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

• K magnetometer

⇒ Elimination of spin-exchange relaxation ⇒ Experimental setup ⇒ Magnetometer performance ⇒ Theoretical sensitivity ⇒ Magnetic field mapping and other applications

• K-3He co-magnetometer

⇒ K-3He spin-exchange ⇒ Self-compensating operation ⇒ Coupled spin resonances ⇒ CPT tests and other fundamental measurements

Outline

Atomic Spin Magnetometers

ω = γB

• Optically pumped alkali-metals:

K, Rb, Cs

• Hyperpolarized noble gases:

3He, 129Xe

• DNP-enhanced NMR:

H

δω = 1 T2Nt

P

Fundamental Sensitivity limit:

• 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 ~ 109 cm-3 ⇒Linewidth ~ 1 Hz

• Fundamental Limitation: Spin-exchange collisions

T 2

–1 = σse v n

σ se = 2 × 10–14cm2

• D. Budker (Berkeley)
• E. Aleksandrov (St. Petersburg)

γ = gµB h(2I + 1) δB = 1fT cm3 Hz

Eliminating spin-exchange relaxation

• Spin exchange collisions preserve total mF, but change F
• For ω á 1/Τse (B á 0.1G)

⇒ No relaxation due to spin exchange B MF=2 MF=1

ω ω

SE B MF=2 MF=1

ω1

ω1 = 3(2I + 1) 3 + 4I(I + 1)ω =2 3ω ω S

B

∆ω ≈ 1/Τse ω

= ± gµ BB h(2I + 1)

F=I±½

S ∆ω ≈ 1/Τsd ω

B

(low P)

Zero-Field Magnetometer

• Residual fields are zeroed out
• Pump laser defines quantization axis
• Detect tilt of K polarization due to a magnetic field
• Optical rotation used for detection

To computer Photodiode Lock-in Amplifier Calcite Polarizer l /4 Single Frequency Diode Laser High Power Diode Laser Probe Beam Pump Beam Field Coils Oven Cell Magnetic Shields Faraday Modulator x z y

y

Pump Probe B S

Measurements of T2

S

B

Chopped pump beam

• Synchronous optical pumping

10 20 30 40 50 Chopper Frequency (Hz)

• 0.1

0.0 0.1 0.2 Lock-in Signal (V rms )

n = 1014 cm−3 1/Tse= 105 sec−1 Lorentzian linewidth = 1.1 Hz

− in phase − out of phase

Magnetic Field Dependence

T2

–1 = Γsd + 5ω2

3Γse

Γsd due to K-K, K-3He collisions, diffusion

• W. Happer and H. Tang, PRL 31, 273 (1973),
• W. Happer and A. Tam, PRA 16, 1877 (1977)

50 100 150 200 250 Chopper Frequency (Hz) 1 2 3 4 5 6 Resonance half-width Dn (Hz)

Spin-Destruction collisions

• Calculated linewidth

⇒ T = 190°C nK = 1×1014 cm-3 ⇒ 3 amg of He nHe = 8 ×1019 cm-3 R = 1 cm

Γsd=12 sec−1(Diff)+7 sec−1(K-K)+13 sec−1(K-He)+2 sec−1 (N2)=34 sec-1

• From measured linewidth Γsd = 6 × 2π ∆ν = 41 sec-1

R

T2

– 1 =

+ σ sd

K vnK +σ sd He vnHe

Dπ 2

2 Alkali Metal

He Ne N2

K 1×10−18 cm2 8×10−25 cm2 1×10−23 cm2 Rb 9×10−18 cm2 9×10−24 cm2 1×10−22 cm2 Cs 2×10−16 cm2 3×10−23 cm2 6×10−22 cm2

Slowing-down factor

Magnetometer Sensitivity

Response to square modulation of vertical field

1 2 3 4 5

Time (sec)

• 3
• 2
• 1

1 2

Magnetometer signal

10 20 30 40 50 Frequency (Hz) 0.1 0.2 0.3 0.4 Hz) Noise spectrum (Vrms/

700 fTrms modulation at different frequencies

SNR = 70 Direct sensitivity measurement gives 10fT/ Hz

Highest demonstrated in an atomic magnetometer

Present Limitation

• Johnson noise currents in magnetic shields
• Removed all conductors from within the 16” inner shield
• Noise estimates 7±2fT/
• No Johnson noise in superconducting shields

I = 4kT∆ f R

Hz

Theoretical Sensitivity Estimates

• Transverse polarization signal
• Probed using optical rotation

⇒ Shot noise for a 1” dia. cell

• Higher than theoretical estimates for SQUID detectors

µ Px = g

BByR

(T2 +R)2

−1

δB = 0.002fT/ Hz

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

Linear Polarizer Multi-Channel Detector Pump Laser Probe Laser S Circular Polarization Linear Polarization K+He B Gas Cell

3He Co-magnetometer

• Simply replace 4He buffer gas with 3He
• 3He is polarized by spin-exchange

⇒TSE = 40 hours for nK=1014cm−3 ⇒T1 ~ 300 hours

K-He He

5 10 15 20 25 30 35 Time (days) 20 40 60 80 100 NMR Signal (mV)

Spin-exchange shifts

• Polarized 3He creates a magnetic field seen by K atoms

⇒Enhanced due to contact interaction: κ0 = 6 ⇒Typical value: 1-10 mG

• Polarized 3He does not see its own classical field in a spherical cell

⇒Long range field average to zero ⇒No contact interaction

• Polarized K creates a magnetic field seen by 3He atoms

⇒Typical value 10-50 µG

BK = 8π 3 κ 0M He

m m m m B

BHe= 8π 3 κ 0M K

Simultaneous operation

Apply an axial magnetic field that:

• Cancels the field BK due to 3He, so K magnetometer
• perates at zero field
• Provides a holding field for 3He, so it doesn’t relax due

to field gradients

• Allows self-compensating operation

T1

– 1 = D ∇Bx 2 + ∇By 2

Bz

2

Magnetic field self-compensation

Perfect alignment Small transverse field

Pump Laser S Q Bz BK Pump Laser S Q B z BK B x Probe Laser Probe Laser

s s s = 0 s = 0

S – electron spin, Q – 3He spin

• Perfect compensation for Bz = −BK
• 3He polarization adiabatically follows total magnetic field

⇒ For changes slow compared with 3He 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

5 10 15 20 25

Time (sec)

• 10
• 5

5 10

K Signal (arb. units)

1 2 3 4

Vertical Field (µG)

Bz=0.536 mG Bz=0.529 mG

Compensated Slightly uncompensated

Adjustment of self-compensation

• Response changes sign as axial field is scanned across

compensation point

0.51 0.52 0.53 0.54 0.55 0.56

Axial Field (mG)

• 1.0
• 0.5

0.0 0.5 1.0

Response to Vertical Field Step

Frequency response of compensated

3He-K magnetometer

• Apply a sine-wave of varying frequency

20 40 60 80 100

Frequency (Hz)

0.0 0.5 1.0 1.5 2.0 2.5

3He-K magnetometer frequency response

5 10 15 Time (sec)

• 0.6
• 0.4
• 0.2

0.0 0.2 0.4 Signal (arb. units) Bz = 0.868 mG 5 10 15 Time (sec)

• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

0.0 Signal (arb. units) Bz = 1.24 mG 2 4 6 8 10 12 Time (sec)

• 2.5
• 2.0
• 1.5
• 1.0
• 0.5

0.0 Signal (arb. units) Bz = 1.05 mG

Transient Response

10 20 30 40

• 0.0004
• 0.0002

0.0002

• 60. mG

10 20 30 40

• 0.0003
• 0.0002
• 0.0001

0.0001 0.0002 0.0003

• 50. mG

10 20 30 40

• 0.0015
• 0.001
• 0.0005

0.0005 0.001 0.0015

• 10. mG

Transient Response - Bloch Model

Large 3He Perturbation

50 100 150 Time (sec)

• 6
• 4
• 2

2 4 6 Signal (arb. units)

Non-linear 3He magnetization relaxation (similar to LXe)

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

⇒bµ 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

L =–bµψγ5γµψ=–bi σi

be

i; 10¡3be

bn;p

i

; 10¡3bn;p cn;p

ik ; 10¡3cn;p 00

de

0i; 10¡3de 00

dn;p

0i ; 10¡3dn;p 00

electron g ¡ 2 [25] 10¡24GeV 10¡21 p ¡ ¹ p [26] 10¡26

201Hg-199Hg [27]

10¡29GeV 10¡27 10¡26

21Ne-3He [28]

10¡27 Cs-199Hg [24] 10¡27 GeV 10¡30 GeV 10¡25 10¡28

3He-129Xe[29]

10¡31GeV 10¡28 Polarized Solid [30] 10¡28 GeV K-3He (This proposal) 10¡31 GeV 10¡34 GeV 10¡29 10¡32

10fT/ Hz bie = 10−30 GeV, bin = 10−33 GeV

Integration time of 106 sec 2 orders of magnitude improvement over best existing limits

Expected Sensitivity

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

Other Applications

• EDM search ?

⇒ Cs

→Higher density at lower temperature →Larger relaxation cross-sections

⇒129Xe

→Higher enhancement factor κ0 →Larger relaxation cross-sections

⇒Application of electric field?

• Axion, exotic forces ….

Conclusions

• Sensitive K magnetometer

⇒Spin-exchange relaxation eliminated

• 3He-K co-magnetometer

⇒Effective compensation of magnetic fields by 3He ⇒Noise reduction at low frequency

• Collaborators

⇒Tom Kornack ⇒Iannis Kominis ⇒Joel Allred ⇒Rob Lyman ⇒Marty Boyd

• Support

⇒NSF ⇒NIST Precision Measurement ⇒NIH ⇒Packard Foundation ⇒U. of Washington, Princeton U. Princeton

• U. of Washington