1. CAVITY QUANTUM ELECTRODYNAMICS IN PHOTONIC CRYSTAL STRUCTURES Photonic Crystal Doctoral Course PO-014 Summer Semester 2009 Konstantinos G. Lagoudakis

2. Outline Light matter interaction Light matter interaction Normal mode splitting Normal mode splitting Trapping light and matter in small volumes Trapping light and matter in small volumes Experiments Experiments

3. How do we describe the interaction of light and matter? We have to get an expression of the total Hamiltonian describing the system. We have to get an expression of the total Hamiltonian describing the system. It will consist of three terms, one for the unperturbed two level system, one for the free field, and one for the interaction. It will consist of three terms, one for the unperturbed two level system, one for the free field, and one for the interaction. γ g κ

4. We can calculate the eigenvalues of the energy before and after the interaction Excited atom with n photons present, or Excited atom with n photons present, or atom in ground state with n+1 photons present. atom in ground state with n+1 photons present. Emission of photon is reversible: Exchange of energy Emission of photon is reversible: Exchange of energy The states with which we describe the system are in the general case: The states with which we describe the system are in the general case: Excited state with n photons Ground state with n+1 photons

5. Energy level diagram Energy level diagram E 2n E e,n E g,n+1 ħδ>0 ħ(Rn+δ)ħ(Rn+δ)ħ(Rn+δ)ħ(Rn+δ) E 1n Uncoupled system Coupled system ENERGY AXIS R n is the Quantum Rabi frequency depends on n R n is the Quantum Rabi frequency depends on n The effect is called Normal Mode Splitting The effect is called Normal Mode Splitting

6. Energy level diagram Energy level diagram E 2n E e,n E g,n+1 ħR n E 1n Uncoupled system Coupled system ENERGY AXIS R n is the Quantum Rabi frequency R n is the Quantum Rabi frequency The effect is called Normal Mode Splitting The effect is called Normal Mode Splitting

7. Energy level diagram Energy level diagram E 2n E e,n E g,n+1 E 1n Uncoupled system Coupled system ENERGY AXIS R n is the Quantum Rabi frequency R n is the Quantum Rabi frequency The effect is called Normal Mode Splitting The effect is called Normal Mode Splitting ħδ≈0 ħδ<0 ħδ>0 ħ(Rn+δ)ħ(Rn+δ)ħ(Rn+δ)ħ(Rn+δ)

8. Crossing and Anticrossing Uncoupled system: tuning photon energy → crossing with energy of 2level system Uncoupled system: tuning photon energy → crossing with energy of 2level system Strongly coupled system: Anticrossing Strongly coupled system: Anticrossing E e,n E g,n+1 E 1n E 2n ħR n

9. How would the spectrum look like? We would see two delta-like function peaks corresponding to the two new eigenenergies We would see two delta-like function peaks corresponding to the two new eigenenergies Normalised Transmission E 1n E 2n

10. In reality there are losses There is a decay rate for the excited state of the atom (γ) There is a decay rate for the excited state of the atom (γ) There is a decay rate for cavity photons (κ) There is a decay rate for cavity photons (κ) γ g κ We define a quantity ξ as We define a quantity ξ as If ξ<1 weak coupling regime If ξ<1 weak coupling regime If ξ≈1 intermediate coupling regime If ξ≈1 intermediate coupling regime For ξ>>1 Strong coupling regime For ξ>>1 Strong coupling regime

11. Realistic transmission spectrum The peaks become broadened into Lorentzians The peaks become broadened into Lorentzians Normalised Transmission E’ 1n E’ 2n

12. Experimental observations of the normal mode splitting Source: H.J.Kimble “Observation of the normal-mode splitting for atoms in optical cavity” P.R.L. 68:8 1132, (1992)

13. TRANSMISSION SPECTROMETER SIDELIGHT EMISSION Source: M. S. Feld “Normal Mode Line Shapes for Atoms in Standing-Wave Optical Resonators ” P.R.L. 77:14 2901, (1996)

15. Up to now we investigated the effects in atomic cavity QED How can we manage this by means of solid state photonic crystals?? How can we manage this by means of solid state photonic crystals?? Replace atoms by QDs Replace atoms by QDs  (atomic like spectra) Replace simple mirror cavities with PC cavities Replace simple mirror cavities with PC cavities  High Q factors and tiny mode volumes

16. Cavity QED in PC structures Cavity construction Cavity construction placing QD placing QD Source: K. Hennesy “Quantum Nature of a strongly coupled single quantum dot-cavity system ” Nature 445 896, (2007)

17. Tuning exciton resonance or cavity? Two available options : Two available options : Cavity tuning by condensation of innert gases on surface of PC Cavity tuning by condensation of innert gases on surface of PC Exciton resonance tuning by varying a gate voltage (when applicable) Exciton resonance tuning by varying a gate voltage (when applicable) Source: K. Hennesy “Quantum Nature of a strongly coupled single quantum dot-cavity system ” Nature 445 896, (2007) Here the first method was applied Here the first method was applied

18. Away from resonance: cross correlation measurements show an unknown channel of communication. cross correlation measurements show an unknown channel of communication. Source: K. Hennesy “Quantum Nature of a strongly coupled single quantum dot-cavity system ” Nature 445 896, (2007)

19. Tuning exciton resonance or cavity? When tuning cavity resonant to QD exciton: When tuning cavity resonant to QD exciton: Source: K. Hennesy “Quantum Nature of a strongly coupled single quantum dot-cavity system ” Nature 445 896, (2007) Anticrossing is evidenced → Signature of strong coupling Anticrossing is evidenced → Signature of strong coupling Note the existence of central peak Note the existence of central peak

20. Cavity QED in PC structures Complementary second order autocorrelation measurements For the ‘trio’ of peaks Complementary second order autocorrelation measurements For the ‘trio’ of peaks Source: K. Hennesy “Quantum Nature of a strongly coupled single quantum dot-cavity system ” Nature 445 896, (2007) Antibunching of emitted photons Antibunching of emitted photons  (one photon at a time) Reduction of X lifetime Reduction of X lifetime

21. Alternate method :Tuning exciton resonance Changing Bias voltage Changing Bias voltage Use of quantum confined stark effect Use of quantum confined stark effect Changes exciton resonance Changes exciton resonance A. Laucht "Electrical control of spontaneous emission and strong coupling for a single quantum dot" NJPh 11 023034, (2009)

22. Alternate method :Tuning exciton resonance Strong coupling Strong coupling No empty cavity peak? No empty cavity peak? A. Laucht "Electrical control of spontaneous emission and strong coupling for a single quantum dot" NJPh 11 023034, (2009)

23. Cavity QED in PC structures Advantages: Monolithic structures Advantages: Monolithic structures Possibility of devices “photon on demand” Possibility of devices “photon on demand” Single photon gun Single photon gun Cavity QED on a chip Cavity QED on a chip

24. Summary cavity QED suggests the appearance of effects that cannot be described classically cavity QED suggests the appearance of effects that cannot be described classically they are experimentally observable in two fundamentally different communities they are experimentally observable in two fundamentally different communities these effects are of great interest because they are direct evidence of the quantised nature of field in cavities these effects are of great interest because they are direct evidence of the quantised nature of field in cavities