Laser MEOP of 3 He: Basic Concepts, Current Achievements, and Challenging Prospects

Polarization in Noble Gases, October 8-13, 2017 Laser MEOP of 3 He: Basic Concepts, Current Achievements, and Challenging Prospects Pierre-Jean Nacher Geneviève Tastevin Laboratoire Kastler-Brossel ENS Paris www.lkb.science/polarisedhelium/

First MEOP experiment 1963 For nuclear polarisation of I=½ noble gases two OP-based methods: Ø Spin Exchange (SEOP) tomorrow Ø Metastability Exchange (MEOP) for 3 He 1 Higher SNR for optical detection of NMR First rf detection of polarized gas

First MEOP experiment to contemporary MEOP systems 1 1963 From tiny to huge cells: OP using dedicated lasers, in pure He gas with discharge.

First MEOP experiment to contemporary MEOP systems 2 From tiny to huge cells: OP using dedicated lasers, in pure He gas with discharge. A weak rf discharge promotes a small fraction (10 6 ) of the atoms into the excited metastable state 2 3 S S and I strongly entangled in the 2 3 S state by hyperfine coupling: OP simultaneously creates electronic and nuclear orientation ME collisions (a very short interaction between a 2 3 S state atom and a ground state atom), induce a fast exchange of electronic excitations with no loss of total angular momentum. ME collisions 1 1 S 0 2 3 P 1083 nm OP 2 3 S Two key processes: Ø Optical Pumping Ø Metastability exchange s+ He cell mirror OP beam B circular polariser rf

OUTLINE 1 Basics of MEOP of He (low B and high B) General considerations on OP Optical transitions and OP Basics of ME MEOP operation and performance 2 Understanding MEOP limits Models OP-induced relaxation: evidence, consequence, origin Prospects

Basics of MEOP Principle of OP 3 Optical pumping (OP) is the redistribution of atoms among the energy sublevels of the ground state by resonant absorption of light (out of thermal equilibrium). (A. Kastler, Physica 17,191,1951) Ingredients : - 2 atomic levels connected by an optical transition - sublevels (fine structure, hyperfine structure, magnetic, ) DE=hn Simple 2-level system (model) : J =1/2 J=1/2 m J : -1/2 1/2 Grotrian diagram (E vs. ang. mom. m J ) Convenient to display optical transitions

Basics of MEOP Principle of OP 3 Optical pumping (OP) is the redistribution of atoms among the energy sublevels of the ground state by resonant absorption of light (out of thermal equilibrium). (A. Kastler, Physica 17,191,1951) Ingredients : - 2 atomic levels connected by an optical transition - sublevels (fine structure, hyperfine structure, magnetic, ) Simple 2-level system (model) : J =1/2 DE=hn J=1/2 m J : -1/2 1/2 s + light : Transition between selected sublevels

Basics of MEOP Principle of OP 3 Optical pumping (OP) is the redistribution of atoms among the energy sublevels of the ground state by resonant absorption of light (out of thermal equilibrium). (A. Kastler, Physica 17,191,1951) Ingredients : - 2 atomic levels connected by an optical transition - sublevels (fine structure, hyperfine structure, magnetic, ) Simple 2-level system (model) : J =1/2 DE=hn J=1/2 m J : -1/2 1/2 With radiative decay: Net depopulation of the illuminated state after several OP cycles

Basics of MEOP Principle of OP 3 Optical pumping (OP) is the redistribution of atoms among the energy sublevels of the ground state by resonant absorption of light (out of thermal equilibrium). (A. Kastler, Physica 17,191,1951) Ingredients : - 2 atomic levels connected by an optical transition - sublevels (fine structure, hyperfine structure, magnetic, ) Simple 2-level system (model) : J =1/2 DE=hn J=1/2 m J : -1/2 1/2 With relaxation: Still net depopulation of the illuminated state

Basics of MEOP Atomic levels of He 4 Atomic state characterised by: e - excitation level (n=1,2, ) e - orbital angular momentum L e - spin ang. momentum S J = L + S nuclear spin ang. momentum I F = I + J Energy depends on quantum numbers magnetic field B 4 He (I=0) 3 He (I=1/2) orbitals 1s 2s 2p L=0 L=0 L=1

Basics of MEOP Atomic levels of He 5 For OP, ground state is metastable 2 3 S 1 state (no suitable optical transition from the true g.s.) L=0, S=1, I=0 or I=1/2 0-5 -10 4S 3S 2S 4P 3P 2P 4D 3D 4F 4S 4P 4D 4F n=4 3P 3D 3S n=3 2S 2P Closed optical transition n=2 Hydrogen levels 2 3 P J 2 3 S 1 J=0 J=1 J=2 J=1 4 He ev -20 1S Parahelium S=0 Orthohelium S=1 Helium energy levels -25 0 1 2 3 0 1 2 3 n=1 D 2 D 1 lines helium-4 D 0 line T=300K Orbital angular momentum L

Basics of MEOP OP of 4 He 6 In contrast with simple 2-level model, 3 sublevels in ground state : n - n 0 n D 0 line : + total population N=n + + n 0 + n - orientation µ n + - n - n + = n 0 = N/2 orientation : 66% helium-4 D 2 line : OP without relaxation orientation 100%

An important application: He4 magnetometers 7 Helium magnetometers : wide range of operating conditions (T), cell lifetime, Usual technique (in He4 He3 nuclear magnetometers on Wednesday) D 0 line RF resonance in ground state: F L =g/2p B (28.023561 Hz/nT) Discharge lamp OP source, Space borne, e.g. (late) Cassini mission: https://saturn.jpl.nasa.gov/magnetometer/

Basics of MEOP Atomic levels of He 8 For OP, ground state is metastable 2 3 S 1 state (no optical transition from the true ground state) L=0, S=1, I=0 or I=1/2 0-5 -10 4S 3S 2S 4P 3P 2P 4D 3D 4F 3S 2S 4S 4P 3P 2P 4D 3D 4F Closed optical transition J=0, F=1/2 J=2, F=5/2 F=1/2 F=3/2 C 8 C 9 3 He 4 He 2 3 P J 1083 nm OP transitions 2 3 S 1 J=0 J=1 J=2 D 0 J=1 ev Parahelium S=0 Orthohelium S=1 helium-3 helium-4-20 1S Helium energy levels -25 0 1 2 3 0 1 2 3 Orbital angular momentum L 0 20 40 60 80 OP transitions to the 2 3 P 0 state are normally used: C 8, C 9, and D 0

Basics of MEOP Atomic levels of 3 He 9 B 18 B 17 2 3 P 0 F=1/2 J=0, F=1/2 3 He 2 3 P J OP line C 8, s + J=2, F=5/2 C 8 F=1/2 F=3/2 1083 nm OP transitions 2 3 S 1 helium-3 helium-4 A 5 A 6 2 3 S 1 F=1/2 A 1 A 2 A 3 A 4 F=3/2-3/2-1/2 1/2 3/2 0 20 40 60 80 OP processes when using C 8 in He3

Basics of MEOP Atomic levels of 3 He 10 OP line C 8, s + B 18 B 17 2 3 P 0 F=1/2 Discussion of photon efficiency h = Dm F : Net change of atomic angular momentum per absorbed photon in an OP cycle No collisions Fast collisions C 8 OP: h = 0.9 h = 0.5 A 5 A 6 2 3 S 1 F=1/2 A 1 A 2 A 3 A 4 F=3/2-3/2-1/2 1/2 3/2

Basics of MEOP Atomic levels of 3 He 10 OP line C 9, s + B 18 B 17 2 3 P 0 F=1/2 Discussion of photon efficiency h = Dm F : Net change of atomic angular momentum per absorbed photon in an OP cycle No collisions Fast collisions C 8 OP: h = 0.9 h = 0.5 C 9 OP: h = 1.05-0.9 h = 1.26-0.5 depends on relative populations a 1, a 2 in A 1 & A 2 (ranges: from a 1 =a 2, P He =0 to a 2 >>a 1, high P He ) A 5 A 6 2 3 S 1 F=1/2 A 1 A 2 A 3 A 4 F=3/2-3/2-1/2 1/2 3/2

Basics of MEOP Atomic levels of 3 He 10 Discussion of photon efficiency h = Dm F : Net change of atomic angular momentum per absorbed photon in an OP cycle No collisions Fast collisions C 8 OP: h = 0.9 h = 0.5 C 9 OP: h = 1.05-0.9 h = 1.26-0.5 depends on relative populations a 1, a 2 in A 1 & A 2 (ranges: from a 1 =a 2, P He =0 to a 2 >>a 1, high P He ) D 0 OP: h = 1

OP in more detail Atomic levels of 3 He: more complex in high B 11 Level energies in 2 3 S and 2 3 P states computed from H=H fs +H hfs +H zeeman 2 3 P level B=0 B=1.5T 2 3 S level Angular momentum m F Field B (0 to 1.5 Tesla) Angular momentum m F

OP in more detail Atomic levels of 3 He: more complex in high B 12 Structure of atomic levels and absorption spectra are deeply modified. Yet, photon efficiency h ~ 1 for the strong lines B = 1.5 T f - 4 f - 2 f + 4 f + 2 3 He, s - 3 He, s + 2 3 P level B=1.5T -50 0 50 100 GHz 50 GHz B 15 B 10 B 13 B 9 f - 2 B1 B 10 B 6 B5 B 2 B 9 (c) 2 3 S level 50 GHz A 4 A 6 A3 A5 f - 4 A 4 A 6 A 5 A3 A 1 A 2 A 1 A 2-5/2-3/2-1/2 1/2 3/2 5/2 m F -5/2-3/2-1/2 1/2 3/2 5/2 Angular momentum m F

ME collisions Low B and high B 13 1S 2S 2S ME collision : He + He* He + He* ± > A i > Tr elec. A i ><A i ± > < ± ÄTr nucl. A i ><A i E S /h (GHz) 1S 50 25 0-25 A 6 A 5 A 4 A 3 Y 3 Y 2 A 2 A 1 Y -50 1 0.0 0.5 1.0 1.5 B (T) 2 3 S states have electronic and nuclear parts In m J,m I > basis: A 6 = -sinq + 0, +> + cos q + 1, - > A 5 = 1, + > B=0 : sin 2 q + =1/3 and sin 2 q - =2/3 B=1.5T : sin 2 q +» sin 2 q -» 0.55 10-2 Low B : strong entanglement of electronic and nuclear orientations spin temperature distribution of populations High B : 3 pairs of states of (almost) given electronic state and opposite m I each ME collision mixes populations within a pair of states 1/ sin 2 q collisions (200) required to transfer between pairs of states

ME collisions Isotopic mixtures 14 1S He3 2S 2S He4 ME collision in He3-He4 mixtures : He3 + He4* He4 + He3* ± > Y i > ± > < ± Ä Y i ><Y i E S /h (GHz) 50 25 0-25 1S A 6 A 5 A 4 A 3 Y 3 Y 2 A 2 A 1 Y -50 1 0.0 0.5 1.0 1.5 B (T) In m J > basis, 2 3 S He4 eigenstates are: Y 3 = 1 >, Y 2 = 0 >, Y 1 = -1 >, He3 metastable atoms are indirectly polarised from OP of He4* atoms

ME collisions Isotopic mixtures 15 1S He4 2S 2S He3 ME collision in He3-He4 mixtures : He4 + He3* He3 + He4* A i > Tr elec. A i ><A i Tr nucl. A i ><A i 1S 2 3 P J 1083 nm OP transitions 2 3 S 1 He4* populations are coupled to He3* populations He3 metastable atoms are indirectly polarised from OP of He4* atoms ME collisions The 3 types of ME collisions jointly contribute to MEOP operation in isotopic mixtures 1 1 S 0 I=1/2 I=0 3 He 4 He

ME collisions and spin temperature 16 metastable state ground state x x 2 A 5 A 6 2 3 S 1, F = 1/2 1 x x 2 x 3 A 1 A 2 A 3 A 4 1-3/2-1/2 +1/2 +3/2 m F Populations for P He =0.5 (x=3) x 2 3 S 1, F = 3/2 metastability exchange collisions 1 1 S 0, F = 1/2 ME collisions tend to enforce a spin-temperature distribution in 2 3 S, ruled by the (majority) 1 1 S nuclear polarisation P He : x β = e = ai+ 1 / a He He 1/b: spin temperature a i : relative population of 2 3 S sublevel A i i 1+ P = 1- P P He* =SL i a i, L i from sin 2 q ± (B) P He* = P He Key property of ME collisions: spin orientation is fully preserved

ME collisions and spin temperature + OP 17 Low B : ME collision rate g e =3.75 10 6 s -1 /mbar maximum OP rate g p <10 7 s -1 (radiative decay in 2 3 P state) ME collisions are the leading process, OP only perturbs the spin-temperature distribution of populations Absorption spectra low B 2 3 P level P He* > P He Drives P He build-up 2 3 S level

ME + OP results at low B 18 1 - OP light absorption decreases with Ø Ø Incident light intensity Nuclear polarisation P He 2 High P He are achieved (p-dependent) Absorption coeff. (m -1 ) C 9 OP 1 P He 0 0.1 0.5 0.8 0.01 0.01 0.1 1 10 g ij / (g T ij ) Reduced OP rate, Steady-state P He limited by losses

Compression of polarised gas the 'spin factories' 19

ME collisions and spin temperature + OP - high B 20 High B : 2 pairs of states efficiently depopulated into third pair by four strong pumping lines (within Doppler width) if g p > g e sin 2 q Spin temperature distribution only inside pumped pair of states High B : 3 pairs of states of (almost) given electronic state each ME collision mixes population within a pair of states 1/ sin 2 q collisions required to transfer orientation between pairs of states

ME collisions and spin temperature + OP - high B 21 1 - High P He are achieved in spite of HF decoupling 2 - Decrease of P He with p strongly reduced

Compression of polarised gas Easier at high B 22 Collier et al. J. Appl. Phys. 113, 204905 (2013) P He : 33-50%

General comment Orders of magnitude 23 Typical pumped atom density ~ 10 11 cm -3 «pressure ~ 10-9 bar, OP can only address a tiny fraction at a time of a sizeable sample 1 W IR light (l~1µm) «5 10 18 photons/s or 1.8 10 22 photons/hour 1 liter of gas contains 2.7 10 22 atoms photon efficiency h ~1 OP of individual atoms can be very fast and efficient but Polarising large amounts of gas requires high absorbed light power and significant time. Efficient OP usually requires: Ø good control of laser spectral features Ø good control of ground-state polarisation losses (relaxation)

Understanding MEOP limits 24 Detailed model: Write and solve rate equations for P He and all populations Ø Exact treatment of ME collisions Ø Light absorption/emission processes velocity-dependent in gas, position-dependent in cell coarse-grained description (crude!) Ø Collisional population transfer within 2 3 P ab-initio calculations in He4 line broadening measurements vs. pressure single rate, random transfer (crude!) Ø Relaxation in g.s., 2 3 S (phenomenological) 2 3 P level He3 (He4) 18 b j (+9 z j ) 6 a i (+3 y i ) Outputs: ü all populations vs. P He ü OP light absorption, photon efficiency h ü ME transfer to g.s., dp He /dt 2 3 S level

Understanding MEOP limits 25 Simple model: Use ang. momentum conservation Inputs: Ø absorbed OP light power, W las Ø photon efficiency h Ø Relaxation rate G R in g.s., dp dt W He abs = 2h - GR PHe NVcell! w ü W abs : measured ü h: computed or measured from build-up at P He =0 ü decay rate G D = G R (W abs =0)

Understanding MEOP limits Simple model: Use ang. momentum conservation Inputs: Ø absorbed OP light power, W las Ø photon efficiency h Ø Relaxation rate G R in g.s., Experiments: G r increases with W abs 25 dp dt W He abs = 2h - GR PHe NVcell! w ü W abs : measured ü h: computed or measured from build-up at P He =0 ü decay rate G D = G R (W abs =0) Batz et al. (2011) J. Phys. Conf. Ser. 294, 012002.

Understanding MEOP limits 26 cell cell Slopes Ang. momentum conservation in steady state from compiled data Upper limits for P He scale as 1/p

Understanding MEOP limits 27 Physical origin of OP-induced relaxation? G R scales with W abs, i.e. with 2 3 P atom density Ø Radiation trapping Ø Relaxation by He 2 * (metastable dimers) both experimentally ruled out.

Understanding MEOP limits 27 Physical origin of OP-induced relaxation? G R scales with W abs, i.e. with 2 3 P atom density n 23P Ø Radiation trapping Ø Relaxation by He 2 * (metastable dimers) both experimentally ruled out. Exchange with (depolarised) 2 3 P atoms? Ø Ø fast population mixing within 2 3 P: low P He** (large J-changing collision rate above 1 mbar) ME-like transfer of P He** to the ground state (large computed rate coefficients k 23P for 1 1 S -2 3 P excitation transfer) k 23P Loss rate for P He** =0 G loss =k 23P n 23P = {k 23P / (ghn)} W abs /V cell numerically, k 23P / (ghn) = 640 cm 3 /J

Understanding MEOP limits 27 Physical origin of OP-induced relaxation? G R scales with W abs, i.e. with 2 3 P atom density n 23P Ø Radiation trapping Ø Relaxation by He 2 * (metastable dimers) both experimentally ruled out. Exchange with (depolarised) 2 3 P atoms? Ø Ø fast population mixing within 2 3 P: low P He** (large J-changing collision rate above 1 mbar) ME-like transfer of P He** to the ground state (large computed rate coefficients k 23P for 1 1 S -2 3 P excitation transfer) Loss rate for P He** =0 G loss =k 23P n 23P = {k 23P / (ghn)} W abs /V cell numerically, k 23P / (ghn) = 640 cm 3 /J

Understanding MEOP limits - Prospects 28 Goal: elucidate the origin of G R at low and high B Method: fully characterise populations in 2 3 P state by absorption spectroscopy at various p, B, P He, in He3 and He3-He4 3 3 S 2 3 P P 0 P x P 1 P y P 2 706 nm probe 2 3 S 1.6 mbar 8 mbar

Understanding MEOP limits - Prospects 29 Goal: elucidate the origin of G R at low and high B Method: fully characterise populations in 2 3 P state by absorption spectroscopy at various p, B, P He, in He3 and He3-He4 Objectives: Explain (and alleviate) current MEOP limits Extend to higher B, lower T, He3-He4 mixtures for existing and emerging applications