Atomic magnetometers: new twists to the old story Michael Romalis - PowerPoint PPT Presentation

Atomic magnetometers: new twists to the old story Michael Romalis Princeton University

Outline • K magnetometer ⇒ Elimination of spin-exchange relaxation ⇒ Experimental setup ⇒ Magnetometer performance ⇒ Theoretical sensitivity ⇒ Magnetic field mapping and other applications • K- 3 He co-magnetometer ⇒ K- 3 He spin-exchange ⇒ Self-compensating operation ⇒ Coupled spin resonances ⇒ CPT tests and other fundamental measurements

Atomic Spin Magnetometers ω = γ B • Optically pumped alkali-metals: K, Rb, Cs • Hyperpolarized noble gases: 3 He, 129 Xe • DNP-enhanced NMR: H 1 δω = Fundamental Sensitivity limit: T 2 Nt P

• State-of-the-Art magnetometers: D. Budker (Berkeley) ⇒ Alkali-metal: K or Rb ⇒ Large cell: 10 - 15 cm diameter E. Aleksandrov (St. Petersburg) ⇒ Surface coating to reduce spin relaxation ⇒ Alkali-metal denstity ~ 10 9 cm -3 ⇒ Linewidth ~ 1 Hz • Fundamental Limitation: Spin-exchange collisions g µ B –1 = σ se v n T 2 γ = σ se = 2 × 10 – 14 cm 2 h (2 I + 1) cm 3 δ B = 1fT Hz

Eliminating spin-exchange relaxation • Spin exchange collisions preserve total m F , but change F g µ B B S ω = ± M F=2 F=I ± ½ h (2 I + 1) SE M F=1 ω B ∆ω ≈ 1/Τ se ω B ω • For ω á 1/Τ se (B á 0.1G) M F=2 S ω 1 M F=1 B B ∆ω ≈ 1/Τ sd 3(2 I + 1) 3 + 4 I ( I + 1) ω = 2 ω 1 = 3 ω ω ⇒ No relaxation due to spin exchange (low P)

Zero-Field Magnetometer Faraday Modulator Magnetic Shields B Single Frequency Probe Diode Laser Pump Pump Beam Field Coils l /4 Cell S High Power Probe Beam Oven Diode Laser x Calcite Polarizer Photodiode z y Lock-in Amplifier To computer • Residual fields are zeroed out • Pump laser defines quantization axis • Detect tilt of K polarization due to a magnetic field y • Optical rotation used for detection

Measurements of T 2 • Synchronous optical pumping B Chopped pump beam S − in phase n = 10 14 cm − 3 0.2 ) − out of phase rms 1/T se = 10 5 sec − 1 Lock-in Signal (V 0.1 Lorentzian linewidth = 1.1 Hz 0.0 -0.1 10 20 30 40 50 Chopper Frequency (Hz)

Magnetic Field Dependence –1 = Γ sd + 5 ω 2 6 T 2 3 Γ se (Hz) 5 Γ sd due to K-K, K- 3 He collisions, Resonance half-width Dn 4 diffusion 3 2 1 0 0 50 100 150 200 250 Chopper Frequency (Hz) W. Happer and H. Tang, PRL 31 , 273 (1973), W. Happer and A. Tam, PRA 16 , 1877 (1977)

Spin-Destruction collisions D π 2 – 1 = + σ sd K vn K + σ sd He vn He T 2 2 R Alkali Metal He Ne N 2 1 × 10 − 18 cm 2 8 × 10 − 25 cm 2 1 × 10 − 23 cm 2 K 9 × 10 − 18 cm 2 9 × 10 − 24 cm 2 1 × 10 − 22 cm 2 Rb 2 × 10 − 16 cm 2 3 × 10 − 23 cm 2 6 × 10 − 22 cm 2 Cs • Calculated linewidth n K = 1 × 10 14 cm -3 ⇒ T = 190°C n He = 8 × 10 19 cm -3 ⇒ 3 amg of He R = 1 cm Γ sd =12 sec − 1 (Diff)+7 sec − 1 (K-K)+13 sec − 1 (K-He)+2 sec − 1 (N 2 )=34 sec -1 • From measured linewidth Γ sd = 6 × 2π ∆ν = 41 sec -1 Slowing-down factor

Magnetometer Sensitivity Response to square 700 fT rms modulation at modulation of vertical field different frequencies 2 0.4 Hz) SNR = 70 1 Magnetometer signal Noise spectrum (Vrms/ 0.3 0 0.2 -1 0.1 -2 -3 0 0 1 2 3 4 5 0 10 20 30 40 50 Time (sec) Frequency (Hz) Direct sensitivity measurement gives 10fT/ Hz Highest demonstrated in an atomic magnetometer

Present Limitation • Johnson noise currents in magnetic shields 4 kT ∆ f I = R • Removed all conductors from within the 16” inner shield • Noise estimates 7 ± 2fT/ Hz • No Johnson noise in superconducting shields

Theoretical Sensitivity Estimates • Transverse polarization signal µ P x = g B B y R − 1 ( T 2 + R ) 2 • Probed using optical rotation ⇒ Shot noise for a 1” dia. cell δ B = 0.002fT/ Hz • Higher than theoretical estimates for SQUID detectors

Magnetic Gradient Imaging Multi-Channel • Higher buffer gas pressure Detector • Higher K density Linear Polarizer • Higher pumping rate ⇒ Reduce diffusion B ⇒ Increase bandwidth Pump Laser S ⇒ Suppress Johnson noise Circular Polarization K+He • Applications Gas Cell ⇒ Magnetic fields produced by Probe Linear brain, heart, etc Laser Polarization ⇒ Replacement for arrays of SQUIDs in liquid helium

3 He Co-magnetometer • Simply replace 4 He buffer gas with 3 He • 3 He is polarized by spin-exchange K-He ⇒ T SE = 40 hours for n K =10 14 cm − 3 He ⇒ T 1 ~ 300 hours 100 80 NMR Signal (mV) 60 40 20 0 0 5 10 15 20 25 30 35 Time (days)

Spin-exchange shifts • Polarized 3 He creates a magnetic field seen by K atoms B K = 8 π 3 κ 0 M He ⇒ Enhanced due to contact interaction: κ 0 = 6 ⇒ Typical value: 1-10 mG • Polarized 3 He does not see its own classical field in a spherical cell ⇒ Long range field average to zero m ⇒ No contact interaction B m m • Polarized K creates a magnetic field seen by 3 He atoms m B He = 8 π 3 κ 0 M K ⇒ Typical value 10-50 µ G

Simultaneous operation Apply an axial magnetic field that: Cancels the field B K due to 3 He, so K magnetometer • operates at zero field Provides a holding field for 3 He, so it doesn’t relax due • to field gradients 2 + ∇ B y – 1 = D ∇ B x 2 T 1 2 B z • Allows self-compensating operation

Magnetic field self-compensation B Bz B x z B K B K S s s S Pump Pump Laser Laser Q Q Probe Probe Laser Laser s = 0 s = 0 Small transverse field Perfect alignment S – electron spin, Q – 3 He spin • Perfect compensation for B z = − B K • 3 He polarization adiabatically follows total magnetic field ⇒ For changes slow compared with 3 He Larmor frequency • K spins do not see a magnetic field change • Also works for magnetic field gradients

Response of the co-magnetometer to a step in vertical magnetic field B z =0.536 mG B z =0.529 mG 10 4 K Signal (arb. units) Vertical Field ( µ G) 5 3 0 2 -5 1 -10 0 0 5 10 15 20 25 Time (sec) Slightly Compensated uncompensated

Adjustment of self-compensation • Response changes sign as axial field is scanned across compensation point Response to Vertical Field Step 1.0 0.5 0.0 -0.5 -1.0 0.51 0.52 0.53 0.54 0.55 0.56 Axial Field (mG)

Frequency response of compensated 3 He-K magnetometer • Apply a sine-wave of varying frequency 3 He-K magnetometer frequency response 2.5 2.0 1.5 1.0 0.5 0.0 0 20 40 60 80 100 Frequency (Hz)

Transient Response B z = 0.868 mG B z = 1.24 mG 0.4 0.0 Signal (arb. units) Signal (arb. units) 0.2 -0.1 0.0 -0.2 -0.2 -0.3 -0.4 -0.4 -0.6 -0.5 0 5 10 15 0 5 10 15 B z = 1.05 mG Time (sec) Time (sec) 0.0 Signal (arb. units) -0.5 -1.0 -1.5 -2.0 -2.5 0 2 4 6 8 10 12 Time (sec)

Transient Response - Bloch Model - 60. mG 50. mG 0.0003 0.0002 0.0002 0.0001 0 0 - 0.0001 - 0.0002 - 0.0002 - 0.0004 - 0.0003 0 10 20 30 40 0 10 20 30 40 - 10. mG 0.0015 0.001 0.0005 0 - 0.0005 - 0.001 - 0.0015 0 10 20 30 40

Large 3 He Perturbation Non-linear 3 He magnetization relaxation (similar to LXe) 6 4 Signal (arb. units) 2 0 -2 -4 -6 0 50 100 150 Time (sec)

CPT Violation • CPT is an exact symmetry in a local field theory with point particles, such as the Standard Model or Supersymmetry • String Theory or any theory of Quantum Gravity is not a local field theory with point particles • Symmetry tests is one of very few possible ways to access Quantum Gravity effects experimentally. • Lorentz Symmetry can also be broken in String Theory • Symmetry violation can be due to Cosmological anisotropy - Was the Universe really created isotropic?

How to detect CPT violation ? • Compare properties of particles and anti-particles ⇒ Masses, magnetic moments, etc ⇒ Anti-particles are difficult to produce and store • Note that CPT violation is a vector interaction L = –b µ ψγ 5 γ µ ψ =–b i σ i ⇒ b µ is a CPT and Lorentz violating vector field in space ⇒ Acts as a magnetic field ⇒ Depends on the orientation of the spin direction in space ⇒ Presumably couples to particles differently from magnetic field ⇒ Can be detected in a co-magnetometer as a diurnal signal

Expected Sensitivity b ie = 10 − 30 GeV, 10fT/ Hz b in = 10 − 33 GeV Integration time of 10 6 sec 2 orders of magnitude improvement over best existing limits b n;p ; 10 ¡ 3 b n;p c n;p ik ; 10 ¡ 3 c n;p d n;p 0 i ; 10 ¡ 3 d n;p b e i ; 10 ¡ 3 b e d e 0 i ; 10 ¡ 3 d e 0 i 0 00 00 00 10 ¡ 24 GeV 10 ¡ 21 electron g ¡ 2 [25] 10 ¡ 26 p [26] p ¡ ¹ 201 Hg- 199 Hg [27] 10 ¡ 29 GeV 10 ¡ 27 10 ¡ 26 21 Ne- 3 He [28] 10 ¡ 27 10 ¡ 27 GeV 10 ¡ 30 GeV Cs- 199 Hg [24] 10 ¡ 25 10 ¡ 28 3 He- 129 Xe[29] 10 ¡ 31 GeV 10 ¡ 28 10 ¡ 28 GeV Polarized Solid [30] 10 ¡ 31 GeV 10 ¡ 34 GeV K- 3 He (This proposal) 10 ¡ 29 10 ¡ 32

Non-magnetic shifts • Light shift suppression ⇒ Pump laser → Perpendicular to probe direction → Tuned exactly on resonance ⇒ Probe Laser → Linearly polarized → Detuned far off-resonance → Perpendicular to field measurement direction • Polarization Shift Suppression → Spherical cell → Polarization perpendicular to the measurement direction → Balanced magnetic fields • Beam Pointing Stability → µ rad stability using active steering ~1/ √ N → Pump power modulation