Optically polarized atoms Marcis Auzinsh, University of atvia Dmitry Budker, UC Berkeley and BN Simon M. Rochester, UC Berkeley 1
Chapter 6: Coherence in atomic systems Exciting a 0ö1 transition with z polarized light Things are straightforward: the 1,0> state is excited What if light is x polarized? 2
Exciting a 0ö1 transition with x polarized light Recipe for finding how much of a given basic polarization is contained in the field E x ö 1 1 0 1 1 E + = ; 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 is excited? Suppose we want to further excite atoms to a level J 4
Compare excitation rate to J =0 for x and y polarized E light 5
Compare excitation rate to J =0 for x and y polarized E light Calculate final-state amplitude as with First, for x polarized light Now repeat for y polarized light! 6
Compare excitation rate to J =0 for x and y polarized E light For y polarized light : + 1 i 0 1 i E = ; E = 0; E = 2 2 Or, with a common phase factor 1 1 0 1 1 E + = ; E = 0; E = 2 2 So, finally, we have : 7
y polarized light x polarized light 8
The state we prepared with x polarized light E is a bright state for x polarized light E At the same time, it is a dark state for y polarized light E A quantum interference effect! Two pathways from the initial to final state; constructive or destructive 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 WI 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 x polarized E light, and have seen an interesting coherence effect (dark( and bright) ) excited states If we choose quantization axis along light polarization,, things look trivial Bright intermediate state for z polarized light E Dark intermediate state for x or y polarized light E 10
Quantum Beats Suppose we prepare a coherent superposition of energy eigenstates with different energies For example, we can be exciting Zeeman sublevels that are split by a magnetic field The wavefunction will be something like 11
Quantum Beats As a specific example, again consider exciting xciting a 0ö1 transition with x polarized light As a specific example, again consider e Assume short, broadband excitation pulse at t=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 between coherently excited states The evolution of the intermediate state can be seen on the plots of electron density Note: : Electron density plots are NOT the same as the angular-momentum probability plots we use a lot in this course! 14
Quantum Beats In this case temporal evolution is simple it is just armor precession 15
Quantum Beats Q: What will be seen with y polarized light E? Q: The same but with opposite phase x: y: Quantum beats in atomic spectroscopy were discovered in 1960s by E. B. Alexandrov in USSR and J.N. Dodd, G.W.Series,, and co-workers in UK 16
Yevgeniy Borisovich Alexandrov 17
The Hanle Effect Now introduce relaxation: : assume that amlitude of state J decays at rate Γ/2 Amplitudes of excited sublevels evolve according to : With x polarized second excitation E, we have 18
The Hanle Effect Assuming that both light fields are cw,, and that we are detecting steady-state state signals as a function of magnetic field, we have: imiting cases: Γ >> 2 ω; Γ ~2 ω; Γ << 2ω This is a nice method for determining lifetimes that does not require fast excitation, photodetectors,, or electronics 19
The Hanle Effect What s s going on is clearly seen on electron-density plot for J ω = 0 ω = Γ /2 ω = Γ ω = 3 Γ /2 ω = 2Γ ω = 5 Γ /2 ω = 3Γ ω = 7 Γ /2 ω = 4Γ 20
The Hanle Effect A similar illustration can be done with angular- momentum probability plots Quite similar physics takes place in Nonlinear Faraday Effect Transverse (w.r.t.. magnetic field) alignment converted to longitudinal alignment The Hanle effect is sometimes called magnetic depolarization of radiation. ω This refers to observation = 0 ω = Γ /2 ω = Γ via emission from the polarized state ω = 3 Γ /2 ω = 2Γ ω = 5 Γ /2 ω = 3Γ ω = 7 Γ /2 ω = 4Γ 21
The Hanle Effect A similar illustration can be done with angular- momentum probability plots Quite similar physics takes place in Nonlinear Faraday Effect Transverse (w.r.t.. magnetic field) alignment converted to longitudinal alignment The Hanle effect is sometimes called magnetic depolarization of radiation. This refers to observation via emission from the polarized state 22