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Optically polarized atoms

Optically polarized atoms. Marcis Auzinsh, University of Latvia Dmitry Budker, UC Berkeley and LBNL Simon M. Rochester, UC Berkeley. Chapter 6: Coherence in atomic systems. Exciting a 0 1 transition with z polarized light Things are straightforward: the |1,0> state is excited

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Optically polarized atoms

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  1. Optically polarized atoms Marcis Auzinsh, University of Latvia Dmitry Budker, UC Berkeley and LBNL Simon M. Rochester, UC Berkeley

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

  3. Exciting a 01 transition with x polarized light • x  • Note: light is in a superposition of σ+and σ - Recipe for finding how much of a given basic polarization is contained in the field E

  4. Exciting a 01 transition with x polarized light • Coherent superposition -|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’’

  5. Compare excitation rate to J’’=0 for x and y polarized E ’ light

  6. 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 !

  7. Compare excitation rate to J’’=0 for x and y polarized E ’ light • For y polarized light : • Or, with a common phase factor • So, finally, we have :

  8. y polarized light x polarized light

  9. 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 statefor 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 rotation • LWI lasing w/o inversion • “slow light” very slow and superluminal group velocities • coherent control of chemical reactions • …

  10. An important comment about bases • We have considered excitation with x polarized Elight, and have seen an “interesting” coherence effect (darkand bright) excited states • If we choose quantization axis along light polarization, things look trivial Bright intermediate state for z polarized light E’ Darkintermediate state for x or y polarized light E’

  11. 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

  12. Quantum Beats • As a specific example, again consider exciting a 01 transition with x polarized light • Assume short, broadband excitationpulse at t=0. Then, at a later time:

  13. 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:

  14. 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 !

  15. Quantum Beats • In this case temporal evolution is simple – it is just Larmor precession

  16. Quantum Beats • Q: What will be seen with y polarized light E ’ ? • A: 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

  17. Yevgeniy Borisovich Alexandrov

  18. The Hanle Effect • Now introduce relaxation: assume that amplitude of state J’ decays at rate Γ/2 • Amplitudes of excited sublevels evolve according to : • With x polarized second excitation E’ , we have

  19. The Hanle Effect • Assuming that both light fields are cw, and that we are detecting steady-state signals as a function of magnetic field, we have: • Limiting cases: • This is a nice method for determining lifetimes that does not require fast excitation, photodetectors, or electronics

  20. The Hanle Effect • What’s going on is clearly seen on electron-density plot for J’

  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

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