Brazilian Microwave Frequency Standards

Using Cold Atoms

Daniel Varela Magalhães

XI Escola de Verão Jorge André SwiecaÓptica Quântica e Óptica Não Linear

Instituto de Física de São CarlosUniversidade de São Paulo

Av. Trabalhador São-Carlense, 40013560-970, São Carlos-SP, Brazil

dvarela@if.sc.usp.br

Outline

The “second”

Frequency Standards

Ramsey Method

Comparisons and Measurements (Stability and Accuracy)

Cold Atoms

Experiments: Fountain & TAC

Frequency Synthesis and Links

Future Prospects

Swieca 08

The “second”

Need of StandardisationConvention du Mètre (20 may 1875)

Establishment of BIPM (Bureau International des Poids et Mesures)Requirement for the growth of international trade in manufactured

and industrial products

Adoption, in 1960, of the Système International d’Unités (SI)Metric, electric and photometric unitsSeven base units, derived

and supplementary unitsAlmost universally used in science

and technology

Swieca 08

Lenghtm

Masskg

Times

ElectricCurrent

A

c Cs µ0

Temp.K

Lum. Int.cd

Sub. Qt.mole

Force

J N

C

W

V

Ω F ε0

2e/h

h/e2

Swieca 08

The “second”

metre - The metre is the length of the path travelled by light in vacuumduring a time interval of 1/299 792 458 of a second.

kilogram - The kilogram is the unit of mass; it is equal to the massof the international prototype of the kilogram.

second - The second is the duration of 9 192 631 770 periods of the radiationcorresponding to the transition between the two hyperfine levels of the groundstate of the caesium 133 atom.

ampere - The ampere is that constant current which, if maintained in twostraight parallel conductors of infinite length, of negligible circular cross-section,and placed 1 m apart in vacuum, would produce between these conductorsa force equal to 2 x 10–7 newton per metre of length.

kelvin - The kelvin, unit of thermodynamic temperature, is the fraction1/273.16 of the thermodynamic temperature of the triple point of water

mole1.The mole is the amount of substance of a system which containsas many elementary entities as there are atoms in 0.012 kilogram ofcarbon 12.2.When the mole is used, the elementary entities must be specifiedand may be atoms, molecules, ions, electrons, other particles, or specifiedgroups of such particles.

candela - The candela is the luminous intensity, in a given direction,of a source that emits monochromatic radiation of frequency 540 x 1012 hertzand that has a radiant intensity in that direction of 1/683 watt per steradian.

Swieca 08

The “second”

Mean solar day Astronomical data Material properties

NBS (NIST) technical note, december, 1964

Swieca 08

The “second”

“The standard to be employed is the transition between the two hyperfine levels F=4 , mf=0 and F=3, mf =0 of the fundamental state 2S1/2 of the atom of cesium 133 undisturbed by external fields and the value 9 192 631 770 hertz is assigned.”

1964

“La seconde est la durée de 9192631770 périodes de la transition correspondant à la transition entre les deux niveaux hyperfinsde l’état fondamental de l’atome de 133Cs”

1967

Experiments since 1955L. Essen and J. Parry (NPL)

New definition dependingon the reliability od the system

Swieca 08

The “second”

Swieca 08

The “second”

Consequences and uses of such reference

Outstanding frequency referencesStability, accuracy, realiability, ...

Development of National Standards

Research in Fundamental PhysicsAtomic Physics – collisions, freq. shifts, ...Tests of Fundamental ConstantsHigh Resolution Absolute SpectroscopyQuantum InformationCold Atoms in Space (ACES, PARCS)

Traceability of other units to the time unit

second

c

meter

2e/hc,ε0

ohm volt

ampere

Force measurement µ0

kilogram

Swieca 08

The “second”

Frequency Standards

Cold H

Cs, Rb:Laser optical pumping

Cs fountain

Ion trap

Ion laser cooling

CoherentPopulationTrapping

Quantum transitionsQuantum transitions

Optical standardsOptical standards Microwave standardsMicrowave standards

Saturatedabsorption

Saturatedabsorption

Othertechniques

Othertechniques

Cells: CH4, I2, OsO4, CO2, Rb,H2O…

Ramseyfringes

Mono-ion

Two-photon

Neutral Atoms

H, Cs, RbH, Cs, Rb Othertechniques

Othertechniques

Optical comb

Swieca 08

Frequency Standards

)NS(Q)(

a

1∝τσQ is for quality (δf/f )

CPT standardsSmall devices for portable applications

Optical domain standards

Excellent prospects – Future redefinition of the second ???Limits related to long term stab. and SNR (Ions x Neutral Atoms)

Sr x Ca – Uncertainty at 1.5x10-16; Stability at 2x10-15

Hg+ x Al+ - Uncertainty at ~2x10-17; Stability at ~2x10-15

Beam standardsGreat number of laboratory and commercial systems, bigger contributor for TAILimitations related with velocity dispersion and accuracy limits

Atomic fountain standardsBest realization of the secondAccuracy at 4x10-16

Stability at 1.6x10-14 at 1s

Swieca 08

The 133Cs as a primary standard

Passive standard – The atom must be interrogated respect to a local oscillator

Transition frequency in the X band – 9192631770Hz

Methods used for microwave spectroscopy - NMR

9192,6MHz2

126 S F=3

F=4

Swieca 08

Frequency Standards

100MHz 10MHz

9.2GHz

100MHz100MHz 10MHz10MHz

9.2GHz9.2GHz

Passive frequency standard

Search for techniques to better interrogate the atomic transition

Swieca 08

Frequency Standards

LocalOscillator

AtomicDiscriminator

ControlSystem

Ramsey Method

The Rabi methodCs oven and stateselection region

<v>

l

Interaction region: Microwave cavity

State analysis anddetection region

Cesium beam

b

a3

k1

k2

k3

ωRτ

ωµw

A

l

CavityLl

Cesium beam<v>

Cavity

k

2

a3(τ+T+τ)

k

2bk1

a3(0)

k3

ωRτ

ωµwa3(τ)

k3

bk1

ωµ

wωRτ

k1

k3

k2

a3(τ+t)ωhf

The Ramsey’s method ofSeparated Oscillatory Fields

π pulse – Mag. field ( b ) & Int. time (τ )

2 x π/2 pulses

Swieca 08

ν

P

µµµµW

ν

P

Increasing the resolutionof the measurement

NMR Methods

Ramsey Method

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∆ν∆ν∆ν∆ν

-80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 800,0

0,5

1,0

Tra

nsiti

on p

roba

bilit

y

Frequency Modulation (Hz)

LT

πυπν ==∆

( ) ( ) ( )2

00

02

2

2

2 sin2

1sin

2

1cos

2

1cos

2

1sin

4

+ΩΩΩΩ−+ΩΩΩ

Ω= φτφτττ TT

bP

22

0b+Ω=Ω

( ) τττ bbP2

1cos

2

1sin4 22

2 =

Ramsey fringe

Ramsey Method

-100 -50 0 50 1000,0

0,2

0,4

0,6

0,8

1,0

ω-ω0(Hz)

P(τ

)

Lrf

Lrf

Lrf

10L

Lrf

Lrf

10L

12Lrf

Swieca 08

•Real gain

•Field homogeneity

•Interference pattern

Comparisons and Measurements (Stability and Accurac y)

Accuracy

Stability

y(t) - Type A uncertainties (statistical)

ε(t) - Type B uncertainties (systematic)

Enviromental effects

Right valueMeasured values

Swieca 08

( ) ( )[ ]tytt ++= )(10 ενν

Tra

nsiti

on p

roba

bilit

y

Modulation (Hz)- ννννm + ννννmνννν0

0

0,5

1,0

Locking the LO to the atomic resonator

Type B uncertainties

Swieca 08

Frequency Shifts

Comparisons and Measurements (Stability and Accurac y)

ν0 ν = ν0 + ε

For atomic references

1. Second order Zeeman effect2. Blackbody radiation3. Colisional effect4. Rabi pulling5. First and second order

Doppler effect6. Cavity pulling7. Light shift8. Microwave leaks

ii σεε ±=Frequency shift

The definition of the second is defined as free of any disturbance

Accuracy budget

( ) 2/1131021 −−×− τ ????τ

(((( ))))tx

(((( ))))ty

τ

(((( ))))tx

(((( ))))ty

Oscillatorunder test

ReferenceOscillator

f / N TimeIntervalCounter

Data rec.f / N

St

Sp

(((( ))))0

01

y

yyty

−−−−====Fractional Frequency

Swieca 08

Comparisons and Measurements (Stability and Accurac y)

( ) ( ) ( )( )2

1

2

2

1tytyy −+= ττσ ( ) ( ) ( )

21

1

1

2112

1

−−

≅ ∑−

=+

M

iiiy yy

Mτσ

( ) ( ) ( )2

12

1

2122

222

1

+−

−≅ ∑

−

=++

N

iiiiy xxx

N ττσ

Finite data

Phase difference data – 1 PPS

Problems with simple variance calculations

Allan variance

Swieca 08

Comparisons and Measurements (Stability and Accurac y)

5 MHz

SR620

Counter

GPSAgilent

GPIB

Counter limitations < 10-11

Comparisons and Measurements (Stability and Accurac y)

Swieca 08

Phase comparisons – Improving performance

LPF

Voltmeter

Comparisons and Measurements (Stability and Accurac y)

Padrão de

Referência

PLL

Síntese de

Microondas

10MHz 10MHz

VCO 10MHz

DS345

DAQ

GPIB

Tempo

Variância de Allan

III

III

Mod

9192631770Hz

( )0

01

ννν −=ty

Padrão de

Referência

PLL

Síntese de

Microondas

10MHz 10MHz

VCO 10MHz

DS345DS345

DAQDAQ

GPIBGPIB

Tempo

Variância de Allan

III

III

Variância de Allan

III

III

Mod

9192631770Hz

( )0

01

ννν −=ty

Comparisons and Measurements (Stability and Accurac y)

Atomic Standards

Why Cold Atoms?

9,192GHz

9192,6MHz2

126 S F=3

F=4

Swieca 08

Why Cold Atoms?

T = 363 KT = 293 K

ττττ

f(ττ ττ)

Swieca 08

Why Cold Atoms?

T = 363 KT = 293 K

ττττ

f(ττ ττ )

Swieca 08

Cold Atoms

H1 = 2.5 mH2 = 5.9 m

Zacharias’ Fountain – Mid 1950’s

Swieca 08

Cold Atoms

First Laser-Cooled Fountain

~ 4 Hz Fringe

Swieca 08

Cold Atoms

Ramsey resonance in a Zacharias fountainA. Clairon, C. Salomon, S. Guellati, W. D. PhillipsEurophys. Lett., 16(2), pp.165-170 (1991)

A Cesium Fountain Frequency Standard:PreliminaryResults

A.Clairon, Ph. Laurent, G. Santarelli, S.N. Lea, S. Ghezali, M. Bahoura

CPEM 1994 Conference Digest, pg. 149

Laboratory Experiments Operational Frequency Standards

1991-1995

Swieca 08

Experiments – Atomic Fountain

Swieca 08

Magneto-optical trap

Six counterpropagating beams – 3 axisAnti-Helmholtz coils108 – 109 Cs atoms in 1-2s

10-20A

MOT

Experiments – Atomic Fountain

Swieca 08

Optical molasses

Six counterpropagating beams – 3 axisAnti-Helmholtz coils offSub-Doppler temperaturesHomogeneity of the atomic cloud100-300ms

MOT mol

Experiments – Atomic Fountain

Swieca 08

Launch of the parabolic flight

Upper beam red tuned, down beamsblue tuned

Initial velocity determined by the detuning1-3ms

MOT mol Launch

Experiments – Atomic Fountain

Swieca 08

Sub-Doppler cooling

Fast detuning and attenuation of thebeams

The atoms are still in the beams zoneThe Cs cloud reach temp. below 10µK1-4ms

MOT mol Launch

S-Dcooling

Experiments – Atomic Fountain

Swieca 08

Selection I – mf = 0

Rabi pulse in the first µwave cavityTransference of the atoms at mf = 0

µµµµW

MOT mol Launch

S-Dcooling

Sel

I

Experiments – Atomic Fountain

Swieca 08

Selection II – mf = 0

Light pulse tuned to push the atoms at mf ≠ 0Transference of the atoms at mf = 0

MOT mol Launch

S-Dcooling

Sel

III

Experiments – Atomic Fountain

Swieca 08

Interrogation I

First pass of the atoms in the µWave cavityPower control to apply a π/2 pulse µµµµW

MOT mol Launch

S-Dcooling

Sel

II

Int

I I

Experiments – Atomic Fountain

Swieca 08

Interrogation II

Dark flight of the cloudDefines the linewidth of the observed transition

MOT mol Launch

S-Dcooling

Sel

II

Int

I III

Experiments – Atomic Fountain

Swieca 08

Interrogation III

Second pass of the atoms in the µWave cavityPower control to apply a π/2 pulse µµµµW

MOT mol Launch

S-Dcooling

Sel

II

Int

I III III

Experiments – Atomic Fountain

Swieca 08

Detection

MOT mol Launch

S-Dcooling

Sel

II

Int

Fluorescence of the cloudDiferential method to minimize fluctuationsEvaluation of Nat in each hyperf. level and T

I III IIIDet

Experiments – Atomic Fountain

Load and launch 107 -109 Cs atoms in 300-1500 ms. Atoms are all in | F= 4, mF > - MOT,molasses,2D-MOT. State Selection π-pulse moves atoms in

| F = 4, mF =0> → | F = 3, mF = 0>. Optical pulse removes remaining | F = 4, mF ≠0>

atoms, leaving a pure | F = 3, mF = 0> sample. Ramsey spectroscopy atoms. (on way UP

and way DOWN.) Detection region measures populations in

| F = 4, mF =0> and | F = 3, mF = 0>.

251MHz201MHz151MHz

D2

852.

1 nm

23

26 P

9192.6MHz2

126 S F=3

F=4

F’=4F’=3F’=2

F’=5

T &

CR

ep

Swieca 08

Experiments – Atomic Fountain

Swieca 08

Vacuum system

Optical system

Diode lasers

AOM’s

Fluorescence detection

Trapping and cooling

Interrogation of the atomic transition

Interrogation signal generation

PLL techniques

Control of the 9.192GHz signal

Experiment Control

Temporal sequence

Signal Acquisition

Data storage

The Laboratory Setup

Experiments – Atomic Fountain

Swieca 08

~109 Cs trapped atoms

0,5 1,0 1,5 2,0 2,5 3,020

40

60

80

100

120

Tem

pera

ture

(10

-6K

)

Detuning (Γ)

0,5 1,0 1,5 2,0 2,5 3,0

0,0

0,2

0,4

0,6

0,8

1,0

Nor

mal

ized

cap

ture

effi

cien

cy

Detuning (Γ)

Experiments – Atomic Fountain

Swieca 08

Loading the sample to be interrogatedMOT – molasses transference

1 2 3 4 5 6 7 810

15

20

25

30

35

40

45

Tem

pera

ture

(10

-6K

)

Detuning (Γ)

1 2 3 4 5 6 7 8

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Num

ber

of a

tom

s in

the

TO

F s

igna

l (no

rm)

Detuning (Γ)

MOT molasses

Some limits in the trap laser

Experiments – Atomic Fountain

E1E2E1E2

80MHz80MHz

80MHz80MHz

DS345DS345

∫∫

∫∫

Escravo

Mestre

TravaFreqüênciaou Fase

Slave

Master

Freq. orPhase lock

Swieca 08

Launching Cold Atoms in a Moving Molasses

laserlaserlaunch v∆= ..3λυ

0,0 0,3 0,6 0,9

0

1

2

3

0,4 0,5 0,6 0,7 0,8 0,9-0,02

0,00

0,02

0,04

0,06

0,08

0,10

0,12

0,14

Inte

nsid

ade

/ V

Tempo / s

19,45 cm after the 2nd cavity5,6 MHz

Flu

or. s

igna

l (V

)

Time (s)

Free fall

InterrogationCavity

SelectionCavity

Cutoff waveguide1 cm

Modo TE 102

4,65 cm

2,286 cm

10 cm

QR = 8358

QP = 1128 1,5 cm

Free flightTube

InterrogationCavity

SelectionCavity

10 c

m

1 cm

a

d

Antinode∆∆∆∆F = ±1 e ∆∆∆∆mF = 0

Copper cavity – Qld > 5000

Mode TE011 – constant phase to avoid first order Doppler

Swieca 08

Experiments – Atomic Fountain

10MHz2f f/10 2f

100MHz

SamplingMixer

4.6GHz

DS345

Isol.~~/ out

in

out

in

out

2f

2f

out

out

in

∫

Maser

HP

OtherChain

ORD

in PC

~~/~/

f/8

3.6MHz

~29MHz

out

∫+offset

∫

∫

∫

High performance oscillators Phase locked loops

Swieca 08

Experiments – Atomic Fountain

1 10 100 1000 10000 100000-160

-140

-120

-100

-80

-60

ORD de 9,192GHz

VCXO de 100MHz

BVA de 10MHz

Sφ,

dB

(rad

2 /Hz)

@10

0MH

z

Freqüência (Hz)

1 10 100 1000 10000 100000-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

Sφ, d

B(r

ad2 /H

z)

@ 9

.192

GH

z

frequency, Hz

Cadeia de Interrogação X Cadeia de Preparação

Pharao X Cadeia de Interrogação

10 1001E-14

1E-13

σσ σσ y(s-1)

ττττ (s)

Oscillators phase noise

Phase noise of the output signalSwieca 08

Use the best spectral partof each oscillator

Experiments – Atomic Fountain

Swieca 08

Experiments – Atomic Fountain

Time of Flight Detection

f = 53 mm f = 20 mm

Photodetector

Atomic cloud

Detection BeamF = 4 ↔↔↔↔ F´ = 5

RepumpF = 3 ↔↔↔↔ F´ = 4

Optical Fiber

Polarizing Cube

Detection Laser

Repump Laser

Differential method to minimizefluctuations

Swieca 08

Experiments – Atomic Fountain

0,0 0,1

0

2

4

Flu

ores

cenc

e S

igna

l (V

)

tof (s)

Cross Talk

0,04 0,06 0,08

0

6

12

Flu

ore

sce

nce

Sig

na

l (V

)

tof (s)

Cross Talk

34

4

==

=

+=

FF

F

NN

NP

TransitionProbability

Detection F=3+4

Detection F=4

Reduction of Crosstalk effectsCollection OpticsAlignement

Time of Flight Detection

-40 -20 0 20 400

2

4

6

8

10

Tra

nsiti

on P

roba

bilit

y (a

.u.)

Frequency Detuning (Hz)

Swieca 08

Experiments – Atomic Fountain

Ramsey Fringesmf = 0

10 1001E-13

1E-12

Squ

are

Roo

t of A

llan

Var

ianc

e (σ

(τ))

Integration Time ( ττττ ) (s)

Tc = 5.2s and Q at = 6.56 x 109

( ) 21121018.5 −−×= ττσ y

-600 -400 -200 0 200 400 600

0

1

2

3

4

5

6

7

8

Tra

nsiti

on P

roba

bilit

y (%

)

Frequency detuning (Hz)

Swieca 08

Experiments – Atomic Fountain

-2,636 x 10-5-2,05 x 10-2Blackbody radiation

0,412,972nd order Zeeman effect

____-2,08 x 10-32nd order Doppler effect

-1,0 x 10-3-1,0 x 10-2Gravitational effect

Uncertainty x 10-12

Shift x 10-12

Effect

Preliminar accuracy budget

1. Colisional effect2. Rabi pulling3. Cavity pulling4. Light shift5. Microwave leaks

Direct probing of cold atoms – no launching

Experiments – TAC

First tests in using an antenna

Direct probing of cold atoms – no launching

-200 0 200 400

-0,1

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

1,1

Model: Lorentz Equation: y = y0 + (2*A/PI)*(w/(4*(x-xc)^2 + w^2))

y0 0.1038 ±0.01651xc 83.2253 ±1.46544w 39.31663 ±5.65373A 61.05288 ±6.29037

Flu

ores

cênc

ia (

U.A

.)

ν − νο (Hz)

Rabi 12 ms (atenuação 0.5) Ajuste lorentziano

( ) 2/111y 104.9 −−×= ττσ

Experiments – TAC

Rabi interrogation39Hz linewidth

-400 -200 0 200 400

-0,1

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

1,1

Experimental Simulation

Flu

ores

cenc

e (a

rb. u

nit)

Frequency (Hz)

-600 -400 -200 0 200 400 600-0,1

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

1,1 Experimental Fringes Simulation

Pro

babi

lity

Frequency (Hz)

Problems with the Ramsey methodPoor contrast observed

Experiments – TAC

Model based on the phase differencebetween the two pulses, dueto the cloud expansion

Experiments – TAC

TAC upgrade

New optical systemMicrowave cavity sculpted in the vacuum chamber

Vacuum chamber in SS-316L

Swieca 08

Frequency Synthesis and links

H - MaserCH1 - KVARZ

Commercial Standards – 5071A

Atomic FountainTime transfer

Other standards or Evaluation Systems

Time transfer – Remote comparisons

Traceability to BIPMCircular T

T T1 T2

One way transfer Two way transfer

Common viewcomparison

Swieca 08

54290 54300 54310 54320 543303876508000

3876508500

3876509000

3876509500

3876510000

3876510500

with frequency offset correction

5071

A-G

PS

(0.

1ns

)

MJD

without frequency offset correction

Swieca 08

Frequency Synthesis and links – Local Standards

54389 54390 54391 54392 54393 54394 54395 54396

9098592600

9098592800

9098593000

9098593200

9098593400

9098593600

9098593800

9098594000

9098594200

Mas

er-G

PS

(0.

1ns

)

MJD

without frequency offset correction

with frequencyoffset correction

GPS comparisons

Calibration of local standards – Long termTraceability to BIPM - TAI

Cs – 5071A – High perf. tube H Maser – CH1

Swieca 08

Frequency Synthesis and links – Local Standards

Allan VarianceDetermination of sample size – Counter limitLong term comparisons

Cs X Maser GPS X Maser

Future Prospects

•Characterization of Current Experiments

•Collisions in a Fountain Clock

•Different Frequencies to Squeeze the Ramsey Fringe

•Magic Wavelength for Cs, Rb

•Remote Comparisons of Current Experiments (ONRJ, LNE-SYRTE)

•Fountain Contribution to TAI

•Absolute Spectroscopy

•Optical Clocks – (LNE-SYRTE Hg Clock)

•New Generation of Microwave LO – Optical to µW sense (LNE-SYRTE OPUS)

The Team

Diego Lencione Renato F. Alves

Aida Bebeachibuli