Dynamical Condensation of Exciton-Polaritons New Quantum liquid and Application to Quantum Emulator S. Utsunomiya, H. Deng, C. W. Lai, G. Roumpos, M. Fraser, N. Masumoto, K. Kusudo and Y. Yamamoto
National Institute of Informatics, University of Tokyo, Stanford University
A. Loeffler, S. Hoefling, and A. Forchel
Technische Physik, Universität Wurzburg

Semiconductor Cavity QED in Strong Coupling Regime
 Dressing Excitons with Electromagnetic Vacuum Field Introduction to microcavity Exciton-Polariton

Polariton is bosonic quasi-particle formed by a strong
coupling of excitons and photon in a semiconductor
cavity.

Exciton - polariton dispersion relation
EMicrocavity photon(mph ~ 10-5 me)

Exciton is bosonic quasi-particle formed by thebound electron –hole pair in quantum wells.
Wave Function

Upper polariton

Total Energy

Rabi splitting(4meV)

crystal latticeeh

QW exciton(mexc ~ 10-1 me)

wexc0electron (negative charge)
hole: vacant orbital left by electron (positive charge)= wph0kL
PUP

cavity photon
 QW exciton
 cavity photon …

//Lower polariton(meff ~ 2 mph)

C. Weisbuch et al., Phys. Rev. Lett. 69, 3314 (1992)

Bose-Einstein Condensation

S. Jiang et al., Appl. Phys. Lett. 73, 3031 (1998)

Experiment Setup

Boson: Particles that can occupy the same quantum statewith the same energy and it follows Bose-Einstein statistics:

BEC phenomenon occurs

Pump laser
sampleL1:removable lens
Red line: Far-field (real space) imaging
Blue line: Near-field (momentum space) imaging

C.W. Lai et al. Nature 450, 529-532 (22 November 2007)

Bogoliubov Excitation Spectrum
S. Utsunomiya et al., to be published in Nature PhysicsFar Field Pattern (momentum space distribution)
Thermal Polaritons  aspect ratio~1:1 (isotropic) 50 ×50 degrees (Dk=7.5 ×104 cm-1)

-25º

+25º
Below Threshold~Threshold

B’
White line：Single particle dispersion
Black line：
Pink line：Bogoliubov theory (polaritonpolariton interaction)

A：D = 1.4meV, p/pth = 4
B：D = 0.82meV, p/pth = 8
B’：D = 0.82meV, p/pth = 0.0001
C：D = 4.2meV, p/pth = 4
D：D = -0.23meV, p/pth = 24

Modeling of exciton-polariton condensates - quantizedvortex dynamics

The formation of a new kind of vortex lattices intriangular lattice potentials

2-dimensional periodic potential
by deposited thin metal patterns

Observed meta-stable condensation at M-points

Inteference indicates the existance ofcoherence between M1 points.

Brillouin Zones

Experimental results indicates the existenceof the new kind of vortex lattices. Vortex andanti-vortex stands like hexagonal lattices as
seen above.

A Bose-Einstein Condensate Computer
Tim Byrnes, Kai Yan, Yoshihisa Yamamoto

Institute for Nano Quantum Information Electronics (INQIE), The University of Tokyo,National Institute of Informatics, and E. L. Ginzton Laboratory, Stanford University
What’s BEC?

How is this useful for computation?

In a BEC, the system has a large concentration of particles in thesystem ground state. In bosonic final state stimulation, thetransition rate is enhanced by a factor N+1, given N particles in
the final state, Bosonic particles have an enhanced cooling rate.

Problem like Graph Partitioning Problem(GPP) can be formulated as a cost
minimization problem.
E

Ground State
Energy Landscape

What the“condensate”
means?

Say, you got many cups with water in it,
when you make them “condensate”, you got
one big bucket with all the water instead ofthe cups put together tightly,
It’s like a fusion.
By the way, in BEC we use bosons, not water.

Example of computational problem

By finding theground state you
can solve GPP?

Yes We Can!
And we use BEC toaccelerate the coolingprocess.

Device idea
Each site is correspondent to a point in thegiven GPP, and has N bosons, each ofwhich can be in one of two states(±1).

Interactions between sites are
modified externally via feedback loop

The Graph Partitioning Problem(GPP)

Given 2N points with arbitrary connections between them, divide the points
into two groups (A and B) of N points, minimizing the number of connections
between them. Any kind of NP-complete problem can be formulated as GPP.

A

Divide the points?
How hard is it for
a computer?

BWell, for some few points it’seasy, but for lots of points it
suddenly becomes very difficult,even cost hundreds of years tofind the best answer.

It’s like disheswith food!

Direct Ising model simulation

Cooling to thermal equilibrium

2 site Isingprobability ofgetting an ↑ona single sitebosonsdistinguishable

2 level system

Increasing boson number increases equilibration speed for both 2 and 4 site
Ising models.
N=14 site Ising

N=502 site IsingE

annealing time

E=+J
E=-J+2λE=-J-2λConclusions• Bosons speed up the equilibriation time of the Ising model by final state
stimulation. An enhanced ground state population is present due to bosonicstatistics.
• Introducing quantum coherence an interesting direction for future study.

The equilibration time forthe 4 site Ising Hamiltonian.
What can we do if theGPP or NP-complete
problem can be solved
faster?

Increasing boson number N
reduces residual energy for thesame annealing time.
Say, we can arrange theshortest path for every
Fedex trucks so that lotsof energy will be saved.
NP-complete do plays a bigrole in bios, medical, IT andmany more fields.

This work is supported by DARPA, JST/SORST, the University of Tokyo, and the Special
Coordination Funds for Promoting Science and Technology.