Optically polarized atoms_ch_6.pdf - The Budker Group

Optically polarized atomsMarcis Auzinsh, University of LatviaDmitry Budker, UC Berkeley and LBNLSimon M. Rochester, UC Berkeley1

Chapter 6: Coherence in atomic systems• Exciting a 0ö1 transition with z polarized light• Things are straightforward: the |1,0> state isexcited• What if light is x polarized ?2

• Exciting a 0ö1 transition with x polarized lightRecipe forfinding howmuch of agiven basicpolarization iscontained inthe field E• x ö1 1 0 1 1E + =− ; E = 0; E− =2 2• Note: light is in a superposition of σ + and σ -3

• Exciting a 0ö1 transition with x polarized light• Coherent superposition -|1, |1,-1>+|1,1> 1>+|1,1> is excited• Why do we care that a coherent superposition isexcited?• Suppose we want to further excite atoms to a level J ’’4

• Compare excitation rate to J ’’=0for x and y polarizedE ’ light5

• Compare excitation rate to J ’’=0for x and y polarizedE ’ light• Calculate final-state amplitude as• with• First, for x polarized lightNow repeat for ypolarized light !6

y polarized lightx polarized light8

• The state we prepared with xpolarized light E is a brightstate for x polarized light E ’• At the same time, it is a darkstate for y polarized light E ’• A quantum interference effect !• Two pathways from the initial tofinal state; constructive ordestructive interference• This is the basic phenomenon underlying :‣ EIT electromagnetically induced transparency‣ CPT coherent population trapping‣ STIRAP stimulated Raman adiabatic passage‣ NMOR nonlinear magneto-optical optical rotation‣ LWI lasing w/o inversion‣ “slow light” very slow and superluminal group velocities‣ coherent control of chemical reactions‣ …9

An important comment about bases• We have considered excitation with xpolarized E light, and have seen an“interesting” coherence effect (dark(andbright) ) excited states• If we choose quantization axis along lightpolarization, , things look trivialBright intermediate state for zpolarized light E’Dark intermediate state for x or ypolarized light E’10

Quantum Beats• Suppose we prepare a coherent superposition ofenergy eigenstates with different energies• For example, we can be exciting Zeeman sublevelsthat are split by a magnetic field• The wavefunction will be something like11

Quantum BeatsAs a specific example, again consider exciting xciting a0ö1 transition with x polarized light• As a specific example, again consider e• Assume short, broadband excitation pulse att=0. Then, at a later time:12

Quantum Beats• Now, as before, we excite further with second cw(but spectrally broad and weak)light field• The amplitude of excitation depends on time:13

Quantum Beats• Excitation probability is harmonically modulated• Modulation frequency ↔ energy intervals betweencoherently excited states• The evolution of the intermediate state can beseen on the plots of electron density• Note: : Electron density plots are NOT the same asthe angular-momentum probability plots we use alot in this course !14

Quantum Beats• In this case temporal evolution is simple – it is justLarmor precession15

Quantum Beats• Q: What will be seen with y polarized light E ’ ?• Q: The same but with opposite phasex:y:• Quantum beats in atomic spectroscopy werediscovered in 1960s by E. B. Alexandrov in USSRand J.N. Dodd, G.W.Series, , and co-workers in UK16

Yevgeniy Borisovich Alexandrov17

The Hanle Effect• Now introduce relaxation: : assume that amlitude ofstate J’ decays at rate Γ/2• Amplitudes of excited sublevels evolve accordingto :• With x polarized second excitation E’ , we have18

The Hanle Effect• Assuming that both light fields are cw, , and thatwe are detecting steady-state state signals as a functionof magnetic field, we have:• Limiting cases:Γ >> 2 ωL; Γ ~2 ωL; Γ

The Hanle Effect• What’s s going on is clearly seen on electron-density plot for J’ω = 0 ω = Γ /2LLωL= Γω = 3 Γ /2 ω = 2Γ ω = 5 Γ /2LLLω = 3Γ ω = 7 Γ /2 ω = 4ΓLLL20

The Hanle Effect• A similar illustration can be done with angular-momentum probability plots• Quite similar physics takes place in Nonlinear FaradayEffect• Transverse (w.r.t.. magnetic field) alignmentconverted to longitudinal alignment• The Hanle effect is sometimes called magneticdepolarization of radiation. ω This refers to observationL= 0 ωL= Γ /2 ωL= Γvia emission from the polarized stateω = 3 Γ /2 ω = 2Γ ω = 5 Γ /2LLLω = 3Γ ω = 7 Γ /2 ω = 4ΓLLL21

The Hanle Effect• A similar illustration can be done with angular-momentum probability plots• Quite similar physics takes place in Nonlinear FaradayEffect• Transverse (w.r.t.. magnetic field) alignmentconverted to longitudinal alignment• The Hanle effect is sometimes called magneticdepolarization of radiation. This refers to observationvia emission from the polarized state22