# Quantum optics Set 4

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## Flashcards on Quantum optics Set 4, created by Tom Schobert on 09/21/2017.

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 Created by Tom Schobert almost 2 years ago
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 Question Answer Recoil limit k_B T_r=(ħk_L )^2/ma last photon which is emitted from the cooled atom in an excited state Cooling 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 Polarisation 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 Rabi oscillations Resonant 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 ) Dipole/rotating wave approximation E ⃗(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) two level atom atom 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⟩ electric dipole Interaction 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〗 classical electro magn. field E ⃗(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. Detuning δ=ω_L-ω_10; deviation from resonance → higher Rabifreq. δ>0 (blue detuning) repelled in trap δ<0 (red detuning) attracted in trap Density matrix pure/mixed states ρ ̂=∑_(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 Spontaneous emission (decay rate) decay of an excited state into all possible modes (Wigner-Weißkopf theory) destroys coherences τ_1=1/γ_10 (lifetime) Optical Bloch Equations - time evolution oft he (components of) density matrix - steady state (long times) - →Population,inversion - Louiville equation Inversion ω=(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 Saturation parameter; Saturation intensity saturation 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) Photon 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