European Laboratory for Non-Linear Spectroscopy
-
Upload
zahir-holmes -
Category
Documents
-
view
30 -
download
1
description
Transcript of European Laboratory for Non-Linear Spectroscopy
![Page 1: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/1.jpg)
European Laboratory European Laboratory for Non-Linear for Non-Linear SpectroscopySpectroscopy
Dipartimento di Dipartimento di Fisica Università di Fisica Università di
FirenzeFirenze
Towards Towards Quantum Magnetism with Quantum Magnetism with
Ultracold Mixtures of Bosonic AtomsUltracold Mixtures of Bosonic Atoms
Towards Towards Quantum Magnetism with Quantum Magnetism with
Ultracold Mixtures of Bosonic AtomsUltracold Mixtures of Bosonic Atoms
Jacopo CataniJacopo CataniESF conference
Obergurgl (AUT), June 2010
INO-CNRINO-CNR
![Page 2: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/2.jpg)
Principal Motivations: why ultracold MIXTURES?
• Optical Lattices: direct mapping on the spin hamiltonian has been shown
-> Quantum Magnetic Phases could be explored- antiferromagnetic (Néel) state, - xy-ferromagnetic state - ….
• Possibility to control a wide number of experimental parameters:
- dipolar and magnetic potentials- strength of interactions can be adjusted by magnetic field
(Feshbach)
• Entropy control of species A exploiting species B: good to achieve low entropy and temperature regimes for quantum phases in OL
Jacopo Catani
OBERGURGL June 2010
CANDIDATE TESTBENCH FOR QUANTUM SPIN MODELS
![Page 3: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/3.jpg)
How an optical lattice is realized?
Exploit:1.the dipolar interaction with EM field: depending on detuning (red or blue) atoms “go” or “escape” from light intensity maxima
2.the coherence of laser light: overlapping two beams, one has a periodic pattern of maxima and minima
Periodicity: /2
Light intensity determines lattice strength: U=sErec
Jacopo Catani
OBERGURGL June 2010
![Page 4: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/4.jpg)
Mixtures in Optical Lattices
• MIXTURES (spin or species): Small tunneling still localizes atomsGround state has a large energetic degeneracy for exactly J=0.
• Atoms in optical lattices For small tunneling atoms localizeSuperfluid-Mott Insulator transition
E. Altman et al., New J. Phys. 2003A.Isacsson et al., PRB 2005G. Soyler et al., NJP 2009
Second order tunneling could induce ORDER !New exotic ordered phases are in principle engineerable (XY-ferro, Checkerboard…) when interactions and tunneling are adjusted
Jacopo Catani
OBERGURGL June 2010
![Page 5: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/5.jpg)
2 Species Bose-Hubbard model
• Starting point: 2 bosons, all atoms in the 1st band, mathematical description given by an extension of the Bose-Hubbard model
• Small tunnelings, ta,b << Va,b perturbation theory (2nd order) can be employed
A. B. Kuklov and B. V. Svistunov
B. PRL 90, 100401 (2003)• MAPPING onto an effective spin Hamiltonian
Jacopo Catani
OBERGURGL June 2010
![Page 6: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/6.jpg)
2 Species Bose-Hubbard model – Mapping onto the Spin Hamiltonian
• Mapping of creation/annihilation operators onto spin operators
A. B. Kuklov and B. V. Svistunov
PRL 90, 100401 (2003)
whith
Effective XXZ hamiltonian, for a balanced mixture with filling factor equal to S per speciesIn principle feasible the SIMULATION of QUANTUM MAGNETIC SYSTEMS
through a Bose Mixture in OL
Jacopo Catani
OBERGURGL June 2010
![Page 7: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/7.jpg)
• In the language of atoms:
- AFM (Néel) phase ! Checkerboard (1 atom per species in alternating sites) - XY Ferromagnet ! Supercounterfluid (h aj
y bji 0, a paired order
parameter exists)
Qualitative phase diagram
(Simplest case: ½ filling per species, i.e., total filling = 1)
A. B. Kuklov and B. V. Svistunov
PRL 90, 100401 (2003)
Jacopo Catani
OBERGURGL June 2010
![Page 8: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/8.jpg)
Phase diagram in the mean-field approach
•Phase diagram with mean-field approach [E. Altman et al., New J. Phys. 5, 113 (2003)]
Similar results: A. Isacsson et al., Phys. Rev. B 72, 184507 (2005)A. Hubener et al., Phys. Rev. B 80, 245109 (2009))
Jacopo Catani
OBERGURGL June 2010
Increasing the lattice height
TRAJECTORIES depend on Tunneling Ratio ta/tb and Interspecies Interactions U (scattering length)
![Page 9: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/9.jpg)
Phase diagram in the QMC approach
• Phase diagram with Quantum MonteCarlo approach
(2D , Hard core bosons Va,b=1)
[S. G. Soyler et al., New J. Phys. 11 (2009)]
Jacopo Catani
OBERGURGL June 2010
![Page 10: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/10.jpg)
Trajectories in the Phase Diagram
• “Knobs to be turned” with a heteronuclear (87Rb-41K ) mixture: 1.Lattice Wavelength (relative tunneling for the 2 species)
2.Lattice Intensity (adjust the absolute value of tunneling for both species, not independently)
3. Interspecies interactions through interspecies Feshbach Resonances
Good for AFM (CB) phases
Good for XY-Ferro (SCF) phases
(sRb=2.4 sK)
(sRb= sK)
Lattice wavelength and intensity
Jacopo Catani
OBERGURGL June 2010
![Page 11: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/11.jpg)
Trajectories in the Phase Diagram
• Reasonable calculated (QMC) parameters for 87Rb-41K exploiting tunability of interaction B. Capogrosso-Sansone et al., Phys. Rev. A 81,
053622 (2010)
Jacopo Catani
OBERGURGL June 2010
Range of parameters is
OK!
![Page 12: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/12.jpg)
Tuning interspecies interactions
• For 87Rb-41K, nice interspecies Feshbach resonances are predicted below 100 G
G. Thalhammer, G. Barontini, L. De Sarlo, J. C., F. Minardi, and M. Inguscio, PRL 100, 210402 (2008)
Jacopo Catani
OBERGURGL June 2010
A. Simoni et al., PRA 77, 052705 (2008).
![Page 13: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/13.jpg)
Effects of Temperature on Phase Diagram
…everything seems to be ready for Quantum Magnetism…
….but HOW COLD should the mixture be?
The finite temperature raises the total ENTROPY of the system, leading to the melting of the phases for a critical value Sc
Finite T QMC predictions for Sc
B. Capogrosso-Sansone et al., Phys. Rev. A 81, 053622 (2010)
3D 3D2D 2D
AFM-Checkerboard
to normal
XY-Ferro to normal
Jacopo Catani
OBERGURGL June 2010
![Page 14: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/14.jpg)
Effects of Temperature on Phase Diagram
…everything seems to be ready for Quantum Magnetism…
….but HOW COLD should the mixture be?
Both should be as low as possible
-Initial ENTROPY/TEMPERATURE-Heating rate during lattice phase
A method to control the ENTROPY of the system at ultralow temperatures
would be desirable in order to ease the realization of ordered phases!
Jacopo Catani
OBERGURGL June 2010
![Page 15: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/15.jpg)
Entropy exchange in an ultracold atomic mixture(collaboration with S. Stringari, University of Trento)
![Page 16: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/16.jpg)
Entropy exchange in a Bose-Bose Mixture
• KEY IDEA: start from an ultracold (degenerate) 2 species mixtureuse a species-selective dipole potential (SSDP) that acts
only on a certain species (K), whereas the other (Rb) is “transparent”
and perform a COMPRESSION.
SINGLE GAS: a (ideal) compression is ISOENTROPIC, In BEC terms: density of energy states decreases
and T increases, T/Tc is not altered
TWO GASES: a compression acting on a single species (SSDP) is still ISOENTROPIC for K+Rb, decreases as before but T increases less.
T/Tc is reduced for the compressed species, entropy is transferred from K to Rb!
In the limit NRb >> NK Rb is a thermal bath, negligible T increase, ISOTHERMAL transformation !
J. C., G. Barontini, G. Lamporesi, F. Rabatti, G. Thalhammer, F. Minardi, S. Stringari, and M. Inguscio, Phys. Rev. Lett. 103, 140401 (2009).
Jacopo Catani
OBERGURGL June 2010
![Page 17: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/17.jpg)
Entropy exchange in a Bose-Bose Mixture
• PROCEDURE we use a selective compression (SSDP) of K to reduce its entropy by transferring it to Rb
M-trap
M-trap+
SSDPK Rb
M-trap freq. for K: 2π × (24, 297,
297)Hz
J. C., G. Barontini, G. Lamporesi, F. Rabatti, G. Thalhammer, F. Minardi, S. Stringari, and M. Inguscio, Phys. Rev. Lett. 103, 140401 (2009).
K
Rb
• Sample is prepared after evaporation and sympathetic cooling in m-trap (400 nK)
• T is right above critical temperature for BEC
• NRb ~ 5 NK
• SSDP beam power is raised to a variable value in 200 ms with =45 ms (adiabaticity is fulfilled)
• Max. compression ratio on K frequencies: ~2
Jacopo Catani
OBERGURGL June 2010
![Page 18: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/18.jpg)
Entropy exchange in a Bose-Bose Mixture
• Selective compression can induce BEC transition on K, and K entropy is transferred to Rb cloud
NO BEC if Rb is absent
[1] S. Giorgini, L. P. Pitaevskii, and S. Stringari, J. Low. Temp. Phys. 109, 309 (1997).[2] L. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Oxford University Press, 2003).[3] M. Naraschewski and D. M. Stamper-Kurn, Phys. Rev. A 58, 2423 (1998).
K
Rb
K
Rb
• Exact quantitative analisys is not possible for interacting gases [1], we start from ideal trapped case [2] to numerically estimate final T after compression using entropy conservation.• We include the effect of interactions in the estimated
fc(T)
[3]
• SELECTIVE COMPRESSION of K
J. C., G. Barontini, G. Lamporesi, F. Rabatti, G. Thalhammer, F. Minardi, S. Stringari, and M. Inguscio, Phys. Rev. Lett. 103, 140401 (2009).
106 Rb atoms105 K atomsT=400 nK
Jacopo Catani
OBERGURGL June 2010
![Page 19: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/19.jpg)
Entropy exchange in a Bose-Bose Mixture
• Is this entropy exchange reversible?For spin mixtures or single species in dimple trapsD. M. Stamper-Kurn et al., PRL 81, 2194 (1998).M. Erhard et al, PRA 70, 031602 (2004). We perform several cycles of
compression/decompression with the SSDP technique (128->216 Hz)
• We observe more than 5 BEC revivals
J. C., G. Barontini, G. Lamporesi, F. Rabatti, G. Thalhammer, F. Minardi, S. Stringari, and M. Inguscio, Phys. Rev. Lett. 103, 140401 (2009).
Jacopo Catani
OBERGURGL June 2010
• Non perfect efficiency can be due to:
1) modest temperature increase of the sample in the process (more than 2 s in trap, 400 -> 500 nK)
2) NRb is decreasing (~ 50%), due to RF shield imposed to compensate for m-trap heating rate
![Page 20: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/20.jpg)
The Species Selective Dipole Potential (SSDP) beam
• SSDP: exploits “naturally” the differences in the fine structure of 2 species
• Wavelength is tuned between D1 and D2 lines Blue and red effects cancel out (for Rb)
KRb
D1 794.8 nm
D2 780.0 nm
• SSDP wawelenght: 789.85 nm
• Max. Beam Power: 32 mW Beam waist: 55 m Beam orthogonal to the weak M-trap axis.
766.5 nm
769.9 nm
! HEATING !
The tighter the manifold, the higher the scattering rate
Cs should be a better “reservoir”
D1-D2= 42 nm !Jacopo Catani
OBERGURGL June 2010
![Page 21: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/21.jpg)
…some “non-magnetic” applications for the SSD potential
• SSDP: gives the possibility to create a wide set of “exotic” geometries
How do particles living in different spatial dimensionality interact?
Different realms of Physics use this concept
eg BRANE THEORY: particles confined in 3 spatial dimensions interact with 3+N dimensions gravitons
SSDP could be employed to confine K in lower dimensions, whereas Rb remains 3D!
Jacopo Catani
OBERGURGL June 2010
![Page 22: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/22.jpg)
Scattering in Mixed Dimensions with ultracold Bose Mixtures(in collaboration with Yusuke Nishida, MIT)
![Page 23: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/23.jpg)
Mix-dimensional scattering with a Bose mixture• IDEA: -employ the species-selective dipole potential (SSDP) in order to confine only the K component in lower dimensions, leaving Rb in 3D
- use a 1D LATTICE configuration: size of K cloud ' losc in the lattice dir.
- use the Feshbach resonance to vary interspecies scattering length
If kBT<< ~!K (lattice levels spacing) the K sample can energetically be considered 1D
Scattering effectively occurs among particles living in different dimensionsJacopo
CataniOBERGURGL June 2010
![Page 24: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/24.jpg)
Mix-dimensional scattering with a Bose mixture• PROCEDURE: -start from an ultracold mixture at 300 nK
-adiabatically ramp the lattice heigth (50 ms exp. ramp, =10 ms)
-we scan the magnetic field across the low field 3D Feshbach resonance
for different lattice strengths s=Vlat / Erec
B field
Lattice strength
We detect enhancement of losses in Nat due to the increase of 2 and 3body recombination rate
Hold time: 65-100 msJacopo Catani
OBERGURGL June 2010
![Page 25: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/25.jpg)
Mix-dimensional scattering with a Bose mixture• OBSERVATIONS: diagram presents a richer spectrum of inelastic losses than 3D!
G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010)
Jacopo Catani
OBERGURGL June 2010
![Page 26: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/26.jpg)
Mix-dimensional scattering with a Bose mixture• QUALITATIVE - energy of incoming K atom is raised by selective confinement. EXPLANATION: - energy of KRb molecule is raised differently (selective confinement)
- no decoupling of CM and internal motion -> CM energy can change
- Each time the molec. Level crosses the treshold -> RESONANCE
M. Olshanii, PRL 81, 938 (1998) for “symmetric” confinementP. Massignan and Y. Castin, PRA 74, 013616 (2006) for “asymmetric” confinement
1- Channel coupling is neglected for n’>0
2- Internal state of molecule does not change
KK
SERIES of resonances
G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010)
Jacopo Catani
OBERGURGL June 2010
![Page 27: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/27.jpg)
Mix-dimensional scattering with a Bose mixture
Dashed lines are predictions of this simple model
ONLY QUALITATIVE AGREEMENTG. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202
(2010)Jacopo Catani
OBERGURGL June 2010
![Page 28: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/28.jpg)
Effective range correction to a scattering model
These predictions are confirmed by a more formal scattering model, derived from previous works, improved by an effective range correction.
P. Massignan and Y. Castin, PRA 74, 013616 (2006)Y. Nishida and S. Tan, PRL 101, 170401 (2008).Y. Nishida and S. Tan, PRA 79, 060701R (2009)
In order to retrieve r0 we employ previous resultson molecular K-RB association@LENS
Measured values for Eb are fitted by the formula
Obtaining the effective range value:
D. S. Petrov, Phys. Rev. Lett. 93, 143201 (2004).
C. Weber et al., Phys. Rev. A 78, 061601(R) (2008)G. Thalhammer et al., New J. Phys. 11, 055044 (2009)
r0 = 168.4 a0r0 = 168.4 a0
G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010)
Jacopo Catani
OBERGURGL June 2010
The model parametrizes the scattering amplitudethrough an effective scattering length aeff
![Page 29: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/29.jpg)
Effective range correction to a scattering model
RESULTS of model:1. Knowledge of the effective Mix-Dim scattering length in the 0-100G
range2. Prediction for the trend in the width of the resonances3. Resonances position still coincides with the harmonic
oscillator predictions4. Selection rules due to coupling term in the Hamiltonian only
allow even resonances
G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010)
Jacopo Catani
OBERGURGL June 2010
S=20
![Page 30: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/30.jpg)
Effects of the band structure on the resonances
• In order to achieve a better agreement, we take in to account the BAND STRUCTURE induced by the lattice On the experimental timescales (' 100 ms) the wells are not perfectly isolated.
G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010)
Jacopo Catani
OBERGURGL June 2010
![Page 31: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/31.jpg)
Results of the improved (lattice) model
Shaded areas are predictions of this improved model
G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010)
Jacopo Catani
OBERGURGL June 2010
NICE AGREEMENT with data
![Page 32: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/32.jpg)
Results of the improved (lattice) model
Shaded areas are predictions of this improved model
G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010)
Jacopo Catani
OBERGURGL June 2010
NICE AGREEMENT with data
![Page 33: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/33.jpg)
Results of the improved (lattice) model
Why the odd resonances ?•The selection rules are strictly valid only for q=0 (Bloch waves are eigenst. of Parity). • The momentum spread in 1st band is of the order of = 0.65qB
for T=300 nK.
pkB Tm=¹h
G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010)
Jacopo Catani
OBERGURGL June 2010
![Page 34: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/34.jpg)
Conclusions and Perspectives
• QUANTUM MAGNETIC PHASES could be investigated through atomic mixtures
• Heteronuclear 87Rb-41K Bose Mixture is a good candidate for QUANTUM MAGNETISM
• Entropy management in the quantum regime using a SSDP potential Entropy exchange among the two
constituents of the mixture reduces entropy of K
• Realization of a mix-dimensional configuration-New scattering resonances-Simple explanation has a fair agreement- Band structure has to be taken into account
Jacopo Catani
OBERGURGL June 2010
![Page 35: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/35.jpg)
BEC3 team , LENS, Florence
M. Inguscio, F. Minardi
Postdocs: J. Catani, G. Lamporesi,
PhD students: G. Barontini (now in Kaiserslautern)
PhD positions and Diploma theses
available!
www.quantumgases.lens.unifi.it
![Page 36: European Laboratory for Non-Linear Spectroscopy](https://reader030.fdocuments.in/reader030/viewer/2022032605/56812b68550346895d8f8acf/html5/thumbnails/36.jpg)
Thank you
Jacopo Catani
ESF conference “Quantum engineering of states and devices”
Obergurgl, June 2010
INO-CNR underEuroCORES
(EuroQUAM-DQS)
EU underNAME-QUAM
andSTREP-CHIMONO