European Laboratory for Non-Linear Spectroscopy Dipartimento di Fisica Università di Firenze...

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

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

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

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

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

2 Species Bose-Hubbard model – Mapping onto the Spin Hamiltonian

• Mapping of creation/annihilation operators onto spin operators


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

• 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)


PRL 90, 100401 (2003)

Jacopo Catani

OBERGURGL June 2010

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)

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

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

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!

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).

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

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

Entropy exchange in an ultracold atomic mixture(collaboration with S. Stringari, University of Trento)

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


• 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


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


• 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


106 Rb atoms105 K atomsT=400 nK

Jacopo Catani

OBERGURGL June 2010


• 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


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

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

…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

Scattering in Mixed Dimensions with ultracold Bose Mixtures(in collaboration with Yusuke Nishida, MIT)

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

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

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

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


Jacopo Catani

OBERGURGL June 2010

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

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


Jacopo Catani

OBERGURGL June 2010

The model parametrizes the scattering amplitudethrough an effective scattering length aeff

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


Jacopo Catani

OBERGURGL June 2010

S=20

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.


Jacopo Catani

OBERGURGL June 2010

Results of the improved (lattice) model

Shaded areas are predictions of this improved model


Jacopo Catani

OBERGURGL June 2010

NICE AGREEMENT with data

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


Jacopo Catani

OBERGURGL June 2010

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

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

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

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