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).