Larmor-resonant Sodium Excitation for

Larmor-resonant Sodium Excitation for

Larmor-resonant Sodium Excitation for Laser Guide Stars Ron Holzlhner S. Rochester 1 D. Budker 2,1 D. Bonaccini Calia ESO LGS Group 1 2 Rochester Scientific LLC, Dept. of Physics, UC Berkeley AO4ELT3 Florence, 28 May 2013 Are E-ELT LGS lasers powerful enough? E-ELT laser baseline: 20W cw with 12% repumping 5 Mph/s/m2 at Nasmyth (at zenith in median sodium; 12 Mph/s/m2 on ground) There may be situations when flux is not sufficient for some instruments (low sodium, large zenith angle, non-photometric night, full moon, etc.) No unique definition of LGS availability; details quite complicated E-ELT Project has expressed interest in exploring paths to raise the return flux Two avenues: 1. Raise cw power Laser development (e.g., Raman fiber amplifiers) 2. Raise coupling efficiency sce Explore new laser formats

Will focus on option 2 Slide 2 Sky Maps Paranal Sim. cw return flux on ground [106 ph/s/m2] = 60 Becoming more independent of field angle would be particularly beneficial in Paranal: Flux varies strongly with angle to B-field B-field inclination is only 21 most of the time this angle is large 3.6! B What factors limit the return flux?

Three major impediments of sodium excitation: 1) Larmor precession (m: angular momentum z-component) B m Laser 2) Recoil (radiation pressure) 3) Transition saturation (at 62 W/m2 in fully pumped sodium) v + 50 kHz spont. emission time excited (P3/2) ground (S1/2) Slide 4

Draw 3D surface where distance from origin equals the probability to be found in a stretched state (m = F) along this direction. z z y z y x y x x Unpolarized Oriented Aligned Sphere centered at origin, equal probability

in all directions. Pumpkin pointing in z-direction preferred direction. Peanut with axis along z preferred axis. Credit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeley Visualization of Atomic Polarization Btorque Credit: E. Kibblewhite causes polarized atoms to precess: Credit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeley Precession in Magnetic Field Efficiency per Atom with Repumping

: Return flux per atom, normalized by irradiance [unit ph/s/sr/atom/(W/m2)] : angle of laser to B-field (design laser for = /2) Symbols: Monte Carlo simulation, lines: Bloch Blue curve peaks near 50 W/m2, close to Na saturation at 60 W/m2: Race to beat Larmor 500 =0 400 q = 0.12 300 200 100 0 -2 10 (ph/s/sr/atom)/(W/m 2)

Model narrow-line cw laser, circular polarization (ph/s/sr/atom)/(W/m 2) Peak efficiency 250 = /2 circular -1 10 0 10 1 10 2

10 3 10 Irradiance (W/m2) 200 150 100 20W cw laser in mesosphere q = 0.12 Transition saturation 62 W/m2 Is there a way to harness the efficiency at peak of green curve? 50 linear q=0

Slide 7 Larmor Resonant Pulsing Pulse the laser resonantly with Larmor rotation: like stroboscope, Larmor period: 3 6.2 s (Field in Paranal: 0.2251G at 92km)s (Field in Paranal: 0.2251G at 92km) Used for optical magnetometry: Yields bright resonance in D 2a of about 20% at 0.31.0 W/m2, narrow resonance of ca. 1.5% FWHM *) Recent proposal by Hillman et al. to pulse at 9% duty cycle, 20W average power, 47/0.09 = 522 W/m2 and a linewidth of 150 MHz 47/15 3 W/m2/vel.class near optimum avg. power (ph/s/sr/atom)/(W/m 2) Paranal simulation: sce = 374 ph/s/W/(atoms/m2),500vs. ca. sce 250 for cw (all at 90 and Paranal conditions) 400 hence about 1.5 times more (!) sce becomes almost independent of field angle 300 200 Increased irradiance also broadens the resonance 100 2 )

0 -2 10 *) PNAS 10.1073/pnas.1013641108 (2011) (arXiv:0912.4310) =0 = /2 circular -1 10 0 10 1 10 10 250 Slide 8

Some Simulation Details B = 0.23 G, = 90, q = 9%, 150 MHz linewidth Return is fairly linear vs. irradiance Steady state reached after ca. 50 periods = 300s (Field in Paranal: 0.2251G at 92km)s (Sdamping time) Slide 9 Simulated Performance Can achieve 14 Mph/s/m2 at 10W, 28 Mph/s/m2 at 20W (D2a+D2b) Peak efficiency reached above 10W Very strong atomic polarization towards (F=m=2) of 6070% Ground States 582 W/m2 Excited States F=m=2

F=m=1 Slide 10 Larmor Detuning A small rep rate detuning shows up first at low peak irradiance Reduces pumping efficiency, induces polarization oscillations Variation in Paranal: 0.22%/year, 0.39%/10km altitude On resonance Ip = 221 W/m2 Ip = 27 W/m2 1% detuned 2% detuned Best Laser Format? Lasers with pulses of ~0.5 s (Field in Paranal: 0.2251G at 92km)s and peak power 200W hard to build (150/2=75 MHz linewidth not large enough to sufficiently mitigate SBS) Multiplex cw laser to avoid wasting beam power? Spatiotemporally: use one laser to sequentially produce multiple stars In frequency: Chirp laser continuously, e.g. from 55... +55 MHz (11 vel.c.) In frequency: Periodically address several discrete velocity classes Or modulate the polarization state? (probably less beneficial)

Can in principle profit from snowplowing by up-chirping, although chirp rate of ~110 MHz/6.2s (Field in Paranal: 0.2251G at 92km)s = 17.7 MHz/s (Field in Paranal: 0.2251G at 92km)s is very high Numerical optimization of modulation scheme; runs are timeconsuming (order 4872 CPU h per irradiance step) Issue: Avoid F=1 downpumping, in particular at 60 MHz offset Slide 12 Downpumping 3S1/2 3P3/2 transition F = I + J : Total angular momentum I = 3/2 : Nuclear spin J = L + S : Total electronic angular momentum (sum of orbital and spin parts) 40 MHz grid Graphic by Unger D2b Excitation from D2a narrow-band laser D2a

Prefer (F = 2, m = 2) (F = 3, m = 3) cycling transition Frequency Scanning Schemes Scan across >= 9 discrete velocity classes Blue-shift to achieve snowplowing via atomic recoil Avoid downpumping leave 40 MHz or >> 60 MHz gaps, but without exceeding the sodium Doppler curve (1.05 GHz FWHM) 9 40 MHz 4 110 MHz Slide 14 Hyperfine State Populations Excitation Time F=1 ground states Larmor period

F=2 ground states Plot hyperfine state evolution for a selection of velocity classes Visualize Larmor precession, downpumping, excitation excited states first pulse Slide 15 Hyperfine State Analysis: 9 40 MHz 60 MHz Slide 16 Conclusions Larmor precession reduces the return flux efficiency by factor 2; forces high irradiance to combat population mixing Can mitigate population mixing by stroboscopic illumination resonant

with Larmor frequency (~160 kHz in Chile, ~330 kHz in continental North America and Europe) Realize with pulsed laser of ~20W average power and < 10% duty cycle, 150 MHz linewidth: Raise efficiency by factor 1.5 ! which is hard to build (> 200 W peak power, M2 < 1.1) Alternative: Frequency modulation (chirping/frequency multiplexing schemes) Caveats: Observe 60 MHz downpumping trap and target ~35 W/m 2/v.c. on time average, frequency sensitive, modulator not easy to build Format optimization is work in progress CW laser format is good, but leaves room for improvement Slide 17 FINE GRAZIE! Slide 18 Frequency Shifters Would like to frequency modulate over 100 MHz (or even 300 MHz) at >80% efficiency Either sawtooth or step function with 160 kHz rep rate (Paranal) Need to maintain excellent beam quality and beam pointing Option1: Free-space AOM. Pro: Proven technique, reasonable efficiency. Con: 100+ MHz is very broadband, variation of beam

pointing or position when changing frequency? Option 2: Free-space EOM using carrier-suppressed SSB. Requires an interferometric setup, may be difficult to realize at high power+efficiency Option 3: Modulate seed laser. Pro: Possibly reduce SBS (fiber transmission time is in s (Field in Paranal: 0.2251G at 92km)s range). Con: Cavity locking difficult (piezo bandwidth would need to be in MHz range), combine with PDH sidebands? Slide 19 Hyperfine State Analysis: 4 110 MHz Slide 20 Some Commercial Frequency Shifters 1 Brimrose Corp. http://www.brimrose.com/pdfandwordfiles/aofshift.pdf Slide 21 No More PlotsHow Do We Build it? Slide 22

Some Commercial Frequency Shifters 2 Brimrose Corp. http://www.brimrose.com/pdfandwordfiles/aofshift.pdf Slide 23 Some Commercial Frequency Shifters 3 A.A http://opto.braggcell.com/index.php?MAIN_ID=102 REFERENCE Materi Wavelength Aperture(mm) Frequency(MHz) al (nm) Polar Deflection angle Efficiency (mrd) MQ200-B30A0.7-244266-Br SiO2 244-266

0.7 x 3 200 +/- 15 Lin 1.3 @266nm > 60 MQ110-B30A1-UV SiO2 325-425 1x2 110 +/- 15 Lin 1.8 @355nm > 60

MCQ110-B30A2-VIS Quartz 458-650 2x2 110 +/- 15 Lin 2.8 @ 532nm > 70 MT350-B120-A0.12-VIS TeO2-L 450-700 0.12 x 2 350 +/- 50 Lin 15.2 @532nm

> 60 MT250-B100-A0.5-VIS TeO2-L 450-700 0.5 x 2 250 +/- 50 Lin 12.6 @532nm > 60 MT250-B100-A0.2-VIS TeO2-L 450-700 0.2 x 1

250 +/- 50 Lin 12.6 @532nm > 60 MT200-B100A0.5-VIS TeO2-L 450-700 0.5 x 2 200 +/- 50 Lin 12.6 @532nm > 60 MT200-B100A0.2-VIS TeO2-L

450-700 0.2 x 1 200 +/- 50 Lin 12.6 @532nm > 60 MT110-B50A1-VIS TeO2-L 450-700 1x2 110 +/- 25 Lin 6.3 @532nm

> 60 MT110-B50A1.5-VIS TeO2-L 450-700 1.5 x 2 110 +/- 25 Lin 6.3 @532nm > 60 MT80-B30A1-VIS TeO2-L 450-700 1x2 80 +/- 15

Lin 3.8 @532nm > 65 MT80-B30A1.5-VIS TeO2-L 450-700 1.5 x 2 80 +/- 15 Lin 3.8 @532nm > 65 Slide 24 To Frequency Shift, or not? Seems that AOM/EOM specs are very challenging (no eierlegende

Wollmilchsau in AOMs, quote by Mr. Jovanovic, Pegasus Optik GmbH) Egg-laying wool milk swine: Broadband, highly efficient, high power, no aberrations, constant pointing. And cheap! Really no way to modulate in the IR and double? Frequency shift is doubled, hence +/ 25 MHz may be enough Could be done after seed laser with fiber-coupled AOM and thus also shift the PDH sidebands Would need fast adjustment of optical path length in cavity (RF active crystal? LBO not suitable, but has been done e.g. with MgO:LiNbO3) or else consider a pulsed laser? Slide 25 Bloch Equation Simulation Schrdinger equation of density matrix, first quantization d/dt = /dt = d/dt = t = A + b = 0

Models ensemble of sodium atoms, 100300 velocity groups Takes into account all 24 Na states, Doppler broadening, spontaneous and stimulated emission, saturation, collisional relaxation, Larmor precession, recoil, finite linewidth lasers Collisions change velocity and spin (v-damping,S-damping) More rigorous and faster than Monte Carlo rate equations Based on AtomicDensityMatrix package, Written in Mathematica v.6+, publicly available

http://budker.berkeley.edu/ADM/ [Optimization of cw sodium laser guide star efficiency, Astronomy & Astrophysics 520, A20] Slide 26 EOMs for Repumping Vendors: New Focus, Qubig Taken from www.qubig.de Used free-space EOM in Wendelstein transportable LGS system Affordable way to retrofit pulsed lasers Issues with peak power (photodarkening, coatings, cooling) Slide 27 What is crucial for good return flux? Most Important:

Laser power, sodium abundance (seasonal) Circular polarization state D2b repumping (power fraction q12%, 1.710 GHz spacing) (Peak) power per velocity class Overlap with sodium Doppler curve (but: implicit repumping) For return flux on ground: zenith angle, atmospheric transmission 2 Somewhat Important: Angle to B-field (), strength of B-field |B| (hence geographic location) Atomic collision rates (factor 10 variation across mesosphere) Less Important: Seeing, launched wavefront error, launch aperture (beware: spot size) Sodium profile, spectral shape (for given number of velocity classes) Could improve on the crucial parameters () Slide 28 Optical pumping Light linearly polarized along z can create alignment along z-axis. z

F = 0 F=1 MF = -1 MF = 0 MF = 1 Credit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeley http://budker.berkeley.edu/Physics208/D_Kimball/ Optical pumping Light linearly polarized along z can create alignment along z-axis. z F = 0 F=1 MF = -1 MF = 0 MF = 1

Medium is now transparent to light with linear polarization along z ! Credit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeley Optical pumping Light linearly polarized along z can create alignment along z-axis. z F = 0 . F=1 MF = -1 MF = 0 MF = 1 Medium strongly absorbs light polarized in orthogonal direction! Credit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeley

Optical pumping Optical pumping process polarizes atoms. Optical pumping is most efficient when laser frequency (l) is tuned to atomic resonance frequency (0). Precession in Magnetic Field Interaction of the magnetic dipole moment with a magnetic field causes the angular momentum to precess just like a gyroscope! B =B = dF dt dF

, F dt = B = gF B F B L = gF B B

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