bose-bose mixtures: atoms, molecules and thermodynamics near the absolute zero bose-bose mixtures:...

Bose-Bose Mixtures: Bose-Bose Mixtures: atoms, molecules and atoms, molecules and

thermodynamicsthermodynamicsnear the Absolute Zero near the Absolute Zero

Bose-Bose Mixtures: Bose-Bose Mixtures: atoms, molecules and atoms, molecules and

thermodynamicsthermodynamicsnear the Absolute Zero near the Absolute Zero

Jacopo CataniJacopo Catani

LENS & CNR-INFMLENS & CNR-INFMUniversità di FirenzeUniversità di Firenze

FerMix ESF MeetingFerMix ESF MeetingTrento, 3-5 June 2009Trento, 3-5 June 2009

European Laboratory European Laboratory for Non-Linear for Non-Linear SpectroscopySpectroscopy

Dipartimento di Dipartimento di Fisica Università di Fisica Università di

FirenzeFirenze

OUTLINE

• 87Rb-41K experimental apparatus

• Double BEC with tunable interspecies interacions

• Association of heteronuclear Bosonic molecules

• Observation of heteronuclear Efimov resonances

• Entropy management in the quantum regime using a SSDP potential

Principal Motivations

• Heteronuclear mixtures are good candidates for Quantum Magnetism: antiferromagnetic Néel state, xy-ferromagnetic state or supercounterfluidity/paired superfluidity

• Long Lived Heteronuclear Dipolar Bosonic Molecules:double Mott insulator with one particle per species per site ideal startingpoint

• Entropy control of species A exploiting species B

The Apparatus

The apparatusThe apparatusThe apparatusThe apparatus

• Triple Chamber Triple Chamber system, 2 high pressure (10-9 mbar), 1 UHV (10-11 mbar)

• Milli-TrapMilli-Trap, low power, low inductance magnetic trapping device

• High Power Fiber laser for Dipole Trap Dipole Trap / Optical LatticeOptical Lattice, 20W @ 1064 nm, <100KHz

• Possibility to tune external magnetic fields (Feshbach resonancesFeshbach resonances) up to 100 G

2D-MOT Rb

2D-MOT K

The Apparatus

• Rb (K) atoms are precooled to 100 K (1mK) by MOTand MOLASSES

• -wave radiation sweep employed for hyperfine spin-flip (F=2->F=1) of Rb@ 6.835 GHz, evaporation and sympathetic cooling

• Fast interspecies thermalization (aRbK=160a0) and repulsive interactions in Rb and K allow for double 87Rb-41K BEC

• Atoms are imaged by resonant light after a variable expansion time (k is mapped on r)

Sympathetic Cooling and 8787Rb-Rb-4141KK Double BEC

41K

87Rb

• The |1,1>|1,1> state has nice tunability of interactions in the 0-100 G range

Tunability of interactions in

8787Rb-Rb-4141KK

G. Thalhammer, G. Barontini, L. De Sarlo, J. C., F. Minardi, and M. Inguscio, PRL 100, 210402 (2008)

Dipole trap loaded at ~ 1 K

wave transfers at 6.3 G

F=2

F=1

K 20 Katoms

Rb40 Katoms

Interaction between K and Rb is tailored during final evaporation to obtain two BECs with

tunable interspecies interactions

A. Simoni et al., Phys. Rev. A 77, 052705 (2008).

• We associate heterospecies Bose molecules by modulating the external magnetic field in proximity of a FR (B0)•K-Rb molecules show permanent e-dipole in the ground state, ~Debye

Association of Heteronuclear Molecules8787Rb-Rb-4141KK

S. T. Thompson, E. Hodby, and C. E.Wieman, PRL 95, 190404 (2005)

• When =Eb/h threshold atoms are stimulated to association

• The mixture is prepared at temperatures in the 200-600 nK range and for a certain value of magnetic field B.

• The Feshbach field is modulated in the 50-200 KHz range, 130 mG amplitude, t=10-1000 ms

• We detect ATOM LOSS after a certain RF time. Molecules relax with lifetime 1/ into deeply bound pairs

C. Weber, G. Barontini, J. C., G. Thalhammer, M. Inguscio, and F. Minardi, Phys. Rev. A 78, 061601(R) (2008)

K. –K. Ni et al., Science 322, 231 (2008)

• 41K-87Rb molecules are good constituents for dipolar BEC ! L. Santos et al., Phys. Rev. Lett. 85, 1791 (2000)

• Binding energies of associated molecules are measured ( ) aside both FR for different values of magnetic field -> comparison with theoretical model ( ) sourcing from different isotopic K-Rb admixtures



A. Simoni et al., Phys. Rev. A 77, 052705 (2008).

• Data are excellently fitted by the theoretical curves (no free parameters) provided the field in the model is shifted by 0.25 G and 1.0 G respectively• The position of the 2B-resonances ( ) are extrapolated using the corrected model ( ) and compared to 3B losses measurement. Small shift.

• molecular association represents a more precise and affordable method (2B) to measure FR position

• The new FR positions are employed to increase the precision on the parameters of the model G Thalhammer, G Barontini J. C., F Rabatti, C Weber, A

Simoni, F Minardi and M Inguscio, NJP 11, 055044 (2009)



• Several nontrivial features appear in the association spectrum:

1)Lines appear broad and asymmetric in frequency;

2)Additional association peaks at fractional frequencies of the binding energy.

3)A shift of the resonant modulation frequency that increases with the modulation amplitude;



1) Lines appear broad and asymmetric in frequency (for a fixed value of Eb)

• It is crucial to take into account temperature (200-600 nK) and energy distribution

NOTE: the broadening/asym. is not observed when degenerate gases are employedJ. J. Zirbel et al., PRL 100, 143201 (2008); J. J. Zirbel et al., PRA 78,

013416 (2008), S. T. Thompson, E. Hodby, and C. E.Wieman, PRL 95, 190404 (2005).



• Model derived combining several ideas from PA to molecular assoc. in harmonic pot. M. Mackie, R. Kowalski, and J. Javanainen, PRL 84, 3803 (2000).

J. F. Bertelsen and K. Mölmer, PRA 76, 043615 (2007).

T. M. Hanna, T. Köhler, and K. Burnett, PRA 75, 013606 (2007).

Thermally averaged

Estimation of molecules lifetime:

(left side of line) 20 s<<5 ms (no decay after RF pulse)



2) Molecular association signal is nonzero for fractional values of Eb: h= Eb /2

• This behavior sources directly from equations of the model, peaks of association for different Fourier components of the excitation.

• ASSUMPTION: B field range is into the universal region of interaction:

• This feature is exploited as a technique to extend the range of B modulation frequency to measure Eb

even if the S/N is worse.



3) An intensity-dependent shift of the association lines appears:

• This feature is directly connected to the quadratic form of the binding energy into the universal regime

• If the amplitude of B field modulation is not negligible compared to Eb , the r.m.s. value of the oscillating field shifts <E> towards higher values respect to B2

Time average:

< E(t)>=h

• In order to measure the “real” Eb we have to extrapolate to zero-modulation the association signal.

130 mG ~ -6 KHz

350 nK15 ms

• In the early ’70s, V. Efimov predicted the existence of trimer states leaning beyond the range where dimers exist (a<0).

• Original field: Nuclear Physics, but first evidencein ultracold homonuclear atomic systems

• Log-periodicity of resonances by a universal scaling factor (e/s0) for (1/a) -> 0

• 3B resonances should occur when threshold is crossed by trimer levels (a<0).

• Peculiar features (oscillations, atom-dimer resonances) are expected for a>0

• Values for s0 and a*/a_ has been predicted and measured for the homonuclear case

• Scaling laws have been found to extract properties on heteronuclear systems.

No experimental evidence for heteronuclear systems

Association of Heteronuclear Efimov Trimers

V. Efimov, Phys. Lett. B 33B, 563 (1970); V. Efimov, Sov. J. Nucl. Phys. 12, 589 (1971), Yadern. Fiz. 12 (1970), 1080-1091.

J. H. Huckans et al., PRL 102, 165302 (2009)

T. Kraemer et al., Nature 440, 315 (2006).

E. Nielsen, H. Suno, and B. D. Esry, PRA 66, 012705 (2002).S. Knoop, et al., Nature Physics 5, 227 (2009)

E. Braaten and H.-W. Hammer, Phys. Rep. 428, 259 (2006).M. Zaccanti et al., arXiv:0904.4453 (2009)

J. P. D’Incao and B. D. Esry, PRA 73, 030702 (2006).

Efimov resonances in a B-B mixture

• Observation of Efimov effect in a heteronuclear system would grant that only two resonant interactions are sufficient to Efimov Effect to take place.

• Efimov physics in a homonuclear system stems from the resonant character of interactions among all three constituents in proximity of a common FR.


• In order to detect a signature of Efimov physics, we observe the atomic losses after a certain hold time around a Feshbach resonance (a<0)

• We have 4 possible decay channels: KKK, RbRbRb (homonuclear) KRbRb, KKRb (heteronuclear), dominating near an interspecies FR.

So, two possible Efimov trimers families should exist in a two species system, different periodicity factors s0

KRbRb

KKRb

V. Efimov, Nucl. Phys. A 210, 157 (1973)

0.3 K, 100 ms


KRbRbKKRb

38.8(1) G, -22000 a0

57.7(5) G-246 a0

• We observe two “candidate” atom loss peaks for a_ (a<0) , aside FR at 38 G

• Single species behaviors are useful for channel assignment (see insets&later)

0.4 K, 500 ms

G. Barontini, C. Weber, F. Rabatti, J. C., G. Thalhammer, M. Inguscio, and F. Minardi, arXiv:0901.4584v2 (2009)


• We compare our data with numerical solutions of a set of 3BR rate equations:


J. P. D’Incao and B. D. Esry, PRA 73, 030702 (2006).

• Things go smoothly for the strongest KRbRb channel…

KRbRb

KKRb

in analogy to the homonuclear case


• … the unitary limit should be taken into account to reproduce the KKRb channel data


KRbRb

KKRb

• The KRbRb channel always dominates except where it is unitary limited by a certain amount

• In this strongly interacting region, the KKRb coefficient exceeds the limited value of the KRbRb

one and a sharp peak appears above the smooth unitary limit of KRbRb ( )

• We assume the unitary limit to be T dependent and of the same order of the homonuclear oneJ. P. D’Incao, H. Suno, and B. D. Esry, PRL 93, 123201 (2004).


• Why should these data (a<0) be Efimov-related signatures?

1) Atom number combinations show loss peaks typical of ABB or AAB 3body processes

3) No FR are predicted, nor measured even for higher momentum

2) No features if only Rb or only K is present

G. Thalhammer et us, NJP 11, 055044 (2009)

4) Atom decay close to an Efimov peak can be reproduced by our 3B numerical model, giving a non-exponential behavior . The ratio of lost particle numbers per specie approaches 2


NRblost/NKlost ~ 1.7(3)

KRbRb channel

B = 56.8 G

Mixtures in Optical Lattices

• Atoms in OL represent a unique testbench for fundamental physical concepts coming from different research areas (crystals, solid state, quantum computing , atom-optics)

• New exotic ordered phases are in principle engineerable (SS, Checkerboard, SCF) when interactions and tunneling are adjusted

• MIXTURES in optical lattices For high lattice heights atoms localize, but a small finite tunneling can induce ORDER

E. Altman et al., New J. Phys. 2003A. Isacsson et al., PRB 2005


• Few experiments has been investigating properties of heteronuclear MIXTURES in OL:

• FERMI-BOSE mixtures

• BOSE-BOSE mixture J. C. et al, PRA(R) 2008

(K. Guenter et al. PRL 2006,S. Ospelkaus et al. PRL 2006,Th. Best et al. PRL 2009)

Still no evidence for ordered quantum phases (BB, FB and FF mixtures) predicted by recent works

• BIG (open) ISSUES: • Which is the highest T (critical temperature) compatible with the onset of an ordered phase?• How to detect these phases?

• Very recent theoretical efforts on the subject of finite TA. Hubener et al., arXiv:0902.2212 (2009)B. Capogrosso-Sansone et al., work in progress

Very low T are required not to melt these phases into disordered phases. For 87RB-41K Tc ~ 50 pK (!)B. Capogrosso-Sansone, preliminary results

S. G. Soyler et al., arXiv:0811.0397 (2008)

QMC


• TEMPERATURE in (deep) Optical Lattices is always a tricky element:

• Difficult to be measured (no feasible method has been implemented)

• …Difficult to be defined (single localized atoms in deep OL)…

IDEA: ordered phases are intrinsically linked to ENTROPY per particle

the higher the order, the lower the entropy

A method to control the ENTROPY of the system at ultralow temperatures would be desirable to ease the realization of ordered phases

S/N ln(/N )S/N ln(/N )

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

…Preliminary results…

Entropy exchange in a Bose-Bose Mixture

• KEY IDEA: use a species-selective dipole potential (SSDP) that acts only on a certain species (K), whereas the other (Rb) is “transparent”

SINGLE GAS: a (ideal) compression is ISOENTROPIC, energy density of states decreases

and T increases

TWO GASES: a compression acting on a single species (SSDP) is still ISOENTROPIC for K+Rb, but entropy is transferred from K to Rb since decreases as before but T increases less.

In the limit NRb >> NK Rb is a thermal bath, negligible T increase, ISOTHERMAL transformation


• ENTROPY EXCHANGE: we use a selective compression (SSDP) of K to reduce its entropyby transferring it to Rb

M-trap

M-trap+

SSDP

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 with =45 ms (adiabaticity is fulfilled)

• Max. compression ratio on K frequencies: ~2 • Residual compression on Rb due to SSDP: VRb/VK =0.08

M-trap freq. for K: 2π × (24, 297, 297)Hz


• K entropy is transferred to Rb cloud, selective compression can induce BEC transition on K

[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


• 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


• Explore the S-T diagram for K (NK=105)

• We can follow different trajectories in the phase diagram combining SSDP compr.+evaporation of Rb

• End Points are assumed to be where NRb becomes nearly equal to NK, that is where symp. cooling efficiency vanishes.

ENTROPY is extracted from exp. Parameters (T, fc) using the relations:

T>Tc

T<Tc

By reducing Nk, lower T and S/N could be reached

The Species Selective Dipole Potential (SSDP) beam

• SSDP: exploits the fine structure of a certain species

• Wavelength is tuned between D1 and D2 lines Blue and red effects cancel out

KRb

D1 794.8 nm

D2 780.0 nm

• SSDP wawelenght: 789.85 nm

• Fine splitting is important as SC scales as I/

Cs-Rb or Cs-K is another good candidate to be employed in SSDP.

• Max. Beam Power: 32 mW Beam waist: 55 m Beam orthogonal to the weak M-trap axis.

M-trap axis (x)

766.5 nm

769.9 nm

…some Perspectives for SSDP technique

• Reduce entropy of a certain species through a SSDP potential could ease the realization of quantum phases in Lattices

• SS Lattice: Study thermalization and scattering between localized K and unperturbed superfluid Rb

• Rb used as a “heatsink” for K excitations

• Thermometry in Deep SS Lattices Few unperturbed Rb atoms represent a temperature probe for the K sample

ACKNOWLEDGMENTS

BEC3 team , LENS, Florence

Staff: M. Inguscio, F. MinardiPostdocs: J. Catani, G. Lamporesi,

G. Thalhammer (now in Innsbruck)PhD students: G. Barontini, C. Weber (now in Bonn)Undergraduate students: F. Rabatti

Thank you

Jacopo CataniFerMix ESF Meeting

Trento, 3-5 June 2009

bose-bose mixtures: atoms, molecules and thermodynamics near the absolute zero bose-bose mixtures:...

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