carrier wave rabi flopping (cwrf) presentation by nathan hart conditions for cwrf: 1.there must...
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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.
The two state wave function
πΌ π½
1 or
i or i
1
πΌ=π₯π +π π¦ π Ξ²=π₯π+ π π¦π
The two state wave function (continued)Identity
πΌ=π₯π +π π¦ π =ππ ππ ππ
π½=π₯π+ π π¦π=ππ ππ ππ
Get : Multiply times
In general (just math):
πβππ π |π β² β©=|π β©=π π β¨π β©+π ππππβ¨πβ©
Identity
ΒΏβ¨π β©The Bloch Vector
ΒΏβ¨π β©Wikipedia: Bloch Vector
The Bloch VectorGet r: Identity on the surface
ΒΏβ¨π β©
ΒΏβ¨π β©Wikipedia: Bloch Vector
Two unknowns Try
|Ο β©=π πΆππ (π /2)β¨π β©+π πππ (π /2)ππ πβ¨π β©
is a measure of the coherence of the two states and .r = 1 βΉ completely coherentr = 0 βΉ completely incoherent
Get
Optical Interpretation of Bloch SphereElectric Dipole
β’ The atomic dipole is in the x-y plane.β’ 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.
|Ο β©
ΒΏβ¨π β©
ΒΏβ¨π β©Wikipedia: Bloch Vector
3D Spatial Interpretation
ΒΏΟ (π ,π β² ,π β²)β©=πβ π π‘β²
|Ο (π , π ,π ) β©
Rotation operator
π =(πβπ (π βπ )π‘ /2+ππ (π+π )π‘ /2)(π΄πβπΞ©t π‘+π΅ππΞ©t π‘)π=(πβπ (π+π ) π‘ /2+ππ (πβπ) π‘ /2)(πΆπβπΞ©t π‘+π·ππΞ©t π‘ )
βThe source for the CWRF is due to fast oscillations in the polarization equations outside the RWA.βHughes, S. "Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses." Physical review letters 81, no. 16 (1998): 3363.
Fast oscillationHigh frequency
Slow oscillationLow frequency
Carrier Wave Rabi Flopping (CWRF)
Dipole acceleration
Frequency spectrum
|sβ©|pβ©
π π
Beating the Frequencies
πβπβ 0 β π΄=π΅=πΆ=π·
π β(1+ππππ‘)(πβπΞ©t π‘+ππΞ©t π‘ )πβ(πβ πππ‘+1)(πβπΞ©π‘ π‘+Ο+ππΞ© π‘π‘+Ο)
Electric Dipole
List of frequencies:
(π+π ) π‘2
=π
Approximations:
β’ 2
β’ 2
β’ 2
β’ 2
Probability amplitudes:
Pulse Area Theorem:
The laserβs electric field :The Rabi frequency :The pulse area Pulse Area Theorem: The laser pulse phase is not changed (only delayed in time) if the pulse area , where is an integer. Self-Induced Transparency
π=ππππππππππππ‘
|π (π‘ )|2=β
π=0
β
π΄ππΆππ (πππ‘ )+βπ=0
β
π΅ππππ(πππ‘)
Fourier Series Waveform Reconstruction
M.βF. Ciappina, J.βA. PΓ©rez-HernΓ‘ndez, A.βS. Landsman, T. Zimmermann, M. Lewenstein, L. Roso, and F. Krausz, Phys. Rev. Lett. 114, 143902
Wikipedia: Fourier Series, 2015
Pulse is delayed and distorted by Rabi Flopping Pulse 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.
βFor 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.β M.βF. Ciappina, J.βA. PΓ©rez-HernΓ‘ndez, A.βS. Landsman, T. Zimmermann, M. Lewenstein, L. Roso, and F. Krausz, Phys. Rev. Lett. 114, 143902
Ξ©π π
Time [fs]
Prob
abili
ty
3s
4s
continuum
5p
Density Matrix Simulation of Sodium Atom Level Population
Linear polarization
Nathan Hart
β’ Transient population inversion of ground state 3s and the excited state 5p at sufficiently high intensities.
β’ Possible applications for new laser mediumsNathan Hart
Density Matrix Simulation of Sodium Atom Dipole Spectrum
1st
3rd
5p
energy [eV]
phot
on y
ield
[au]
Linear polarizationBroadened odd harmonic orders
Final Notes
β’ M.βF. Ciappina et. al. showed that sodium does not satisfy the condition #1 (slide 1) for CWRF.
β’ 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.βF. Ciappina, J.βA. PΓ©rez-HernΓ‘ndez, A.βS. Landsman, T. Zimmermann, M. Lewenstein, L. Roso, and F. Krausz, Phys. Rev. Lett. 114, 143902
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