1. Yakup Boran Spring-2016 689-Modern Atomic Physics
Carrier-Wave Rabi Flopping Signatures in High-Order Harmonic Generation for Alkali Atoms
Yakup Boran Spring Modern Atomic Physics
Phys. Rev. Lett. 114, – 2015

2. MOTIVATION
Theoretical investigation of carrier wave Rabi flopping has been studied by employing numerical simulations of HHG in alkali atoms.
This letter mainly focuses on the features of the third harmonic of Na and K
For Na atoms; for pulse areas of 2π, a characteristic unique peak was predicted and it is correlated with conventional Rabi Flopping.
For larger pulse areas, area theorem fails and Carrier wave Rabi flopping occurs so that more complex structures have been predicted in the third harmonic.

3. Rabi Flop(Rabi Cycle)
The Rabi flop is the cyclic behavior of a two level system in the presence of an oscillatory driving field.
When an atom is illuminated by a coherent light, it will cyclically absorb photons and re-emit them by stimulated emission. This phenomenon is known as Rabi Flopping which named after the Nobel Prize winner Isidor Isaac Rabi.
This effect is usually shown using the Bloch Sphere.
If the Rabi frequency between the ground state and the first excited state is comparable to the laser frequency, Carrier Wave Rabi Flopping(CWRF) occurs.

4. RABİ FLOPPİNG
Conventional Rabi flopping plotted on Bloch sphere for pulse area of 2π . The Rabi frequency is much smaller than the light frequency.
The optical oscillation corresponds to an orbiting of the Bloch vector parallel to uv plane, the oscillation of the inversion to a motion in the uw plane.
Starting from the south pole( all electrons are in the ground state) the Bloch vector spirals up to the north pole(all electrons are in the excited state) and back to the south pole
[Mücke et. al. Phys. Rev. Lett. 87, (2001)]

5. CARRİER WAVE RABİ FLOPPİNG
Results for pulse area of 4π and for a much shorter pulse, such that the Rabi period equals the light period.
Bloch vector does not come back to the south pole.
Optical polarization becomes strongly distorted and it is not harmonically.
[Mücke et. al. Phys. Rev. Lett. 87, (2001)]

6. What happens when larger input areas are injected....?
Multiple of 2π describes a complete rabi floppings.
If the pulse area large enough, the area under the individual carriers may themselves cause Rabi flopping.
Incomplete Rabi flops will be occurred instead of the anticipated integer numbers and Area Theorem will fail and CWRF signatures will show up
[Hughes Phys. Rev. Lett. 81, 3363 (1998)]

7. Methods Alkali atoms are used to avoid electron-electron correlations.
Both ground and excited states of K and Na atoms combined with realistic laser parameters and clearly distinct features have been observed in the third harmonic.
A system is created by K atoms with a transition energy between the ground state and the excited state of 1.61eV (765nm) which is close to the laser source photon energy 1.55eV(800)
HHG of Na atoms is also computed since the transition energy between the ground and excited state is 2.1eV(590nm)and it is not resonant with driven light.
In order to create the conditions for CWRF, an atomic system in which the period of a Rabi oscillation is similar to one period of laser light is used.

8. Results
2.103eV
1.61eV
2.097eV
1.622eV
Ground 3s and first excited state 3p for Na and ground 4s and first excited state 4p have been theoretically calculated.
Numerical results are in excellent agreement with the experimental results

9. Potassium
Sodium
θK ̴2π , θNa ̴ 5.4
θK ̴8.4 , θNa ̴ 7.2
θK ̴4π , θNa ̴ 10.1
For K atoms, there is significant change around the third harmonic as the envelope pulse area increases
For Na atoms, regardless of the envelope pulse area the characteristic peak is present at third harmonic

10. The CWRF phenomenon in atoms could also emerge as an alternative for CEP characterization for long pulses.
In the case of Na(out of resonance), the third harmonic does not show any significant difference
It is known that HHG spectra are only sensitive to CEP changes when driving laser field is a few cycle pulse. The third harmonic of K is strongly affected even the driving laser is rather long(20 cycles) in total duration

11. Conclusions
The signatures of CWRF in real atoms, by studying the third harmonic of alkali atoms have been found.
Accurate values for the atomic wave function of both ground and excited states and accurate values for the laser parameters are used so that this experiment can be easily done with current laser technology. A Ti:sapphire laser provides nm wavelengths which is close to the 765 nm value corresponding to the transition energy 4s-> 4p in K.
CWRF can be used as an alternative to CEP characterization for long pulses.

12. THANK YOU!