COLD DIPOLAR EXCITONS ON A CHIP –
FROM FUNDAMENTAL MANY-BODY
PHYSICS TO MULTI-FUNCTIONAL
CIRCUITRY
Ronen Rapaport
The Racah Institute of Physics and the School of
Engineering,
The Hebrew University of Jerusalem
Yehiel Shilo
Paulo Santos
Kobi Cohen
Snezana Lazic
Ronen Rapaport
Adriano Violante
Boris Laikhtman
Rudolph Hey
The nanophotonics group
Loren Pfeiffer
Ken West
Outline
Fundamental aspects:
I - experiments on trapped dipolar excitons –
evidence for strong particle correlations, dark excitons
condensate
Dipolar exciton functional devices:
II - Demonstration of an exciton acoustic multiplexer circuit
III (not presented) - Remote dipolar interactions
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Dipolar excitons in semiconductor bilayers
Energy
CB
-
z
-
AlGaAs
+
-
+
+ GaAs
-
+
+
-
VB
+
-
z
d
Energy
CB
CB
e∆V
+
e∆V
z
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AlGaAs
-+
+
-
+
-
VB
VB
z
d
-+
-
-
+ GaAs
+
+
-
∆V
dipolar excitons
2D dipolar fluid – aligned dipoles – repulsive interaction
+
Boson quasi-particles (integer spin) – Bose fluid at low T
(<4K)
+
r
-
-
Spin degeneracy of 4: 2-bright excitons (S=±1),
2-dark excitons (S=±2)
Long tunable lifetime (nanoseconds to microseconds)
z
Easy to observe and measure – emit photons!
We can “see” excitons…
+
+
-
-
d
-
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+
∆V
Weakly interacting quantum fluids
Cold atoms
Exciton-polaritons in semiconductor microcavities
Common feature:
weakly interacting particles →
Local (contact) interactions
→
Point particles – weak spatial
correlations – mean field
description (generally speaking)
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Cold dipolar fluids in two dimensions
Composed of particles with a permanent dipole moment
Longer range interactions
→
Non-trivial particle correlations in both quantum
and classical regimes
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Cold dipolar fluids in two dimensions (2D)
→
BEYOND MEAN FIELD
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Cold dipolar fluids in two dimensions
new correlation regimes and phases are expected, e.g.:
• Classical and quantum particle correlations
• Gas – liquid transitions (both quantum and classical)
• beyond Bogoliubov excitation spectrum – rotons
• Superfluidity and crystalization.
Schindler, Zimmerman, PRB, (2008)
Astrakharchik et al. Phys. Rev. Lett. (2007).
Buchler et al. Phys. Rev. Lett. (2007).
Boning et al. Phys. Rev. B (2011).
Berman et al.Phys. Rev. B (2012).
Measuring particle correlations is
essential to understand the manybody classical and quantum physics
of dipolar fluids
BL, RR, PRB 2009
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Observation of spontaneous coherence of a cold
dipolar exciton fluid
A. A.High. et al. Nature 483, 584–588 (2012).
A. A. High et al. Nano Letters 12, 2605-2609 (2012).
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I – Dipolar exciton correlation
measurements
dipolar excitons
Excitons emit photons  an optical probe of the system:
Energy of emitted Photon:
+
E ph = EX + Eint (nX ,T )
Single exciton energy
-
r
+
-
interaction energy with other dipoles
z
Direct measurement of d-d interaction!
+
+
+
∆V
→
d
Direct window to particle
- correlations,
fluid phases
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Can we see evidence for particle correlations?
Technique: time resolved spectroscopy of
trapped dipolar excitons Advantages:
• Homogeneous fluid in thermal equilibrium with no
particle source
• Allows density calibration (at least relative) by “photon
counting” and knowledge of the thermal distribution
• Allows to see fast dynamics
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Trapped dipolar exciton fluid
Position (microns)
Exciton electrostatic traps – dipoles are trapped under a
semitransparent gate via electrostatic forces
Wavelength (nm))
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Trapped dipolar exciton fluid
Note:
- Spatial confinement
- Flat density distribution
- Reduction of interaction
energy as density decays
Position (microns)
Exciton electrostatic traps – dipoles are trapped under a
semitransparent gate via electrostatic forces
Wavelength (nm))
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Mapping
Eint (nX ,T) from trapped fluid dynamics
Single exciton energy
E ph = EX + Eint (nX ,T )
Dipolar interaction energy
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Mapping
Eint (nX ,T) from trapped fluid dynamics
Mean field prediction:
No temperature dependence!
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Mean field prediction
Eint
T>2.5K
T independent
• beyond mean field prediction- dipolar correlations!
• Two correlation regimes
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High T: r0 > T - Classical correlations
Balance between thermal motion and
repulsion
2 2
ez
Ek » T = U(r0 ) = 03
e r0
r0
Temperature dependence
æ e 2 z02 ö
Þ r0 (T ) = ç
÷
e
T
è
ø
13
Lower T: r0 < T - Quantum correlations
Balance between quantum motion and repulsion

2
M Xr
2
2
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~
e d
r
3
2
No temperature dependence
Deviation from thermal distribution below ~2.5K
 Missing particles!
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Mapping
Eint (nX ,T)
T< 2.5K
 less bright excitons
 missing particles
 larger ΔE
 larger density
 more particles
(S=±1)
(S=±2)
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<0.1meV?
Dark exciton (S=±2)
accumulation
(condensation)?
(S=±1)
(S=±2)
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Mapping
Eint (nX ,T) from trapped fluid dynamics
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II – Multi-functional exciton
circuit
Why?
Vision: Future coherent exciton •
circuitry
More control and manipulation •
tools  more access to
investigate interesting physical
phenomena
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Dipolar exciton devices: How to control exciton
motion?
Surface acoustic waves (SAW) •
introduce a traveling strain field.
Causes bandgap modulation. •
Allows for exciton transport inside •
potential minima.
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Transport by surface acoustic waves
SAW is generated •
using RF transducers.
Propagation distance •
of milimeters!
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A transistor with surface acoustic waves
Transport using SAW. •
Electrical switching •
between ON/OFF states.
Based on:
High et al. Opt. Lett. (2007).
High, et al. Science (2008).
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Switching using surface acoustic waves
Channel switching by interfering SAWs •
Simulation based on nonlinear
exciton diffusion model:
RR, GC, SS, APL (2006)
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A demonstration of a multi-functional device
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III – Remote dipolar interactions
(not presented in the talk)
Remote dipolar interactions
Dipolar interaction is relatively long range. •
Can it have an effect over a macroscopic •
distance?
+
Intra-fluid
Fluid A
Inter-fluid
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r
+
Fluid B
Remote interaction for density calibration
Interaction energy of a homogeneous trapped fluid
But, for a remote dipole
Local correlations not important – only geometry
Model independent relation between density and density
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KC, PS, and RR, PRL 2011
Using remote interactions to manipulate exciton
flow
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KC, PS, and RR, PRL 2011
Measuring remote interactions
Measure the interaction of one fluid on •
another
Pump-probe experiment •
Time and space resolved spectroscopy •
Pump
density
Probe
energy
Time
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Probe laser
(CW)
Pump laser
(pulsed)
Time
Can remote dipolar interactions be measured?
+
-
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Energy profile
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Time resolved pump-probe experiments
Probe
indirect
t=1800ns
afterexciton
pulse
Position (m)
0
50
100
150
200
810
815
820
Wavelength (nm)
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Observing remote interactions
Better long time
electrostatic stability
is still required for a
reliable density
calibration
∆E
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Intensity
nmax » 1011 cm2
Thank you!
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