BoseEinstein Condensation of ExcitonPolaritons

1
Bose-Einstein Condensation of Exciton-Polaritons i
n a Two-Dimensional Trap
D.W. Snoke R. Balili V. Hartwell University of
Pittsburgh L. Pfeiffer K. West Bell Labs,
Lucent Technologies
Supported by the U.S. National Science Foundation
under Grant 0404912 and by DARPA/ARO Grant
W911NF-04-1-0075
2
Outline 1. What is an exciton-polariton? 2.
Are the exciton-polaritons really a delocalized
gas? Can we trap them like atoms? 3. Recent
evidence for quasiequibrium Bose- Einstein
condensation of exciton-polaritons 4. Some
quibbles
3
What is an exciton-polariton? A) What is an
exciton?
Coulomb attraction between electron and hole
gives bound state
net lower energy for pair than for free electron
and hole ? states below single-particle gap
Wannier limit electron and hole form atom like
positronium
Excitonic Rydberg
Excitonic radius
4
B) What is a cavity polariton?
microcavity
J. Kasprzak et al., Nature 443, 409 (2006).
cavity photon
quantum well exciton
5
Tune Eex(0) to equal Ephot(0)
Mixing leads to upper polariton (UP) and
lower polariton (LP) LP effective mass 10-4
me
r
r
r
r
6
Light effective mass ideal for Bose quantum
effects
Why not use bare cavity photons?
...photons are non-interacting.
Excitons have strong short-range interaction
Lifetime of polariton 5-10 ps Scattering time
4 ps at 109 cm-2 (shorter as density increases)
7
Nozieres argument on the stability of the
condensate Interaction energy of condensate
Interaction energy of two condensates in
nearly equal states, N1N2N
1
1
E
V
N
(
N
1
)
V
N
(
N
1
)
2
V
N
N

-

-

0
1
1
0
2
2
0
1
2
2
2
1
2

V
N
V
N
N

0
0
1
2
2
Exchange energy in interactions drives the phase
transition! --Noninteracting gas is
pathological-- unstable to fracture
8
Trapping Polaritons
How to put a force on neutral particles?
hydrostatic stress
shear stress
9
Bending free-standing sample gives hydrostatic
expansion
finite-element analysis of stress
strain (arb. units)
x (mm)
hydrostatic strain
shear strain
10
Using inhomogenous stress to shift exciton states
GaAs quantum well excitons
Relative Energy (meV)
x (mm)
Negoita, Snoke and Eberl, Appl. Phys. Lett. 75,
2059 (1999)
11

• Typical wafer properties
• Wedge in the layer thickness
• Cavity photon shifts in energy due layer
  thickness
• Only a tiny region in the wafer is in strong
  coupling!

Reflectivity spectrum around point of strong
coupling
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Sample Photoluminescence and Reflectivity
Photoluminescence Reflectivity
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Reflectivity and luminescence spectra vs.
position on wafer
false color luminescence grayscale reflectivity
increasing stress
trap
Balili et al., Appl. Phys. Lett. 88, 031110
(2006).
14
Motion of polaritons into trap
unstressed
positive detuning
resonant creation
accumulation in trap
15
Do the polaritons really move? Drift and
trapping of polaritons in trap
Images of polariton luminescence as laser spot
is moved
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Toward Bose-Einstein Condensation of Cavity
Polaritons
? superfluid at low T, high n
log T
normal
superfluid
log n
17
Critical threshold of pump intensity
Luminescence intensity at k 0 vs. pump power
Nonresonant, circular polarized pump
Pump here! 115 meV excess energy
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Spatial profiles of polariton luminescence
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Spatial narrowing cannot be simply result of
nonlinear emission
model of gain and saturation
20
Spatial profiles of polariton luminescence-
creation at side of trap
21
General property of condensates spontaneous
coherence
Andrews et al., Science 275, 637 (1997).
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Measurement of coherence Spatially imaging
Michelson interferometer
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Michelson interferometer results
Below threshold
Above threshold
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Spontaneous linear polarization --symmetry
breaking
kBT
small splitting of ground state
aligned along 110 cystal axis
Cf. F.P. Laussy, I.A. Shelykh, G. Malpuech, and
A. Kavokin, PRB 73, 035315 (2006), G. Malpuech
et al, Appl. Phys. Lett. 88, 111118 (2006).
25
Degree of polarization vs. pump power
Note Circular Polarized Pumping!
26
Threshold behavior
k0 intensity
k0 spectral width
degree of polarization
27
In-plane k is conserved ? angle-resolved
luminescence gives momentum distribution of
polaritons.
28
Angle-resolved luminescence spectra
50 mW
400 mW
600 mW
800 mW
29
Intensity profile of momentum distribution of
polaritons
0.4 mW
0.6 mW
0.8 mW
30
Occupation number Nk vs. Energy
Maxwell-Boltzmann fit Ae-E/kBT
min
31
Can the polariton gas be treated as an
equilibrium system? Does lack of equilibrium
destroy the concept of a condensate?
lifetime larger, but not much larger, than
collision time continuous pumping
Ideal equilibrium Bose-Einstein distribution
32
Occupation number vs. Energy
MB 80 K
BE 80 K
33
Kinetic simulations of equilibration
Exciton distribution function in Cu2O
D.W. Snoke and J.P. Wolfe, Physical Review B 39,
4030 (1989). - collisional time scale for BEC
Quantum Boltzmann equation Fokker-Planck
equation
Maxwell-Boltzmann distribution
Snoke, Braun and Cardona, Phys. Rev. B 44, 2991
(1991).
34
Kinetic simulations of polariton equilibration
Tassone, et al , Phys Rev B 56, 7554
(1997). Tassone and Yamamoto, Phys Rev B 59,
10830 (1999). Porras et al., Phys. Rev. B 66,
085304 (2002). Haug et al., Phys Rev B 72,
085301 (2005). Sarchi and Savona, Solid State
Comm 144, 371 (2007).
35
Full kinetic model for interacting polaritons
V. Hartwell, unpublished
36
Angle-resolved data
Unstressed-- weakly coupled
bottleneck
Weakly stressed
Resonant-- strongly coupled
37
Power dependence
38
Fit to experimental data for normal but highly
degenerate state
39
Strong condensate component
above threshold
far above threshold
below threshold
logarithmic intensity scale
thermal particles
condensate (ground state wave function in
k-space)
linear intensity scale
40
Quibbles and other philosophical questions

• Are the polaritons still in the strong coupling
  limit when the
• threshold effects occur?
• i.e., are the polaritons still polaritons?
• (phase space filling can reduce coupling, close
  gap between LP and UP)

mean-field shift blue shift for both LP, UP
phase-space filling LP, UP shift opposite
41
Power dependence of trapped population
Images of polariton luminescence as laser power
is increased
42
2. Does the trap really play a role, or is this
essentially the same as a 2D Kosterlitz-Thouless
transition?
43
Spatially resolved spectra
below threshold
above threshold
at threshold
Flat potential
Trapped
44
3. Optical pump, coherent emission Is this a
laser?
normal laser
lasing without inversion
stimulated scattering
stimulated emission
exciton-exciton interaction coupling (inversion
can be negligible)
radiative coupling (oscillators can be isolated)
45
Two thresholds in same sample
Deng, Weihs, Snoke, Bloch, and Yamamoto, Proc.
Nat. Acad. Sci. 100, 15318 (2003).
46
Conclusions 1. Cavity polaritons really do move
from place to place and act as a gas, and can
be trapped 2. Multiple evidences of
Bose-Einstein condensation of
exciton-polaritons in a trap in two
dimensions 3. Bimodal momentum distribution is
consistent with steady-state kinetic models 4.
Coherent light emission without lasing Lasing
in the strongly coupled regime or, Lasing
without inversion