Tests of Lorentz Invariance with alkali- metal noble-gas - - PowerPoint PPT Presentation

Tests of Lorentz Invariance with alkali- metal– noble-gas co-magnetometer (+ other application)

Michael Romalis Princeton University

Tests of Fundamental Symmetries

• Parity violation → weak interactions
• CP violation → Three generations of quarks

Lorentz and CPT symmetry

• Exact in standard field theory
• Can be broken in many ways by quantum gravity effects

⇒For example, Plank mass introduces an energy scale, so a particle given a Lorentz boost to p ~ Mpl should experience different physics due to quantum gravity effects. Symmetry violations found before corresponding particles were produced directly

• Lorentz Symmetry

⇒ Motivations for possible violation ⇒ Experimental signatures

• Development of sensitive co-magnetometer

⇒ Elimination of alkali-metal spin-exchange broadening ⇒ Alkali-metal noble gas co-magnetometer ⇒ Limits on Lorentz-violating spin coupling

• Applications

⇒ Sensitive magnetometer for detection of brain fields ⇒ Nuclear spin gyroscope

Outline

Parametrizing Lorentz and CPT Violation

• Use effective field theory:
• Many mechanisms:

⇒ spontaneous symmetry breaking: vector fields with VEV ⇒ Modified dispersion relationships: E2 = m2 + p2 + η p3/MPl ⇒ Non-commutative space time [xµ,xν] = θµν

a,b - CPT-odd, dimension of energy c,d - CPT-even, dimensionless

Kostelecky et al.

D = 3

L = – ψ (m + aµγ µ + bµγ5γ µ)ψ + i

2 ψ (γν + c

µν γ µ + dµν γ5 γ µ)∂νψ

D = 4 + higher dimension operators

Jacobson, Amelino-Camelia Myers, Pospelov, Sudarsky Witten, Schwartz, Pospelov

Experimental Signatures

• Spin coupling:
• Limiting velocities for particles different from c
• Photon effects: vacuum dispersion, vacuum birefringence,

directional dependence of the speed of light

L = – bµψγ5γ µψ = – b ·S

S B⋅ − = = m ge A e 2 ψ γ ψ

µ µ

L

c.f.

i L = 2 ψ c

µν γ µ ∂ ν

ψ

(cπ-c)/c ~ c00

In general, spin coupling seems to be the most robust effect in most models.

Spin coupling experiments

• Vector interaction gives a sidereal signal in the lab frame
• Need a co-magnetometer to distinguish from regular magnetic fields

and avoid cancellation by magnetic shields

• Assume coupling is not in proportion to the magnetic moment
• Don’t need anti-particles to search for CPT violation
• Preferred direction bµ

could be the direction of motion relative to CMB

bµ hν1= 2µ1 B + 2β1 (b·nB) hν2= 2µ2 B + 2β2 (b·nB) ) ( 2

2 2 1 1 2 2 1 1 B

h n b⋅         µ β − µ β = µ ν − µ ν

Atomic Spin Magnetometers

B µ ω

ω = 2µB h

T2 1/(πT2)

FFT

Quantum noise limit for N atoms:

δω = 1 T2Nt

Choice of Active Species:

• Unpaired electron - high magnetic moment
• 2S1/2 ground state - relatively small collisional spin relaxation rate
• Easy to polarize using optical pumping

Alkali metal atoms: Na, K, Rb, Cs

Collisions between alkali atoms, with buffer gas and cell walls

• Spin-exchange alkali-alkali collisions

⇒ Increasing density of atoms decreases spin relaxation time ⇒ Under ideal conditions:

T 2

–1 = σse v n

σ se = 2 × 10–14cm2

δB ¥ 1fT

cm3 Hz T2N = σsevV

Mechanisms of spin relaxation

Why do spin-exchange collisions cause relaxation?

• Spin exchange collisions preserve total angular momentum
• They change the hyperfine states of alkali atoms
• Cause atoms to precess in the opposite direction around the magnetic field

SF=1 B SF=2 ω ω SE

ω = ± gµB B h(2I + 1)

F=I±½

∆ω ≈ 1/ΤSE

S ω

F=2 F=1 mF = −2 −1 0 1 2

Ground state Zeeman and hyperfine levels

Zeeman transitions +ω Zeeman transitions −ω

SE

Eliminating spin-exchange relaxation

• 1. Increase alkali-metal density
• 2. Reduce magnetic field

ω << 1/ΤSE

Atoms undergo spin-exchange collisions faster than the two hyperfine states can precess apart

• No relaxation due to spin exchange

B SF=2 SF=1 ω1

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

S ω

• W. Happer and H. Tang, PRL 31, 273 (1973)

Complete elimination of spin-exchange broadening

• Residual linewidth due to spin-

destruction collisions

⇒ Convert spin angular momentum to rotational momentum of atoms

S

B

Chopped pump beam

10 20 30 40 50 Chopper Frequency (Hz)

• 0.1

0.0 0.1 0.2 Lock-in Signal (V rms ) − in phase − out of phase

Spin-exchange width: 3 kHz Observed width: 1 Hz

• J. C. Allred, R. N. Lyman, T. W. Kornack, and MVR,
• Phys. Rev. Lett. 89, 130801 (2002)

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

Turning spin-exchange broadening back on

Magnetometer Schematic

• Multi-layer magnetic shields eliminate external fluctuations
• Residual fields are zeroed out with internal coils
• Cell heated to 180°C to obtain alkali density of 1014 cm-3

Pump Laser Probe Laser

Alkali metal cell Polarizer Photodetector

Magnetometer Performance

• I. K. Kominis, T. W. Kornack, J. C. Allred and MVR, Nature 422, 596 (2003)

Magnetic shield noise 7 fT/Hz1/2 Gradiometer Sensitivity 0.5 fT/Hz1/2 Volume : 0.3 cm3 Baseline: 3 mm Best SQUID

• Fundamental sensitive limit at 5 aT/ Hz

Previously best atomic magnetometer : ~1.8 fT/Hz1/2 with a volume 1800 cm3

3He Co-magnetometer

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

⇒T1 ~ 300 hours

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

3He Co-magnetometer

• 1. Replace 4He with 3He (I = 1/2)
• 2. 3He nuclear spin is polarized by spin-exchange

collisions with alkali metal

• 3. Polarized 3He creates a magnetic field felt by

K atoms

• 4. Apply magnetic field Bz to cancel field BK

⇒K magnetometer operates near zero field

• 5. In a spherical cell dipolar fields produced by

3He cancel

⇒3He spins experience a uniform field Bz ⇒Suppress relaxation due to field gradients

BK = 8π 3 κ 0MHe

m m m m B

T1

– 1 = D

∇Bx

2 + ∇B y 2

Bz

2

Magnetic field self-compensation

Magnetic field compensation

Slightly uncompensated Compensated

Frequency Response

T.W. Kornack and MVR, PRL 89, 253002 (2002)

Cancellation of magnetic field effects

Noise Compensation Gradient Compensation

Thermal Shields Magnetic shields with insulation Pump Laser Box Probe Laser Box Table Position Sensors

Environmental Shields Environmental Shields

Development Run Data

S = Ax sin(Ωt)+Ay cos(Ωt) Ω - sidereal Earth rotation rate Ax = −0.76 ± 0.74 fT Ay = 0.59 ± 0.81 fT

Periodic zeroing of fields

Limits on Lorentz and CPT violating spin coupling

|bn| < 1.4 ×10−31 GeV |be| < 1.0 ×10−28 GeV

Limits from development run

|bn| < 1.1 ×10−31 GeV |be| < 0.3 ×10−28 GeV

Existing best limit

3He-129Xe co-magnetometer

Walsworth, Harvard-Smithonian Magnetic torsion pendulum Heckel, Adelberger, U of Washington

Natural size for Lorentz violation ?

pl

M m b

2

~ η

m - light mass scale: fermion mass SUSY breaking scale Pospelov, hep-ph/0505029

Existing limits: η ~ 10−9 − 10−12 1/Mpl effects are already highly excluded

What’s next?

• Low frequency noise dominates
• Current result 2-3 orders of magnitude below best sensitivity

⇒Further work on drift reduction and continuous data taking ⇒Constructing a miniature (30 cm size) system that can be placed on a rotating table to increase modulation frequency

1 day

Other applications of co-magnetometer

• Search for a permanent electric dipole moment (EDM)

⇒ EDM violates CP symmetry, but very suppressed in the SM ⇒ Large EDMs generated in SUSY, other extensions

• Need heavy atoms
• Cs- 129Xe co-magnetometer

⇒Sensitivity 1 fT/Hz1/2 ⇒E = 10kV/cm, t = 107 sec

) sin( 24 ~

SUSY SUSY

2

φ π α M m e d

da ∝ deα2Z 3

δde= 10−29 e-cm, δdXe= 10−30 e-cm

Factor of 100 improvement in both limits

Cs-129Xe cell

Atomic Magnetoencephalography Setup

• DC Shielding Factor ~ 10000
• 256 channel 2D photodiode array
• No conductive materials inside
• 10 measurement positions
• Optimization in progress

Atomic Gyroscope

• Rotation creates an effective magnetic field Beff = Ω/γ

Ω         − =

Ω

1

n e z

R P S γ γ

For 3He 0.001 deg/hour1/2 ⇒ 1 fT/Hz1/2 For 21Ne 0.001 deg/hour1/2 ⇒ 10 fT/Hz1/2

Rotation signal

• Motion and rotation agree with no free parameters
• Short term noise is 2.2 × 10−7 rad/s / Hz1/2
• Competitive with compact ring laser and fiber gyros
• T. W. Kornack, R. K. Ghosh and MVR, PRL (in press)

Conclusions

• Lorentz and CPT symmetry tests provide one of the few

ways to experimentally probe Quantum Gravity

• Noble-gas - alkali-metal co-magnetometers allow

sensitive tests of Lorentz violation and other precision measurements.

Support: NIST, NASA, NSF, NIH, Packard

Foundation, Princeton University

Igor Savukov Igor Savukov Tom Kornack Tom Kornack Rajat Ghosh Rajat Ghosh Micah Ledbetter Micah Ledbetter Scott Seltzer Scott Seltzer Hui Xia Hui Xia Dan Hoffman Dan Hoffman Georgios Vasilakis Georgios Vasilakis Parker Meares Parker Meares

• Collaborators

⇒Tom Kornack ⇒Iannis Kominis ⇒Scott Seltzer ⇒Igor Savukov ⇒Georgios Vasilakis ⇒Andrei Baranga ⇒Rajat Ghosh ⇒Hui Xia ⇒Dan Hoffman ⇒Joel Allred ⇒Robert Lyman