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CAVITY QUANTUM ELECTRODYNAMICS IN PHOTONIC CRYSTAL STRUCTURES

CAVITY QUANTUM ELECTRODYNAMICS IN PHOTONIC CRYSTAL STRUCTURES. Photonic Crystal Doctoral Course PO-014 Summer Semester 2009 Konstantinos G. Lagoudakis. Outline. Light matter interaction Normal mode splitting Trapping light and matter in small volumes Experiments.

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CAVITY QUANTUM ELECTRODYNAMICS IN PHOTONIC CRYSTAL STRUCTURES

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  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 • Normal mode splitting • Trapping light and matter in small volumes • 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. • It will consist of three terms , one for the unperturbed two level system, one for the free field, and one for the interaction. γ κ g

  4. We can calculate the eigenvalues of the energy before and after the interaction • Excited atom with n photons present, or atom in ground state with n+1 photons present. • Emission of photon is reversible: Exchange of energy • 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 Uncoupled system Coupled system E1n ENERGY AXIS Ee,n ħRn Eg,n+1 E2n • Rn is the Quantum Rabi frequency • The effect is called Normal Mode Splitting

  6. Energy level diagram Uncoupled system Coupled system E1n ħδ>0 ENERGY AXIS Ee,n ħδ≈0 ħ(Rn+δ) ħδ<0 Eg,n+1 E2n • Rn is the Quantum Rabi frequency • The effect is called Normal Mode Splitting

  7. E1n Ee,n ħRn E2n Eg,n+1 Crossing and Anticrossing • Uncoupled system: tuning photon energy →crossing with energy of 2level system • Strongly coupled system: Anticrossing

  8. How would the spectrum look like? • We would see two delta-like function peaks corresponding to the two new eigenenergies Normalised Transmission E2n E1n

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

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

  11. 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)

  12. 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)

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

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

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

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

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

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

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

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

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

  22. Summary • cavity QED suggests the appearance of effects that cannot be described classically • 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

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