Sub-Doppler Spectroscopy of H3+

James N. Hodges, Adam J. Perry, Brian M. Siller, Benjamin J. McCall

Outline

• Motivation– Fundamental Physics– Astronomy

• Instrument Description• Transition Frequency Results• Wavelength Calibration Testing

H3+ Fundamental Benchmark

• Simplest polyatomic ion• Benchmark for ab initio theory

– Accuracy of order 300 MHz @ low energy

• QED corrections are frontier– Accuracy of order 30 MHz @ low energy

• Requires higher precision data

O. L. Polyansky, J. Tennyson, J. Chem. Phys. (1999), 110, 5056-5064.J. Komasa, et al. J. Chem. Theor. Comp. (2011), 7, 3105-3115.

H3+ Astronomically Important

• Abundant in Interstellar Medium• Deuterium Fractionation• Found in Ionospheres of Gas

Giants• Measure Speed of Auroral Winds • Limited by Laboratory Accuracy

T. R. Geballe and T. Oka, Nature (1996), 384, 334.P. Drossart et al. Nature (1989), 340, 539.D. Rego et al. Nature (1999), 399, 121.

Images From: http://solarsystem.nasa.gov/planets/profile.cfm?Object=Jupiterhttp://www.ucl.ac.uk/~ucaptss/work/publications/royalsoc/energy.htm

Spectroscopic TechniqueLarge Signal

Low Noise

Ion Selectivity

Cavity Enhancement

Heterodyne Spectroscopy

Velocity Modulation

NICE-OHVMS

Noise Immune Cavity Enhanced Optical Heterodyne Velocity Modulation Spectroscopy

B. M. Siller, et al. Opt. Express (2011), 19, 24822-7.

Instrumental Layout

OPO

YDFL

EOMLock-In

Amplifier

X & YSignal

Lock-In Amplifier

X & YSignal

Wave-meter

40 kHzPlasma

Frequency

80 MHz1 × Cavity Free Spectral Range

90o Phase Shift

IPS

2f

ni = np - ns

Freq. CombAOM

K. N. Crabtree, et al. Chem. Phys. Lett. (2012), 551, 1-6.

Comb Calibration

Wave-meter

Freq. CombAOM

[…]

Signal Pump

Comb Calibration

Wave-meter

Freq. CombAOM

[…]

Signal Pump

Comb Calibration

Wave-meter

Freq. CombAOM

[…]

Signal PumpSignal

H3+ Spectra

Sig

nal

Signal

Doubly Degenerate n2 Band

H3+ Transition Notation

𝐺≡|𝑘− 𝑙|{𝑃∨𝑄∨𝑅 }( 𝐽 ,𝐺){𝑢∨𝑙 }

Lamb Dips & Saturation• High Power Optical Saturation Lamb dips• Second Comb Calibrated Observation of Lamb dips

• In NICE-OHVMS fm-triplet causes many Lamb dips

H.-C. Chen et al. Phys. Rev. Lett. (2012), 109, 263002.K.N. Crabtree et al. Chem. Phys. Lett. (2012), 551, 1.

Lamb Dips & Saturation• High Power Optical Saturation Lamb dips• Second Comb Calibrated Observation of Lamb dips

• In NICE-OHVMS fm-triplet causes many Lamb dips

H.-C. Chen et al. Phys. Rev. Lett. (2012), 109, 263002.K.N. Crabtree et al. Chem. Phys. Lett. (2012), 551, 1.

Lamb Dips & Saturation• High Power Optical Saturation Lamb dips• Second Comb Calibrated Observation of Lamb dips

• In NICE-OHVMS fm-triplet causes many Lamb dips

H.-C. Chen et al. Phys. Rev. Lett. (2012), 109, 263002.K.N. Crabtree et al. Chem. Phys. Lett. (2012), 551, 1.

Lamb Dips & Saturation• High Power Optical Saturation Lamb dips• Second Comb Calibrated Observation of Lamb dips

• In NICE-OHVMS fm-triplet causes many Lamb dips

H.-C. Chen et al. Phys. Rev. Lett. (2012), 109, 263002.K.N. Crabtree et al. Chem. Phys. Lett. (2012), 551, 1.

Lamb Dips and Fits

R(2,2)l Transition

Transition Frequencies

𝜎 𝜇=𝜎√𝑛

St. Err. = St. Dev. Of Mean

Lamb Dip Signal-to-Noise-RatioLamb Dip SNR:

𝑆𝑁𝑅=𝑆𝑖𝑔𝑛𝑎𝑙𝑝𝑘−𝑝𝑘𝜎𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙𝑠

Lamb Dip Signal-to-Noise-Ratio

R(1,0)R(3,2)l

Frequency Calibration Test

• First use of a comb with this instrument• Need to ensure proper calibration• Lamb dips of methane

Instrumental Layout

OPO

YDFL

EOMLock-In

Amplifier

X & YSignal

Lock-In Amplifier

X & YSignal

Wave-meter

40 kHzPlasma

Frequency

80 MHz1 × Cavity Free Spectral Range

90o Phase Shift

IPS

2f

ni = np - ns

Freq. CombAOM

1.4 kHzModulationFrequency

3f

Frequency Calibration Test

• First use of a comb with this instrument• Need to ensure proper calibration• Lamb dips of methane• Acquired Lamb dips for F1

(2) component of P(7) transition of n3 band

Frequency Calibration Test

Lamb dip of methaneFit with 2nd derivative of Lorentzian

5 kHz diff. from Takahata et al. ~30 kHz st. dev. from fit

K. Takahata et al. Phys. Rev. A. (2009) 80, 032518.

ConclusionsComb calibrated H3

+ transitions reported

Higher S/N lines have sub-MHz precision

Methane used to validate comb calibration

Values differ than Chen et al. H.-C. Chen et al. Phys. Rev. Lett. (2012), 109, 263002.

Acknowledgements

Springborn FellowshipNSF GRF (DGE 11-44245 FLLW)