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: Hyperpolarized noble gases: DNP-enhanced NMR: K, Rb, Cs 3 He, 129 Xe H Fundamental Sensitivity limit: δω = P 1 T 2 Nt
State-of-the-Art magnetometers: Alkali-metal: K or Rb Large cell: 10-15 cm diameter Surface coating to reduce spin relaxation Alkali-metal denstity ~ 10 9 cm -3 Linewidth ~ 1 Hz Fundamental Limitation: Spin-exchange collisions T 2 1 = σ se v n σ se = 2 10 14 cm 2 D. Budker (Berkeley) E. Aleksandrov (St. Petersburg) γ = g µ B h(2i +1) δb=1ft cm 3 Hz
Eliminating spin-exchange relaxation Spin exchange collisions preserve total m F, but change F S B For ω á 1/Τ se gµ ω = ± B B F=I±½ h(2i +1) ω 1/Τ se ω (B á 0.1G) M F=1 ω SE B M F=2 ω M F=2 S B M F=1 ω 1 B ω 1/Τ sd ω No relaxation due to spin exchange ω 1 = 3(2I +1) 3+4I (I +1) ω = 2 3 ω (low P)
Zero-Field Magnetometer Pump B Probe S Single Frequency Diode Laser l /4 Faraday Modulator Pump Beam Magnetic Shields Field Coils Cell High Power Diode Laser Probe Beam Oven x Calcite Polarizer y z Lock-in Amplifier Photodiode To computer Residual fields are zeroed out Pump laser defines quantization axis Detect tilt of K polarization due to a y magnetic field Optical rotation used for detection
Synchronous optical pumping Measurements of T 2 Chopped pump beam B S Lock-in Signal (V rms ) 0.2 0.1 0.0 in phase out of phase n = 10 14 cm 3 1/T se = 10 5 sec 1 Lorentzian linewidth = 1.1 Hz -0.1 10 20 30 40 50 Chopper Frequency (Hz)
Magnetic Field Dependence Resonance half-width Dn(Hz) 6 5 4 3 2 1 0 0 50 100 150 200 250 Chopper Frequency (Hz) T 2 1 = Γ sd + 5 ω 2 3Γ se Γ sd due to K-K, K- 3 He collisions, diffusion W. Happer and H. Tang, PRL 31, 273 (1973), W. Happer and A. Tam, PRA 16, 1877 (1977)
T 2 1 = Spin-Destruction collisions D π 2 2 R + σ K sd vn K +σ He sd vn He Alkali Metal He Ne N 2 K 1 10 18 cm 2 8 10 25 cm 2 1 10 23 cm 2 Rb 9 10 18 cm 2 9 10 24 cm 2 1 10 22 cm 2 Cs 2 10 16 cm 2 3 10 23 cm 2 6 10 22 cm 2 Calculated linewidth T = 190 C n K = 1 10 14 cm -3 3 amg of He n He = 8 10 19 cm -3 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 Magnetometer signal 2 1 0-1 -2-3 Response to square modulation of vertical field 0 1 2 3 4 5 Time (sec) Noise spectrum (Vrms/ Hz)0.4 0.3 0.2 0.1 0 700 ft rms modulation at different frequencies SNR = 70 0 10 20 30 40 50 Frequency (Hz) Direct sensitivity measurement gives 10fT/ Hz Highest demonstrated in an atomic magnetometer
Present Limitation Johnson noise currents in magnetic shields I = 4kT f 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 BB y R 1 (T 2 +R) 2 Probed using optical rotation Shot noise for a 1 dia. cell δb=0.002ft/ Hz Higher than theoretical estimates for SQUID detectors
Magnetic Gradient Imaging Higher buffer gas pressure Higher K density Higher pumping rate Reduce diffusion Increase bandwidth Suppress Johnson noise Applications Magnetic fields produced by brain, heart, etc Replacement for arrays of SQUIDs in liquid helium Pump Laser Circular Polarization Linear Polarizer Probe Laser K+He S Multi-Channel Detector B Gas Cell Linear Polarization
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 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 No contact interaction B K = 8 π 3 κ 0M He m B m m Polarized K creates a magnetic field seen by 3 He atoms Typical value 10-50 µg B He= 8 π 3 κ 0M K m
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 T 1 1 = D B x 2 + B y 2 B z 2 Allows self-compensating operation
Magnetic field self-compensation Pump Laser s B K S Q B z Pump Laser s B x B z B K S Q Perfect alignment Probe Probe Laser Laser s = 0 s = 0 Small transverse field 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 10 B z =0.536 mg B z =0.529 mg 4 K Signal (arb. units) 5 0-5 3 2 1 Vertical Field (µg) -10 Compensated 0 5 10 15 20 25 Time (sec) 0 Slightly 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)
0.4 B z =0.868mG Transient Response 0.0 B z =1.24mG Signal (arb. units) 0.2 0.0-0.2-0.4 Signal (arb. units) -0.1-0.2-0.3-0.4-0.6 0 5 10 15 Time (sec) 0.0 B z =1.05mG -0.5 0 5 10 15 Time (sec) 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 0.0002 0-0.0002-0.0004 0.0003 0.0002 0.0001-0.0001-0.0002-0.0003 0 0 10 20 30 40 0.0015 0.001 0.0005 0-0.0005-0.001-0.0015-10. mg 0 10 20 30 40 0 10 20 30 40
Large 3 He Perturbation Non-linear 3 He magnetization relaxation (similar to LXe) Signal (arb. units) 6 4 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= bµψγ 5 γ µ ψ= bi 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 10fT/ Hz b i e = 10 30 GeV, b i n = 10 33 GeV Integration time of 10 6 sec 2 orders of magnitude improvement over best existing limits b e i ; 10 3 b e 0 electron g 2 [25] 10 24 GeV 10 21 p ¹p [26] 10 26 201 Hg- 199 Hg [27] 10 29 GeV 10 27 10 26 b n;p i 21 Ne- 3 He [28] 10 27 ; 10 3 b n;p 0 c n;p ik ; 10 3 c n;p 00 d e 0i ; 10 3 d e 00 d n;p 0i ; 10 3 d n;p 00 Cs- 199 Hg [24] 10 27 GeV 10 30 GeV 10 25 10 28 3 He- 129 Xe[29] 10 31 GeV 10 28 PolarizedSolid[30] 10 28 GeV K- 3 He (This proposal) 10 31 GeV 10 34 GeV 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 µrad stability using active steering ~1/ N Pump power modulation
EDM search? Cs Other Applications Higher density at lower temperature Larger relaxation cross-sections 129 Xe Higher enhancement factor κ 0 Larger relaxation cross-sections Application of electric field? Axion, exotic forces.
Conclusions Sensitive K magnetometer Spin-exchange relaxation eliminated 3 He-K co-magnetometer Effective compensation of magnetic fields by 3 He Noise reduction at low frequency
Collaborators Tom Kornack Iannis Kominis Joel Allred Rob Lyman Marty Boyd Princeton U. of Washington Support NSF NIST Precision Measurement NIH Packard Foundation U. of Washington, Princeton U.