Fundamental physics with diatomic molecules:
from particle physics to quantum computation....!
• electron electric dipole moment search (CP, “new” physics)
• sources of ultracold molecules for wide range of
applications:
--large-scale quantum computation
--time variation of fundamental “constants”
--etc.
• parity violation: Z0 couplings & nuclear anapole moments
D. DeMille
Yale University
Physics Department
Funding: NSF, Keck Foundation, ARO, DOE
(Packard Foundation, Sloan Foundation, Research Corporation, CRDF, NIST)
Structure of molecules 0:
“A diatomic molecule has one atom too many.”
--Art Schawlow
(and most atomic physicists)
....or maybe not?
“new” internal degrees of freedom in molecules
useable as a resource…?
Structure of molecules I: electronic states
Energy
Electron
clouds
“merge” in
potential
well
States of
separated
atoms
S+P
Ve(R)
S+S
Vg(R)
Internuclear distance R
Structure of molecules II: vibration
Energy
V(R)
Internuclear distance R
Structure of molecules III: rotation
•
•
•
Moment of intertia
I = MR2;
Angular momentum
J = n;
3Energy
Energy of rotation
E = J2/2I
Angular
momentum
J/
2+
R
10+
Molecular electric dipoles
Wavefunctions of polar molecules
No E-field: no dipole!
J = 1, mJ = 0
“=“ |p>
With E-field:
induced dipole
z, E
+
++
+
+
|> 
|s>+|p>
+
+
++
+
+
+
+
J=0
“=“ |s>
|> 
|s>-|p>
polarized
molecules act like
permanent dipoles
+
+
-
Small splitting (~10-4 eV) between states of opposite parity (rotation)
leads to large polarizability (vs. atoms, ~ few eV)
A permanent EDM Violates T and P
 
 
H Magnetic dipole     B  -  B
d
P
Purcell
Ramsey
Landau
 
 
H Electric dipole  - d  E  - d  E
S
T
CPT theorem  T-violation = CP-violation
Q. How does an electron EDM arise?
A. From cloud of accompanying “virtual” particles
Standard Model
Supersymmetry
t
~
e
W
e e


W d
t s
b
~

~
e
W
ee
Searching for new physics with the electron EDM
Yale
Yale II
Yale II
Berkeley
(projected) (projected)
(2002) (projected)
MultiMultiHiggs
Higgs
Extended
Extended
Technicolor
Technicolor
Left- Right
Left-Right
Symmetric
Symmetric
Lepton FlavorLepton
Flavor Changing
Changing
Standard
Standard
Model
Model
Alignment
Alignment
Split SUSY
Split SUSY
SO(10) GUT
SO(10) GUT
Seesaw Neutrino Yukawa Couplings
Seesaw Neutrino Yukawa Couplings
Accidental
Accidental
Cancellations
Cancellations
-25
10
-26
Exact
Exact
Universality
Universality
Approx.
Approx.
Universality
Universality
Heavy
Heavy
sFermions
sFermions
Naï ve SUSY
Naïve SUSY
10
Approx.
Approx.
CP
CP
10
-27
10
-28
10
-29
10
-30
10
-31
10
de (e×cm)
-32
10
-33
10
-34
~~
10
-39
10
-40
General method to detect an EDM
-2dE
 +2dE
B E
Energy level picture:
S
-2dE
 +2dE

shift
Figure of

merit:
resolution
dE
1/  coh  S / N 
1
 E  coh  N  Tint
Amplifying the electric field E with a polar molecule
Eext
Pb+
Eint
O–
Electrical polarization
of molecule
subjects valence electrons
to huge internal field
Eint > 1010 V/cm
with modest polarizing field
Eext ~ 10 V/cm
Explicit calculations indicate valence electron feels
Eint ~ 2Z3 e/a02 ~ 2.1 - 4.0  1010 V/cm in PbO*
semiempirical: M. Kozlov & D.D., PRL 89, 133001 (2002);
ab initio: Petrov, Titov, Isaev, Mosyagin, D.D., PRA 72, 022505 (2005).
Spin alignment & molecular polarization in PbO (no EDM)
n
-
n
S
+
+
-
-
+
-Brf  z+
a(1)
[3+]
J=1-
m = -1 S
J=1+
-
n
+
m = +1 S
m=0
B E
+
+
+  ||-z
n
-
+
X, J=0+
EDM measurement
in PbO*
Sn
-
Sn
+
+
“Internal
co-magnetometer”:
most systematics
cancel in up/down
comparison!
Sn
B E
+
-
Sn
+
-
The central dogma
of physics (c.f. S. Freedman)
Theorist :: Experimentalist :: Fact
Farmer ::


Pig
:: Truffle
PbO vapor cell and oven
Sapphire
windows
bonded to ceramic
frame with gold
foil “glue”
Gold foil
electrodes and
“feedthroughs”
quartz oven body
800 C capability
wide optical access
w/non-inductive heater
for fast switching
Present Experimental Setup (top view)
PMT
Signal
Data
Processing
Frequency
E
solid
quartz
light
pipes PbO
vapor
cell
B
Larmor
Precession
 ~ 100 kHz
Vacuum chamber
quartz oven structure
Pulsed Laser Beam
5-40 mJ @ 100 Hz
 ~ 1 GHz
B
Vapor cell technology allows high count rate
(but reduced coherence time)
Zeeman quantum beats in PbO
Excellent fit to Monte Carlo w/PbO motion, known lifetime
Shot noise-limited S/N in frequency extraction
(Laser-induced spin alignment only here)
Current status: a proof of principle
[D. Kawall et al., PRL 92, 133007 (2004)]
•PbO vapor cell technology in place
•Collisional cross-sections as expected anticipated density OK
•Signal sizes large, consistent with expectation;
improvements under way should reach target count rate: 1011/s.
•Shot-noise limited frequency measurement
using quantum beats in fluorescence
•g-factors of -doublet states match precisely
co-magnetometer will be very effective
•E-fields of required size applied in cell; no apparent problems
 First useful EDM data ~early 2006;
de ~ 310-29 ecm within ~2 years...?
Applications of ultracold polar molecules
• Precision measurements/symmetry tests: narrow lines improve sensitivity
& molecular structure enhances effects (small energy splittings)
Time-reversal violating electric dipole moments (103 vs. atoms)
Parity violation: properties of Z0 boson & nuclear anapole moments (1011 !!)
New tests of time-variation of fundamental constants? (103 vs. atoms)
• Coherent/quantum molecular dynamics
Novel collisional phenomena (e.g. ultra-long range dimers)
ultracold chemical reactions (e.g. tunneling through reaction barriers)
• Electrically polarized molecules have tunable interactions
that are extremely strong, long-range, and anisotropic--a new regime
Models of strongly-correlated systems (quantum Hall effect, etc.)
Finite temperature quantum phase transitions
New, exotic quantum phases (supersolid, checkerboard, etc.)
novel BCS pairing mechanisms (models for exotic superconductivity)
Large-scale quantum computation
D. DeMille, Phys. Rev. Lett 88, 067901 (2002)
Quantum computation with ultracold polar molecules
Strong
E-field
Standing-wave trap
laser beam
E-field due to each
dipole influences
its neighbors
+V
Weak
E-field
-V
• bits = electric dipole moments of polarized diatomic molecules
• register = regular array of bits in “optical lattice” trap (weak trap low temp needed!)
• processor = rf resonance w/spectroscopic addressing (robust, like NMR)
• interaction = electric dipole-dipole (CNOT gate speed ~ 1-100 kHz)
• decoherence = scattering from trap laser (T ~ 5 s  Nop ~ 104-106 !)
• readout = laser ionization or cycling fluorescence + imaging (fairly standard)
• scaling up? (104- 107 bits looks reasonable: one/site via Mott insulator transition)
CNOT requires bit-bit interactions
With interaction H' = aSaSb
Without interactions
|1>a|1>b
|0>a|1>b
|1>a|0>b
|0>a|0>b
Desired:
a flips if b=1
Undesired:
a flips if b=0
Size of interaction term “a”
determines maximum gate speed:
-1 ~  ~ a
Quantum computation
with trapped polar molecules
• Quantum computer based on ultracold polar molecules
in an optical lattice trap can plausibly reach
>104 bits and >104 operations in ~5 s decoherence time
• Based heavily on existing work & likely progress:
Main requirement is sample of ultracold (T  10 K) polar molecules
with phase space density ~10-3
• Anticipated performance is above
some very significant technological thresholds:
Nop > 104  robust error correction OK?
Crude scaling 
300 bits, 104 ops/s  teraflop classical computer
Cold molecules from cold atoms: photoassociation
•very weak free-bound (but
excited) transition driven by laser
for long times (trapped atoms)
energy
|Ye(R)|2
S+P
Ve(R)
laser
|Yf(R)|2
|Yg(R)|2
S+S
Vg(R)
Internuclear distance R
EK
• electronically excited molecules
decay to hot free atoms
or to ground-state molecules
• Production of polar molecules
requires assembly from
two different atomic species
• molecules can be formed in
single rotational state, at
translational temperature of atoms
(100 K routine, 1 K possible)
BUT molecules are formed in
range of high vibrational states
MOT trap loss photoassociation spectra
RbCs* and Cs2* formation (Ω = 0)
RbCs
•up to 70% depletion of trap for RbCs  near 100% atom-molecule conversion
•spectroscopically selective production of individual low-J rotational states
A.J. Kerman et al., Phys Rev. Lett. 92, 033004 (2004)
Verification of polar molecules:
behavior in E-field
Fitted electric dipole moment for this (=0+) state:  = 1.3 Debye
Detection of vibrationally excited RbCs
Cs,Rb
electrode
+2 kV
670-745 nm
0.5 mJ
time
channeltron
-2 kV
532 nm
5 mJ
10 ns
Vibrationally excited RbCs @T = 100 K
PA
delay
decay time
consistent with
translational temp.
T ~ 100 K
as expected
from atomic temps.
Decay due to ballistic
flight of RbCs molecules
from ~2 mm diam.
detection region
Cold molecules from cold atoms: stopping the vibration
•free-bound (but excited)
transition driven by laser
•excited molecules can decay to
molecular ground state
energy
|Ye(R)|2
S+P
Ve(R)
laser
|Yf(R)|2
|Yg(R)|2
S+S
Vg(R)
Internuclear distance R
EK
• molecules can be formed in
single rotational state, at
translational temperature of atoms
(100 K routine, 1 K possible)
BUT molecules are formed in
range of high vibrational states
•High vibrational states are
UNSTABLE to collisions and have
NEGLIGIBLE POLARITY
need vibrational ground state!
• Laser pulses should be able to
transfer one excited state to
vibrational ground state:
TRULY ultracold molecules
(translation, rotation, vibration)
Production of absolute ground state molecules
Epump= 9786.1 cm-1
Edump =
13622.0
cm-1
•Raman transfer verified on
~6 separate transitions
v=0
3.5
5.5
R [Å]
7.5
•Estimated efficiency ~8%, limited by
poor pulsed laser spectral profiles
Coming next: “distilled” sample of polar, absolute
ground-state RbCs molecules
Lattice
Photoassociation CO2
Trap
in optical trap
allows
accumulation
of vibrationally
excited molecules
v = 0, J = 0
polar molecules
levitated
by electrostatic
potential
+V
STIRAP
transfer
to X(v=0)
w/transformlimited lasers
Dipole
CO2
Trap
Anticipated:
pure, trapped
sample
of >3104
RbCs(v=0)
@n>1011/cm3
T  15 K
-V
other species
(atoms,
excited molecules)
fall from trap
Gravity
Status & Outlook: ultracold polar molecules
• Optical production of ultracold polar molecules now in hand!
[J.Sage et al., PRL 94, 203001 (2005)]
T ~ 100 K now, but obvious route to lower temperatures
• Formation rates of up to ~107 mol/s/level in high vibrational states
AND
efficient transfer to v=0 ground state (~5% observed, 100% possible)
 Large samples of stable, ultracold polar molecules in reach
• molecule trapping (CO2 lattice/FORT),
collisions & manipulation (E-fields, rotational transitions, etc.)
are next
• Ultracold polar molecules are set to open new frontiers in
many-body physics, precision measurements, & chemical physics
Ph.D. Students
DeMille Group
S. Sainis, J. Sage, (F.
Bay), Y. Jiang,
J. Petricka,
S. Bickman,
D. Rahmlow,
N.
Gilfoy,
D. Glenn, A. Vutha,
D. Murphree,
P. Hamilton
Undergrads
Collaborators
(L. Hunter [Amherst]), A. Titov, M. Kozlov [PNPI],
T. Bergeman [Stony Brook], E. Tiesinga [NIST],
R. Paolino [USCGA], J. Doyle [Harvard]
(J. Thompson,
M. Nicholas,
D. Farkas, J. Waks,
J. Brittingham,
Y. Gurevich, Y. Huh,
A. Garvan, C. Cheung,
C. Yerino, D. Price)
Postdocs/Staff:
S. Cahn, (V. Prasad,
D. Kawall, A. J. Kerman)