Atomic magnetometers:new twists to the old story

Michael RomalisPrinceton 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= 1T2 NtP

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 ωω

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 computerPhotodiode

Lock-in Amplifier

Calcite Polarizer

l /4

Single Frequency

Diode Laser

High PowerDiode Laser

Probe Beam

Pump Beam Field Coils

Oven

Cell

Magnetic ShieldsFaraday

Modulator

x

zy

y

Pump ProbeB

S

Measurements of T2

S

BChopped pump beam

• Synchronous optical pumping

10 20 30 40 50Chopper Frequency (Hz)

-0.1

0.0

0.1

0.2

Lock

-in S

igna

l (V r

ms )

n = 1014 cm−3

1/Tse= 105 sec−1

Lorentzian linewidth = 1.1 Hz

− in phase

− out of phase

Magnetic Field Dependence

T2 –1 = Γ sd +

5ω2

3Γ se

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)

0 50 100 150 200 250Chopper Frequency (Hz)

0

1

2

3

4

5

6

Res

onan

ce h

alf-

wid

th D

n (H

z)

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

RT2

– 1 = + σ sdK vnK +σ sd

He vnHeDπ2

2

Alkali Metal He Ne N2K 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 SensitivityResponse to square

modulation of vertical field

0 1 2 3 4 5Time (sec)

-3

-2

-1

0

1

2

Mag

neto

met

ersi

gnal

0 10 20 30 40 50Frequency (Hz)

0

0.1

0.2

0.3

0.4

Hz)

Noi

se sp

ectru

m (V

rms/

700 fTrms modulation atdifferent frequencies

SNR = 70

Direct sensitivity measurement gives 10fT/ HzHighest 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∆ fR

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

µPx =

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

LinearPolarizer

Multi-ChannelDetector

Pump Laser

ProbeLaser

SCircularPolarization

LinearPolarization

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

0 5 10 15 20 25 30 35Time (days)

0

20

40

60

80

100

NM

RSi

gnal

(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 = 8π3 κ 0M He

m

m

m

m

B

BHe= 8π3 κ 0M K

Simultaneous operation

Apply an axial magnetic field that:

• Cancels the field BK due to 3He, so K magnetometeroperates at zero field

• Provides a holding field for 3He, so it doesn’t relax dueto field gradients

• Allows self-compensating operation

T1– 1 = D

∇ Bx2 + ∇ By

2

Bz2

Magnetic field self-compensation

Perfect alignment Small transverse field

Pump Laser

S

Q

Bz

BK

Pump Laser

S

Q

B

zBK

Bx

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 invertical magnetic field

0 5 10 15 20 25

Time (sec)

-10

-5

0

5

10K

Sign

al(a

rb.u

nits

)

0

1

2

3

4

Ver

tical

Fiel

d(µ

G)

Bz=0.536 mG Bz=0.529 mG

Compensated Slightlyuncompensated

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

Res

pons

eto

Ver

tical

Fiel

dSt

ep

Frequency response of compensated3He-K magnetometer

• Apply a sine-wave of varying frequency

0 20 40 60 80 100Frequency (Hz)

0.0

0.5

1.0

1.5

2.0

2.53 H

e-K

mag

neto

met

erfre

quen

cyre

spon

se

0 5 10 15Time (sec)

-0.6

-0.4

-0.2

0.0

0.2

0.4

Sign

al(a

rb.u

nits)

Bz = 0.868 mG

0 5 10 15Time (sec)

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

Sign

al(a

rb.u

nits

)

Bz = 1.24 mG

0 2 4 6 8 10 12Time (sec)

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

Sign

al(a

rb.u

n its

)

Bz = 1.05 mG

Transient Response

0 10 20 30 40

- 0.0004

- 0.0002

0

0.0002

- 60. mG

0 10 20 30 40

- 0.0003- 0.0002- 0.0001

00.00010.00020.0003

50. mG

0 10 20 30 40- 0.0015

- 0.001- 0.0005

00.0005

0.0010.0015

- 10. mG

Transient Response - Bloch Model

Large 3He Perturbation

0 50 100 150Time (sec)

-6

-4

-2

0

2

4

6Si

gna l

(arb

.uni

ts)

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 fieldtheory with point particles

• Symmetry tests is one of very few possible ways to accessQuantum Gravity effects experimentally.

• Lorentz Symmetry can also be broken in String Theory

• Symmetry violation can be due to Cosmological anisotropy - Wasthe 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

bei ; 10¡3be

0bn;pi ; 10¡3bn;p

0cn;pik ; 10

¡3cn;p00

de0i; 10

¡3de00

dn;p0i ; 10

¡3dn;p00

electron g ¡ 2 [25] 10¡24GeV 10¡21

p¡ ¹p [26] 10¡26201Hg-199Hg [27] 10¡29GeV 10¡27 10¡2621Ne-3He [28] 10¡27

Cs-199Hg [24] 10¡27 GeV 10¡30 GeV 10¡25 10¡283He-129Xe[29] 10¡31GeV 10¡28

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

10fT/ Hz bie = 10−30 GeV,

bin = 10−33 GeVIntegration 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