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The Nobel Prize in Physics 2012

The Nobel Prize in Physics 2012. Serge Haroche. David J. Wineland. Prize motivation: "for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems". The Nobel Prize in Physics 2012. BCIT.

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The Nobel Prize in Physics 2012

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  1. The Nobel Prize in Physics 2012 Serge Haroche David J. Wineland Prize motivation: "for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems"

  2. The Nobel Prize in Physics 2012 BCIT Magnetooptical atom trap used in atomicphysicsexperiments

  3. The Nobel Prize in Physics 2012 CavityQuantum Electrodynamics, SCIENTIFIC AMERICAN’1993 Experimental demonstration of cavity induced modification of spontaneous emissoin rate of Rydberg atoms BCIT

  4. The Nobel Prize in Physics 2012 Quantum non-demolitionmeasurement Credit: Nobel Prize

  5. The Nobel Prize in Physics 2012

  6. Lecture 2: Basics of Quantum CavityElectrodynamics Quantum Dots in PhotonicStructures Jan Suffczyński Wednesdays, 17.00, SDT Projekt Fizyka Plus nr POKL.04.01.02-00-034/11 współfinansowany przez Unię Europejską ze środków Europejskiego Funduszu Społecznego w ramach Programu Operacyjnego Kapitał Ludzki

  7. Plan for today Cavity qualityfactor 2. Weakcoupling regime 3. Strongcoupling regime

  8. Reminder • Optical cavity: an arrangement of optical components which allows a beam of light to circulate in a closed path. • Optical cavitymode: EM field distribution which reproduce itself (if no losses) after one cavityround trip. A condtion: a phase shift afterone round trip = an integer multiple of 2π. Modefrequencies: N • Qualityfactor: a measure of the rateatwhichopticalenergydecays from the cavity (absorption,scattering, leakagedue to imperfectmirrors). Lifetime of the photonwithin the cavity: τ= 1/Γ= Q/ωc • Quantum fluctuations of the vacuum and the Casimir effect d

  9. Quality factor Q R R Blackboardcalculation

  10. Quality factor Q 1. Definition of Q via energy storage: Decay of the photon froma cavitydue to absorption,scattering, leakagedue to imperfectmirrors. Considerelectric field at a given point inside a cavity: E = Electric field magnitude u = Energy density 1 1/e 0 2/ Γ – opticalenergydecaytime Optical period T = 1/fc= 2/c Energy density decay:

  11. 2. Definition of Q via resonance bandwidth: Fouriertransform  Time domain Frequency domain 1 1/e Lorentzian 2/ • The two definitions for Q are equivalent • Thisishow on canmeasure Q (not in the case of microcavities with QDs!)

  12. Quality factor vs. Finesse F F- a measure of the rateatwhichopticalenergydecays from the cavity, but theoptical cycletime T(in the case of Q) is replaced by round trip time tRT: Δ Finesse: the ratio of freespectralrangeΔω (the frequencyseparationbetweensuccessivelongitudinalcavitymodes) to the linewidthΓ of a cavitymode: F = „resolving power or spectral resolution of the cavity”

  13. Quality factor vs. Finesse • Quality factor: number of optical cycles (times 2) before stored energy decays to 1/e of original value. • Finesse: number of round trips (times 2) before stored energy decays to 1/e of original value. Q = F = • When mirror losses dominate cavity losses: • F and Q similar in the case of micrometersizecavities • (as Δω~ωcin thatcase) • Q can be increased by increasing cavity length • Fis independent of cavity length !

  14. Quality factor and typicalvalues • For Q = 5000 and λ = 700 nm, cavitylength = λ/2 = 350 nm: • photondecaytimeτ = Q/ωc = 1.86 ps • Total run = τ*(speed of the light) = 557 µm • Number of bounces = 2*TotalRun/(λ/2) = 2Q/π = 3183 • Number of the field oscillations: 7854

  15. Light-mattercoupling: Weakcoupling regime

  16. Spontaneous emission in a free space 1887 (Wiena) – 1961 (Wiena) Nobel Prize 1933 Helium emission spectrum

  17. Spontaneousemission in a freespace 1887 (Wiena) – 1961 (Wiena) Nobel Prize 1933 Helium emission spectrum Perturbation necessary! • Spontaneousemission in a freespace: • Exponentialdecay with time: • Charactersticdecayconstant 1/Γ • Irreversibleprocess

  18. Anemitter in the simplestcase : a twolevel system Excited state Fundamentalstate + Photon E E1 E1 + Spontaneousemission E0 E0

  19. Density of modes in a freespace Let’ consider a LxLxL box of vacuum: (l,m,narepositive integers) Blackboardcalculation

  20. Density of modes in a freespace N(ω) Frequencyω

  21. Density of states in a freespace - example Consider 1m3of vacuum and l=500 nm : ~50000 photon states per 1 Hz

  22. Density of modesinsidecavity • Cavitymodifiesdensity of states of the field • Energy of emitteremissioncounts much morethen in freespace!

  23. Emitter in the cavity • Completelydifferentsituationthan in a freespace! • Spontaneous emission in the cavity: • Exponential, irreversibledecaymodifieddecayrateor • Reversibleprocess mirror mirror Spontaneousemissioninhibited Spontaneousemissionenhanced Spatialposition of the emittercounts!

  24. Fermi’sGoldenRule • Spontaneousemissionrateis not aninherentproperty of the emitter • It depends on: Dipol moment of the emitter Density of photonstates atemitterwavelength Electric field intensity atemitterposition Emissionrate

  25. Enrico Fermi 1901 (Rzym) – Chicago (1954) Nobel Prize 1938

  26. Fermi’sGoldenRule Rate of decay from the initial, excited state of the emitter: Spectralmatching: Spatialmatching: How manyfinalstates are there for the photon? (+ a constraint: photonenergy = excited-groundenergy level difference) Whatis a modeintensityat the emitterspatialposition?

  27. Light-matterinteraction: Weakcoupling Energy S1 S2 CavityMode Emitter Optical Modes outside the cavity • When S1< S2 and Emitter in resonance with the CavityMode: • photon „quickly” decays to the outside of the cavity • Increasedrate of the spontaneousemissioninto the cavitymode

  28. Density of modes inside cavity Ecav – energyposition of the mode Cavity + density of states Outside Emitter

  29. Purcell effect

  30. G+G13 Ql03G1 FP==+ G04p2V n3 G0 Purcell effect • Purcell effect: acceleration of spontaneousemission for a factor of FP Edward M. Purcell (1912–1997) Nobel Prize 1952 Spontaneousemission intoleakymodes Spontaneousemission to resonantcavitymode Spontaneousemission to nonresonantmodes

  31. Purcell effect – the firstobservation Europium ions Spacer thickness d Silver mirror

  32. Emission in front of a mirror – „almost” cavitycase Europium ions Spacer thickness d Silver mirror Drexhage (1966): fluorescence lifetime of Europium ions dependson source position relative to a silver mirror (l=612 nm) • The bettercavity, the largeremisionrateenhancement

  33. Whatiffurtherimprovecavityparameters?

  34. Light-matterinteraction: Strongcouplingregime

  35. Light-matterinteraction: Strongcoupling Energy S1 S2 CavityMode Emitter Optical Modes outside the cavity When S1> S2 and Emitter in resonance with the CavityMode: Photonpreserved in the cavity „for long” Reabsorption and reemission of the photon by the mitter

  36. Strongcoupling –Rabisplitting Out of the resonence: |1,0> : Emptycavity Excited emitter |0,1> : Photon insidecavity Emitter in groundstate

  37. In resonance: Energy Rabbi SplittingDR (|0,1>|1,0>)/ (|0,1>+|1,0>)/ Eigenstates : Entengledstatesemitter-photon 2 2 ↔ |0,1> |1,0> Oscillations with Rabifrequency = R / h Strongcoupling –Rabisplitting Out of the resonence: |1,0> : Emptycavity Excited emitter |0,1> : Photon insidecavity Emitter in groundstate

  38. Strongcouplingregime When emitter in the resonance with the cavity mode: Isidor Isaac Rabi 1898 (Rymanów) – 1988 (New York) Nobel Prize 1944 Emitter and cavity mode levels anticrossed for E Oscillations with Rabi frequency  = E / h: |emitter in a groundstate,photon in the cavity> |excitedemitter,emptycavity>

  39. Strongcoupling regime emitter – cavitymodedetuning • Energylevels versus detuning: • Anticrossing of levelsatemitter – cavitymoderesonance

  40. Strongcouplingregime- the firstexperiments [R. J. Thompson et al., Phys. Rev. Lett. (1992). • Evidence for the stronglight-mattercoupling • Increasinglightmattercuplingwihtincreasingnumber of atomsinsidecavity

  41. Summary • Spontaneous emission rate depends on the photonic environment: • itcan be enhancedorsupressed (weakcoupling), or • reversed!(strongcoupling) • Fermi’s Golden Rule: spontaneousemission rate depends on: • availability of final states (spectraloverlapemitter-mode) and • spatialposition of the emitter with respect to the modedistribution and • emitter dipol moment

  42. Jaynes, F.W. Cummings model It describes the system of a two-level atom interacting with a quantized mode of an optical cavity, with or without the presence of light (in the form of a bath of electromagnetic radiation that can cause spontaneous emission and absorption). E.T. Jaynes, F.W. Cummings (1963). "Comparison of quantum and semiclassical radiation theories with application to the beam maser". Proc. IEEE51 (1): 89–109.

  43. Ocena wykładu • Rok studiów: • Za łatwy • Łatwy • Akurat • Trudny • Za trudny • Nierówny: komentarz • Nuda • Może być • Super! • Nierówny: komentarz

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