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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 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. Hˆ total o † † † ˆˆ ˆ z ˆ ˆ g ˆ ˆ 2 γ g κ 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: e, n g , n 1 Excited state with n photons Ground state with n+1 photons Energy level diagram Coupled system E1n Ee,n Eg,n+1 ħRn ENERGY AXIS Uncoupled system E2n Rn is the Quantum Rabi frequency The effect is called Normal Mode Splitting Energy level diagram ħδ>0 Ee,n Eg,n+1 ħδ≈0 Coupled system E1n ħ(Rn+δ) ħδ<0 ENERGY AXIS Uncoupled system E2n Rn is the Quantum Rabi frequency The effect is called Normal Mode Splitting Crossing and Anticrossing Uncoupled system: tuning photon energy → crossing with energy of 2level system Strongly coupled system: Anticrossing Energy axis E1n Ee,n ħRn E2n Eg,n+1 0 Detuning How would the spectrum look like? We would see two delta-like function peaks corresponding to the two new eigenenergies Normalised Transmission -3 -2 E-12n 0 E11n 2 3 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) γ κ g We define a quantity ξ as 4g 2 2 2 If ξ<1 weak coupling regime If ξ≈1 intermediate coupling regime For ξ>>1 Strong coupling regime Realistic transmission spectrum The peaks become broadened into Lorentzians Normalised Transmission E’1n Lossless system Realistic system E’2n 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) 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) Source: M. S. Feld “Normal Mode Line Shapes for Atoms in Standing-Wave Optical Resonators ” P.R.L. 77:14 2901, (1996) 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 Replace like spectra) simple mirror cavities with PC cavities High Q factors and tiny mode volumes 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) 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) 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) 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) 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) 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) Cavity QED in PC structures Advantages: Monolithic structures Possibility of devices “photon on demand” Single photon gun Cavity QED on a chip 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