fundamental physics with diatomic moleculesg2pc1.bu.edu/lept10/demille-lm2010-pdf.pdf ·...
TRANSCRIPT
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Fundamental physics with diatomic molecules
• electron EDM in PbO ThO (G. Gabrielse talk)
• parity violation (S. Cahn and E. Kirilov poster) Z0 semileptonic couplings & nuclear anapole moments
• ultracold molecules for wide range of applications: --time variation of fundamental “constants” --next-generation EDM, PV experiments --large scale quantum computation --many-body physics, ultracold chemistry, etc.
• recent result: laser cooling of molecules
D. DeMille Yale University
Physics Department
DeMille
Group
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Status of the Electron EDM Search using PbO*
• Basic physics of PbO* system • Experimental approach • Results from initial data run • Ongoing improvements • (time permitting) a sophomore-level explanation of the electron EDM “enhancement” factor
D. DeMille Yale University
Physics Department Funding: NSF
DeMille
Group
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Amplifying the electric field E with a polar molecule
Eint
Pb+
O–
Eext
Inside molecule, EDM interacts with effective internal field
Eeff ~ α2Z3 e/a02 2.6 × 1010 V/cm in PbO*
[Petrov, Titov, Isaev, Mosyagin, D.D., PRA 72, 022505 (2005)]
Complete polarization P ~ 1 achieved with Eext ~ 10 V/cm
for PbO*
[ ] +30% -10%
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Populating the a(1) [3Σ+] state of PbO
1+ 1-
~11 MHz
X(0) [1Σ+]
0+
1-
2+
~10 GHz
• • •
a(1) [3Σ+]
2+ 2-
• • •
Laser pulse ~ 571 nm bandwidth ~ 1 GHz ~ ΔνDoppler
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EDM measurement in PbO*
+
- n
+
-
n
+
- n
+
-
n
B E E E E
S
S
S
S
Ω-doublet states
Internal co-magnetometer:
B-field drift AND
most systematics cancel
in up/down comparison
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Experimental Setup (top view)
Pulsed Laser Beam 5-40 mJ @ 100 Hz Δν ~ 1 GHz ε ⊥ B
Larmor Precession ν ~ 100 kHz
PMT B
solid quartz light pipes
Data Processing
Vacuum chamber
E
quartz oven structure
PbO vapor
cell T~700 C
Vapor cell technology allows high count rate (but modest coherence time & contrast)
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Sapphire windows
bonded to ceramic frame with
gold foil “glue”
Gold foil electrodes and “feedthroughs”
PbO vapor cell and oven
Opaque quartz oven body: 800 C capability;
wide optical access; non-inductive heater;
fast eddy current decay w/shaped audio freq. drive
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The PbO EDM lab (before magnetic shields)
.001 km
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The PbO EDM lab with 2 of 4 shields
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m=0 m=+1 m=-1
Pb+
O-
Pb+
O-
Pb+
O-
Pb+
O-
State preparation v3.0: “Microwave erasure”
Net result: 50% useful signal
from one doublet state + 50% background
x-polarized laser pulse
28.2 GHz µwave
Laser prepares “grand superposition” state
Strong, inhomogeneous microwave drive
decoherence of one doublet
S
S
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Raw quantum beat data with fit ca. 2008
Small contrast (3-4% typical) due to laser excitation of “wrong” molecules
(hot sample, poor laser)
Large background
due to blackbody radiation
from oven
Extract spin precession freq.
from fit
Small signals: PbO vapor density ~30 smaller than originally expected (remainder Pb2O2, Pb4O4)
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Cancellation of B-field drift w/Omega doublets
Single magnetic shield for this data
also >103 rejection of magnetic (e.g. leakage currents) & other (e.g. geometric phase) systematics
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1st generation data (Spring 2008)
Needed: ~20× better statistical sensitivity to surpass Berkeley limit in one day
0.01s B E
Avg 16 shots each & fit
Ω Ω E
Repeat 1440 times (~2 hr), then reverse B
41 hours total data collection
~1 hour data ~2×10-26
e⋅cm/√day 1.1-1.2 shot noise
repeat 32 times (~5s) Reverse E & repeat
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Zeroth-order analysis of systematics: odd vs. even
Imperfect reversal of B-field
spurious B-field due to leakage currents
Imperfect reversal of E-field
False signals due to spurious fields suppressed by
multiple small factors
Result: δde (syst.) < 1 ×10-27 e⋅cm (95% c.l.)
All spurious & non-reversing components consistent with zero
Various combos allow extraction of specific isolated imperfections
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Recent/ongoing improvements to statistical sensitivity
Better heat shielding: >5x decrease in blackbody Excitation from v=0: 3x more signal Broader detection bandwidth: 2x more signal Polarization sensitive detection: 2x decrease in background Improved state preparation: 2x sensitivity
Expected sensitivity de ~1x10-27 ecm/√day in immediate future (?)
?? New excitation laser: ~4x decrease in background and ~5x increased signal
Present demonstrated sensitivity: de 4x10-27 ecm/√day
(~8x improvement in S/N since 2008)
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E-field dependence of Ω-doublet g-factors
Provides mechanism to measure E-field nonreversal & better method of state preparation
2-level model (Ω-doublet only)
Model including mixing with
“distant” J=2 rotational level
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Improved state preparation from g-factor difference
Simpler (no microwaves) 100% signal,
no added background
Simultaneous co-magnetometry
Reduced dynamic range for E & B
m=0 m=+1 m=-1
Pb+
O-
Pb+
O-
Pb+
O-
Pb+
O-
x-polarized laser pulse
S
S
Background-subtracted beat signal @ high E & B
shows distinguishable beats
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• Only ~20% of the molecular fluorescence is from the desired transition • Ideal laser would reduce time-dependent background to below signal
Excitation transition!
What an improved laser could do for us (part 1)
Scan of excitation laser over rotational lines
Excitation transition!
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What an improved laser could do for us (part 2)
Wasted laser power…
• Broad spectral wings (from pump laser mode beating) lead to excitation of nearby large rotational lines big background
• Narrow longitudinal modes saturate velocity classes inefficient excitation (~10% of molecules excited)
from a lousy laser spectrum
2 GHz
12 GHz
Random longitudinal
modes
signal
background
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Home-built, improved laser system
• 4 pass pulsed amplification of CW seed laser • CW seed laser =
IR diode laser + tapered amp. + 1-pass PPLN waveguide SHG High power + large, controlled linewidth for visible seed laser
• Injection-seeded, transform-limited Nd:YAG pump laser
Schwettmann et al. Appl. Opt. 46, 1310 (2007).
Everything in place, ready to look at PbO signals…
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Summary and conclusions
• PbO* is a working EDM experiment
• Ω-doublet noise & systematic cancellation mechanism demonstrated
• Initial data run (41 hours, 2008) yielded de = -19 ± 20 (stat.) ± 1 (syst.) ×10-27 e⋅cm
• S/N improved ~8× since 2008
• Further improvement (~5× ??) in S/N from new laser expected, to be tested soon
• Goal: >100 hour data run with new laser
• Final generation of PbO*…. ACME ThO is next
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DeMille
Group
PbO* at Yale Postdocs:
(D. Kawall, V. Prasad), E. Kirilov Grad students:
(F. Bay, S. Bickman, Y. Jiang), Paul Hamilton
Undergrads: (C. Cheung, Y. Gurevich,
N. Sedlet), Hunter Smith, I. Kozyryev
Paul & family 6/21/2010
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Effects of E-field in an atom
s
But still, net electric field = 0… Simple proof: <Etot> = < Eint + Eext> ∝ <Ftot> = 0
s + ηp
Eext
With external E-field typical atomic ground state wavefn.
Rigorous proof in non-relativistic Q.M. (Schiff ’s Thm/Schroedinger Eqn) BUT well-known that eEDM shifts don’t vanish in relativistic treatment
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B µ
B B
E-field on an electron? [my own slide, 2000-2008] electric forces can be cancelled by magnetic forces:
<Ftot> = <Fel + Fmag> = 0, <Eeff> = -<Fmag>/e
(spin-orbit energy)
Strongly peaked near nucleus (r < a0/Z):
v, E, large v ~ Zc; E ~ Ze/r2
Eeff Z32
magnetic forces arise from
spin-orbit interaction:
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E-field on an electron?
Simple to prove that <E>=0 for electron inside atom at rest even in fully relativistic treatment (Dirac Eqn)
[2-line proof, exact analogue of non-relativistic Schiff Thm proof]
E. Commins, J.D. Jackson, DD
Am. J. Phys. 75, 532 (2007)
Alternate proof that spin-orbit forces are irrelevant for de: --Add anomalous magnetic moment by hand to Dirac Eqn. --Make usual nonrelativistic reduction (Foldy-Wouthuysen)
--Which terms are proportional to g-factor?
Spin-orbit
Darwin
Rel. K.E.
e-EDM
Independent of g Proportional to g
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E-field on an electron?
simple estimate: |<Eeff>| Z3α2 (e/a02) ⋅ P
~ P ⋅ 1011 V/cm @ Z~80!
H = de⋅E = 2deS⋅E <H> = <de⋅E> ≠ <de>⋅<E> if de , E ≠ const
de varies inside atom due to relativistic length contraction Eint varies in atom due to point charge at nucleus
<H> = <de⋅E> = <δde⋅E> ≡ de⋅Eeff
P. Sandars
Near nucleus, BOTH δde [v2/c2]de AND Eint large
Polarization P causes electron to spend more time on one side of nucleus ⇒ vector avg. <δdeE> P.
E. Commins, J.D. Jackson, DD
Am. J. Phys. 75, 532 (2007)