Carrier Wave Rabi Flopping (CWRF) Presentation by Nathan Hart Conditions for CWRF: 1.There must exist a one photon resonance with the ground state 2.The Rabi frequency between the ground state and the first excited state must be on the order of the laser frequency Result of CWRF: 1.Asymmetric Bloch sphere path for the block vector. 2.Broad frequency generation resulting from beating between the atomic dipole and the laser frequency.

i 1

Wikipedia: Bloch Vector

Optical Interpretation of Bloch Sphere The atomic dipole is in the x-y plane. The electric field of the laser may also be in the x-y plane.

NMR: In a semiclassical description of spin, the magnetic dipole points in the direction of the Bloch vector and precesses with it. Wikipedia: Bloch Vector 3D Spatial Interpretation Rotation operator

“The source for the CWRF is due to fast oscillations in the polarization equations outside the RWA.” Hughes, S. "Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses." Physical review letters 81, no. 16 (1998): Fast oscillation High frequency Slow oscillation Low frequency Carrier Wave Rabi Flopping (CWRF) Dipole acceleration Frequency spectrum |s ⟩ |p ⟩

Beating the Frequencies Approximations: Probability amplitudes:

Pulse Area Theorem:

Fourier Series Waveform Reconstruction M. F. Ciappina, J. A. Pérez-Hernández, A. S. Landsman, T. Zimmermann, M. Lewenstein, L. Roso, and F. Krausz, Phys. Rev. Lett. 114, Wikipedia: Fourier Series, 2015

Pulse is delayed and distorted by Rabi FloppingPulse is slightly delayed in medium Hughes, S. "Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses." Physical review letters 81, no. 16 (1998): 3363.

Absorption Absorption & Frequency generation Hughes, S. "Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses." Physical review letters 81, no. 16 (1998): 3363.

“For these pulses, peculiar behavior emerges when the driven light intensity is so high that the period of one Rabi oscillation is comparable with that of one cycle of light.” M. F. Ciappina, J. A. Pérez-Hernández, A. S. Landsman, T. Zimmermann, M. Lewenstein, L. Roso, and F. Krausz, Phys. Rev. Lett. 114,

Time [fs] Probability 3s 4s continuum 5p Density Matrix Simulation of Sodium Atom Level Population Nathan Hart Transient population inversion of ground state 3s and the excited state 5p at sufficiently high intensities. Possible applications for new laser mediums Nathan Hart

Density Matrix Simulation of Sodium Atom Dipole Spectrum 1st 3rd 5p energy [eV] photon yield [au]

Final Notes M. F. Ciappina et. al. showed that sodium does not satisfy the condition #1 (slide 1) for CWRF. However, sodium may have a CWRF-like 3-photon resonance with the 5p energy level, allowing for broad frequency generation at each odd harmonic. M. F. Ciappina, J. A. Pérez-Hernández, A. S. Landsman, T. Zimmermann, M. Lewenstein, L. Roso, and F. Krausz, Phys. Rev. Lett. 114,