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European Laboratory for Non-Linear Spectroscopy Dipartimento di Fisica Università di Firenze Towards Quantum Magnetism with Ultracold Mixtures of Bosonic Atoms Towards Quantum Magnetism with Ultracold Mixtures of Bosonic Atoms Jacopo Catani ESF conference Obergurgl (AUT), June 2010 INO-CNR TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA A A A A AAA

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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 CataniOBERGURGLJune 2010 CANDIDATE TESTBENCH FOR QUANTUM SPIN MODELS

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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=sE rec Jacopo CataniOBERGURGLJune 2010

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Mixtures in Optical Lattices MIXTURES (spin or species): Small tunneling still localizes atoms Ground state has a large energetic degeneracy for exactly J= 0. Atoms in optical lattices For small tunneling atoms localize Superfluid-Mott Insulator transition E. Altman et al., New J. Phys. 2003 A.Isacsson et al., PRB 2005 G. 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 CataniOBERGURGLJune 2010

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2 Species Bose-Hubbard model Starting point: 2 bosons, all atoms in the 1 st band, mathematical description given by an extension of the Bose-Hubbard model Small tunnelings, t a,b << V a,b perturbation theory (2 nd order) can be employed A.B. Kuklov and B. V. Svistunov B.PRL 90, 100401 (2003) MAPPING onto an effective spin Hamiltonian Jacopo CataniOBERGURGLJune 2010

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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 species In principle feasible the SIMULATION of QUANTUM MAGNETIC SYSTEMS through a Bose Mixture in OL Jacopo CataniOBERGURGLJune 2010

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In the language of atoms: - AFM (Néel) phase ! Checkerboard (1 atom per species in alternating sites) - XY Ferromagnet ! Supercounterfluid ( h a j y b j i 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 CataniOBERGURGLJune 2010

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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 CataniOBERGURGLJune 2010 Increasing the lattice height TRAJECTORIES depend on Tunneling Ratio t a /t b and Interspecies Interactions U (scattering length)

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Phase diagram in the QMC approach Phase diagram with Quantum MonteCarlo approach (2D, Hard core bosons V a,b = 1 ) [S. G. Soyler et al., New J. Phys. 11 (2009)] Jacopo CataniOBERGURGLJune 2010

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Trajectories in the Phase Diagram Knobs to be turned with a heteronuclear ( 87 Rb- 41 K ) 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 (s Rb =2.4 s K ) (s Rb = s K ) Lattice wavelength and intensity Jacopo CataniOBERGURGLJune 2010

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Trajectories in the Phase Diagram Reasonable calculated (QMC) parameters for 87 Rb- 41 K exploiting tunability of interaction B. Capogrosso-Sansone et al., Phys. Rev. A 81, 053622 (2010) Jacopo CataniOBERGURGLJune 2010 Range of parameters is OK!

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Tuning interspecies interactions For 87 Rb- 41 K, 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 CataniOBERGURGLJune 2010 A. Simoni et al., PRA 77, 052705 (2008).

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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 2D AFM-Checkerboard to normal XY-Ferro to normal Jacopo CataniOBERGURGLJune 2010

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Effects of Temperature on Phase Diagram …everything seems to be ready for Quantum Magnetism… ….but HOW COLD should the mixture be? Bothshould 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 CataniOBERGURGLJune 2010

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

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Entropy exchange in a Bose-Bose Mixture KEY IDEA: start from an ultracold (degenerate) 2 species mixture use 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 N Rb >> N K 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 CataniOBERGURGLJune 2010

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Entropy exchange in a Bose-Bose Mixture PROCEDUREwe use a selective compression (SSDP) of K to reduce its entropy by transferring it to Rb M-trap + SSDP K 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 N Rb ~ 5 N K 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 CataniOBERGURGLJune 2010

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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 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 f c (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). 10 6 Rb atoms 10 5 K atoms T=400 nK Jacopo CataniOBERGURGLJune 2010

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Entropy exchange in a Bose-Bose Mixture Is this entropy exchange reversible? For spin mixtures or single species in dimple traps D. 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 CataniOBERGURGLJune 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) N Rb is decreasing (~ 50%), due to RF shield imposed to compensate for m-trap heating rate

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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 CataniOBERGURGLJune 2010

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…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 CataniOBERGURGLJune 2010

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

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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 ' l osc in the lattice dir. - use the Feshbach resonance to vary interspecies scattering length If k B T<< ~ ! K (lattice levels spacing) the K sample can energetically be considered 1D Scattering effectively occurs among particles living in different dimensions Jacopo CataniOBERGURGLJune 2010

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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=V lat / E rec B field Lattice strength We detect enhancement of losses in N at due to the increase of 2 and 3body recombination rate Hold time: 65-100 ms Jacopo CataniOBERGURGLJune 2010

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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 CataniOBERGURGLJune 2010

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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 confinement P. 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 K K SERIES of resonances G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010) Jacopo CataniOBERGURGLJune 2010

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Mix-dimensional scattering with a Bose mixture Dashed lines are predictions of this simple model ONLY QUALITATIVE AGREEMENT G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010) Jacopo CataniOBERGURGLJune 2010

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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 r 0 we employ previous results on molecular K-RB association@LENS Measured values for E b 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) r 0 = 168.4 a 0 G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010) Jacopo CataniOBERGURGLJune 2010 The model parametrizes the scattering amplitude through an effective scattering length a eff

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Effective range correction to a scattering model RESULTS of model: 1.Knowledge of the effective Mix-Dim scattering length in the 0-100G range 2.Prediction for the trend in the width of the resonances 3.Resonances position still coincides with the harmonic oscillator predictions 4.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 CataniOBERGURGLJune 2010 S=20

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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 CataniOBERGURGLJune 2010

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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 CataniOBERGURGLJune 2010 NICE AGREEMENT with data

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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 CataniOBERGURGLJune 2010 NICE AGREEMENT with data

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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 1 st band is of the order of = 0.65q B for T=300 nK. G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010) Jacopo CataniOBERGURGLJune 2010

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Conclusions and Perspectives QUANTUM MAGNETIC PHASES could be investigated through atomic mixtures Heteronuclear 87 Rb- 41 K 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 CataniOBERGURGLJune 2010

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BEC 3 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

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Thank you Jacopo Catani ESF conference Quantum engineering of states and devices Obergurgl, June 2010 INO-CNR under EuroCORES (EuroQUAM-DQS) EU under NAME-QUAM and STREP-CHIMONO

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