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Laboratory interests
Interactions of atoms with bulk materials / Measurement of small forces
Forces of
Nature
Electromagnetic Gravitational
Nuclear
weak
Nuclear
strong
Parity
Violation
Atom manipulation
Laser cooling
Mass and
Gravity
Accessible physics
• Measurement of mass
• Measurement of G
• New short range forces of gravitational kind
• Study of the Casimir-Polder Force
• Light induced tunneling
• Characterization of surfaces
• Preparation of macroscopic quantum states
• Measurement of a
• Tests of the weak equivalence principle
• Study of the weak force
Some numbers
m (Rb) = 1.4 X 10-25 kg
M (mm sphere) =3 X 10-15 kg = 2 X 1010 m
= 2p 104 s-1
For the first excited state
x = 1.8 X 10-7 m
X = 1.2 X 10-12 m
For room temperature
n = kBT/ħ = 6 X 108
Coupling
31
0
5
0 10102102
p
gM
mg a
a
Improvements: increase m, decrease M, make larger, or make the coupling insensitive to m/M.
MHz12p Q
TkB
Mass difference introduces an impedance mismatch that produces an small coupling constant.
For the strong regime go should be larger than the decoherence. In particular for the bulk material we have
Limits to new forces of the Yukawa type
Correction to the gravitational force due to new interactions
FG
FG
1 er
Scaling of the gravitational force
r=6000 km
mgGrmr
GMmF p
3
42
Grg p3
4
p 3
3
4rM
r’ For r’=0.06 m gives g’=10-8g
Measurement of g
e-iw1t
e-iw2t
E1=ħw1
z E2=ħw2=E1+mgz
Dw=w2-w1=mgz/ħ
m (Rb) = 1.4 X 10-25 kg z=1 mm
Dw=2p (2.2 kHz)
Pushing the sensitivity of g
Dw=mgz/ħ=2p (220 MHz)
If we measure for 1s then the measurement width is 1 Hz. If we measure with
a signal to noise of 106 then the precision is 1 mHz.
Suppose that z=0.1 m
The relative precision is one part in 2.2 X 1014
The state of the art is one part in 109 plenty of room at the bottom!
The above precision gives sensitivity to a sphere with r=0.1 mm
A human could be gravitationally detected at a distance of 100 m
Applications for accelerometers
• Navigation
• Exploration
• Improved tests of the weak equivalence principle
• Gravitational force at short distances
• Measurements of a
Interferometric measurement
detector
cos (kz-wt) = cos (107z-wt)
l=600 nm k=2p/l=107 m-1
A change of z of 0.1 mm gives a phase change of order p.
Michelson fringes
S = cos2 (f1-f2) = (1/2) (1+cos (2kz))
z
S Dza = l/4 = 150 nm
Precision in the measurement of z
fmNS
zP a 150
/
D For a signal to noise of 106
Evolucion of a superposition
│Y> = (1/√2) ( exp(-ibt)│b> + exp(-iet)│e> )
│Y> = (1/√2) ( │b> + exp(-iWt)│e> ) W = e - b
Real
Imaginary
Plane wave
y = A exp (-ilt)
Atomic interferometer
│e>
│b>
Time
Popu
lation in e
│Y> = (1/√2) ( │b> + exp(-iWt)│e> )
time heig
ht
0
0.2
0.4
0.6
0.8
1
deBroglie wavelength
velocity
Pro
babili
ty d
istr
ibution
Room temperature gas
p = h / l
l = h / (mv)
Hot gas
Cold gas
Laboratory control system
System
Hardware
System
Software
Digital
outputs 5V
Analog
outputs
-10 to 10 V
Control
program
Image
analysis
Laser system
Laser 780 nm
Hyperfine DAVLL lock
AOM
AOM
l/4
Amplifier Isolator
fiber l/4
Isolator
MOT Resonant beam
Rev. Sci. Instrum. 83, 015111 (2012)
MOT characterization
Lifetime: 13 ± 1 s
Atom number: 8 X 108
With a 10% precision
Cloud size: 0.7 mm
Peak density: 5 X 1010 atoms/cm3
KTMOT m1730
Postdoc
Luis Octavio Castaños
Graduate students
Lorenzo Hernández Víctor Jiménez Saeed Hamze Loui
Undergraduate students
Francisco Salces María del Cármen Ruíz
Eslava del Río Eduardo Uruñela
$ CONACYT, PROMEP, UASLP, TWAS
Mónica Gutiérrez Galán Nieves Arias Tellez
Diffraction grating
x
y
q
kpy 2D
dBx
y
h
k
p
p
lq
/
2tan
D
For small angles
qq sintan
dBlql
sin2
Gives the Bragg condition
Band structure
p
E E=p2/2m
Free particle spectrum
p
E
bands
Periodic potential spectrum
V(x)=V0cos(2kx)
Bloch oscillations
Band structure Two photon transition
H=p2/2m+V(x)
V(x+a)=V(x) Yn,q(x)=eiqxun,q(x)
Oscillations period
z
V
DV
2/lmgmghV D
D
k
mgmg
222/ pl
From the band structure perspective
gtv D
If t=T
kmgTvmp 2DD
Temperature requirement
p=mv=h/l
v=1 mm/s
From equipartition
mvrms2/2= 3kBT/2
T=3 nK
You need very cold atoms!
Velocity of the atom at the edge of the Brillouin zone
Casimir Polder force experiment
Measure the change in gravitational
acceleration as a function of the
distance to the surface.
Use Bloch oscillations to confine
the atoms and measure the
gravitational acceleration to high
precision.
g
Limits to new forces of the Yukawa type
Correction to the gravitational force due to new interactions
FG
FG
1 er
Raman transitions
2
2
1
2
2
1
2
1 fbia mvEmvE
Energy and momentum conservation in a Raman transition
21 kvmkvm fi
Resonance condition
212121
2kk
mvkk iHFS
Doppler Recoil
Velocity selection
D
WWW
2
*
21R
Rabi frequency of a Raman transition
W1
W2
For a p pulse
tpt /1WW RR
The transition probability drops when
Rvkk WD 21
The velocity selection is then
21
1
kkv
D
t
Polarizador
Optical fiber
Fast detector
ROSA OPLL
ADF4007
Synthesizer
ADF4360-8
Spliter cube
Phase locked lasers
Laser1
Laser2
amplifier
filter
Measurement of a
)52(03599880.1374 0
2
c
e
pa
Relevance of the measurement of a
•Verification of QED
•Sensitivity to new physics
•Variations of a
Connection between a and h/m
chRcme 22
2
1a
a is related to the Rydberg constant (in hydrogen)
The determination requires the following ratio
e
x
Xe m
m
m
h
m
h
The remaining ratio is determined from deBroglie
vm
h
X
l
hk
mg
2D
The ratio comes from the frequency of Bloch oscilations
The FrPNC Experiment,
Atomic PNC in Francium at TRIUMF
FrPNC colaboration
Supported by NSF, DOE, NSERC, CONACYT
Collaborator Institution Country
Seth Aubin College of William and Mary
John Behr TRIUMF
Eduardo Gómez Universidad Autonoma de San Luis Potosí
Gerald Gwinner University of Manitoba
Victor Flambaum University of New South Wales
Dan Melconian Texas A&M
Luis Orozco University of Maryland
Matt Pearson TRUIMF
Gene Sprouse SUNY Stony Brook
Yanting Zhao Sahnxi University
Graduate students and postdocs
Maryland: Jiehang Zhang
Manitoba: Robert Collister
TRIUMF: Michael Tandecki, Annika Voss and Olivier Shulbaya
Parity violation in atoms
Weak Hamiltonian of the e-p interaction
Non-relativistic approximation for p
Non-relativistic approximation for e
Atomic transitions
Atomic transition
Mixing of states due to the weak force
Induced transition 1S
2S 2P
012 SreEP
allowed
012 SreES
forbidden
PSS
Energy shift=0
Dependence on nuclear spin
Weak e-p Hamiltonian
a 5
2r
2
wQGH
)(12
rII
IKGH ia
a
WQiaiiK
I
K
K
12/12
anapole Tree level Spin independent
+ hyperfine
Nuclear spin dependent part