James Bounds Organization Dipole and Quadrupole transitions Special Laser beam types Using special laser beams to induce Quadrupole transitions Experimental Realization Possible extensions EM Fields ID: 555632
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Slide1
Optical Vortices and Electric Quadrupole transitions
James BoundsSlide2
Organization
Dipole and Quadrupole transitions
Special Laser beam types
Using special laser beams to induce Quadrupole transitions
Experimental Realization
Possible extensionsSlide3
E-M FieldsSlide4
Gauge FreedomSlide5
Perturbing Term in Length GaugeSlide6
Classical correspondance of perturbing termSlide7
Time-Dependent Perturbation TheorySlide8
Problem is reduced to finding expansion coefficientsSlide9
Separation of emission and absorption termsSlide10
Dipole Matrix ElementSlide11
Probability of being in state bSlide12
Relation to Einstein CoefficientsSlide13
Classical Dipole RadiationSlide14
Higher Order terms
By including higher order terms, the field gradients become more important.Slide15
Selection RulesSlide16
Quadrupole selection Rules
Selection rules are then for hydrogen like systems:Slide17
Fundamental Laser Modes
Hermite
-Gaussian Beam
Mode usually found in lasers
Laguerre-Gaussian
Beam
Contains a sharp amount of orbital angular momentum
Bessel Beam
Diffraction Free
Not possible with finite apertureSlide18
Huygen's principleSlide19
Approximated Fresnel IntegralSlide20
Helmholtz EquationSlide21
Relation to Schrodinger equationSlide22
Substitution into Helmholtz equationSlide23Slide24
Hermite-Gaussian Modes
Solution of the paraxial wave equation in cartesian coordinatesSlide25
Hermite-Gaussian ModesSlide26
Laguerre-Gaussian Modes
Arise when there is cylindrical symmetry
Usually not favored due to astigmatism
Carry sharply defined amount of orbital angular momentum (OAM)Slide27
Leguerre-Gaussian ModesSlide28
Ince-Gaussian Modes
Solution of paraxial wave equation in elliptic coordinates
Provides smooth connection between HG and LG beams
OAM not as sharply definedSlide29
The non-zero Leguerre-Gaussian modes form optical vorticesSlide30
Orbital Angular momentum
The
Laguerre-Gaussian
Beams are special in that they carry a very sharp amount of orbital angular momentum
The
Poyting
vector
reperesents
a helical spiralSlide31
Orbital Angular Momentum (OAM)
Property of individual photons and not just beam
Can be coupled to external systems
Rotation of Ion crystals
Forbidden transitions
Communication Systems
OAM MultiplexingSlide32
Generation of LG beams
Computer Generated Hologram
Diffracts plane wavefronts into helical wavefronts
Spatial light modulator
Laser etched gratingsSlide33
Holographic PlatesSlide34
Construction of Laser etched gratingsSlide35
Phase-Amplitude modulation from phase only gratingSlide36
Difficulty for pulsed operation
Pulsed operation not favored for holographic plates
Angular chirp
Pulse front tilt
2f-2f setupSlide37
Spatial Light modulator
LCD Crystals respond to computer generated image
Can be used to not only generate, but characterize LG beams
Work done by
James Strohaber
Holographic Knife
edge techniqueSlide38
Holographic Knife Edge
Similar to a mechanical knife edge technique, we can use the SLM to diffract part of the beam awaySlide39
Knife Edge for LG BeamsSlide40
Knife Edge for LG BeamsSlide41
Simultaneous Generation and characterization of LG beamsSlide42
Experimental Realization of quadrupole transitions
Schmiegelow, “Excitation of an Atomic Transition with a Vortex Laser Beam”Slide43
State is easily probed
3
2
D State is metastable
Transition wavelengths accessible
Calcium Quadrupole TransitionSlide44
3
2
D state depopulated
854nm transition
3
2
D state is metastable
Population vs. 729 nm LG pulse length gives Rabi frequency
State PreparationSlide45
Population Detection
4
2
S poulation determined by 866nm fluorescenceSlide46
Zeeman Splitting of Ca+ Quadrupole Transition at 729nm
Quadrupole TransitionSlide47
Relative strengths of transitionsSlide48
Large Gradient and zero field = electric quadrupole transitionSlide49
Conclusions
We have demonstrated the origin of the quadrupole transition
Selection rules
Investigated fundamental beam modes
Generation and characterization
Orbital Angular momentum
Experimental realization of coupling of OAM to
atoms