European Laboratory for Non-Linear Spectroscopy

1. INO-CNR Towards Quantum Magnetism with Ultracold Mixtures of Bosonic Atoms Dipartimento di Fisica Università di Firenze Jacopo Catani ESF conference Obergurgl (AUT), June 2010 EuropeanLaboratoryforNon-LinearSpectroscopy TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAA

2. Principal Motivations: why ultracold MIXTURES? CANDIDATE TESTBENCH FOR QUANTUM SPIN MODELS • Possibility to control a wide number of experimental parameters: • - dipolar and magnetic potentials • - strength of interactions can be adjusted by magnetic field (Feshbach) • Optical Lattices: direct mapping on the spin hamiltonian has been shown • -> Quantum Magnetic Phases could be explored • - antiferromagnetic (Néel) state, • - xy-ferromagnetic state • - …. • 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

3. How an optical lattice is realized? • Exploit: • the dipolarinteractionwith EM field: depending on detuning (red or blue) atoms “go” or “escape” fromlight intensitymaxima • the coherenceof laser light: overlappingtwobeams, onehas a periodic pattern ofmaxima and minima Periodicity: l/2 Light intensity determines lattice strength: U=sErec Jacopo Catani OBERGURGL June 2010

4. Mixtures in Optical Lattices • Atoms in optical lattices • For small tunneling atoms localize • Superfluid-Mott Insulator transition • MIXTURES (spin or species): • Small tunneling still localizes atoms • Ground state has a large energetic degeneracy • for exactlyJ=0. Second order tunneling could induce ORDER ! New exotic ordered phases are in principle engineerable (XY-ferro, Checkerboard…) when interactions and tunneling are adjusted • E. Altman et al., New J. Phys. 2003 • Isacsson et al., PRB 2005 • G. Soyler et al., NJP 2009 Jacopo Catani OBERGURGL June 2010

5. 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,bperturbation theory (2nd order) can be employed • B. Kuklov and B. V. Svistunov • PRL 90, 100401 (2003) • MAPPING onto an effective spin Hamiltonian Jacopo Catani OBERGURGL June 2010

6. 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 Sper species In principle feasible the SIMULATIONof QUANTUM MAGNETIC SYSTEMS through a Bose Mixture in OL Jacopo Catani OBERGURGL June 2010

7. Qualitative phase diagram • In the language of atoms: • - AFM (Néel) phase !Checkerboard(1 atom per species in alternating sites) • - XY Ferromagnet ! Supercounterfluid (hajybji0, a paired order parameter exists) (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

8. Phase diagram in the mean-field approach • Phase diagram with mean-field approach [E. Altman et al., New J. Phys. 5, 113 (2003)] TRAJECTORIES depend on Tunneling Ratio ta/tband Interspecies Interactions U(scattering length) Increasing the lattice height 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

9. 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

10. Trajectories in the Phase Diagram • “Knobs to be turned” with a heteronuclear (87Rb-41K ) mixture: • Lattice Wavelength (relative tunneling for the 2 species) • Lattice Intensity (adjust the absolute value of tunneling for both species, not independently) • Interspecies interactions through interspecies Feshbach Resonances Lattice wavelength and intensity (sRb= sK) (sRb=2.4 sK) Good for XY-Ferro (SCF) phases Good for AFM (CB) phases Jacopo Catani OBERGURGL June 2010

11. 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) Range of parameters is OK! Jacopo Catani OBERGURGL June 2010

12. Tuning interspecies interactions • For87Rb-41K, nice interspecies Feshbach resonances are predicted below 100 G A. Simoni et al., PRA 77, 052705(2008). G. Thalhammer, G. Barontini, L. De Sarlo, J. C., F. Minardi, and M. Inguscio, PRL 100, 210402 (2008) Jacopo Catani OBERGURGL June 2010

13. 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 B. Capogrosso-Sansone et al., Phys. Rev. A 81, 053622 (2010) Finite T QMC predictions for Sc 2D 3D 2D 3D AFM-Checkerboard to normal XY-Ferro to normal Jacopo Catani OBERGURGL June 2010

14. Effects of Temperature on Phase Diagram …everything seems to be ready for Quantum Magnetism… ….but HOW COLD should the mixture be? • Initial ENTROPY/TEMPERATURE • Heating rate during lattice phase Both should be as low as possible 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

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

16. Entropy exchange in a Bose-Bose Mixture • KEY IDEA:start from an ultracold (degenerate) 2 species mixture • use aspecies-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 r 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, r decreases as before but T increases less. T/Tc is reduced for the compressed species, entropy is transferredfrom K to Rb! In the limit NRb >> NKRb 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

17. 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 freq. for K: 2π × (24, 297, 297)Hz M-trap + SSDP Rb K Rb M-trap • 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 t=45 ms (adiabaticity is fulfilled) • Max. compression ratio on K frequencies: ~2 K 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

18. Entropy exchange in a Bose-Bose Mixture • SELECTIVE COMPRESSION of K 106 Rb atoms 105 K atoms T=400 nK Rb K Rb K • Selective compression can induce BEC transition on K, and K entropy is transferred to Rb cloud • NO BEC if Rb is absent • 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. [3] • We include the effect of interactions in the estimated fc(T) [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). 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

19. Entropy exchange in a Bose-Bose Mixture 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). • Is this entropy exchange reversible? • We perform several cycles of • compression/decompression with • the SSDP technique (128->216 Hz) • We observe more than 5 BEC revivals • Non perfect efficiency can be due to: • 1) modest temperatureincrease 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 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

20. 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) Rb K D1 794.8 nm • SSDP wawelenght: 789.85 nm D2780.0 nm 769.9 nm • Max. Beam Power: 32 mW • Beam waist: 55 mm • Beam orthogonal to the weak M-trap axis. 766.5 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

21. …some “non-magnetic” applications for the SSD potential • SSDP: gives the possibility to create a wide set of “exotic” geometries SSDP could be employed to confine K in lower dimensions, whereas Rb remains 3D! 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 Jacopo Catani OBERGURGL June 2010

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

23. 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 dimensions Jacopo Catani OBERGURGL June 2010

24. 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, t=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 ms Jacopo Catani OBERGURGL June 2010

25. 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

26. 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 K K SERIES of resonances 1- Channel coupling is neglected for n’>0 2- Internal state of molecule does not change G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010) Jacopo Catani OBERGURGL June 2010

27. 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 Catani OBERGURGL June 2010

28. 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) The model parametrizes the scattering amplitude through an effective scattering length aeff • In order to retrieve r0we employ previous results • on molecular K-RB association@LENS • Measured values for Ebare fitted by the formula • Obtaining the effective range value: C. Weber et al., Phys. Rev. A 78, 061601(R) (2008) G. Thalhammer et al., New J. Phys. 11, 055044 (2009) D. S. Petrov, Phys. Rev. Lett. 93, 143201 (2004). r0 = 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

29. Effective range correction to a scattering model • RESULTS of model: • Knowledge of the effective Mix-Dim scattering length in the 0-100G range • Prediction for the trend in the width of the resonances • Resonances position still coincides with the harmonic oscillator predictions • Selection rules due to coupling term in the Hamiltonian only allow even resonances S=20 G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010) Jacopo Catani OBERGURGL June 2010

30. 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

31. Results of the improved (lattice) model Shaded areas are predictions of this improved model NICE AGREEMENT with data G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010) Jacopo Catani OBERGURGL June 2010

32. Results of the improved (lattice) model Shaded areas are predictions of this improved model NICE AGREEMENT with data G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010) Jacopo Catani OBERGURGL June 2010

33. 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. G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010) Jacopo Catani OBERGURGL June 2010

34. 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

35. BEC3 team , LENS, Florence PhD positions and Diploma theses available! M. Inguscio, F. Minardi Postdocs: J. Catani, G. Lamporesi, PhD students: G. Barontini (now in Kaiserslautern) www.quantumgases.lens.unifi.it

36. INO-CNR under EuroCORES (EuroQUAM-DQS) EU under NAME-QUAM and STREP-CHIMONO Thank you Jacopo Catani ESF conference “Quantum engineeringofstates and devices” Obergurgl, June 2010