1. Harvard-Smithsonian Center for Astrophysics
Laser Frequency Combs for Precision Radial Velocity Measurements in Astrophysics
David F. Phillips
Harvard-Smithsonian Center for Astrophysics
A collaboration between astronomers (CfA), physicists (CfA) and electrical engineers (MIT)
~15 scientists

2. “Astro-Comb”
• Precision spectroscopy essential for advances in astrophysics
• Currently limited by spectrograph wavelength calibration
• Laser frequency combs can solve calibration problem
• Rapid progress in last 3 years:
concept => lab demo => operation at observatories
• Coming soon: discovery & characterization of Earth-like planets
• years: direct measurement of cosmological dynamics
Diddams et al., Nature 445, 627 (2007).
Murphy et al., MNRAS 380, 839 (2007).

3. Unique Opportunity Origins of Life in the Universe
Over the next decade, we will:
• Discover the first Earth-like planets around other stars
• Search these planets for chemical signatures of life
• Image planets directly
Is the Earth special, or just another planet?
=> Complete Copernican revolution?

4. Extrasolar Planets 400 exoplanets found to date Hot Jupiters
Primarily hot Jupiters
“Super Earths” now being found
Soon, earth-like planets
Hot Jupiters
Jupiter mass planets close to their stars
Primarily Radial Velocity Method to date
Sensitive to massive close-in planets
Automated transit surveys underway
Will find earth-like planets
Super-Earths
Radial velocity sensitivity
Habitable zone
(Sasselov 2008)

5. Super Earths
Image: S.Cundiff
Planets could have similar size, but be very different in mass and composition
(Sasselov 2008)

6. Exoplanet Detection Methods
Direct detection ( brightness difference)
Radial velocity (determine mass – m sin(i) – from reflex motion)
Transit method (determine radius from eclipses)
Microlensing (no follow-up possible)
Pulsar timing (exotic environment for planets)

7. Direct Detection HR 8799 d=129 lt-yr Rplanets = 20-70 AU m = 10 mJ
Challenging
Stars are bright, planets are dim and close to stars
Two techniques -- adaptive optics and a coronagraph -- to minimize the glare from the star and reveal the dim glow of the much fainter planets.

8. Spitzer space telescope at 8 µm
Transit Method
HD B
Hot jupiter
63 light-years away
Mass = 1.13 MJ
Radius = 1.14 RJ
T=1000 K
P = 2.2 days
secondary eclipse
Spitzer space telescope at 8 µm
primary eclipse
Heather Knutson & Dave Charbonneau (2007)

9. Transits: Kepler spacecraft
launched 3/6/09
Transit method, free of Earth’s atmosphere
Search 100,000 nearby stars over next 3 years
Expect to find many Earth-size planets in “habitable zone”
43 days of science data on more than 156,000 stars recently released
Only gives planet size & orbit period, not mass

10. Radial Velocity Method
Unseen exoplanet
Reflex motion of star due to planet
• Heavier planet causes larger Doppler shift in star light
• Gives planet mass and orbital period, not size
• Doppler-shift from Earth-mass planet is VERY SMALL

11. Stellar Spectrum
100,000 absorption lines

12. Spectrograph
Small frequency shifts => Use echelle spectrograph => broad spectral coverage & high-resolution
corrector
collimator
slit
2D CCD array
From telescope
cross disperser (low-dispersion)
echelle grating (high dispersion)
Slit is often a multimode fiber, allowing the spectrograph to reside in an environmentally controlled room, away from the telescope
State-of-the-art astrophysical spectroscopy is broadband, photon-starved => spectrograph resolution R = λ/Δλ ~ 100,000
=> minimum resolution element Δν > 5 GHz

13. Resolution Linewidth of typical stellar lines ~1 GHz
Doppler shift: Δλ/λ = ΔRV/c
Δλ ΔRV
10–7 Å 1 cm/s
10–6 Å cm/s
10–5 Å 1 m/s
0.01 Å 1 km/s
Earth-mass planet around Sun-like star
Pre-comb sensitivity
“Hot Jupiter”
Resolution of spectrograph Δλ/λ ~ 105
at 500 nm: 5 GHz
line splitting: ,000
Need high signal-to-noise ratio and many lines

14. Octave-Spanning Femtosecond Ti:Sapphire Laser
pump laser
532 nm
BaF2 plate & wedge
lens
Ti:Sa crystal
red comb • octave-spanning • ~1 GHz rep rate • 105 comb lines
PZT
Double-chirped mirror pairs => compensate broadband dispersion
• Stabilize ωr => feedback to external cavity length
• Stabilize ωCE => feedback to pump laser power
< 4 fs
Broadband gain, Kerr effect => octave spanning Kerr-lens mode-locking => stabilize pulsing Cavity sets Trep ~1 GHz

15. Octave-Spanning Femtosecond Ti:Sapphire Laser
pump laser
532 nm
BaF2 plate & wedge
lens
Ti:Sa crystal
red comb • octave-spanning • ~1 GHz rep rate • 105 comb lines
PZT
Double-chirped mirror pairs => compensate broadband dispersion
• Stabilize ωr => feedback to external cavity length
• Stabilize ωCE => feedback to pump laser power
< 4 fs
=> spectrograph resolution R = λ/Δλ ≤ 100,000
=> minimum resolution element Δν > 5 GHz
=> optimal calibrator line-spacing > 10 GHz
But such high-repetition-rate, octave-spanning combs do not yet exist…

16. Astro-Comb
Phase lock box
Synthesizer
Photo-detector
Fabry-Perot cavity
Astro-comb beam
Octave-spanning 1-GHz
laser frequency comb
PZT
λ/2
EOM
Photo-detector
Diode laser
PID lock box
Synthesizer
Remove most comb lines with a stabilized Fabry-Perot Cavity to yield line-spacing up to ~30 GHz

17. Astro-Comb intensity wavelength Fabry-Perot cavity Astro-comb beam
PID lock box
λ/2
Photo-detector
Fabry-Perot cavity
PZT
Octave-spanning 1-GHz
laser frequency comb
Diode laser
Astro-comb beam
EOM
Synthesizer
Phase lock box
intensity
wavelength

18. Astro-Comb intensity wavelength Fabry-Perot cavity Astro-comb beam
PID lock box
λ/2
Photo-detector
Fabry-Perot cavity
PZT
Octave-spanning 1-GHz
laser frequency comb
Diode laser
Astro-comb beam
EOM
Synthesizer
Phase lock box
intensity
wavelength

19. Filter Cavity Dispersion-compensating mirrors Bragg-Stack Mirror Pair
Effective path
wavelength
Layers of alternating refractive index
Complementary-Chirped Mirror Pair
wavelength
Effective path
Layers of alternating refractive index

20. Astro-comb
Astro-comb tested using a 1.5 m telescope with high-resolution echelle spectrograph (TRES)
TRES spectrograph
R~40,000

21. Calibration Spectrum Th:Ar calibrator Astro-comb spectrum
2D CCD
echelle grating (high dispersion)
100 µm fiber
lens
cross disperser (low-dispersion)
Th:Ar calibrator
Astro-comb spectrum
Red astro-comb and Th:Ar spectrum
TRES spectrograph on 1.5 m Tillinghast reflector at Mt. Hopkins
2 dimensional spectrum on spectrograph CCD

22. Red Astro-Comb 100 nm bandwidth 32 GHz spacing
10 GHz FWHM on spectrograph
100 nW per line
counts in 5 minutes through integrating sphere.

23. Red Astro-Comb SNR A ≈ 0.7 FWHM ≈ 10 GHz (S/N)300 s ≈ 200
(S/N)max ≈ 300
n ≈ 6 pixels
∆ν ≈ 15 MHz or 15 m/s for one peak
250 peaks/order: ∆ν ≈ 1 MHz in one order
Murphy (2007)

24. One order of comb lines superimposed
Fit Model
Comb
∆ν = 1 GHz S • δI/I
S = side mode suppression
∆ν = 3 MHz • δI/I
Negligible at the 1 m/s level
Fiber
100 µm fiber
Modeled as flat top in 2D
Half circle in 1D
Add skew
Optics
Modeled as Hermite- Gaussians
Up to 16 terms
CCD
Model as flat
Tails from charge diffusion don't appear to help
One order of comb lines superimposed
Residuals of fit
near shot noise floor

25. Calibration Calculate wavelength calibration as above order by order.
Compare calibration to reference frame.
Calculate deviation of all orders from mean drift.

26. Calibration ≤ 1 m/s uncertainties
Calculate wavelength calibration as above order by order.
Compare calibration to reference frame.
Calculate deviation of all orders from mean drift.

27. Blue Astro-Comb 1 GHz Ti:Sapphire source laser BBO doubling crystal
50 nm bandwidth
Fabry-Perot cavity:
Bragg stack mirrors
Bandwidth limited by air dispersion to ~15 nm
Improved flux to spectrograph
Phase scrambling

28. One order of comb lines superimposed
Blue Astro-Comb
One order of comb lines superimposed
faster data rate
Residuals of fit
50 cm/s resolution
Much closer to shot noise!
420 nm with less fringing.
Fiber shaking active.

29. Green Astro-Comb Photonic Crystal Fiber (PCF)
PID lock box
λ/2
Photo-detector
Fabry-Perot cavity
PZT
Octave-spanning 1-GHz
laser frequency comb
Diode laser
Astro-comb beam
EOM
Synthesizer
Phase lock box
Photonic Crystal Fiber (PCF)
High nonlinear coefficient
Zero-dispersion wavelength ~700 nm
Four-wave mixing
Near Gaussian mode profile
FP Cavity
Complementary-Chirped Mirror Pair

30. Green Astro-Comb 45 GHz green astro-comb Various Ti:Sapphire settings
Astro-comb lines not resolved on OSA
Lab demo. Next, test at telescope
240 GHz green astro-comb
demo for low-resolution OSA
Side suppression minimal

31. What’s Next? • Observe Earth candidates found by Kepler
HARPS clone for northern hemisphere
Astro-comb calibrator => ΔRV < 10 cm/s
William Herschel telescope,
Canary Islands, 4.2 meter mirror
• Observe Earth candidates found by Kepler
• Use Doppler-shift method to distinguish new Earths from exotics
Harvard, Smithsonian, Geneva Observatory

32. Calibration
Wavelength calibration sufficient for RV <10 cm/s => only combs can do the job
Murphy et al., Mon. Not. R. Astron. Soc. 380, 839 (2007)

33. RF beat frequencies => lock ωr & ωCE
Octave-Spanning Comb
Octave-spanning comb => atomic clock accuracy & stability for all comb lines
τpulse < 4 fs
• 105 comb lines • narrow lines (<kHz) • coherent • equally-spaced • intense (10 μW/line)
ωr ~ 1 GHz
~300 nm
nH = 2nL
RF beat frequencies => lock ωr & ωCE
to atomic clock