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Physics with Atomic : Beyond What Is It? •How Atomic Clocks work •Cold Collisions - Rb • photon recoils –Is the photon momentum ħk? •Juggling in fountains •Optical Clocks –How do you count at optical frequencies? Penn State Tyler Anderson Seongsik Chang Russ Hart Chad Fertig Theory Ruoxin Li Ron Legere Dr. Lingze Duan Irfon Rees Servaas Kokkelmans Dr. Steve Gensemer Veronica Savu (now Asst. Prof.) Dr. Paul Lammert Dr. Sid Cahn Boudewÿn Verhaar Dr. Wenko Süptitz Kurt Gibble Dr. Ivan Mistrik Eindhoven Technological Dr. Xinye Xu University, the Netherlands Jérémie Bouttier Quentin Beaufils Support from NASA, ONR, NSF, NIST, & Penn State.

Atomic Clocks ? State 2 Accurately Eh= υ P#2() Determine Center

State 1 X Microwave or Laser ν. Current Atom of Choice is 133Cs. Quantum Mechanics 1 valence e−: 6S If nucleus S= 1/2 Nuclear : I= 7/2 Then or

2 Well Defined Energy States F = I + S = 4 z F = 4 G JG 6S Δ=Ehυ I •S 12 υ ≡ 9,192,631,770Hz F = 3 3/20/2007-2 Atomic Beam Clocks Oscillator 9.192 GHz Cs N N beam F = 3 F=3 F=4 4 or S F = 4 F=3 S F=4 3 Detector FF= 3+=e iGHzt 29.192 π ( ) 4 Ψ= 2 Analogy Can’t observe an atomic (quantum) pendulum. Precession time T 1 Δ=f T=0.005s ⇒100Hz “Ramsey 2T Versus voscillator Fringes” F=4 Probability Accuracy: δν =±110 × −14 or pendulum ν amplitude υ osc ±100 μHz υ atom 3/20/2007-3

Laser-Cooled Fountain Clocks & the Cold Collision Frequency Shift • Microwave Spectroscopy • Collisions can shift the phase – laser-cooling: Doppler of the atomic coherence shifts & narrow linewidth i2π ()9GHz t+iϕ phase shifts coherence by ϕ 3 + e c 4 c Ψ = 6 2 2 σ=−10 Å Cs 6s ground state 9 F = 4 ν≡9,192,631,770 Hz 1.0 GHz F = 3 Cs 0.5 1.0 The dominant 0.0 problem for 0.5 Cs fountain -0.5 Frequency (mHz) Δν clocks Cs -1.0 012345 Transition Probability 0.0 -4 -2 0 2 4 Density (108 cm-3) ν−6.834 GHz (Hz) Tiesinga, Verhaar, Stoof, & van Bragt, PRA 45, 2671 (’92).

Gibble & Chu, PRL 70, 1771 (’93) 3/20/2007-4 Cold Atom Scattering Semi-classically: R Cs-Cs at 1μK bmax v=1 V(R cm/s ) bmax ≈200Å μ=m/2 −1μK R-6

Lvbhmax=≈μ max 0.3 h Quantum Mechanics λ =≈3,000Åb >> dB μv max Lllh=+( 1) No p-wave ∴A = 0

λ 2 s-wave scattering for T → 0: σδ=≈dB sin262() 10 Å 00π Spherical outgoing waves → isotropic scattering

Cs-Cs - 99.9(1)% s-wave @ 0.89 μK KG, Chang, Legere, PRL (1995). 3/20/2007-5

87Rb

1.0

Rb 34 0.5 cm Δν 6.8 GHz Transition Probability Transition

0.0 -4 -3 -2 -1 0 1 2 3 4 ν − 6,834,612,611 Hz (Hz)

Δν = 0.953 Hz −13 −1/2 σy(τ) = 2.1×10 τ S/N = 200:1 (local oscillator) 3/20/2007-6 87Rb Cold Collision Frequency Shift

1.0 • -0.38(8)mHz @ n=1.0(6)109×cm−3 • 50× less than 133Cs 0.5 • Consistent with calculations δ = −Γ • GPS & SI

0.0 δ = 0

-0.5 δ = +Γ Rb Frequency (mHz) Frequency 34 cm ΔνCs -1.0 0 0.1 0.2 0.3 0.4 0.5 6.8 GHz Density (109 cm-3)

Cs: Gibble & Chu, PRL 70, 1771 (‘93) Rb: Fertig & Gibble, PRL 85, 1622 (‘00) Sortais Bize, Nicolas, Clairon, Salomon, & Williams, PRL 85, 3117 (‘00) Theory: Kokkelmans, Verhaar, Gibble, & Heinzen, PRA 56, RC4389 (‘97)

Kempen, Kokkelmans, Heinzen, & Verhaar, PRL 88, 093201 (‘02) 3/20/2007-7

87Rb Cold Collision Frequency Shift

1.0 • -0.38(8)mHz @ n=1.0(6)109×cm−3 • 50× less than 133Cs 0.5 • Consistent with calculations δ = −Γ • GPS & SI second

RECOMMENDATION0.0 CCTFδ = 0 1 (2004): Concerning secondary representations of the second The Consultative Committee for Time and Frequency, -0.5 … δ = +Γ Rb recommends (mHz) Frequency that the unperturbed ground-state hyperfine quantum34 Δν cm transitionCs of 87Rb may be used as a secondary representation of the -1.0 second with a frequency of fRb = 6 834 682 610.904 324 Hz and an 0 0.1 0.2 0.3 0.4 0.5 -15 6.8 estimated relative standard uncertainty (1σ) of 3 × 10 , … . GHz Density (109 cm-3)

CCTFCs: Gibble (2006): & Chu, PRL 70, 1771 (‘93) 199 + 88 + 171 + recommendsRb: Fertig & Gibble,Hg PRL@ 282nm,85, 1622 (‘00)Sr @ 674nm, & Yb @ 436nm. Sortais Bize, Nicolas, Clairon, Salomon, & Williams, PRL 85, 3117 (‘00) Theory: Kokkelmans, Verhaar, Gibble, & Heinzen, PRA 56, RC4389 (‘97) Kempen, Kokkelmans, Heinzen, & Verhaar, PRL 88, 093201 (‘02) Atomic Clocks 6 834 682 610.904 324 17(7) Hz

Doppler shift for atoms at room temperature.

Doppler shift for a slow walk.

Gravitational red-shift for 2m. δν 1 v 2 for walking. =− ν 2 c 2

5s in the of the universe!

3/20/2007-9

Better Clocks - Applications 200 Global Positioning System (GPS) Handheld $200 receiver. 0 – 24 satellites with atomic clocks Lime Rock, CT

– Accuracy of 15 feet. N (m) – Many applications -400 • Auto, marine, & aviation navigation-600 0 400 • surveying & mapping E (m) • agriculture, construction, mining, fleet management 100 Car racing & teaching physics Lime Rock, CT v (mph) Time50 North (m) East (m) 13:53:54 102.1 -259.4 13:53:551 86.8 -222.1 200 13:53:57 48.4 -143.4 13:53:58 28.9 -101.2 13:53:59 9.4 -57.6 0 13:54:01 -31.9 32.2 13:54:03(g's) 0 -75.7 127.8

13:54:04tr -98.2 174.9 a 13:54:06 -136.0 248.2 N (m) 13:54:07 -151.9 282.5 -400 13:54:08-1 -167.8 305.6 0 1000-600 0 2000 400 E (m) 3/20/2007-10 distance (m) Better Clocks • Global Positioning System (GPS) – earth-based - ionosphere & water vapor are current limitations Mars – Interplanetary - VLBI () – NASA Deep Network • Academic interest: How accurately can we measure? – Fundamental constants – new techniques • High speed Communication networks • Tests of – 100 to 104 better • Time variation of constants dα e 2 1 α =≈ – string theory dt =c 137 – Cs & Rb clocks, optical clocks • Unforeseen applications

3/20/2007-11

NASA DSN (Deep Space Network)

3 sites: Goldstone, Canberra, & Madrid. 24 m to 70 m radio telescopes. Uses the most stable & fieldable clocks. Different atmospheric delays.

3/20/2007-12 Atomic Clock for Space Atomic Clock Experiment: RACE Much longer observation times. T=10s (Δν = 50 mHz)

Vapor Trap v=10 m/s Transition Probability ν 6.8 GHz shutter

v=5cm/s

UHV Trap • Local Oscillator 0.5 m • ISS vibrational noise Penn State & JPL • 2 clocks for accuracy evaluation

• Clock , red-shift, c 3/20/2007-13

High Performance Clocks in a Space-Based DSN Δx Δs r

b

Very Long Baseline Initial range comes from 2-way. Geo Synch orbit & Different than GPS - transmit only. 10 m @ Mars bsΔ Geometry is very different than GPS. Δ=Δxbθ = = 2.5mm r ΔxfΔ Precise timing allows <10 m error. = =×1.4 10−14 Time differences are key. rf Δ=tcx Δ =8.5 ps Differential relative to Mars station.

3/20/2007-14 Clock Accuracy & Stability Uncertainty in Frequency SYRTE NIST PTB IEN (10−16) FO2 F1 CSF1 CsF1 Cold collisions 2.0 1 7 12 Black-body radiation 2.5 2.6 2 0.7 1st order Doppler - Distributed <3 <0.3 5 <0.3 cavity phase Electronics, microwave leakage 4.3 1.4 2 <2

Microwave Lensingphoton recoil 1.4 Total uncertainty (10−16) 6.5 3.3 9 16 Instability @ 1s 280 6000 2000 3000

• Biggest offset is 40 days R. Li & KG, Metrologia ’04. • Black-body is difficult – differential AC Stark shift • Cold collisions inhibit evaluation of other systematics

Wynands & Weyers, Metrologia (2005) 3/20/2007-15

Microwave Photon Recoil?

Infinite plane wave

=k mvx = = k

vmsx ≈ 0.1μ /

Recoil Frequency Shift: E Conserve E & p. F = 2

δυω==22k F = 1 == v v υ 22mmc=ω 2 r =±1.5 × 10−16

3/20/2007-16 Is an atom’s recoil equal to the photon’s momentum?

Finite beam: nk= x Maxwell: (∇+22kE) =0 2222 so kkkkxyz++= & kkx < 2 k yz, ≈ ⇒=−δ kppbx 8 wmm0 = 2 Three good choices: zˆ xˆ 1. The photon momentum comes in discrete units of k, in the x direction. =k

2. The atom has a recoil of kx in the x direction; v & v are unchanged. y z =kx 3. The atom has a recoil of kx in the x =k = direction, and also ±ky & ±kz. ± kz =kx Wicht…, Chu, Phys. Script (2002) Gould, Ruff, Pritchard, PRL (1986) Cladé…, Biraben, PRL (2006) Wicht, … Chu, PRA (2005) 3/20/2007-17

Transverse (Microwave) Photon Recoils? zˆ xˆ There is no grating in the z direction. =k → No recoil in z direction. ±=kz =kx “Microwave” Stern-Gerlach regime: Same problem for atomic clocks: The dipole force of the microwave field acts as a lens on the atomic wavefunction. 2 E Shift: ≈ ±4nm ħħkkx Δwidth: ≈ ±2nm 1 2 z ee 22 δϕPt=Ψ⎡⎤2 −Ψ 1 t sin⎡ kkx cos ⎤ 2 2 ()22() ⎣ ()zx ( )⎦ 1 Ψ ()t2 2 Ψ ()t2 ⎣⎦⎢⎥⎛⎞ω 1 G −itω ⎜⎟2 Ω()rte, 2 2 Hint = ⎜⎟ =k w1 ⎜⎟1 G itω ω δυ⎜⎟≠Ω−()rte, δυ=Δ ϕ()kzR υ f ⎝⎠2 4π m 2 w δυ δυ 2 ≠×1.5 10−16 ≈×310−17 υ υ KG PRL (‘06) 3/20/2007-18 Juggling Atomic Fountains

10−10 −11

) 10 2 10−12 10−13 s-wave

Size (cm 10−14 10−15 2 10 100 200 Ec (μK)

mg22Δ t E = c 4

T= 300nK Δt Launch= 7ms E =19μK •State-to-state velocity-selected •Ramsauer-Townsend effect differential crossed-beam •Next generation of clocks scattering at µK energies. will juggle.

Legere & Gibble, PRL (‘98) 3/20/2007-19

Juggling Frequency Shift

0.05 22ms 44ms 66ms

Rb 0.00 6.8 GHz

Frequency Shift (mHz) Frequency -0.05 0.0 0.5 1.0 1.5 2.0 E (mK)

• Optimal delay is 22 ms • Higher partial waves – other patterns • Avoid 44 ms

S. Kokkelmans & KG 3/20/2007-20 Direct Measurement of s−wave Phase Shifts • Juggle “clock” atom in a coherent superposition of 2 states with an atom in F,m (4,4). • Detect only scattered atoms. • Phase shift of Ramsey fringes is independent of atomic density. • Clock-like accuracy - 104× more accurate interactions. PPM scattering lengths. ⎡⎤eeikr ikr ψδδψ ++=+++=+1 ⎡⎤eee ikz 334 4iδ3 sin 3 eiδ4 sin 4 2 ⎢⎥⎣⎦() 34 ⎣⎦kr kr

unscatteredn1 (arb.) scattered state 3 & 4 0 0.5 1 arb.)

0 3 20 15 n(vz) 10 −0.1 10

(rad) 100×

4 5 20 −δ 0.2 scattered atoms (arb.) 3 − 0

δ 0 -10 0 10 -2 -1 0 1 2 vz (cm/s) Microwave Detuning (Hz) unscattered atoms (10 A (arb.) 0 −0.3 01Hart, Xu, Legere, & KG, quant-ph/0702146 (in3/20/2007-21 press) n1 (arb.)

A Quantum Scattering Interferometer

•Mach-Zehnder 20

10

Detected Atoms (arb.) 0 Δφ -10 -5 0 5 10 Microwave Detuning (Hz) T (s) 0 0.1 0.2 0.3 0.4 0.5 0 Δ=φ δδ34- 4,0 + 3,0 frequency shift 2 (rad.)

4 −0.1 −δ

Δφ 3 δ

−0.2 •Phase shift, not frequency shift •8 mrad statistical error 3/20/2007-22 Optical Clocks • Fractional frequency is the key δυυΔ performance measure. = υπυSN/ υ ≈ 1015 Hz 100,000 × opt Count optical cycles! • How do you make a very short pulse of (sound)? A laser with a million colors!

Pulse rate

3/20/2007-23

2005

Roy Glauber Jan Hall Ted Hänsch Harvard JILA, Max Planck USA, 1925 - USA, 1934 - Germany, 1941 - "for his contribution "for their contributions to … to the quantum precision spectroscopy, including theory of optical the optical " coherence"

3/20/2007-24 Counting the Ticks of Light

Pulse rate f 2f

f 2f Stable Laser Crystal

2f – f = (Pulse Rate) × 429,228 = f

• Measure f by measuring the difference between f & 2f! • Much better clocks - also huge impacts for chemistry.

Diddams et al., PRL 84, 5102 (‘00); Rafac et al., PRL 85, 2462 (‘01). 3/20/2007-25

Directly Locking Lasers with Large FM Noise to High Q Cavities

• Pound-Drever-Hall locking Laser EOM • Laser linewidth ffmà cavity linewidth Δν Servo PD • Gravity wave detectors - LIGO ω vω ≡ • What if the laser sweeps through SPDH Δω 2 faster than the build up time? • Previous analyses in time domain. 20 dE cav =−(1 −iv t ) E + iE -10 10 30 dt ω cav in -20 20 40 ν/Γ • Distortions when v à1→can’t lock ω t • Frequency domain .01 – 3.5 kHz cavity, 3 MHz laser fm “noise”

Drever et al., Appl. Phys. B 31, 97 ’83. Rohde et al., JOSA B 19, 1425, ’02.

Lawrence et al., JOSA B 16, 523, ’99. Duan & Gibble, Opt. Lett 30, 3317, ’05. 3/20/2007-26 Laser Lock to Cavity

40 66,600 30 Finesse 20 6.97 kHz 10 Transmission 0 -20 -10 0 10 20 Detuning (kHz) 99.995% reflectivity. Photon lives for 22 μs! δυ 6.97kHz = Laser Stability υ 3.8× 1014 Hz S/ N

20 10

(Hz) 4 Hz

y 4

22.7 Hz σ 2 1.6Hz τ Intensity 100 200 300 0.01 0.1 0.2 0.5 1 f (Hz) τ (s) 3/20/2007-27

Summary • Laser-cooled atoms 1.0 – TAI – international atomic time Rb 0.5 • 87Rb Cold collision shift 6.8 GHz 0.0 87 – 50 times smaller for Rb -0.5 Frequency (mHz)

– cancel collision shift -1.0 0.0 0.1 0.2 0.3 0.4 0.5 – Juggling clocks Density (109 cm-3) – Rb clocks will be the GPS system clocks • RACE: High Performance Rb – French clock ACES (Cs) in 2008?? • Atom’s recoil is less than ħk. – No discrete transverse recoils – Lensing frequency shift • Juggling Cs fountain – Direct measurement of scattering phase shifts SPDH • Optical clocks and oscillator -20 -10 10 20 30 40 ν/Γ 3/20/2007-28 t