Quantum optics Set 2

Tom Schobert
Flashcards by , created almost 2 years ago

Flashcards on Quantum optics Set 2, created by Tom Schobert on 09/21/2017.

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Tom Schobert
Created by Tom Schobert almost 2 years ago
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Question Answer
Laser cooling (temperature measurement) Temperature of a lot of cold atoms expansion (from trap or molasses) image after time Δt measurement of position spread Δx T∝(Δx/Δt)^2
Magnetic trap class: E=-μ_m B cos⁡ϑ quant: E=gμ_B m_F B for an atom in state mF a trap is formed if E(mF) has a local minimum gmF>0 local minimum low field seekers gmF<0 local maximum high field seekers the trap centre is always where B has local minimum
Majorana losses - due to non-adiabatic transitions - spin flips for small or vanishing B-Fields - if magnetic field is finite like in a Joffe-Pritchard trap, Majorana a losses are supressed
Optical lattices - 1D: the electrical field of a one-dim. standing wave formed by two counter prop. lasers - to avoid interference:  polarisations orthogonal  frequency detuning - one can have Bragg scattering on lattices
Trap geometries - simplest optical trap: Gaussian beam (red detuned δ<0) potential can be approximated as harmonic - weak confinement along laser beam axis - crossed dipole trap: overlap of two laser beams - Advantage: strong confinement in all directions - but: small volume
Magnetooptical trap(MOT) combination of optical (laserfield) trap and magnetic field F=0 →F‘=1 transition F=-β ̃v-kz (damped harmonic oscillator) 0-10 ms overdamped capture velocity ≈50 m/s
Optical traps trapping due to optical potential U_opt (r ⃗ )≈(ħδ_0 γ_10^2)/8δ δ>0 atoms are repelled δ<0 atoms are attracted (due to radiative force)
MOT: Temperature vs. density regime temperature limited: overdamped oscillator 1/2 k_B T=1/2 mv_rms^2=1/2 kz_rms^2 z_rms=√((k_B T)/κ) density limited if the atom number is increased atoms start to interact →repulsion max. ≈10^11 atoms/cm³→ Volume increases with number of atoms
Evaporative cooling o fast particles escape o „rest“ thermalizes through collisions o Abkühlung o E/N↓→T↓ - theoretical: o infinitly slow evaporation o But: in experiment are losses
Evaporation in a magnetic trap - transfer all energetic atoms to a magnetic sublevel, that is not trapped - RF Knife - inharmonic trap: density may increase while atom number shrinks - run away evaporation: nσv (n=NT-3/2→∞T1/2) - RF induced: manipulate potential such, that fast atoms evaporate
Feshbach resonances - tune the scattering length by applying an external field (magnetic)
What is a BEC? quantum mechanical phase transition from thermal gas at T≠0 nλ_dB^3=2.612; caused by quantum statistics not interactions |p ⃗=0⟩ has macroscopic occipation can be described as matter wave Atomic oven → Zeeman slower → MOT →optical molasses → magnetic trap → evaporative cooling → BEC n(ε_p )=1/(e^β(ε_p-μ) -1) ;μ≤min(εp) for n≥0
Critical temperature macroscopically occupation below Tc the ground state is occupied with N0 atoms in the ground state T_c=(2πħ^2)/(mk_B (2.612)^(2/3) ) p^(2/3) N_0=N(1-(T/T_c )^(3/2)
BEC in a harmonic trap - Δx ist Breite des harmonischen Potentials
Gross-Pitiaevski-Equation iħ ∂/∂t Φ(r ⃗,t)=(-(ħ^2 ∇^2)/2m+V_ext (r ⃗ )+g|Φ(r ⃗ )|^2 „Mean field“: eff.Potential =trap potential +U meanfield Φ(r ⃗,t)=√(ρ(r ⃗ ) ) e^iΦ(r ⃗,t) valid for ρa³ <<1 (a is scattering length) Interaction energy of BEC much larger than kinetic