Download Quantum Information Processing with 1010 Electrons ?

Quantum Information Processing
with 1010 Electrons ?
René Stock
IQIS Seminar, October 2005
People:
• Barry Sanders
• Peter Marzlin
• Jeremie Choquette
Motivation
Quantum information
processing realizations
Ions
Solid State systems
Photons
NMR
Need for hybridization
and interfacing of
different technologies
Neutral Atoms
Superconductors
Surface Plasmons ?
coherent charge density
oscillations involving
1010 electrons
Outline
• What are surface plasmons: Introduction
• Excitation of surface plasmons at surfaces
• Entanglement and surface plasmons
• Surface plasmons in quantum information implementations
Outline
• What are surface plasmons: Introduction
• Excitation of surface plasmons at surfaces
• Entanglement and surface plasmons
• Surface plasmons in quantum information implementations
What are surface plasmons ?
•
Electric field propagating at surface
r
E
z
metal
x
− − − + + + − − − + + + − − −
dielectric
ε1
ε2
€
Hy •
•
Maxwell Equations and continuity
D = ε0E + P = ε E (linear medium)
€
divD = 0
€
€
 E x1 
 
E1 =  0  exp[i( kx1 x − k z1z − ωt )]
 
 E z1 
 0 
 
H1 =  E y1  exp[i( kx1 x − k z1z − ωt )]
 
 0 
1 ∂D
=0
→
c ∂t
divB =€
0
rot H −
€
E x1 = E x 2
→
ε1 E z1 = ε2 E z 2
H y1
kz1
H y1
ε1
 Ex2
 
E 2 =  0  exp[i( kx 2 x + k z2 z − ωt )]
 
 Ez2 
 0 
 
H 2 =  E y 2  exp[i( kx 2 x + k z2 z − ωt )]
 
 0 
SP Dispersion relation
kx =
Hy 2
k
= − z 2 Hy 2
ε2
=
€
ω ε1ε2
c ε1 + ε2
2
ω
kx2 + kzi2 = εi 2
c
What are surface plasmons ?
•
Evanescent electric field propagating at surface
z
r
E
z
metal
x
− − − + + + − − − + + + − − −
dielectric
Ez ∝ e−kz z
ε1
ε2
Hy •
Surface Plasmon: Longitudinal charge
€ density oscillations involving 1010 electrons€
Ez
ω ε1ε2
ksp =
c ε1 + ε2
Surface Plasmon Polariton: Polaritons are quasiparticles
resulting from
€
strong coupling of electromagnetic waves with an electric or magnetic dipolecarrying excitation, in this case plasmons.
€
What are surface plasmons ?
•
Evanescent electric field propagating at surface
z
r
E
z
metal
x
− − − + + + − − − + + + − − −
dielectric
Ez ∝ e−kz z
ε1
ε2
Ez
Hy •
€
€

ε1 = ε1′ + i ε1′′
ε2 is real
ω ε1ε2
kx =
c ε1 + ε2
ω ε1′ε2 
kx′ = 

c  ε1′ + ε2 
3
2
ω  ε1′ε2  ε1′′
kx′′ = 

c  ε1′ + ε2  2(ε1′) 2
ε1′′ < ε1′
€
e.g.
Ag ε = −22.4 − 0.91i
Au ε = −23.0
€ − 0.77i
1
2
[also ε(ω )]
€
What are surface plasmons ?
•
Evanescent electric field propagating at surface
z
r
E
z
metal
x
− − − + + + − − − + + + − − −
dielectric
ε1
ε2
Hy •
Ez ∝ e−kz z
δm
Ez
δd
€
€
3
2
[Figures courtesy of Barnes et al., Nature 424, p824 (2003)]
ω  ε1′ε2  ε1′′
δsp ⇔ k x′′ = 

c  ε1′ + ε2  2(ε1′) 2
Extremely short lifetimes for surface plasmons ( 10-15 s to 10-12 s)
€
Outline
• What are surface plasmons: Introduction
• Excitation of surface plasmons at surfaces
• Entanglement and surface plasmons
• Surface plasmons in quantum information implementations
Excitation of Surface Plasmons
•
Attenuated total reflection
ksp =
ω ε1ε2
ω
<
c ε1 + ε2 c
[Figures courtesy of Barnes et
al., Nature 424, p824 (2003)]
ω
€kx = sin θ ε0 c
r
klight
θres
r
kx
r
metal film
ksp
attenuated total reflection at surface plasmon resonance
€
€
[other figures courtesy of R. Stock, Thesis, UNM (2001)]
Excitation of Surface Plasmons
•
0.4
Attenuated total reflection
prism
gold
air
0.3
ksp =
ω ε1ε2
ω
<
c ε1 + ε2 c
2
normal
incidence
E (z )
0.2
E0
0.1
ω
€kx = sin θ ε0 c
0
-200
0
r
klight
6
5
2
θres
E (z ) 4
E0
400
600
distance (Å)
8
7
200
prism
gold
air
surface
plasmon
resonance
angle
3
r
2
kx
1
r
metal film
0
-200
0
200
400
600
ksp
strong field enhancement effect due to surface plasmons
€
€
[Figures courtesy of R. Stock, Thesis, UNM (2001)]
Excitation of Surface Plasmons
•
Periodic structure
r
r
r
r
ksp = k x ± m Gx ± n Gy
→
€
•
ε1ε2
m +n λ=D
ε1 + ε2
2
2
Periodic sub wavelength hole array
€
versatile wavevector matching using periodic structures
[Figures courtesy of Ghaemi et al., PRB 58, p6779 (1998) and Altewischer et al., Nature 418, p304 (2002)]
Excitation of Surface Plasmons
•
Periodic sub wavelength hole array
700 nm
ksp
200 nm
200 nm
ksp
Enhanced optical transmission through array of sub
wavelength holes (compared to diffraction theory)
[Figures courtesy of Ghaemi et al., PRB 58, p6779 (1998) and Altewischer et al., Nature 418, p304 (2002)]
Outline
• What are surface plasmons: Introduction
• Excitation of surface plasmons at surfaces
• Entanglement and surface plasmons
• Surface plasmons in quantum information implementations
Implementations using Surface Plasmons
•
Field enhancement effect
– Surface enhanced spectroscopy
– Strong coupling to waveguides
– Biophotonics: Biological and chemical detectors (sensitivity to ε2 at the surface)
•
Nanoscale technology
– Nano-optics and nano-circuitry on surfaces:
• Mirrors (reflectivity> 90%)
• Nanowires (waveguides) for plasmons
– “Plasmonic” computer chips and other nanoscale technology
– Data storage
•
Quantum nature of surface plasmons
– SPASERS (surface plasmon amplification
by spontaneous emission of radiation)
– Single photon light sources
– Quantum information processing
Seidel et al., PRL 94, 177401 (2005)
Surface Plasmons and Entanglement
•
Polarization entangled photons
ψ =
•
1
X1Y2 + e iφ Y1 X 2
(
2
)
Experimental setup
€
Nature 418, p304 (2002)
Coincidence detection
after transmission
through hole array
Surface Plasmons and Entanglement
•
Experiment
Reduced visibility
due “which-path”
information in
solid?
Surface Plasmons and Entanglement
•
Which-path information: include state of solid
E. Moreno, F.J. Garcia-Vidal, D. Erni, J. I. Cirac, L. Martin-Moreno
PRL 92, 236801(2004)
•
€
€
Interaction models?
a) all Sab are orthogonal: solid and biphoton entangled
→ trace over solid: mixed state for biphoton, “which-polarization” information
b) all Sab are equal: no entanglement between solid and photon states
→ trace over solid: biphoton entangled depending on tab
• Choose b): no which-path labels introduced in solid
• Observed visibilities can be explained by polarization dependent
transmission of hole array
Surface Plasmons and Entanglement
•
Energy-time entanglement
S. Fasel, N. Gisin, H. Zbinden, D. Erni, E. Moreno, F. Robin
PRL 94, 110501(2005)
ψ =
€
1
( 1,0;1,0
2
AB
+ e iφ 0,1;0,1 AB )
→ energy-time entanglement especially robust against environmental disturbance
→ telecom wavelength particularly interesting for quantum communication
Surface Plasmons and Entanglement
•
Energy-time entanglement
S. Fasel, N. Gisin, H. Zbinden, D. Erni, E. Moreno, F. Robin
PRL 94, 110501(2005)
→ macroscopic cat states (surface plasmons) living at different “epochs”
that differ by more than the cats (surface plasmon) lifetime
Outline
• What are surface plasmons: Introduction
• Excitation of surface plasmons at surfaces
• Entanglement and surface plasmons
• Surface plasmons in quantum information implementations
Surface Plasmons in Quantum Information
•
Proposal: Cavity QED with Surface Plasmons
D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin
quant-ph/0506117
• efficient coupling of emitter (quantum • plasmon cavity created by plasmon
dot, atom) to plasmon mode of nanowire mirrors (2k|| grating on surface) with
reflectivity > 0.9
• evanescent coupling of nanowire to
dielectric waveguide
→ single photon source
• field enhancement: stronger coupling and faster interaction times
• one photon sources
Surface Plasmons in Quantum Information
•
Proposal: Cavity QED with Surface Plasmons
D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin
quant-ph/0506117
→ calculation of plasmons modes
→ efficiency of single photon generation
P
• fractional power emitted into fundamental plasmon mode
• one photon source efficiency: 0.7 (coupling to wire), 0.9 coupling to cavity
Summary
Summary
• Entanglement survives excitation and deexcitation of surface plasmons
• Applications for hybridization of different QIP implementations
• Problems:
– Short Coherence time (usually < 10-12 s)
– Limited spatial propagation (usually < 1 mm)
References
• General review:
• Surface Plasmons:
• Entanglement experiments
– Theoretical analysis
– Time-energy entanglement
•
Hybrid proposal
J. Opt. A 5, S16-S50 (2003)
H. Raether: Surface Plasmons, Springer 1988
Nature 418, 304 (2002)
PRL 92, 236801(2004)
PRL 94, 110501(2005)
quant-ph/0506117