Quantum Information Processing with 1010 Electrons ? René Stock. ⢠Barry Sanders. ⢠Peter Marzlin. ⢠Jeremie Choquette. People: IQIS Seminar, October 2005 ...
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
