The CH radical offers a sensitive way to test the hypothesis that fundamental
constants measured on earth may differ from those observed in other parts of
the universe. The starting point for such a comparison is to have accurate
laboratory frequencies. Here we measure the frequency of the lowest
millimetre-wave transition of CH, near 535 GHz, with an accuracy of 0.6 kHz.
This improves the uncertainty by roughly two orders of magnitude over previous
determinations and opens the way for sensitive new tests of varying constants.Comment: 5 pages, 5 figure

Hendricks, R. J.

Hinds, E. A.

Tarbutt, M. R.

Truppe, S.

The Astrophysical Journal

English

arXiv

S. Truppe

R. J. Hendricks

E. A. Hinds

M. R. Tarbutt

Crossref

MEASUREMENT OF THE LOWEST MILLIMETER-WAVE TRANSITION FREQUENCY OF THE CH RADICAL

The CH radical offers a sensitive way to test the hypothesis that fundamental constants measured on earth may differ from those observed in other parts of the universe. The starting point for such a comparison is to have accurate laboratory frequencies. Here, we measure the frequency of the lowest millimeter-wave transition of CH, near 535 GHz, with an accuracy of 0.6 kHz. This improves the uncertainty by roughly two orders of magnitude over previous determinations and opens the way for sensitive new tests of varying constants

Truppe, S

Hendricks, RJ

Hinds, EA

Tarbutt, MR

Spiral - Imperial College Digital Repository

The Astrophysical Journal, 780:71 (4pp), 2014 January 1 doi:10.1088/0004-637X/780/1/71C© 2014. The American Astronomical Society. All rights reserved. Printed in the U.S.A.MEASUREMENT OF THE LOWEST MILLIMETER-WAVE TRANSITION FREQUENCY OF THE CH RADICALS. Truppe, R. J. Hendricks, E. A. Hinds, and M. R. TarbuttCenter for Cold Matter, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW72AZ, UK; m.tarbutt@imperial.ac.ukReceived 2013 September 12; accepted 2013 November 18; published 2013 December 12ABSTRACTThe CH radical offers a sensitive way to test the hypothesis that fundamental constants measured on earth maydiffer from those observed in other parts of the universe. The starting point for such a comparison is to haveaccurate laboratory frequencies. Here, we measure the frequency of the lowest millimeter-wave transition of CH,near 535 GHz, with an accuracy of 0.6 kHz. This improves the uncertainty by roughly two orders of magnitudeover previous determinations and opens the way for sensitive new tests of varying constants.Key words: methods: laboratory: atomic – molecular data – submillimeter: generalOnline-only material: color figures1. INTRODUCTIONThe CH radical is an important constituent of stellar atmo-spheres and interstellar gas clouds and plays an essential rolein most combustion processes. It is a well-established tracer formolecular hydrogen and a basic constituent of interstellar chem-istry, being one of the building blocks for more complex species.Recently, the lowest-lying Λ-doublet transitions of CH, and thelowest rotational transition, have been identified as highly sensi-tive to a possible variation of the fine-structure constant, α, or ofthe electron-to-proton mass ratio, μ (Kozlov 2009; de Nijs et al.2012). Such variations—in time, in space, or with local matterdensity—are expected in some higher-dimensional theories thataim to unify gravity with the other forces, and in some theories ofdark energy (Uzan 2003). The ground-state Λ-doublet transition,at 3.3 GHz, has been detected in numerous interstellar clouds ofthe Milky Way (Rydbeck et al. 1976; Hjalmarson et al. 1977) andin several other galaxies (Whiteoak et al. 1980) and has beenused to study the velocity structure, physical conditions, andchemistry of these clouds. The Λ-doublet transition of the firstrotationally excited state, at 0.7 GHz, has also been detected inseveral clouds (Ziurys & Turner 1985). Constraints on the vari-ation of α and μ with local matter density have recently beenobtained using astronomical observations of the CH Λ-doublets,along with new laboratory measurements (Truppe et al. 2013).As pointed out by de Nijs et al. (2012), very sensitive and ro-bust measurements could be obtained by observing the lowestrotational transition of CH, which has components at 532.8 and536.8 GHz, along with the two Λ-doublets at 3.3 and 0.7 GHz,all from the same cloud. Since this test uses only the four lowest-lying states of a single species, it is quite robust against system-atic shifts caused by spatial segregation. Using the Herscheltelescope, the lowest rotational transition has recently been de-tected in emission from star-forming regions of the Milky Way(van der Wiel et al. 2010) and in absorption in interstellar cloudsagainst the millimeter-wave background of star-forming regions(Gerin et al. 2010; Qin et al. 2010). Using the Atacama LargeMillimeter/submillimeter Array, this transition has also nowbeen observed in the absorber PKS 1830-211 at a redshift of z =0.89 (S. Muller 2013, private communication), opening up theprospect of using CH to search for variation of the constants overcosmological time, as well as with matter density. For these teststo reach the highest possible sensitivity, an improved laboratorymeasurement of the rotational transition frequency is needed.Figure 1 shows the relevant energy levels in the ground state ofCH. The two lowest levels, having angular momenta J = 1/2and J = 3/2, are separated by a combination of rotationaland spin–orbit energy. Each of these is split into a Λ-doublet,consisting of two levels of opposite parity, p. The magneticmoment of the hydrogen nucleus causes a further splittinginto hyperfine components labelled by F, the total angularmomentum quantum number. We use the notation (Jp, F ) tolabel these levels. Precise measurements of the Λ-doublingfrequencies are given in Truppe et al. (2013). The previousmost precise measurements of the J = 3/2–1/2 transitionsare given by Amano (2000), with uncertainties between 30 and100 kHz. Rotational and spin–orbit transitions between higher-lying rotational levels were measured with similar precision byDavidson et al. (2001), who then used all the available data onthe v = 0 level of the X2Π state to determine a precise setof molecular parameters. Here, we measure the J = 3/2–1/2frequencies with a precision of 0.6 kHz.2. EXPERIMENTFigure 2 shows the experimental setup. We produce a super-sonic beam of CH by photodissociating bromoform. At 4 barpressure, a carrier gas of He, Ne, Ar, or Kr is bubbled throughliquid bromoform (CHBr3, 96% purity stabilized in ethanol)and then expands through the 1 mm-diameter nozzle of a pulsedsolenoid valve into a vacuum chamber (Lindner et al. 1998;Romanzin et al. 2006). Light from an excimer laser (wavelengthof 248 nm, duration 20 ns, and energy up to 220 mJ) is focusedin front of the nozzle to a spot 1 mm high (along y) and 4 mmwide (along z), where it dissociates the bromoform to producethe CH. This source is pulsed with a repetition rate of 10 Hz.At z = 86 mm, the molecules pass through a 2 mm-diameterskimmer into a second vacuum chamber where the pressure isbelow 10−7 mbar. Here, they enter a magnetically shielded re-gion, and then, at z = 241 mm, they pass through a beam ofmillimeter-wave radiation that drives a selected hyperfine com-ponent of the 3/2+–1/2− transition. The radiation propagatesalong x and is linearly polarized along y. After leaving the mag-netic shield, the molecules are detected at z = 780 mm bydriving the A2Δ(v = 0) ← X2Π(v = 0) transition with a cwlaser beam (from a frequency-doubled titanium-sapphire laser)and imaging the resulting fluorescence onto a photomultipliertube. This probe light propagates along x, is linearly polarized1The Astrophysical Journal, 780:71 (4pp), 2014 January 1 Truppe et al.+__+J=1/2J=3/2X 2∏ (v=0, N=1)01011212Parity F 3335479.356 3263793.447 3349192.556 701677.682 724788.315 722487.624532723889.3Figure 1. Relevant energy levels in the X2Π(v = 0) ground state of CH, usingHund’s case (b) notation. Transition frequencies are in kHz and are given bythe present measurement in combination with the Λ-doublet transitions given inTruppe et al. (2013).x54Gas in Pulsed valveDissociationlaserSkimmerSynthesizerLensmultiplier chainHornProbelaser86 mm241 mm780 mmPMTzxMagneticshieldFigure 2. Schematic of the experiment.along z, has a wavelength near 430.15 nm, and has a powerof about 5 mW in a rectangular cross section 4 mm high and1.4 mm wide. The pulse of fluorescence is recorded with a tem-poral resolution of about 5 μs. To measure the depletion of theJ = 1/2 population, or the increase in the J = 3/2 population,the laser drives the transitions to the J = 3/2 or J = 5/2 levelsof the A2Δ(v = 0, N = 2) state, respectively. The frequenciesof these transitions are given by Zachwieja (1995), where theyare designated as R22ff(1/2) and R11ff(3/2).The millimeter-wave radiation comes from an amplifier-multiplier chain (Virginia Diodes, AMC) that generates the54th harmonic of a frequency synthesizer, phase-locked toa 10 MHz GPS reference. A WR1.5 diagonal horn antennacouples the radiation out of the waveguide, delivering about13 μW at 535 GHz. The electric field distribution at the outputis approximately Gaussian with a waist of 1 mm. This beam iscollimated by a plano-convex teflon lens of 30 mm focal lengthand then passes into the vacuum chamber through a quartzwindow. At the position of the molecular beam, the electricfield profile of the millimeter-wave beam is approximatelye−(y2+z2)/w2 , where w  5 mm. After accounting for reflectionand absorption losses in the lens and window, the powerdelivered to the molecules is about 7 μW. For the transitionbetween (3/2+, 2,M = 1) and (1/2−, 1,M = 1), we estimatea Rabi frequency of 2π × 23 kHz.1.1 1.2 1.3 1.4 1.5 1.60.250.300.350.400.450.50Arrival time msSignalFigure 3. Time-of-flight profiles for molecules having J = 3/2 before (redpoints) and after (blue points) driving the (3/2+, 2)–(1/2−, 1) transition. Thesolid lines are Gaussian fits to the data. The molecules used in the analysis arethose that arrive between the dashed lines.(A color version of this figure is available in the online journal.)150 100 50 0 50 10025303540Frequency 532723889.3 kHzSignalFigure 4. J = 3/2 signal vs. millimeter-wave frequency, showing the(3/2+, 2)–(1/2−, 1) transition. The line is a Gaussian fit to the data.(A color version of this figure is available in the online journal.)3. RESULTS AND DISCUSSIONWith Ar as the carrier gas, Figure 3 shows the time-of-flightprofile for molecules in the J = 3/2 state, both with and withoutthe millimeter-wave radiation applied. From the peak and widthof these profiles, we deduce that the molecules have a meanspeed of 567 m s−1 and a translational temperature of 0.4 K.When Kr is the carrier gas, the speed is 412 m s−1, and for Neit is 791 m s−1. When the millimeter-wave radiation is off, theJ = 3/2 fluorescence signal is about 5% of the J = 1/2 signal.When the millimeter-wave radiation is on, and resonant with themolecular transition, the J = 3/2 signal increases by a factorof 8.Figure 4 shows how the laser-induced fluorescence signalfrom the (3/2+) state depends on the millimeter-wave frequency,which is tuned near the (3/2+, 2)–(1/2−, 1) transition andstepped between shots of the experiment in a random order. Eachpoint in the spectrum is the integral of the time-of-flight profilebetween the limits indicated by the dashed lines in Figure 3. Tounderstand the line shape, we have modeled the experimenttaking into account the Gaussian intensity distribution andwavefront curvature of the millimeter-wave beam and theDoppler broadening due to the range of transverse velocitiesthat are detected. Broadening due to the Zeeman effect (seebelow) is negligible. This model predicts a Gaussian line shapewith an FWHM of 44 kHz for a speed of 412 m s−1, 58 kHz for567 m s−1, and 79 kHz for 791 m s−1. Gaussian fits to our data2The Astrophysical Journal, 780:71 (4pp), 2014 January 1 Truppe et al.0 200 400 600 8000-10-20-30-40Velocity (m/s)Frequency - 532723889.3 (kHz)Figure 5. Doppler shift of the (3/2+, 2)–(1/2−, 1) transition frequency as afunction of velocity, for two different angles of the millimeter-wave beam.(A color version of this figure is available in the online journal.)give reasonably good agreement with these predictions: we findFWHMs of 51 ± 4 kHz, 62 ± 2 kHz, and 79 ± 4 kHz for thesethree speeds, where the uncertainties are the standard deviationsof several measurements. The fit indicated by the solid line inFigure 4 determines the line center with a precision of 0.3 kHz.Inevitably, there is a Doppler shift because the millimeter-wave beam is not exactly perpendicular to the molecular beam.We correct for this by measuring at all three beam velocitiesand extrapolating the line center to zero velocity, as plottedin Figure 5. For each velocity, we repeat the measurement anumber of times and take the weighted mean of the line centers.As expected, we observe a linear shift of the frequency withvelocity due to the Doppler shift. To check the reliability of thismethod, we change the propagation direction of the millimeter-wave beam and repeat the measurements, as also plotted inFigure 5. The two sets of data have different slopes due tothe change in angle, but they have the same zero-velocityintercept, which we take as the true resonance frequency.The slopes correspond to angles of 28 and 22 mrad withthe x-axis. The same procedure is also used to measure thefrequency of the (3/2+, 1)–(1/2−, 1) hyperfine component of thetransition.Next, we consider systematic shifts due to the Zeeman effect.The g-factor is close to zero when J = 1/2, whereas forJ = 3/2 it is 1.081 when F = 1 and 0.648 when F = 2.The (3/2+, 2)–(1/2−, 1) transition is therefore split by a smallmagnetic field into five equally spaced components separated by9.07 Hz/nT. In the shielded region where the molecules interactwith the millimeter-wave beam, we measure a magnetic fieldcomponent along z of 13 nT, with the components along x andy being at least 10 times smaller. The linear Zeeman splittingin this field is only 120 Hz. Furthermore, this linear splittingshould not shift the line center because, for a linearly polarizedmillimeter-wave beam, the shifted components are symmetricabout the line center. We have verified this by applying afield large enough to resolve the Zeeman splitting. We havealso measured the effect of the quadratic Zeeman shift due tomagnetic dipole matrix elements off diagonal in F. We applymagnetic fields along z that are large enough to observe a shiftof the line center. As expected, this shift is quadratic and hasa curvature of −20 Hz/μT2. We conclude that in our residualfield, shifts due to both linear and quadratic Zeeman shifts arenegligible at the current level of precision.The dc Stark shift due to stray static electric fields, themotional Stark shift due to the motion of the molecules throughthe magnetic field, and the ac Stark shift due to frequencyTable 1Frequencies of All Components of the (N = 1,J = 3/2)–(N = 1, J = 1/2) Transition of 12CHTransition Frequency (kHz)(3/2−, 1)–(1/2+, 0) 536,795,569.5 ± 0.6(3/2−, 1)–(1/2+, 1) 536,781,856.3 ± 0.6(3/2−, 2)–(1/2+, 1) 536,761,046.3 ± 0.6(3/2+, 1)–(1/2−, 0) 532,793,274.6 ± 0.6(3/2+, 2)–(1/2−, 1) 532,723,889.3 ± 0.6(3/2+, 1)–(1/2−, 1) 532,721,588.6 ± 0.6sidebands are all negligible in the experiment. Also negligibleare frequency shifts due to collisions, blackbody radiation, andthe second-order Doppler shift.Our measured frequencies for the (3/2+, 2)–(1/2−, 1) and(3/2+, 1)–(1/2−, 1) transitions are 532,723,889.3 ± 0.7 kHzand 532,721,588.5 ± 1.4 kHz, respectively. When taken togetherwith the measured J = 1/2 and J = 3/2 Λ-doublet transitionfrequencies (Truppe et al. 2013), these results determine the fre-quencies for all components of the (N = 1, J = 3/2)–(N = 1,J = 1/2) transition in 12CH. These are given in Table 1. Theuncertainties in the table are slightly smaller than those of theindividual measurements quoted above because there are moremeasurements than independent frequencies. Our results arebetween 50 and 150 times more precise than the previous bestmeasurements (Amano 2000) and differ from those by up to3.6 standard deviations. Subtracting our results from those ofAmano (2000) and taking the weighted mean, we find a differ-ence of 79±15 kHz, indicating an uncontrolled systematic errorin those previous measurements.The absolute accuracy of these new laboratory frequencies isimproved to almost one part per billion, at which level the un-certainty no longer hinders the search for varying fundamentalconstants. This improvement will also allow more accurate ve-locity determinations to be made in astrophysical measurements.If some need were to emerge for measuring the laboratory fre-quency even more accurately, then this could be readily achievedusing Ramsey’s method (Ramsey 1950) of two excitation zones.In the present apparatus, this would increase the frequency reso-lution by a factor of 100 without any loss of molecular flux. Theuse of resonant cavities around the two excitation zones wouldeliminate the residual Doppler shift and increase the amount ofavailable power for driving the transition. With careful shield-ing to reduce systematic shifts due to magnetic fields (Truppeet al. 2013), a measurement of this THz frequency interval withan accuracy of 1 Hz is feasible. Precise measurements of sub-millimeter-wave transition frequencies in other molecules couldalso be made using this method.We thank Ben Sauer and Heather Lewandowski for usefuldiscussions and assistance in the lab. This work was supportedin the UK by the EPSRC and the Royal Society.REFERENCESAmano, T. 2000, ApJL, 531, L161Davidson, S. A., Evenson, K. M., & Brown, J. M. 2001, ApJ, 546, 330de Nijs, A. J., Ubachs, W., & Bethlem, H. L. 2012, PhRvA, 86, 032501Gerin, M., de Luca, M., Goicoechea, J. R., et al. 2010, A&A, 521, L16Hjalmarson, Å., Sume, A., Elldér, J., et al. 1977, ApJS, 35, 263Kozlov, M. G. 2009, PhRvA, 80, 022118Lindner, J., Ermisch, K., & Wilhelm, R. 1998, CP, 238, 329Qin, S. -L., Schilke, P., Comito, C., et al. 2010, A&A, 521, L143The Astrophysical Journal, 780:71 (4pp), 2014 January 1 Truppe et al.Ramsey, N. F. 1950, PhRv, 78, 695Romanzin, C., Boyé-Péronne, S., Gauyacq, D., et al. 2006, JChPh, 125, 114312Rydbeck, O. E. H., Kollberg, E., Hjalmarson, Å., et al. 1976, ApJS, 31, 333Truppe, S., Hendricks, R. J., Tokunaga, S. K., et al. 2013, NatCo, 4, 2600Uzan, J. P. 2003, RvMP, 75, 403van der Wiel, M. H. D., van der Tak, F. F. S., Lis, D. C., et al. 2010, A&A,521, L43Whiteoak, J. 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Measurement of the lowest millimeter-wave transition frequency of the CH radical

Measurement of the lowest millimetre-wave transition frequency of the CH
  radical

Measurement of the lowest millimetre-wave transition frequency of the CH radical

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