# CAVITY QUANTUM ELECTRODYNAMICS

Document Sample

```					      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.
o
ˆ
H total   
2
  z       g    
ˆ         †
ˆ ˆ      †
ˆ ˆ ˆˆ   
†

γ
κ
g
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            Excited state with n photons
          
 g, n  1        Ground state with n+1 photons
Energy level diagram
Uncoupled system   Coupled system

ENERGY AXIS
E1n
Ee,n
Eg,n+1                   ħRn

E2n

   Rn is the Quantum Rabi frequency
   The effect is called Normal Mode Splitting
Energy level diagram
Uncoupled system    Coupled system
E1n

ENERGY AXIS
ħδ>0
Ee,n            ħδ≈0
ħ(Rn+δ)
Eg,n+1       ħδ<0

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

E1n
Energy axis

Ee,n
ħRn
Eg,n+1                 E2n

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     E2n
-1                     0         E1n
1     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

g                                  κ

   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
Lossless system
Realistic system

E’1n                             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   like spectra)
 Replace   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

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
 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

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 7 posted: 6/8/2012 language: Latin pages: 22
How are you planning on using Docstoc?