The Fit and the Pendulum Quantum Mechanics and New Clocks M. Crescimanno Department of Physics and Astronomy Youngstown State University & R. Walsworth, D. Phillips, I. Novikova and C. Wang Harvard -Smithsonian Center for Astrophysics

$$$ : ONR, NASA, Research Corporation, Cluster Ohio Program, YSU PACER funds

IDEAL CLOCK Bright : need good SNR to "split" the line. Dark : period needs to be immune from environment. Based on regularity of periodic behavior must be: (Same Problem as : Quantum Computing, Art, Democracy (!!)...)

Gerard David "Rest on the Flight into Egypt" 1512(?)

A Brief History of Time......Measurement Mercury Ion Stability Size/Cost Rooms Table Quarter ?

Why Small Atomic Clocks? " Cell Phone Repeaters " GPS System

Rb Atomic Clock 6.8 GHz 87 Rb microwave cavity Optical table: lasers, optics and magnetic shields Q L = 15,000 • split endplate design for double bulb • mechanical tuning • access for fiber optical detector (Source: D. Phillips)

Level Scheme What the experimentalist knows... Level Scheme Simplified What the theorist thinks...

Atomic Clock: Traditional Maser Good: Bad: Simple, Bright Light shifts, environment couplings large, bulky Microwave Cavity Shield Light RF Pickup

Need to shine some dark on this clock... (Use interference) Fountain Clocks (Reduce time atoms spend in cavity) CPT Clock

Coherent Population Trapped Clock = optical pumping to a superposition hyperfine ground states  bc  ac |a> |c> |b>  ab Atomic population's dipole vanishes "Dark State" No microwave cavity Small Size Simple construction Low light readout

CPT =Electromagnetically Induced Transparency Static Solution (exact) Im(rho_01) = probe beam absorption Little spike of transparency in middle... Dispersion: Large index of refraction = slow- and stopped light

EIT window CPT clock : lock to center of EIT window Factor of 10 4 Closup...

CPT Clock: Elements 2 Lasers Shield Photodetector

Schematic of "All-Optical" Atomic Clock cell oven solenoid shields  bc  ac |a> |c> |b>  ab (Source: D. Phillips, R. Walsworth) isolator power level = +17 dBm freq=6.834 GHz x2 Multplier VCXO 12 GHz photodetector cell oven solenoid shields 6.84 GHz LO 3.42 GHz drive 3.42 GHz EOM DC feedback signal laser diode

Why so good? " Environmental susceptibility (Data from I. Novikova) " Medium Term stability at the Level

Simulation vapor cell inputs: gas, pressure, laser power, beam diameter diffusion coefficient, line shifts, broadenings...  bc  ac |a> |c> |b>  ab 3-level density matrix solver velocities, diffusion, AC effects  dv v output lineshapes calculations performed in C/GSL/IDL parameters chosen to match experimental conditions from literature and our measurements Detection

CPT Quantum Optics : Basic Model Light Collisions, etc. RWA

Parameters of Basic Model

Simulation Doppler effect + Motional Averaging (Lamb-Dicke) Analytic solution for steady state AC Stark Effect due to carrier Lockin detection modulation dependent effects - (EIT line asymmetry) Includes...

Analytic solution for steady state Exact Expressions -Steady state (No additional AC fields) Numerical Evaluation -Atom(s) at rest Pulse-Probe Limit

Doppler effect + Diffusive Averaging (Lamb-Dicke Effect) Refns: MIT atomic physics notes -simplified- R. H. Dicke, Phys. Rev. 89 (1953) 472. Two Effects of particle motions: Doppler Effect: (time) Coherence wash-out by diffusion: (space) Select velocity from ensemble, doppler shift atomic response and add distinct motional channels. UPSHOT:

Doppler Effect: Diffusion: Beat Pump: No diffusion: UPSHOT : replace 'w' by 'w +iDk 2 '

Do it at same time you do Doppler; via convolution: NOW: combine diffusion kernel and doppler kernel by essentially multiplying them...total kernel is;

AC Stark Effect due to Carrier Three light fields: Carrier and (2) Hyperfine sidebands Carrier : Bright but far detuned. With Refns: F.Bloch and A. Siegert, Phys. Rev. 57 (1940) 522. J. H. Shirley, Phys. Rev. 138 (1965) B979. Don't dress atoms

Develop density matrix as series in Order: Instead... Zero'th DC First, Oscillatory Second: DC and Oscillatory BIG!! Second Order DC term causes: Shift Lineshape asymmetry

AC Stark: 1 st Order

AC Stark : 2 nd Order, DC part Ex: Can be Large...not (A/s)^2! Mixes Real and Imaginary parts of density matrix

Line Shape Change due to AC Stark Effect Center, Width and Skew Example on EIT line (3 states) Without Carrier With Carrier (A ~ ½ Mhz) In 2-state model, expect only shift in leading order. In multi-state model expect lineshape changes as well. NOTE:Hemmer, et. al. :EIT in solids/third beam used to narrow width

Preliminary Comparisons So many knobs to twist ! DATA THEORY

DATA THEORY Detuning Slope w1/w0 ~ 10 mHz/MHZ Slope is negative !

Dependence on Modulation DATA THEORY

Carrier Intensity Stark Effect DATA THEORY 1-2 Mhz Carrier Rabi -10 Hz shift ~ ½ Mhz Rabi Slope change is presumably increase in line asymmetry

CONCLUSIONS: CPT clock may be promising Experiment and QO theory are converging QO theory informing design compromises