Carrier-Wave Rabi Flopping Signatures in High-Order Harmoni
Carrier-Wave Rabi Flopping Signatures in High-Order Harmoni

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Yakup Boran Spring2016 689Modern Atomic Physics Phys Rev Lett  114 143902 2015 MOTIVATION Theoretical investigation of carrier wave Rabi flopping has been studied by employing numerical simulations of HHG in ID: 540833 Download Presentation

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Carrier-Wave Rabi Flopping Signatures in High-Order Harmonic Generation for Alkali Atoms

Yakup BoranSpring-2016689-Modern Atomic Physics

Phys. Rev. Lett. 


, 143902



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 2



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


in the third harmonic.Slide3

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.



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


loch vector parallel to



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, 057401 (2001)]Slide5


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, 057401 (2001)]Slide6

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)]Slide7


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.


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.Slide8

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













̴ 5.4θK ̴8.4 , θNa ̴ 7.2θK ̴4π , θNa ̴ 10.1

For K atoms, there is significant change around the third harmonic as the envelope

pulse area increasesFor Na atoms, regardless of the envelope


area the characteristic peak is present at third harmonicSlide10

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 differenceIt 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 durationSlide11


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 750-800nm 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.Slide12