The 6th International Conference on Spontaneous
Coherence in Excitonic Systems
Closing Remarks
David Snoke
Department of Physics and Astronomy, University of Pittsburgh
ICSCE6, Stanford University, USA
2012 August 27-31
Bloch sphere picture
standard laser with inversion
spontaneous symmetry breaking
gives exact phase of oscillation
See D.W. Snoke, “Polariton Condensation and Lasing,” in Exciton Polaritons in Microcavities,
(Springer Series in Solid State Sciences 172, V. Timofeev and D. Sanvitto, eds., (Springer,
2012). (arXiv:1205.5756)
Bloch sphere picture
Excitonic condensate
coherent oscillation without
inversion
See D.W. Snoke, “Polariton Condensation and Lasing,” in Exciton Polaritons in Microcavities,
(Springer Series in Solid State Sciences 172, V. Timofeev and D. Sanvitto, eds., (Springer,
2012). (arXiv:1205.5756)
Amplified stimulated emission (ASE)
fast dephasing
scales with size of system, with critical size
Lasing
Requires inversion.
Spontaneous symmetry breaking gives amplification of phase coherent fluctuation
Superfluorescence (SF)
Same as lasing, but without mirrors or continuous pump: a spontaneous coherent
pulse following inversion (after time delay)
Superradiance (SR)
Same mechanism as SF, but starts with coherent driving pulse. Maps to classical
case of coupled antennas. Can still have spontaneous symmetry breaking in emission
direction.
Exciton condensation
No inversion: amplification of phase coherent fluctuation through pair-pair
interaction (“stimulated scattering”)
Photon condensation (Weitz et al.)
Only possible through effective photon-phonon interaction via incoherent medium
inversion?
coherent
medium?
spontaneous
phase?
amplified stimulated emission
(ASE)
yes
no
no
superfluorescence
yes
yes
yes
superradiance
yes
yes
no
lasing
yes
yes
yes
dielectric medium
no
yes
no
excitonic BEC
no
yes
yes
photon BEC
no
no
yes
Terminology debates
 “condensation but not BEC” is silly.
 BEC occurs when a macroscopic fraction of all particles enter the ground
quantum state (in some reference frame; moving condensate is allowed)
-that ground state often includes a component with off-diagonal longrange order (ODLRO). Long-range = extensive with system size
-but not always, if ground state is not extensive with system (e.g. a trap)
 more controversial: BEC occurs spontaneously via thermalization
-requires examination of excited states (should have a thermal tail)
-“perfect” equilibrium not required and never happens anyway
-“quasiequilibrium” = subset of system can be well described by equilibrium
e.g. electron or exciton gas not in equilibrium with lattice
-system must have a mechanism by which the excited states and ground
state approach equilibrium
 By this definition, BCS is a type of BEC (and so is bilayer quantum Hall condensate)
and so are trapped atom BEC and helium-4 and helium-3
 By this definition, lasing is not BEC, and OPO is not BEC
- but laser is an example of spontaneous coherence which is a special case of
spontaneous symmetry breaking (SSB)
-spontaneous coherence is SSB with a complex (two-component) order parameter
i.e. amplitude and phase
BEC is a special case of spontaneous coherence
 By this definition, polariton and photon BEC (and magnon BEC) can be BEC
-may not always be BEC: sometimes spontaneous coherence far from equilibrium
may be occurring (“polariton laser”)
Variations:
 “Quasicondensate” = macroscopic fraction in tiny region of state space near
ground state but not exactly one state (dephased, or fluctuating, BEC)
- can occur in equilibrium, e.g. 2D BKT, possibly attractive 3D Bose gas
- can occur as transitory stage in path to equilibrium
-2D system can become quasicondensate, not true BEC, in infinite system,
but large, trapped 2D system can be true BEC.
- no significant difference between 2D and 3D trapped BEC
- in practice quasicondensate may be hard to tell from full BEC
(e.g. superfluid helium on a surface)
 “Nonequilibrium BEC” = not far from equilibrium, but nonequilibrium effects
large enough to measure differences from equilibrium solution
-probably greatest contribution of polariton community to fundamental
physics so far: many equilibrium BEC phenomena preserved even as system
deviates significantly from equilibrium
 “Bose glass” = locally BEC but strong disorder prevents long-range phase coherence
- also interesting to look at crossover to full BEC
(e.g. phase locking seen in polaritons)
Superfluidity
Not the same as BEC.
Can have ~100% superfluid and 0% BEC (e.g. BKT superfluid in 2D)
and 100% BEC and 0% superfluid (e.g. ideal Bose gas)
But they are related: stimulated scattering makes it strongly unfavorable
for particles to act independently as is required for drag.
Need at least a quasicondensate for superfluidity, and ideal BEC may be
viewed as superfluid with zero critical velocity.
Superfluidity is defined by transport measurements: flow without drag.
Two-fluid model: only normal part feels drag.
“Just” classical waves
Why are there classical waves at all, if we live in a quantum world?
A macroscopic Fock state (definite number of particles, indeterminate phase)
is a physically possible state
A water wave = macrocopic number of bosons in single k-state
Fock state = superposition of different phases, definite amplitude
Snoke, Liu, and Girvin, Annals of Physics 327, 1825 (2012)
infinite homogeneous Bose gas
in-flow: negligible at low density (~N2)
out-flow: negative
out-scattering normally leads to “dephasing” but for highly occupied states
(near k=0) “enphasing” occurs. True for Planck as well as BEC systems
Our normal experience of superpositon of low-frequency waves with definite
phase (= “classical wave approximation”) arises from this.
Planck distribution
occupation number
f(E)
classical regime
normally no
average coherence,
no single state dominates
unless BEC
f(E)D(E)
E/kBT
macroscopic coherent
classical wave can arise
via non-spontaneous
symmetry breaking
“driven condensate”?
= classical wave (e.g. bell
hit by hammer)
E/kBT
Progress
1. Room temperature condensate very doable
already reasonable claims in polariton systems; RT in weak coupling
with photons; also magnons
2. Equilibrium condensate of excitonic systems doable
permanent bilayer (BCS-like); long-lifetime polaritons
3. Long-range transport of polaritons doable
continuously pumped solitons, long-lifetime polaritons, wires
4. Crossovers interesting: BEC/BCS, PBEC/laser, strong coupling/weak coupling,
equilibrium/nonequilibrium/far-from-equilibrium
5. Lots of ways to control and manipulate polaritons
stress, laser AC Stark, laser exciton cloud, surface patterning, acoustic
lattices...
M. Gonokami
T. Ogawa
The University
of Tokyo
Osaka University