spectroscopy and evaporative cooling in a radio-frequency ... · intro rf-dressed traps rf issues...
TRANSCRIPT
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Spectroscopy and evaporative cooling in a
radio-frequency dressed trap
Raghavan Kollengode Easwaran
Laboratoire de physique des lasers, Universite Paris Nord
PhD Defence
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
OUTLINE
1 Introduction
2 Ultracold atoms confined in a radiofrequency dressed magnetic trap
3 Influence of the radiofrequency source properties
4 Spectroscopy and evaporative cooling in a rf dressed trap
5 Conclusion and prospects
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
INTRODUCTION
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Introduction1995: Bose-Einstein condensation (BEC)
BEC is a phenomenon in which, below a critical temperatureTC , a macroscopic number of bosons occupy the lowest singleparticle state with the rest distributed over the excited states.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Introduction1995: Bose-Einstein condensation (BEC)
BEC is a phenomenon in which, below a critical temperatureTC , a macroscopic number of bosons occupy the lowest singleparticle state with the rest distributed over the excited states.
In recent years, the investigation of quantum gases in lowdimensional trapping geometries has significantly attractedthe attention of the physics research community.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
IntroductionA classical 2D gas
A classical 2D gas is realized if the temperature satisfies theinequality kBTC < kBT < ~ωz :
az is the harmonic oscillator length.
kBTC < ~ωz =⇒ N < 1.2ω2
z
ωxωy
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
IntroductionA quantum 2D gas.
A quasi 2D quantum gas is realized if one has both T < TC
and µ < ~ωz
quasi 2D quantum gas surrounded by a 3D thermal gas
µ < ~ωz =⇒ N < 0.4azω
2z
aωxωy,
where a is the scattering length.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Introduction
Aim: reaching quantum degeneracy in a quasi 2D geometry⇒ an anisotropic trap is needed
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Introduction
Aim: reaching quantum degeneracy in a quasi 2D geometry⇒ an anisotropic trap is needed
O. Zobay and B.M. Garraway, 2001: use radiofrequencyinduced adiabatic potentials to realize a quasi two dimensionaltrap.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Introduction
Aim: reaching quantum degeneracy in a quasi 2D geometry⇒ an anisotropic trap is needed
O. Zobay and B.M. Garraway, 2001: use radiofrequencyinduced adiabatic potentials to realize a quasi two dimensionaltrap.
Adiabatic potentials are suitable to realize unusual geometries:quasi-2D ‘bubble’ traps, double wells, ring traps (see OlivierMorizot’s thesis)...
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Introduction
Aim: reaching quantum degeneracy in a quasi 2D geometry⇒ an anisotropic trap is needed
O. Zobay and B.M. Garraway, 2001: use radiofrequencyinduced adiabatic potentials to realize a quasi two dimensionaltrap.
Adiabatic potentials are suitable to realize unusual geometries:quasi-2D ‘bubble’ traps, double wells, ring traps (see OlivierMorizot’s thesis)...
rf evaporative cooling is possible in such traps, the effect of asecond rf field was theoretically addressed in the group.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
ULTRACOLD ATOMS CONFINED IN A
RADIO-FREQUENCY DRESSED MAGNETIC TRAP
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Experimental set up
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Magnetic trap
-3,2 -2,4 -1,6 -0,8 0 0,8 1,6 2,4 3,2
x (mm)
-3,2
-2,4
-1,6
-0,8
0
0,8
1,6
2,4
3,2
z (m
m)
-3,2 -2,4 -1,6 -0,8 0 0,8 1,6 2,4 3,2
y (mm)
-3,2
-2,4
-1,6
-0,8
0
0,8
1,6
2,4
3,2
z (m
m)
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Magnetic trap
-3,2 -2,4 -1,6 -0,8 0 0,8 1,6 2,4 3,2
x (mm)
-3,2
-2,4
-1,6
-0,8
0
0,8
1,6
2,4
3,2
z (m
m)
-3,2 -2,4 -1,6 -0,8 0 0,8 1,6 2,4 3,2
y (mm)
-3,2
-2,4
-1,6
-0,8
0
0,8
1,6
2,4
3,2
z (m
m)
νx = 20.1 Hz, νy = νz = 225 Hz,
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Magnetic trap
-3,2 -2,4 -1,6 -0,8 0 0,8 1,6 2,4 3,2
x (mm)
-3,2
-2,4
-1,6
-0,8
0
0,8
1,6
2,4
3,2
z (m
m)
-3,2 -2,4 -1,6 -0,8 0 0,8 1,6 2,4 3,2
y (mm)
-3,2
-2,4
-1,6
-0,8
0
0,8
1,6
2,4
3,2
z (m
m)
νx = 20.1 Hz, νy = νz = 225 Hz,
At the trap center:Bmin = 1.8 G
b′ = 220 G/cm
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Radio frequency set up
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Radio frequency dressed magnetic trap – an introduction
Adiabatic potentials are created by a combination of a staticmagnetic field and an oscillating magnetic field (radiofrequencyfield).
-320 -240 -160 -80 0 80 160 240 320
-4
-2
0
2
4
6
8
Pot
entie
ls U
/h (
MH
z)
z (µm)
U2'
U1'
U0'
U-1'
U-2'
2
1
0
-1-2
|2′〉........| − 2′〉 are called ‘dressed states’.PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Hamiltonian of the system
We define as X , Y and Z the axes of a local frame attached to thestatic magnetic field, Z being the direction of dc magnetic field,chosen as quantization axis.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Hamiltonian of the system
We define as X , Y and Z the axes of a local frame attached to thestatic magnetic field, Z being the direction of dc magnetic field,chosen as quantization axis.Hamiltonian of this system:
HT (r, t) =gFµB
~F.[Bdc(r) + B1(r, t)].
HT (r, t) = ω0(r)FZ + 2Ω1(r)FX cos ω1t (1)
where Ω1 = gFµBB1/(2~) is the Rabi frequency of the rf field andω0(r) = gFµBB0(r)/~ is the local Larmor frequency.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Spin evolution
In the frame rotating at frequency ω1, the ‘Rotating waveapproximation’ leads to a time independent Hamiltonian:
HA(r) = −δ(r)FZ + Ω1FX
= Ω(r)(cos θFZ + sin θFX ) (2)
= Ω(r)Fθ.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Spin evolution
In the frame rotating at frequency ω1, the ‘Rotating waveapproximation’ leads to a time independent Hamiltonian:
HA(r) = −δ(r)FZ + Ω1FX
= Ω(r)(cos θFZ + sin θFX ) (2)
= Ω(r)Fθ.
We have defined Ω(r) =√
δ(r)2 + Ω21 and the flip angle θ by:
tan θ = −Ω1
δ(r)with θ ∈ [0, π]. (3)
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Spin Precession
ZωRF
Fθ
θ
In the presence of the rf field, the eigenstates of the spin are tiltedby an angle θ from the Z axis and precess around it at the angularfrequency ωRF of the rf wave.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Adiabaticity condition
The adiabaticity condition states that the variation rate θ of theeigenstates of the spin Hamiltonian HA must be very small ascompared to the level spacing Ω(r) in the dressed basis:
|θ| ≪√
δ2 + Ω21.
or equivalently
|Ω1δ − Ω1δ| ≪ (δ2 + Ω21)
3/2. (4)
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Adiabaticity condition
The adiabaticity condition states that the variation rate θ of theeigenstates of the spin Hamiltonian HA must be very small ascompared to the level spacing Ω(r) in the dressed basis:
|θ| ≪√
δ2 + Ω21.
or equivalently
|Ω1δ − Ω1δ| ≪ (δ2 + Ω21)
3/2. (4)
At resonance (around δ = 0), it is more restrictive: |δ| ≪ Ω21.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Adiabatic potentials
The total potential for the dressed state m′
F reads:
Um′
F(r) = m′
F ~
√
δ(r)2 + Ω21 + Mgz
= m′
F
√
(~ω1 − gFµBB(r))2 + ~2Ω21 + Mgz . (5)
iso-B surface B(r) = ~ω1gF µB
, i.e. Larmor frequency ω0(r) = ω1.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Adiabatic potentials
The total potential for the dressed state m′
F reads:
Um′
F(r) = m′
F ~
√
δ(r)2 + Ω21 + Mgz
= m′
F
√
(~ω1 − gFµBB(r))2 + ~2Ω21 + Mgz . (5)
iso-B surface B(r) = ~ω1gF µB
, i.e. Larmor frequency ω0(r) = ω1.
-1,5 -1,0 -0,5 0,0 0,5 1,0-0,30
-0,25
-0,20
-0,15
-0,10
-0,05
0,00
0,05
0,10
(a)
x (mm)
z (m
m)
zx
y
(b)
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Loading atoms into the radio-frequency trap
Trap loading stage: The energy diagram is plotted at constant rfcoupling strength Ω1
2π = 180 kHz, for different detunings ω1 − ωmin:
δ =−1.94 Ω1
0.83 Ω1
-100 -50 0 50 100
-1
0
1
a)
Pot
entie
ls U
/h (
MH
z)
z (µm)
-100 -50 0 50 100
-1
0
1
Pot
entie
ls U
/h (
MH
z)
c)
z (µm)
-100 -50 0 50 100
b)
z (µm)
-100 -50 0 50 100
d)
z (µm)
−0.27 Ω1
3.61 Ω1
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Typical loading ramp
0 20 40 60 80 100 120 0
1
2
3
4
5
6
7
8
9
ν RF
(M
Hz)
t (ms)
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
rf dressed trap oscillation frequencies
The oscillation frequency in the z direction can be inferredfrom the coupling strength Ω1 and the vertical gradient:
ω⊥ = α(z0)
√
2~
MΩ1≈ 2π × 0.5 kHz to 2π × 1.5 kHz (6)
where α(z0) = gFµBb′(z0)/~ is the local magnetic gradient inunits of frequency.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
rf dressed trap oscillation frequencies
The oscillation frequency in the z direction can be inferredfrom the coupling strength Ω1 and the vertical gradient:
ω⊥ = α(z0)
√
2~
MΩ1≈ 2π × 0.5 kHz to 2π × 1.5 kHz (6)
where α(z0) = gFµBb′(z0)/~ is the local magnetic gradient inunits of frequency.
The horizontal ‘pendulum’ frequencies ωh1 and ωh2
corresponding, respectively, to the y and x directions read:
ωh1 =
√
g
|z0|≈ 2π × 20 Hz to 2π × 40 Hz, (7)
ωh2 =
√
g
|z0|
ωx
ωz≈ 2π × 4 Hz. (8)
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Measurement of the transverse oscillation frequency ω⊥
The oscillation frequency in the transverse direction is measured bydisplacing suddenly the atomic cloud in the vertical direction andrecording the oscillation of its centre of mass velocity. This is doneby using a rf ramp with a frequency jump:
0 20 40 60 80 100 0
1
2
3
4
5
6
7
8
9
ν RF
(M
Hz)
t (ms)
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Measurement of the transverse oscillation frequency ω⊥
-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
ν z = 545 ± 3 Hz
(a)
Vertical oscillation at 400 mVpp and 5 MHz
Ver
tical
pos
ition
(m
m)
t (ms)
fit by damped sine (first points)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
ν z = 606.7 ± 3 Hz
(b)
Vertical oscillation at 200 mVpp and 5 MHz
Ver
tical
pos
ition
(m
m)
t (ms)
fit by damped sine
0 1 2 3 4 5 6 1.0
1.2
1.4
1.6
1.8
2.0
ν z = 684 ± 9.8 Hz
(c)
Vertical oscillation at 50 mVpp and 5 MHz
Ver
tical
pos
ition
(m
m)
t (ms)
fit up to 2 ms
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Is this a trap for a 2D BEC?
The typical values for the oscillation frequencies in the rfdressed trap are:ωz = 2π × 1 kHzωy = 2π × 20 Hzωx = 2π × 4 Hz.
The trap is very anisotropic
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Is this a trap for a 2D BEC?
The typical values for the oscillation frequencies in the rfdressed trap are:ωz = 2π × 1 kHzωy = 2π × 20 Hzωx = 2π × 4 Hz.
The trap is very anisotropic
2D criterion for a degenerate gas: N < 400 000
2D criterion for a thermal gas: N < 20000
Conclusion:Our typical BEC would be in the 2D regime in this trap............ if it is still degenerate after the loading procedure.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
rf Issues
Non adiabatic transfer of the atoms from the QUIC trap tothe rf dressed trap: the BEC is destroyed.
Heating could originate from excitations along the transversedirection, due to rf frequency noise, phase jumps...
A thorough study on the influence of different properties ofthe rf source on the rf dressed trap is necessary.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
INFLUENCE OF THE RADIO-FREQUENCY SOURCE
PROPERTIES ON THE RF BASED ATOM TRAPS
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Influence of the radio-frequency source propertiesSensitivity to rf defects
The quality of the rf source is very important in the rf based trapsas the cloud position is directly linked to the rf trapping frequency.Defects in the rf field inducing atom losses or heating can be:
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Influence of the radio-frequency source propertiesSensitivity to rf defects
The quality of the rf source is very important in the rf based trapsas the cloud position is directly linked to the rf trapping frequency.Defects in the rf field inducing atom losses or heating can be:
frequency jumps
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Influence of the radio-frequency source propertiesSensitivity to rf defects
The quality of the rf source is very important in the rf based trapsas the cloud position is directly linked to the rf trapping frequency.Defects in the rf field inducing atom losses or heating can be:
frequency jumps
phase jumps
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Influence of the radio-frequency source propertiesSensitivity to rf defects
The quality of the rf source is very important in the rf based trapsas the cloud position is directly linked to the rf trapping frequency.Defects in the rf field inducing atom losses or heating can be:
frequency jumps
phase jumps
frequency noise
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Influence of the radio-frequency source propertiesSensitivity to rf defects
The quality of the rf source is very important in the rf based trapsas the cloud position is directly linked to the rf trapping frequency.Defects in the rf field inducing atom losses or heating can be:
frequency jumps
phase jumps
frequency noise
amplitude noise
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Radio frequency issues
Frequency noise: dipolar excitation heating
Linear heating rate
E =1
4Mω4
⊥Sz(ν⊥) ∝ Srel(ν⊥)
For Bose-Einstein condensation experiments, a lineartemperature increase below 0.1 µK·s−1 is desirable. This ratecorresponds to Srel(ν⊥) = 118 dB·Hz−1.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Radio frequency issues
Frequency noise: dipolar excitation heating
Linear heating rate
E =1
4Mω4
⊥Sz(ν⊥) ∝ Srel(ν⊥)
For Bose-Einstein condensation experiments, a lineartemperature increase below 0.1 µK·s−1 is desirable. This ratecorresponds to Srel(ν⊥) = 118 dB·Hz−1.
Amplitude noise: parametric heating
Exponential heating at a rate
Γ = π2ν2⊥Sa(2ν⊥).
In order to perform experiments with the BEC within a timescale of a few seconds, Γ should not exceed 10−2 s−1. Thisrate corresponds to Sa < −90 dB·Hz−1.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Results
Phase jumps and Frequency jumps
-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180 0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
atom
num
ber
(10
6 )
phase jump at switching (degrees)
experiment theory
0 5000 10000 15000 20000 0,0
0,5
1,0
1,5
2,0
2,5
experiment theory
nb. o
f tra
nsfe
rred
ato
ms
(10
6 )
number of frequency points
0 5000 10000 15000 20000 0 2 4 6 8
10 12 14 16 18 20 22 24 26
tem
p. a
fter
1 s
trap
ping
( µ
K)
number of frequency points
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Results
Frequency noise Measurement of the linear heating rate intwo configurations:
1 Agilent 33250A driven by an external voltage T ≈ 5µK/s.2 Tabor WW1072 DDS T ≈ 80 nK/s.
0 5 10 15 20 25 30 35 40 45 50 0
2
4
6
8
10
Tabor WW1072
Tem
pera
ture
(µK
)
holding time in the trap (s)
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0
Agilent 33250A
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Results
Life time in the rf dressed trap using the Tabor DDS:
0 10 20 30 40 50 0
2
4
6
8
10
12
14
16
τ = 32 s
N (
10 5 )
trapping time (s)
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Results
Life time in the rf dressed trap using the Tabor DDS:
0 10 20 30 40 50 0
2
4
6
8
10
12
14
16
τ = 32 s
N (
10 5 )
trapping time (s)
The lifetime reaches 32 s in this situation – before with the Agilentit was 400 ms.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Conclusions
With the new Tabor synthesizer we could reduce the heatingrate and increase dramatically the life time in the rf dressedtrap.
The adiabaticity condition is still difficult to satisfy in the x
direction due to the low oscillation frequency in this direction(a few Hz).
This heating is difficult to avoid and we failed in transferringdirectly a BEC into the rf dressed trap.
The long life time and the low heating rate in the rf dressedtrap allow the implementation of rf evaporative cooling in therf dressed trap.
This can be done by the adjunction of a second rf source, asstudied theoretically in our group.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
SPECTROSCOPY AND EVAPORATIVE COOLING IN
A RF DRESSED TRAP
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Spectroscopy and evaporative coolingWhy performing spectroscopy?
1 In order to implement a rf evaporative cooling mechanism inthe rf dressed trap, we first performed some spectroscopicmeasurements.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Spectroscopy and evaporative coolingWhy performing spectroscopy?
1 In order to implement a rf evaporative cooling mechanism inthe rf dressed trap, we first performed some spectroscopicmeasurements.
2 A weak additional rf probe field is emitted by an additionalantenna. When the probe rf field is resonant with a transitionbetween dressed states, spin flips to untrapped states occur.This results in trap losses, which are the signature of theresonances.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Spectroscopy and evaporative coolingWhy performing spectroscopy?
1 In order to implement a rf evaporative cooling mechanism inthe rf dressed trap, we first performed some spectroscopicmeasurements.
2 A weak additional rf probe field is emitted by an additionalantenna. When the probe rf field is resonant with a transitionbetween dressed states, spin flips to untrapped states occur.This results in trap losses, which are the signature of theresonances.
3 Unlike for the case of a static magnetic trap, not only one butmultiple resonance frequencies are identified.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Spectroscopy and evaporative coolingWhy performing spectroscopy?
1 In order to implement a rf evaporative cooling mechanism inthe rf dressed trap, we first performed some spectroscopicmeasurements.
2 A weak additional rf probe field is emitted by an additionalantenna. When the probe rf field is resonant with a transitionbetween dressed states, spin flips to untrapped states occur.This results in trap losses, which are the signature of theresonances.
3 Unlike for the case of a static magnetic trap, not only one butmultiple resonance frequencies are identified.
4 These transitions are used to induce evaporative cooling in therf dressed trap.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Hamiltonian for the rf spectroscopy
In the presence of two rf sources, in the case where ω2 ≈ ω1
and the probe rf polarization ⊥ to Z direction, theHamiltonian is:
HT (r, t) = ω0(r)FZ + 2Ω1 cos ω1t FX + 2Ω2 cos ω2t FX .
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Hamiltonian for the rf spectroscopy
In the presence of two rf sources, in the case where ω2 ≈ ω1
and the probe rf polarization ⊥ to Z direction, theHamiltonian is:
HT (r, t) = ω0(r)FZ + 2Ω1 cos ω1t FX + 2Ω2 cos ω2t FX .
After a first rotating wave approximation, the Hamiltonianreads:
H(r, t) = HA(r) + Ω2[cos(∆t)FX + sin(∆t)FY ]
∆ = ω2 − ω1 and HA(r) = Ω(r)Fθ, |∆| ≪ ω1.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Hamiltonian for the rf spectroscopy
In the presence of two rf sources, in the case where ω2 ≈ ω1
and the probe rf polarization ⊥ to Z direction, theHamiltonian is:
HT (r, t) = ω0(r)FZ + 2Ω1 cos ω1t FX + 2Ω2 cos ω2t FX .
After a first rotating wave approximation, the Hamiltonianreads:
H(r, t) = HA(r) + Ω2[cos(∆t)FX + sin(∆t)FY ]
∆ = ω2 − ω1 and HA(r) = Ω(r)Fθ, |∆| ≪ ω1.
We introduce a rotation at frequency |∆| = ε∆ around Fθ
and apply a ‘second rotating wave approximation’:
H ′
A(r) = −(|∆|−Ω(r))Fθ+Ω2
2(1+ε cos θ(r))F⊥θ = Ω∆(r)Fθ∆
.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Spin evolution
Fθ∆= cos(θ∆)Fθ + sin(θ∆)F⊥θ
with tan(θ∆) = −Ω2[1 + ε cos θ(r)]
2(|∆| − Ω)for θ∆ ∈ [0, π].
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Resonant coupling for the rf probe
E∆ = m′′
F ~Ω∆(r), where
Ω∆(r) =
√
(|∆| − Ω(r))2 +Ω2
2
4(1 + ε cos θ(r))2.
m′′
F states are called ‘doubly dressed states’.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Resonant coupling for the rf probe
E∆ = m′′
F ~Ω∆(r), where
Ω∆(r) =
√
(|∆| − Ω(r))2 +Ω2
2
4(1 + ε cos θ(r))2.
m′′
F states are called ‘doubly dressed states’.
0,15 0,20 0,25 0,30 -1,0
-0,5
0,0
0,5
1,0
π - θ 0 π/2 θ
0
3 2 1
-2"
2''
Angle ( θ )
I.R O.R
E/h
(M
Hz)
z (mm)
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
The expected resonances
Two resonances around the dressing frequency ω2 ∼ ω1:
From the expression of the Hamiltonian, a resonance appearsfor |∆| = Ω(r) & Ω1, that is for ω2 & ω1 + Ω1 (∆ > 0) orω2 . ω1 − Ω1 (∆ < 0).
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
The expected resonances
Two resonances around the dressing frequency ω2 ∼ ω1:
From the expression of the Hamiltonian, a resonance appearsfor |∆| = Ω(r) & Ω1, that is for ω2 & ω1 + Ω1 (∆ > 0) orω2 . ω1 − Ω1 (∆ < 0).
One additional low frequency resonance ω2 ∼ Ω1:
For a π-polarized coupling i.e. if the probe rf field is orientedalong the direction of the static magnetic field, we can derivethe time independent Hamiltonian
H ′′
A = (Ω(r) − ω2)Fθ +Ω1Ω2
ω2Fθ⊥.
A resonance at ω2 = Ω(r) appears naturally, with a couplingstrength Ω1Ω2
ω2.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Interpretation of the resonances in terms of photon transfer
(a)
∆ > 0, ω2 ≃ ω1 + Ω(r)
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Interpretation of the resonances in terms of photon transfer
(b)
∆ < 0, ω2 ≃ ω1 − Ω(r)
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Interpretation of the resonances in terms of photon transfer
(c)
ω2 ≃ Ω1
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Spectroscopy of the rf-dressed QUIC trap
Time sequence:
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
ResultsResonances close to dressing rf frequency
η = 0.5-600 -400 -200 0 200 400 600 0
50
100
150
200
250
∆ν
∆ν = 130 kHz
Inte
grat
ed o
ptic
al d
ensi
ty
∆/2 π (kHz)
The rf attenuator is controlled from the computer using aparameter η between 0 and 1, setting the relative rf amplitude:Ω1 = ηΩmax .
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Results
The low frequency resonance:
0 50 100 150 200 250 300 350 400
150
200
250
300
350 η = 0.5 Probing rf amplitude = 0.1 Vpp
Inte
grat
ed o
ptic
al d
ensi
ty
ω 2 /2 π (kHz)
Direct probing of the resonance at ω2 ≈ 2π×50 kHz.
This is an efficient way to measure the rf coupling strength Ω1.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
ResultsVariation with dressing amplitude
(a)
(c)
-150 -100 -50 0 50 100 150 0
50
100
η = 0.3 Probing amplitude = 0.1Vpp
inte
grat
ed o
ptic
al d
ensi
ty
∆ /2 π (kHz)
-200 -100 0 100 200 0
100
200
η = 0.75 Probing amplitude = 0.1 Vpp
inte
grat
ed o
ptic
al d
ensi
ty
∆ /2 π (kHz)
(b)
-600 -400 -200 0 200 400 600 0
100
200
∆ 1 = 2 π x 8 MHz
η = 0.5 Probe rf amplitude = 0.2 Vpp
∆ /2 π (kHz)
inte
grat
ed o
ptic
al d
ensi
ty
(a): η = 0.3, ∆res = ±30 kHz(b): η = 0.5, ∆res = ±50 kHz(c): η = 0.75, ∆res = ±75 kHz
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
ResultsVariation with dressing frequency
(a)
(c)
-600 -400 -200 0 200 400 600 0
100
200
∆ 1 = 2 π x 8 MHz
η = 0.5 Probe rf amplitude = 0.2 Vpp
∆ /2 π (kHz)
inte
grat
ed o
ptic
al d
ensi
ty
-150 -100 -50 0 50 100 150 200 0
50
100
150
200
ω 1 = 2 π x3 MHz
η = 0.5 Probe rf amplitude = 0.2 V
PP
inte
grat
ed o
ptic
al d
ensi
ty
∆ /2 π (kHz)
(b)
(a):(b):(c):
-100 -50 0 50 100 0
50
100
150
200
ω 1 =2 π x 6 MHz
η =0.5 Probe rf amplitude = 0.2V
PP
inte
grat
ed o
ptic
al d
ensi
ty
∆ /2 π (kHz)
ω1 = 8 MHz, ∆res = ±50 kHzω1 = 6 MHz, ∆res = ±60 kHzω1 = 3 MHz, ∆res = ±80 kHz
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Evaporative cooling in the rf dressed trap
The rf which was used to probe the spectroscopy is now usedto perform evaporative cooling.
In order to remove dynamically the higher energy atoms alinear rf ramp is applied either around ω1 ± Ω1 or around Ω1.
Evaporative cooling is more efficient close to Ω1
This may be due to a more symmetric outcoupling whichinvolves a 2 photon process at both O.R. and I.R.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
ResultsResonances close to dressing rf frequency
RECALL
η = 0.5-600 -400 -200 0 200 400 600 0
50
100
150
200
250
∆ν
∆ν = 130 kHz
Inte
grat
ed o
ptic
al d
ensi
ty
∆/2 π (kHz)
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Results: Evaporative cooling in the rf dressed trap:
preliminary results
60 70 80 90 100 110 120 0
1
2
3
4
5 T
z , N
, PS
D
T z in µ K
PSD x 10 -4
N x 10 5
ν rf (kHz)
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Efficiency of evaporation
The evaporation is not efficient enough to reach quantumdegeneracy.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Efficiency of evaporation
The evaporation is not efficient enough to reach quantumdegeneracy.
The efficiency of evaporative cooling can be checked using aparameter ηevap ≡ ∆E
kBT.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Efficiency of evaporation
The evaporation is not efficient enough to reach quantumdegeneracy.
The efficiency of evaporative cooling can be checked using aparameter ηevap ≡ ∆E
kBT.
Efficient evaporation is possible when ηevap > 3. Runawayevaporation requires ηevap > 5.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Efficiency of evaporation
The evaporation is not efficient enough to reach quantumdegeneracy.
The efficiency of evaporative cooling can be checked using aparameter ηevap ≡ ∆E
kBT.
Efficient evaporation is possible when ηevap > 3. Runawayevaporation requires ηevap > 5.
ηevap between 7 and 10 is a good compromise.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Efficiency of evaporation
The evaporation is not efficient enough to reach quantumdegeneracy.
The efficiency of evaporative cooling can be checked using aparameter ηevap ≡ ∆E
kBT.
Efficient evaporation is possible when ηevap > 3. Runawayevaporation requires ηevap > 5.
ηevap between 7 and 10 is a good compromise.
In our case this parameter ηevap decreases during evaporationfrom 6 to 2.5.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Efficiency of evaporation
The evaporation is not efficient enough to reach quantumdegeneracy.
The efficiency of evaporative cooling can be checked using aparameter ηevap ≡ ∆E
kBT.
Efficient evaporation is possible when ηevap > 3. Runawayevaporation requires ηevap > 5.
ηevap between 7 and 10 is a good compromise.
In our case this parameter ηevap decreases during evaporationfrom 6 to 2.5.
The initial density of ≈ ×1011cm
−3 is too low, as well as the≈ 2 collisions per second, compared to the usual 500 or morecollisions per second.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
How to improve this situation?
This situation can be improved by increasing the oscillationfrequencies in the trap which will improve the initial density inthe trap and the collision rate.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
How to improve this situation?
This situation can be improved by increasing the oscillationfrequencies in the trap which will improve the initial density inthe trap and the collision rate.
As we have only a few Hz along the x direction it is difficult tohave an adiabatic transfer of the atoms from the QUIC trapto the dressed QUIC trap, and to cool the atoms efficiently.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
How to improve this situation?
This situation can be improved by increasing the oscillationfrequencies in the trap which will improve the initial density inthe trap and the collision rate.
As we have only a few Hz along the x direction it is difficult tohave an adiabatic transfer of the atoms from the QUIC trapto the dressed QUIC trap, and to cool the atoms efficiently.
One solution to improve the situation of the evaporativecooling would be to start from a quadrupolar trap instead ofQUIC trap.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
How to improve this situation?
This situation can be improved by increasing the oscillationfrequencies in the trap which will improve the initial density inthe trap and the collision rate.
As we have only a few Hz along the x direction it is difficult tohave an adiabatic transfer of the atoms from the QUIC trapto the dressed QUIC trap, and to cool the atoms efficiently.
One solution to improve the situation of the evaporativecooling would be to start from a quadrupolar trap instead ofQUIC trap.
The horizontal oscillation frequencies are indeed larger in thiscase.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Atoms in a dressed quadrupolar trap
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Atoms in a dressed quadrupolar trap
5 10 15 20 25 22
24
26
28
30
32
34
36
38
40
N G
*10
5
Power (W)
5 10 15 20 25
8
10
12
14
16
18
20
Life
tim
e (s
)
Power (W)
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Conclusions
Improvement of the life time of the atoms in the rf dressedtrap
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Conclusions
Improvement of the life time of the atoms in the rf dressedtrap
Spectroscopic studies allow a measurement of Ω1
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Conclusions
Improvement of the life time of the atoms in the rf dressedtrap
Spectroscopic studies allow a measurement of Ω1
Preliminary results of evaporative cooling in a rf dressed trap
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Conclusions
Improvement of the life time of the atoms in the rf dressedtrap
Spectroscopic studies allow a measurement of Ω1
Preliminary results of evaporative cooling in a rf dressed trap
Ultracold atoms confined in a dressed quadrupole trap
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Conclusions
Improvement of the life time of the atoms in the rf dressedtrap
Spectroscopic studies allow a measurement of Ω1
Preliminary results of evaporative cooling in a rf dressed trap
Ultracold atoms confined in a dressed quadrupole trap
To reach 2D degeneracy:1 Increase the trap oscillation frequencies
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Conclusions
Improvement of the life time of the atoms in the rf dressedtrap
Spectroscopic studies allow a measurement of Ω1
Preliminary results of evaporative cooling in a rf dressed trap
Ultracold atoms confined in a dressed quadrupole trap
To reach 2D degeneracy:1 Increase the trap oscillation frequencies2 Improve the initial density in the rf dressed trap
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Conclusions
Improvement of the life time of the atoms in the rf dressedtrap
Spectroscopic studies allow a measurement of Ω1
Preliminary results of evaporative cooling in a rf dressed trap
Ultracold atoms confined in a dressed quadrupole trap
To reach 2D degeneracy:1 Increase the trap oscillation frequencies2 Improve the initial density in the rf dressed trap3 Perform evaporative cooling inside the rf dressed trap
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Prospects
Search for quantum degeneracy in the rf dressed trap
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Prospects
Search for quantum degeneracy in the rf dressed trap
Implementation of the atomic ring trap
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Prospects
Search for quantum degeneracy in the rf dressed trap
Implementation of the atomic ring trap
Rotation of the superfluid condensate
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Prospects
Search for quantum degeneracy in the rf dressed trap
Implementation of the atomic ring trap
Rotation of the superfluid condensate
Observation of persistent currents
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
Prospects
Search for quantum degeneracy in the rf dressed trap
Implementation of the atomic ring trap
Rotation of the superfluid condensate
Observation of persistent currents
⇒ a renewed experiment is currently under construction!
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap
Intro rf-dressed traps rf issues Spectro/cooling Conclusion
The end
Thank you for your attention.
PhD Defence Spectroscopy and evaporative cooling in a rf-dressed trap