PT-Quantum Mechanics In 1998, Bender and Boettcher found that a wide class of Hamiltonians, even though non-Hermitian, can still exhibit entirely real spectra if they obey parity-time requirements or PT symmetry.
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PT-Quantum Mechanics
In 1998, Bender and Boettcher found that a wide classof Hamiltonians, even though non-Hermitian, can stillexhibit entirely real spectra if they obey parity-timerequirements or PT symmetry.
Parity Time (PT)Optics
Demetri Christodoulides,
Kostas Makris, Ramy El-Ganainy, and George Siviloglou,CREOL/ UCF
Roberto Morandotti,
David Duchesne, INRS-Canada
Greg Salamo,Aqiang Guo, K. Yeruva,Department of PhysicsUniversity of Arkansas
PT-
OpticsPT-symmetrysystem
Real part: evenImaginary part: odd Gain/loss
One example a PT Optical Potential is thePT directional coupler
Gain Loss
Gain = Loss
Index
x
Passive PT directional couplerExperiment measurable --- Output Power
TotalOutputPower
Lossless
Loss
PT-
OpticsHow should we make the PTdirectional coupler?
Gain Loss
Gain = Loss
x
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The effort to understand and designstructures at the nano size and seektheir application
Line up 50 atoms end-to-endand you get one nanometer
Take the diameter of a hair and divideby 100,000 and you have a diameter ofnanometer size
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Same element but
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Element in the Periodic Table
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the same element orcompound will havevery different optical,electrical, ormechanicalproperties dependingon its size!
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CdSe CdSe –– but each a different size! but each a different size!
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?
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Molecular Beam Epitaxy (MBE)
Source of Atoms
III
V
substrate
Heater
Beam ofAtoms
substrate
Mono-Layer
13.5
nm
0
nm
15nm
13.5
nm
0
nm
13.5
nm
0
nm
15nm200 nm x 200nm
Strainrelaxation
Surface energy
Stablesurfacesor facets
What Nanoscience can do for you in researchExplore the new rules at the nanoscale
Starting GaAs
InAs
2.2 ML InAs
on AlAs2.1 ML InAs
on AlAs
Scanning Tunneling Microscopy(STM)
A
Piezo
Tip
= 5 Å
Bias+
–
200nm
Even More Than Size = New Behavior!We can form Molecules or Chains or Solids
made of Quantum Dots
Dots in aPeacock Feather
400nm
400nm
Arkansas GrownQuantum Dots
Color in a peacockfeather
PT-
OpticsHow should we make the PTdirectional coupler?
No Loss Loss
x
Design of a PT Coupler
3.5 μm
1.88 μm Al0.20Ga0.80As
Al0.26Ga0.74As
GaAs: substrate
Tuning loss byVarying Cr-Width
8 μμ 2.0 μμ
0.62 μm
index=3.3695
index=3.24956
index=3.27739
62°
The introduction of loss must be done in way that does not perturb the even refractiveprofile. This is physically demanding since The presence of loss is typicallyaccompanied by an index perturbation (because of the Kramers-Kronig relations).
Top-view: Loss = 35 cm-1
Cr width = 4 μμ
2 μμ
ESEM cross view
ESEM image of one PTcoupler
Experimental Set-Up
IPG Fiber Laser IR Camera
X40 Obj X20 Obj
Sample
Detector
CylindricTelescorpe
Aperture
B.S
Ar Laser
Camera
B.S
Sample image (top)
Loss of Isolated waveguide structure as a function of Crwidth
Lossless
Loss
Experimental observation of PT-symmetry breaking
Conclusions
•We show for the first time that passivePT-symmetry breaking can be observedwithin the realm of optics.
•This abrupt phase transition leads to acounterintuitive loss induced opticaltransparency in specially designedpseudo-Hermitian potentials.
for PT
PT symmetry in QM PT symmetry in Optics
Schrödinger-like equations appear in In optics (paraxial equation )
Potential V(x)
Index of refraction n(x)
Passive PT directional couplerExperiment measurable --- Output Power
TotalOutputPower
Lossless
Loss
Real and imaginary parts of the optical dielectric function ofCr
Appl. Opt. 37, 5271-5283 (1998)
Choose Cr:
At 1.55mm, themetal leads to heavylosses while the realpart of indexmismatch atminimum!
At 1.55μμ
Gain LossLoss = Gain
PT directional coupler supermodes below and above phase transition
below phase transitionabove phase transition
Gain Loss
Gain = Loss
Lossless Loss
Passive PT directional coupler: Gain = 0
Lossless (Gain=0) and LossLossless Loss
Passive PT directional coupler: Gain = 0
below phase transition above phase transition
Output Power?
Z
Passive PT directional coupler
Supermode at z (below phase transition)
Lossless
Loss
Input
Output Power?
Z
Passive PT directional couplerExperiment measurable --- Output Power
Supermode at z (above phase transition)
Lossless
Loss
Input
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