger V0 values, higher perturbative orders in the Stark interaction energy must be considered, whereupon the effect of an EHL is no longer simply described by Eq. 22. 

Q10. What is the relationship between KS and KCs?

KS and KCs are proportionality constants, µCs is the magnetic dipole of the Cs nucleus, µB the Bohr magneton, Ry the Rydberg constant, and F (α) is a dimensionless function accounting for relativistic effects in Cs, whose dependence on α is to the power of 0.83. 

Q11. What is the rovibrational band of CF3H?

it has a fundamental, strong rovibrational band (CF3 degenerate stretch, υ5) at 8.63 micron (1158.75 cm−1) [21], where high-performance quantum cascade lasers (QCLs) are available and effective optical frequency combs can be developed. 

Q12. Why can't the beam parameters be characterized and optimized?

In this case, due to the lack of a reliable prediction model, the main beam parameters can only be characterized and optimized through comprehensive experimental investigations. 

Q13. What is the frequency-dependent amplitude of the QCL beam?

Concerning the frequency-dependent amplitude, it can be expressed as D20(ω) = µ21µ10|E|2/[~2(ω10 − ω)] ≡ −µ21µ10|E|2/(~δ), where ω10 ≡ [Ero−vib(|1⟩) − Ero−vib(|0⟩)]/~, |E|2 is proportional to the intensity of the Ramsey laser beam, and µ21 (µ10) denotes the dipole matrix element corresponding to the transition |2⟩ ↔ |1⟩ (|1⟩ ↔ |0⟩). 

Q14. What is the probability of finding a molecule in the state of a symmetrictop?

In the case of a symmetrictop molecule, and considering the electronic and vibrational ground states, e ≡ eg and υg ≡ (0, 0, 0, 0, 0, 0), one can safely assume peg ≃ pυg ≃ 1 and then writepeg ,υg ,r ≃ peg · pυg · pJ,K ≃ pJ,K(T ) = gJ,Ke −EJ,K/kBT∑ J,K gJ,Ke−EJ,K/kBT (8)where EJ,K ≡ E(J,K) is the rotational energy defined above and gJ,K the corresponding degree of degeneracy. 

Q15. What is the energy of a given ro-vibrational level?

To determine the detuning δ of the virtual level from the intermediate one, the authors start with the general consideration that the energy of a given ro-vibrational level is the sum of a vibrational and a rotational term, Ero−vib = Evib + Erot. 

Q16. What is the spectral spectra of the DFG pump?

More in detail, the DFG pump laser beam comes from the main output which, consisting of an Er-doped fiber amplifier (EDFA) followed by a dispersion compensation system, provides 1.55-µm-wavelength pulses with a duration less than 70 fs and an average output power of 340 mW; the DFG signal beam comes from the second output that, comprising an independent EDFA plus a supercontinuum generation module, delivers an average output power greater than 300 mW over the entire spectrum (1050 − 2100 nm). 

Q17. What is the simplest way to minimize the fringe periodicity?

In this scheme one first wants to minimize the fringe periodicity P , given by the ratio of the mean longitudinal speed of the molecules in the beam, u, to the distance D between the two interaction zones: P = u/(2D). 

Q18. what is the speed of sound in an expanding gasa?

by inserting Eq. 13 into Eq. 12 and introducing the speed of sounda =√ γkBTm , (14)one derives the following expression for the sound velocity in an expanding gasa = a0√1 + γ − 1 2M2 (15)where the Mach number M = u/a has been introduced and a0 is the initial sound velocity, i.e. inside the cell (note that u0 = M0 = 0). 

Q19. How can the authors narrow the divergence figure to skim?

The divergence figure, as determined by Eq. 6, can be further narrowed down to ∆θskim by the use of a skimmer which, however, inevitably reduces the beam flux to Fskim; a good compromise is obtained using a 2-mm-input-diameter skimmer (2 cm length and 35◦ full aperture angle) placed at 3 cm from the cell hole. 

Q20. What is the price to pay for a decrease in the molecular beam flow?

The price to pay is a tenable decrease in the molecular beam flow (between 1 and 2 orders of magnitude), against a reduction in the longitudinal speed by some factor. 

Q21. What is the frequency-dependent probability for a molecule to be in the level?

As a result of the Ramsey excitation, the final, frequency-dependent probability for a molecule to be in the level |2⟩ is given byP(ω) ≃ B(ω) { A+ C cos ω − ω20/2P} (24)In the above equation, ω20 ≡ [Ero−vib(|2⟩)−Ero−vib(|0⟩)]