Flashcards
Quantum optics Set 4
Cards in this deck (15)
- 1Recoil limitk_B T_r=(ħk_L )^2/ma
last photon which is emitted from the cooled atom in an excited state - 2Cooling below Recoil limit- Recoil limit: polarisation gradient cooling
- atoms with p=0 should not be excited anymore (dark state)
- achieved when we use VSCPT cooling - 3Polarisation gradient cooling- polarization gradient by two counter prop. lasers with lin┴lin configuation
- „dressed states“
- when atoms reach a position where potential energy large they are pumped into another state for which the energy is close to minimum
- atoms against potential, where pumped, fall in a minimum and then begin again - 4Rabi oscillationsResonant Rabi freq. Ω_0=((d_10 ) ⃗ε ⃗E_0)/ħ
|C_0 (t)|^2=cos^2〖(Ω_0/2t);|C_1 (t)|^2=sin^2〖(Ω_0/2t)〗 〗
oscillation of population between ground and excited state (periodic alternation of stim. absorption and emission)
generalized Rabifreq. : Ω=√(δ^2+Ω_0^2 ) - 5Dipole/rotating wave approximationE ⃗(r ⃗,t)≈E ⃗(t)≈ε ⃗E_o cos(ω_L t);for a_0≪λ_L
neglect rapidly oscillating terms (ω_L+ω_10) (non-resonant, to fast for field(atom) to react) - 6two level atomatom with a closed two level transition (does not exist/sketch)
Ψ(r ⃗,t)=C_0 (t) e^(-iω_0 t) |├ 0⟩+C_1 (t) e^(-iω_1 t) |├ 1⟩ - 7electric dipoleInteraction energy: V(t)=-(d_el ) ⃗E ⃗(t)
d ⃗_el=∫▒〖ρ ⃗_el (r) r ⃗ d^3 r〗 ; ρ_el=-e|ψ(r ⃗ )|^2
Eigenfunction of atomic Hamiltonian(12S1/2) →del=0
superposition state:
d ⃗_el^ind ∞E ⃗(t)
d ⃗_ij=〈i|d ⃗|j〉=-e ∫▒〖u_1^* (r ⃗ ) r ⃗ u_0 (r ⃗ ) d^3 r〗 - 8classical electro magn. fieldE ⃗(r ⃗,t)=ε ⃗E_o cos(ω_L t-k ⃗_L r ⃗ )
k_L=2π/λ_L =ω_L/c
classical Laser field, Maxwell eq. wave eq. - 9Detuningδ=ω_L-ω_10; deviation from resonance → higher Rabifreq.
δ>0 (blue detuning) repelled in trap
δ<0 (red detuning) attracted in trap - 10Density matrix pure/mixed statesρ ̂=∑_(i=0)^n▒〖p_n ├ |Ψ_n ⟩⟨Ψ_n |┤ 〗 off diagonal elements (coherences phase relation)
Pure states: Superposition→1/√2(|0>+|1>)
Mixed states: Mixture source - 11Spontaneous emission (decay rate)decay of an excited state into all possible modes (Wigner-Weißkopf theory)
destroys coherences
τ_1=1/γ_10 (lifetime) - 12Optical Bloch Equations- time evolution oft he (components of) density matrix
- steady state (long times)
- →Population,inversion
- Louiville equation - 13Inversionω=(ρ_11 ) ̂-(ρ_00 ) ̂ ; Population exited state – Population ground state
ω=-1/(1+δ)
not possible to invert the population in a 2-level atom (ρ_11 ) ̂→1/2 as maximum in steady state - 14Saturation parameter; Saturation intensitysaturation parameter: S=(S_0 γ_10^2)/(γ_10^2+4δ^2 );
res. S_0=(2Ω_0^2)/(γ_10^2 )
S_0=I/I_s (measures how strong laser field compared to atomic quantities) - 15Photon scattering rate- the rate at which an atom absorbs a photon and reemitts it
- γ_phase: a Lorentzian curve as function of detuning
- FWHM is γ10 for low intensities
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- Created by Tom Schobert · Sep 21, 2017
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