Third order nonlinear optics 1. Two Photon pumping 2.. Third harmonic generation 3. Doppler free spectroscopy 4. Lambda structures

Two-photon absorption and optical pumping ri W Purpose: create a two photon population inversion As before: But we need to be ON resonance Adiabatic approximation breaks down!

Two-photon absorption and optical pumping ri W Alternate to pi pulse pumping:

Two-photon absorption and optical pumping The dilemma: if The adiabatic approximation breaks down, and the energy Gets stored in the intermediate levels by absorption!? Too high powers are required to reach an inversion If Is there a solution? Is there a problem worth looking for a solution? “Light travels undisturbed for billions of years - only to get its wavefront distorted in the last few milliseconds” Yes, there is a problem: atmospheric distortion of out of space radiation:

What are the solutions to atmospheric distortions? Send an observer into space …they selected Mr. Hubble

2nd solution: Correct for the atmosphere a) Correct the telescope to minimize the size of the image of the point source. Choose/create a point source within 2 arcsec of the object to be observed. b) But how?

Two-photon absorption and optical pumping 2 photon coherent excitation of Sodium Which we approximate by The ideal solution: create an artificial star by optical pumping of Na

now 1 st approach: off-resonance zero area pulse excitation

now

1 st approach: off-resonance zero area pulse excitation now

1 st approach: off-resonance zero area pulse excitation The purist will tell you that you have to include the full hyperfine structure

1 st approach: off-resonance zero area pulse excitation The result of listening to the purist:  t = 650 ps  = 100 ps F 589 =.90  J/cm 2 F 1140 = 2.2  J/cm 2   = 14.6 GHz   = 2.39 GHz => 3.1 mW / cm 2

Second approach: the two-photon “pi pulse”  10 ps, 4.58  J/cm 2 (each)  1 = 1.91 GHz and  2 = 2.39 GHz.

Full hyperfine structure (including Doppler-distribution)  = 25 ps F 589,1140 = 14.1  J/cm 2   = 58.6 MHz   = 0 => 30 mW / cm 2

Sodium temperature: 190 K. Pulse duration: 10 ps, Single pulse fluence: 4.58  J/cm 2 (each) Detunings:  1 = 1.91 GHz and  2 = 0 GHz.  -pulse yields 5 times more signal than cw excitation at roughly the same energy expenditure Photon return is 25 times above detection limit for an un-cooled PMT  -pulse excitation leads to a signal per excitation Comparison of coherent excitation versus cw More details in J.~Biegert and J.~C.~Diels, “Feasibility study to create a polychromatic guidestar in atomic sodium", Physical Review A, 67: (2003). Much

2. Third harmonic generation Bloch vector model for two-photon resonance Max value of = 1,, therefore Shortest two photon absorption length Shortest harmonic generation length Linear absorption length Linear absorption length for 3rd harmonic

Shortest two photon absorption length Shortest harmonic generation length Linear absorption length Linear absorption length for 3rd harmonic Maximum conversion efficiency L 0 0 L L photon resonance Low efficiency, but low power needed small large small + 3 photon resonance Highest efficiency, but highest power needed 2. Third harmonic generation

Simple characteristics: Reversibility Zero-area pulse excitation E F=E P d=P Mechanical analogy Do we need to look at a 2 level-system? Each successive cycle of the pulse constitutes a zero-area pulse sequence Cumulative (coherent) effects in the attosecond scale!

Intracavity interaction in a mode-locked laser Atomic beam  pulse ZERO-AREA PULSE What are they good for?

2. Third harmonic generation Exploit coherent propagation effects to minimize the two-photon absorption losses. U V W

Third order nonlinear optics 1. Two Photon pumping 2.. Third harmonic generation 3. Doppler free spectroscopy 4. Lambda structures Does it apply to ultrashort pulses?

3. Doppler Free two-photon spectroscopy PMT Tunable laser Doppler cancels – one measures lines with their natural linewidth

Doppler Free two-photon spectroscopy PMT Doppler cancels – one measures lines with their natural linewidth Tunable short pulse laser Shorter pulses  stronger signal? But… can one get better resolution than the pulse bandwidth? Yes… continuous train of pulses

Doppler Free two-photon spectroscopy PMT Tunable short pulse laser “Transit time” broadening Shorter pulses  stronger signal? Doppler does not cancel anymore i[  v]t  c e i[  v]t  c e cc v   

Third order nonlinear optics 1. Two Photon pumping 2.. Third harmonic generation 3. Doppler free spectroscopy 4. Lambda structures