Upload
others
View
3
Download
0
Embed Size (px)
Citation preview
Coherence and decay within Coherence and decay within BoseBose--Einstein condensates Einstein condensates ––
beyond beyond BogoliubovBogoliubov
N. KatzN. Katz11, E. Rowen, E. Rowen11, R. Pugatch, R. Pugatch11, N. Bar, N. Bar--gillgill11 and and N. DavidsonN. Davidson11, ,
I. MazetsI. Mazets22 and and G. KurizkiG. Kurizki22
((R. R. OzeriOzeri and J. and J. SteinhauerSteinhauer))
1. Department of Physics of Complex Systems1. Department of Physics of Complex Systems,,2. Department of Chemical Physics,2. Department of Chemical Physics,
WeizmannWeizmann Institute of Science, Institute of Science, RehovotRehovot 76100, Israel76100, Israel
For more information For more information –– see my webpage: see my webpage: www.weizmann.ac.il/home/katznwww.weizmann.ac.il/home/katzn
OutlineOutline
• Weak Bogoliubov excitationsFringe spectroscopy
• Strong Excitations Spectrum of BEC oscillating in a latticeTime domain – suppression of dephasingDecay of these states
• Probing many-body correlation times (theory)
Experimental setExperimental set--upup
• 87Rb atoms in the ground state.
• N0 = 1-5x10 5 atoms.
• T ~ 0.3 Tc ~ 100 nK
• ~95% of atoms in the ground state
• Chemical potential µ/h = 2 – 4 kHz
2,2, =FmF
Time of flight (absorption imaging)Time of flight (absorption imaging)
z (mm)
r (m
m)
optical density - no background
100 200 300 400 500 600
20
40
60
80
100
120
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4-0.5
0
0.5
1
1.5
2
2.5
3Z direction
z [mm]
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-0.1
0
0.1
0.2
0.3Z direction
z [mm]
optic
al d
ensi
ty (a
.u.)
T>Tc T=Tc T
TOF image of an excited condensate
ωω +o oω
pk θ pk
⎟⎠⎞
⎜⎝⎛=2
sin2 θpkk
Bragg SpectroscopyBragg Spectroscopy
J. Stenger et al., PRL 82, 4569 (1999) (Ketterle); M. Kozuma et al., PRL 82, 871(1999) (Phillips); J. Steinhauer et al., PRL 88, 120407 (2002) (Davidson).
BogoliubovBogoliubov spectrumspectrum
( )gnkkk 200 += εεε
k(ξ−1)
E(µ)
mk
2
2
1−ξgn=µ
ck
ckk =εPhonon regimelow k limit:
µεε += 0kk
Free particle high k limit: regime
0 2 4 6 8 10 12 140
2
4
6
8
10
12
14
2πR-1 ξ-1
ω/(2
π) (k
Hz)
k (µm-1)J. Steinhauer et al., PRL 88, 120407 (2002) (Davidson.
Excitation Spectrum: a roadmapExcitation Spectrum: a roadmap
0 2 4 6 8 10 12 140
2
4
6
8
10
12
14
2πR-1 ξ-1
ω/(2
π) (k
Hz)
k (µm-1)
Can possibly observe singleparticle excitations!
Fringe visibility: a spectroscopic toolFringe visibility: a spectroscopic tool
−300 −200 −100 0 100 200 3000
0.05
0.1
0.15
0.2
0.25
ω/2π (Hz)
frin
ge v
isib
ility
Fringe visibility
N. Katz, R.Ozeri, J. Steinhauer, N. Davidson, C. Tozzo and F. Dalfovo, PRL 93, 220403 (2004).
Heterodyne detection – matter wave interference
counting visibility
y (m
m)
(a)
−0.2 0 0.2
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
(b)
−0.2 0 0.2
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
z (mm)
y (m
m)
(c)
−0.2 0 0.2
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
z (mm)
(d)
−0.2 0 0.2
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
π/6 π/2
~π ~12π
Strong excitations at high Strong excitations at high momentamomenta
N. Katz, R. Ozeri, E. Rowen, E. Gershnabel and N. Davidson, Phys. Rev. A 70, 033615 (2004)
Strong excitation Strong excitation –– splitting in spectrumsplitting in spectrum
−2kL 0 2kL
pumpprobe
E. Rowen, N. Katz, R. Ozeri, E. Gershnabel and N. Davidson, cond-mat/0402225 (2004).time (µsec) frequency (kHz)
For a dressed state view of atomicmode mixing –see Eitan Rowen’s poster (Mo-15)
Dynamics: Dynamics: decoherencedecoherence vs. vs. dephasingdephasing
y (m
m)
x (mm)
(a)
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
Decoherence+dephasingMomentum measurement
Tota
l mom
entu
mEx
cita
tion
frac
tion
Only dephasingAgrees with Gross-Pitaevskii!!
Population measurement:
0 200 400 600
0.0
0.2
0.4
0.6
0.8
1.0
exci
ted
popu
latio
n
time (µsec)
Exci
tatio
n fr
actio
n
N. Katz, R. Ozeri, E. Rowen, E. Gershnabel and N. Davidson, Phys. Rev. A 70, 033615 (2004)
Suppression of mean field broadeningSuppression of mean field broadening
Detuning (kHz)
Gain mean-field
Pay mean-field
0.4 0.5 0.6 0.7 0.8 0.9 11
1.5
2
2.5
3
3.5
lattice momentum
E/E
r
0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
2.5
lattice momentum
E/E
r
Weak Strong
Suppression of mean field Suppression of mean field and Doppler broadeningand Doppler broadening
E0k E0k
Exci
ted
popu
latio
nResult:Coherence enhanced by more than a factor of 10.
Collisions in theCollisions in thelatticelattice
(a)
kz/k
L
k y/k
L
−2 −1 0 1 2
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
(b)
kz/k
L
−2 −1 0 1 2
experiment
Bloch band model
Stochastic GPE simulation
Coupling to a nontrival continuum…
E. Rowen, N. Katz, R. Ozeri, E. Gershnabel and N. Davidson, cond-mat/0402225 (2004).
A.A. Norie, R. J Ballagh and C.W. Gardiner, cond-mat/0403378
Probing correlations Probing correlations -- RamanRamanScheme:
• Excite off resonance (positive detuning ∆) Raman momentum states (q),• Monitor the decay products of these states as a function of time
Raman beams
Off-resonanceRaman excitation
Decay products
I. Mazets, G. Kurizki, N. Katz and N. Davidson, cond-mat/0411301
Zeno effects in BECZeno effects in BEC
0 3 6 9 12mtê—
0
0.5
1
1.5
GHt
LêG
GR
t corr0.2=∆
µ
66.0=∆µ
07.0=∆µ
Observing Zeno effectsObserving Zeno effects
0 0.1 0.2 0.3 0.4t HmsL
0
0.01
0.02
0.03
PHt
L
Pair production rate
Golden Rule result
Modulated frequency
Summary Summary -- physics beyond physics beyond BogoliubovBogoliubov
• Heterodyne detection of few excitations
• Strong excitations – spectra and decay
• Many-body correlation time for Raman
excitations
Dynamical instabilities (simulations)Dynamical instabilities (simulations)What happens when the Bragg pulse is at intermediate intensity
(comparable to the mean-field)?
1 2 3 4 5 6 7 8
1950
2000
2050
2100
2150
2200
2250
2300
2350
24001.5 2 2.5 3 3.5 4 4.5 5
1950
2000
2050
2100
2150
2200
2250
2300
2350
2400
2/µ≈Ω µ2≈Ω
A. Vardi and J. R. Anglin, Phys. Rev. Lett. 86, 568 (2001).