Pelle Grin

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Decoherence protection and quantum logic gatesin photonic bandgap structures

Sophie Pellegrin, Gershon Kurizki

Chemical Physics DepartmentWeizmann Institute of Science

Rehovot 76100, Israel

[email protected]

Quantum information – optically manipulated atomsChallenge: protection of the quantum states from decoherence – spontaneous emission

Photonic crystals – photonic bandgap structures

Quantum logic gates: dynamical aspectsadiabatic / nonadiabatic

Periodic sudden changes

Decoherence protection and quantum logic gatesin photonic bandgap structures

Sophie Pellegrin, Gershon Kurizki

Chemical Physics DepartmentWeizmann Institute of Science

Rehovot 76100, Israel

[email protected]

Quantum information – optically manipulated atomsChallenge: protection of the quantum states from decoherence – spontaneous emission

Photonic crystals – photonic bandgap structures

Quantum logic gates: dynamical aspectsadiabatic / nonadiabatic

Periodic sudden changes

http://www.weizmann.ac.il/






Photonic crystals

1D

2D

3D

photonic crystals - light

periodic refractive index

semi conductors - electrons

periodic atomic potential

Band structure

K. Lim et al., GaAs and AlGaAs 1.8µ m, λ =4.5 µ m and 1.5 µ m

AIST, Japan, TiO2 pillars of

640 nm and height 2 µ m

Fan et al., Si (dark) and SiO2 (light), large

and complete submicron bandgap.

S. G. Johnson and J. D. Joannopoulos,APL 77, 3490-3492 (Nov. 2000)

J. G. Fleming and S. Y. Lin,Opt. Lett. (1999)



Defects

Breaking the periodicity• point like defects: cavities

frequency

bandgap

• linear defects: waveguide

90 bend: 98 of the power transmission(30 in analogous dielectric waveguide)

2 µ m



Density of modes

Neglecting the vectorial nature of the electromagnetic field:analytic scalar dispersion relation

isotropic density of modes (gap = sphere) ∝ (ω

- ω c)

-1/2

qualitative results, limited to the description of the bandgap neighborhood

Quantitative results: non isotropic density

Densityo

fmodes

ω 2

ωc

Scalar, isotropic approximation

ω c ω



Coupling with an atom – static aspects

0.0 10.0 20.0 30.00.2

0.4

0.6

0.8

1.0

time (dimensionless(

Excit

edstatep

opulatio

n

A. G. Kofman, G. Kurizki, B. Sherman, J. of Mod. Opt. 41, 353 (1994)

Strong interaction between the atomand its own photon : splitting

of the atomic transitionone part is stable, the other one decays.

Static position of the atomic transition inside the gap.

ωat



α dyn (t) = α Astat (τ ) α B

stat (t-τ ) +

β ω ,Astat (τ ) β ω ,B

stat (t- τ ) ρ (ω ) dω , tτ0

+

Dynamic aspects – periodic shifts (1)


Excite

dstatepop

ulation ω

A→ ω B

ωB→ ω

A

ωA

ωB

static

densityof modes

ωA

ωB

α A/Bstat = excited state amplitude

at a fixed frequency ω A (ω B)

β ω ,A/Bstat = mode ω amplitude

0 20 40 600.6

0.7

0.8

0.9

1.0

Exciteds

tatepopulation


static

one change



Dynamic aspects – periodic shifts (2)

0 20 400.65

0.75

0.85

0.95

Excitedstatepo

pulation


densityof modes

ωA

ωB

…

0 20 0.65

0.75

0.85

0.95

Exciteds

tatepopulation


Finite transition times

0 5 10 150.0

0.2

0.4

0.6

0.8

1.0

fid

elity


gate

“control phase gate”:excited atomic statephase shift of π / 2performed adiabatically

8 9 10 110.90

0.95

fid

elity




Conclusion and perspectives

• Periodic modulation of the detuning is able to protect the atomic statefrom spontaneous emission more effectively

than fixing the largest possible detuning value

• Sudden changes outperform the adiabatic modulation

• First attempts to apply the resultsto quantum logic gates are very encouraging

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