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. Magnetooptical atom trap used in atomic physics experiments BCIT The Nobel Prize in Physics 2012

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

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

5. The Nobel Prize in Physics 2012

6. Quantum Dots in Photonic Structures Wednesdays, 17.00, SDT Jan Suffczyński 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 Lecture 2: Basics of Quantum Cavity Electrodynamics

7. Plan for today 1.Cavity quality factor 2. Weak coupling regime 3. Strong coupling regime

8. Reminder d

9. Quality factor Q RR Blackboard calculation

10. Quality factor Q 1 1/e 2/  Decay of the photon from a cavity due to absorption,scattering, leakage due to imperfect mirrors. Consider electric field at a given point inside a cavity: Optical period T = 1/f c = 2  /  c 0 E =Electric field magnitude u =Energy density 1. Definition of Q via energy storage: Energy density decay: Γ – optical energy decay time

11. 1 1/e 2/  Time domainFrequency domain Fourier transform  The two definitions for Q are equivalent This is how on can measure Q (not in the case of microcavities with QDs!) Lorentzian 2. Definition of Q via resonance bandwidth:

12. F Quality factor vs. Finesse F - a measure of the rate at which optical energy decays from the cavity, but the optical cycle time T (in the case of Q) is replaced by round trip time t RT : Finesse: the ratio of free spectral range Δω (the frequency separation between successive longitudinal cavity modes) to the linewidth Γ of a cavity mode: „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. When mirror losses dominate cavity losses: F and Q similar in the case of micrometer size cavities (as Δω~ω c in that case) Q can be increased by increasing cavity length F is independent of cavity length !

14. For Q = 5000 and λ = 700 nm, cavity length = λ/2 = 350 nm: photon decay time τ = Q/ω c = 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 Quality factor and typical values

15. Light-matter coupling: Weak coupling regime

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

17. Spontaneous emission in a free space Helium emission spectrum Perturbation necessary! 1887 (Wiena) – 1961 (Wiena) Nobel Prize 1933

18. An emitter in the simplest case : a two level system E Excited state Fundamental state + Spontaneous emission Photon+ E1E1 E0E0 E1E1 E0E0

19. Density of modes in a free space (l,m,n are positive integers) Let’ consider a L x L x L box of vacuum: Blackboard calculation

20. N(ω) Frequency ω Density of modes in a free space

21. Density of states in a free space - example Consider 1m 3 of vacuum and =500 nm: ~50000 photon states per 1 Hz

22. Density of modes inside cavity Cavity modifies density of states of the field Energy of emitter emission counts much more then in free space!

23. Emitter in the cavity mirror Spontaneous emission inhibited Spontaneous emission enhanced Spatial position of the emitter counts!

24. Fermi’s Golden Rule Emission rate Density of photon states at emitter wavelength Electric field intensity at emitter position Dipol moment of the emitter Spontaneous emission rate is not an inherent property of the emitter It depends on:

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

26. How many final states are there for the photon? (+ a constraint: photon energy = excited-ground energy level difference) Fermi’s Golden Rule Spectral matching: What is a mode intensity at the emitter spatial position? Spatial matching:

27. Light-matter interaction: Weak coupling Emitter Cavity Mode Optical Modes outside the cavity Energy S1S1 S2S2 When S 1 < S 2 and Emitter in resonance with the Cavity Mode: photon „quickly” decays to the outside of the cavity Increased rate of the spontaneous emission into the cavity mode

28. Density of modes inside cavity Emitter Cavity + density of states Outside E cav – energy position of the mode

29. Purcell effect

30. Edward M. Purcell (1912–1997) Nobel Prize 1952 Spontaneous emission to resonant cavity mode  Purcell effect: acceleration of spontaneous emission for a factor of F P F P = = +    3 Q 0 3    0 4  2 V n 3  0 Spontaneous emission to nonresonant modes Spontaneous emission into leaky modes

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

32. Drexhage (1966): fluorescence lifetime of Europium ions depends on source position relative to a silver mirror ( =612 nm) The better cavity, the larger emision rate enhancement Emission in front of a mirror – „almost” cavity case Silver mirror Spacer thickness d Europium ions

33. What if further improve cavity parameters?

34. Light-matter interaction: Strong coupling regime

35. Emitter Cavity Mode Energy S1S1 S2S2 When S 1 > S 2 and Emitter in resonance with the Cavity Mode: Photon preserved in the cavity „for long” Reabsorption and reemission of the photon by the mitter Light-matter interaction : Strong coupling Optical Modes outside the cavity

36. Strong coupling –Rabi splitting |0,1> : |1,0> : Emitter in ground state Excited emitter Empty cavity Photon inside cavity Out of the resonence:

37. Strong coupling –Rabi splitting Energy Eigenstates : Entengled states emitter-photon Rabbi Splitting  R (|0,1> + |1,0>)/ 22 (|0,1>  |1,0>)/ 22 |0,1>|0,1> ↔ In resonance: Oscillations with Rabi frequency  =  R / h |1,0>|1,0> |0,1> : |1,0> : Emitter in ground state Excited emitter Empty cavity Photon inside cavity Out of the resonence:

38. Strong coupling regime Isidor Isaac Rabi 1898 (Rymanów) – 1988 (New York) Nobel Prize 1944 Oscillations with Rabi frequency  =  E / h: |emitter in a ground state, photon in the cavity> |excited emitter, empty cavity> When emitter in the resonance with the cavity mode: Emitter and cavity mode levels anticrossed for  E

39. Strong coupling regime emitter – cavity mode detuning Energy levels versus detuning: Anticrossing of levels at emitter – cavity mode resonance

40. Strong coupling regime- the first experiments [R. J. Thompson et al., Phys. Rev. Lett. (1992). Evidence for the strong light- matter coupling Increasing light matter cupling wiht increasing number of atoms inside cavity

41. Summary Spontaneous emission rate depends on the photonic environment: it can be enhanced or supressed (weak coupling), or reversed!(strong coupling) Fermi’s Golden Rule: spontaneous emission rate depends on: availability of final states (spectral overlap emitter- mode) and spatial position of the emitter with respect to the mode distribution and emitter dipol moment

42. Jaynes, F.W. Cummings model E.T. Jaynes, F.W. Cummings (1963). "Comparison of quantum and semiclassical radiation theories with application to the beam maser". Proc. IEEE 51 (1): 89–109. 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).

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