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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