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

The kilogram

Coupled oscillators

m

M

x X

2

max

22

max

2

2

1

2

1XMxmE

2

X

xmM

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

Optical coupling

arXiv:1103.1820v1 (2011)

Optical coupling

PRL 103, 063005 (2009)

Macroscopic oscillators

Nature 464, 697 (2010)

Interactions of atoms and surfaces

Precision measurement of the Casimir Polder force

g

Limits to new forces of the Yukawa type

Correction to the gravitational force due to new interactions

FG

FG

1 er

Measurement of G

G = 6.67428 (67) x 10-11 m3/kg s

R∞ = 10973731.568527 (73) m-1

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

Displacement measurement

z

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

Classical measurement of g

time

he

igh

t

Quantum measurement of g

time

he

igh

t

Interaction of atoms with light

│e>

│b>

Time

Po

pu

latio

n in

e

0

0.2

0.4

0.6

0.8

1

Atomic interferometer

│e>

│b>

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

Mach-Zender interferometer

frequency

spectr

um

White light

deBroglie wavelength

velocity

Pro

babili

ty d

istr

ibution

Room temperature gas

p = h / l

l = h / (mv)

Hot gas

Cold gas

Laser cooling (MOT)

Laser cooling (MOT)

kzvF a

MOT and Dipole trap

Trap laser

Laser Saturation

spectroscopy

Lock-in

and PID

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

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

Interaction of atoms and light

Optical lattice

eikx e-ikx

laser laser

eikx + e-ikx = 2 cos(kx)

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

Gravimeter

time

heig

ht

Gravimeter

time

heig

ht

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

Cornell experiment

PRL 98, 063201 (2007)

Limits to new forces of the Yukawa type

Correction to the gravitational force due to new interactions

FG

FG

1 er

Dipole laser

Frequency meter

Shutters

Rev. Sci. Instr. 82, 046102 (2011)

Frequency filter

10 ms 12 ms

14 ms 16 ms

Compresion

Dipole trap

l = 785.7 nm, P = 900 mW, N = 3 X 106, t = 8 ± 2 ms Rev. Sci. Instr. 83, 015111 (2012)

Wave function in a parabolic potential

z

V

Wave function in a periodic potential

V

z

Ligth induced tunneling

z

V

Ligth induced tunneling

PRL 106, 213002 (2011)

Ligth induced tunneling

PRL 106, 213002 (2011)

Raman transitions

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

Phase locked lasers

Laser1 Fiber

modulator

frequency frequency

RF

AOM

Blue detuned optical trap

Zeeman pumping and

Faraday spectroscopy

Raman transition

Magnetic dipole (M1) transition

AC Stark shift of the trap

Rev. Sci. Instrum. 83, 043106 (2012)

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

Optical PNC experiment

Stable No Yes

Source Trap Atomic beam

Z 87 55

Atom Francium Cesium

Constants on limits

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

Quiral current

)(2 rJdrra

Anapole moment

Current

Magnetization

Limits on constants

Measurement of the anapole

moment

1g

2g

Transition between

hyperfine levels

i(E1×M1)•B Observable

Systematic effects

Systematic effects

Gomez et. al. Phys. Rev. A 75, 033418 (2007)

High efficiency trap

Aubin et. al. Rev. Sci. Instr. 74, 4342

(2003)