Breathing modes of a 1D Bose gas - Seras Club Nautique
Experimental tools. 2. Hydrodynamic breathing mode. Theory. Measurement. 3. Beyond .... Images taken at focus (tv = 15ms) for different initial temperatures ..... Fit using YY of the wings. 100 ... Change the 1D-ness (difficult) or add a lattice.
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Breathing modes of a 1D Bose gas Bess Fang , Isabelle Bouchoule, Thibaut Jacqmin, Tarik Berrada, Aisling Johnson Institut d’Optique, Palaiseau.
Institut d’Optique, 30 Mai 2013
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Outline 1
Experimental techniques and physical background Apparatus Regimes of 1D Bose gases Experimental tools
2
Hydrodynamic breathing mode Theory Measurement
3
Beyond self similar solution Observations Origin ?
4
frequency and lifetime
5
Long-lived out-of-equilibrium stationnary states
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Outline 1
Experimental techniques and physical background Apparatus Regimes of 1D Bose gases Experimental tools
2
Hydrodynamic breathing mode Theory Measurement
3
Beyond self similar solution Observations Origin ?
4
frequency and lifetime
5
Long-lived out-of-equilibrium stationnary states
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Realisation of very anisotropic traps on an atom chip Magnetic confinement of 87 Rb by micro-wires A 3-wire guide
z
ω⊥ /2π = 2 − 40 kH ωz /2π = 5 − 10 Hz
1D : T, µ ~ω⊥ g = 2~ω⊥ a chip mount trapping wire z
CCD camera
In-situ images absolute calibration (a)
0.69 −0.077
y B
T ' 400 − 15nK ' 3.0 − 0.1~ω⊥ N ' 5000 − 1000.
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
1D Bose gas with repulsive contact interaction H=−
~2 2m
Z
dzψ +
g ∂2 ψ+ 2 ∂z 2
Z
dzψ + ψ + ψψ,
Exact solution : Lieb-Liniger Thermodynamic : Yang-Yang (60’) n, T Length scale : lg = ~2 /mg, Energy scale Eg = g2 m/2~2 Parameters : t = T/Eg , γ = 1/nlg = mg/~2 n 1e+08
nearly ideal gas
1e+06
deg
ther
10000
t
mal
ene
rat
classical
Bosonic bunching g(2) (0) ' 2 µ ~/ξ
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Outline 1
Experimental techniques and physical background Apparatus Regimes of 1D Bose gases Experimental tools
2
Hydrodynamic breathing mode Theory Measurement
3
Beyond self similar solution Observations Origin ?
4
frequency and lifetime
5
Long-lived out-of-equilibrium stationnary states
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Hydrodynamic breathing mode Long wave length perturbation : hydrodynamic equations ∂t ρ + ∂z(ρv) = 0 mρ∂t v + ρ∂z (V + mv2 /2) + ∂z p = 0 Quasi-condensate equation of state : p = −∂E/∂V = gn2 /2 √ V = 0, small perturbations : phonons ω = ck, c = ρg V harmonic and ρ(t = 0) inverted parabola : self similar solution ρ
z
ρ(t, z) = ρ(t = 0, z/η)/η
v
z
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Experimental observation V
Quench of the longitudinal confinement z Mom ent um profile
21
6.0
20
5.5
19
5.0
18
rm s widt h
rm s widt h
Insit u profile
17 16
4.5 4.0 3.5
15
3.0
14
2.5
13
0
100
200
300
400 t
500
600
700
2.0
0
100
200
300
400
500
600
700
t √ Insitu profile : ωB = 0.94 3ωD Momentum profile : ωBp = 2ωB Very large amplitude in momentum space : P ' (~/ξ)∆σ/σ First observation in momentum space.
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Breathing mode excited by strong evaporation Cutting into the Thomas-Fermi profile by RF knife Cut into quasi−condensate
5 × 104 Nat
U µ
µU
0 −1200 −800 −400 t
Mom ent um profile 3.2
√ ωBp = 0.98 × 2 3ω
3.1
rm s widt h
3.0 2.9 2.8 2.7 2.6 2.5 2.4 2.3
50
100
150 t
200
250
0
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Outline 1
Experimental techniques and physical background Apparatus Regimes of 1D Bose gases Experimental tools
2
Hydrodynamic breathing mode Theory Measurement
3
Beyond self similar solution Observations Origin ?
4
frequency and lifetime
5
Long-lived out-of-equilibrium stationnary states
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Ab-normal breathing mode resulting from evaporation Insitu profile
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
rms width (pixels)
Co-existence of both modes
3.5
3
2.5 0
250 t (ms) √
√ 3ω
500
2 3ω
S(ω)
40 30 20 105 0 0
5
10
15
20
ω/(2π)
25
30
35
40
750
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
g
rms width (pixels)
Effect of a quench of g
5 ms g ∝ ω⊥
3g1
Insitu profile √ ω = 3ωD
18 16 14
g1 0
t
250 500 t (ms)
750
√ 2 3ωD
14 12
3.2
10
S(ω)
rms width (pixel)
Momentum distribution
2.8
8 6 4
2.4
2
0
200
400 t (ms)
600
Both frequency visible.
0 0.0 0.5
3.0 √ ω/( 3ωD )
1.0 1.5 2.0 2.5
3.5 4.0
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Physical origin ? Adiabatic temperature change to the compression of the gas ? Not the good order of mangnitude Gross-Pitaevski calculations. Initial thermal state : use Local density approximation h(θ(z) − θ(z0 ))2 i = mT/(~2 ρ)|z − z0 | ⇒ Random walk p 0 hδρ(z)δρ(z0 )i = mT/(~2 ) mg/(~2 ρ)e−2|z−z |/ξ ⇒ Ornstein-Uhlenbeck 1.8
1.4
0.5
1.2
ρ
1.6
1
θ
1.5
0
1
0.8 −0.5
0.6
−1
0.4 0.2
−1.5 2000
2500
3000
3500
z
4000
4500
0 1000
1500
2000
2500
3000
z
3500
4000
4500
5000
5500
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Gross-Pitaevski calculations
momentu width
Time evolution according to Gross-Pitaevski after a quench of ωz Result of GP fitted by a prabola
1.0 0.9 0.8
Self-similar solution
0.7 0.6 0.5 0.4 0.3
Effect of compression
0.2 0.1 0.0 0
1
2
3
4
5
6
7
tω
Do not account for experimental observation
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Gross-Pitaevski calculations : quench of g Time evolution according to Gross-Pitaevski after the quench of g. Experimental parameters used
Do not account for experimental observation
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Outline 1
Experimental techniques and physical background Apparatus Regimes of 1D Bose gases Experimental tools
2
Hydrodynamic breathing mode Theory Measurement
3
Beyond self similar solution Observations Origin ?
4
frequency and lifetime
5
Long-lived out-of-equilibrium stationnary states
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Breathing mode frequency Quasi-condensation cross-over : ω :
√
3ω → 2ω
Dimensionnal pcrossover (within quasi-bec) : √ ω : 3ω → 5/2ω Insit u profile Insit u profile 27
15
26 25 rm s widt h
rm s widt h
14 13 12
ωB = 1.89ωD T from profile : 80 nK, T from fluctuations : 20 nK
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Lifetime of the breathing mode 3D case : lifetime limited by phonons/phonons coupling at non zero temperature. 1D case ? Insit u profile Insit u profile
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Outline 1
Experimental techniques and physical background Apparatus Regimes of 1D Bose gases Experimental tools
2
Hydrodynamic breathing mode Theory Measurement
3
Beyond self similar solution Observations Origin ?
4
frequency and lifetime
5
Long-lived out-of-equilibrium stationnary states
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Long-lived out-of-equilibrium stationnary states Predictions for Tprofile
Qusi-condensate (T=)
60
hδN 2 i
Prediction for T=) 30
0 0
40
80
hNi Experimental data
Relax time of 950 ms !
80
N
Modified Yang-Yang profile : T= 140 nK Contribution of transverse excited states
40
0 100
z (pixels)
200
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Long lived states with strange profile
Experimental data
80
Best YY fit
N
Thomas−Fermi parabola Fit using YY of the wings
40
0 100 z (pixel)
200
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Satbility of the non-equilibrium state
T from fluctuation T from profile
T
120
70
20 450
1050 t(ms)
1350
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Outline 1
Experimental techniques and physical background Apparatus Regimes of 1D Bose gases Experimental tools
2
Hydrodynamic breathing mode Theory Measurement
3
Beyond self similar solution Observations Origin ?
4
frequency and lifetime
5
Long-lived out-of-equilibrium stationnary states
Experimental techniques and physical background Hydrodynamic breathing mode Beyond self similar solution frequency and lifetime Long-li
Conclusion and prospetcs Conclusion First observation of the breathing mode in momentum space A strange behavior of the momentum distribution associated with breathing mode at finite temperature Very long lived out of thermal equilibrium states Prospects Investigating the breathing mode frequency and lifetime across the quasi-condensation. Investigate the breathing mode frequency and lifetime across the dimensional crossover Relation of the long lived out of thermal equilibrium states with intergrability ? Change the 1D-ness (difficult) or add a lattice. Investigating effect of quenches of g. Going towards strongly interacting gases
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