tunable fröhlich polarons of slow-light polaritons in a 2d bec
TRANSCRIPT
(1) Dept. of physics & research center OPTIMAS
Technische Universität Kaiserslautern(2) Dept. of physics, Harvard Universiy
Dense light, KITP, Santa Barbara 06.10.2015
Tunable Fröhlich polarons of
slow-light polaritons in a 2D BEC
Michael Fleischhauer (1), Fabian Grusdt (1,2)
F. Grusdt, M. Fl.
arXiv 1507.08248
polarons in solids
in solid-state systems
Fröhlich model, Adv. Phys. (1954)
polarons in solids
coupling strength impurity mass
polarons in solids
coherent displacement of phonon field
phonon-phonon scattering
weak coupling strong couplingintermediate
coupling
coupling strength
polarons in solids
coupling strength
weak coupling strong couplingintermediate
coupling
perturbative
mean-field
Lee, Low, Pines,
Phys Rev (1953)
self-trapping
Landau, Pekar
Zh. Exp. Th. Phyz.
(1946)
Feynman variational approach
no phase
transition
Gerlach, Löwen
RMP (1991)
polarons in BEC
impurity in a Bose-Einstein condensate
interaction with
Bogoliubov phonons
in unperturbed condensate
Fröhlich polaron bubble polaron
deformation of
condensate
Blinova et al.
PRA (2013)
polarons in BEC
phase transition vs. crossover ?
Gerlach - Löwen proof does not hold here
Grusdt et al.
Sci. Rep. 2015
Casteels et al.
PRA 2012
phase
transition ?
mass of polaron vs. bare mass
Fröhlich polarons in 2D BEC: extended RG
F. Grusdt, M. Fleischhauer, arXiv 1507.08248
renormalization group approach
F. Grusdt, Y. Shchadilova, A. Rubtsev, E. Demler, Sci. Rep. (2015)
F. Grusdt, arXiv 1509.08974
light impurities are needed !
Elm. Induced Transparency & slow light
large small
=
dispersion
M.Fl., M. Lukin, PRL 84, 5094 (2000); PRA 65, 022314 (2002)
dark-state polaritons
dark-state polariton
bright-state polariton (decays)
(a) (b)
free Hamiltonian
atom-light interaction
dark-state polariton impurity
BEC in ground state
dark-state polariton in a BEC
dark-state polariton impurity
non-adiabatic couplingbright-excited state
coupling
dark-state polariton impurity
problem: DSP is super-sonic
2D confinement of light
2D confinement of BEC
to avoid interaction- induced
scattering
(a) (b) (c)
0 2 4 6 80
10
20
30
40
50
Frank-Condon reduction
free polariton hamiltonian
polariton dispersion
impurity mass
dark-state polariton impurity
cavity decay of elm. part
Fröhlich polarons of dark-state polaritons
Interactions with Bogoliubov phonons
Fröhlich Hamiltonian
Interaction strength
polaronic mass renormalization
0 20 40 60 80 1000
50
100
150
200
250
MF
RG
tunable by coupling laser
phase diagram
phase diagram
100
102
104
106
108
10−1
100
101
102
103
st rong
coupling
interm .
coupling weak
coupling
some numbers
agg = 100.4 a0 ags = 98 a0
87Rb
(a) (b)
preparation of DSP polarons
(a)
(b)
(c)
0
2
4
6
8
010
20
30
40
50
storage of few-photon pulse
preparation of DSP polarons
(a)
(b)
(c)
0
2
4
6
8
010
20
30
40
50
partial retrieval
detection of DSP polarons
(a)
(b)
(c)
0
2
4
6
8
010
20
30
40
50
curved mirrors harmonic confinement potential
excite finite transverse k-values
absorption spectrum momentum resolved spectral function
Z = quasi-particle weight
= polaron energy
intermediate
coupling
100
102
104
106
108
10−1
100
101
102
103
st rong
coupling
weak
coupling
validity of Fröhlich model
validity of Fröhlich model
100
102
104
106
108
10−1
100
101
102
103
st rong
coupling
interm .
coupling weak
coupling
summary
nature of self-trapping transition of BEC polarons is unclear
Feynman: sharp transition for small impurity masses
RG: extended intermediate coupling regime
Dark-state polaritons in 2D cavity + 2D BEC = polaron with
widely tunable parameter
Detection of momentum-resolved spectral function, polaron mass etc.
Self-trapping transition in steady-state of open system?
Detection of beyond-Fröhlich effects, bubble polarons
SFB TR 49
Eugene Demler (Harvard)
Yulia Shadilova (Harvard)
thanks to
2010
Fabian Grusdt
