Transcript Diapositiva 1

European Laboratory
for Non-Linear
Spectroscopy
Dipartimento di
Fisica Università di
Firenze
Bose-Bose Mixtures:
atoms, molecules and
thermodynamics
near the Absolute Zero
Jacopo Catani
LENS & CNR-INFM
Università di Firenze
FerMix ESF Meeting
Trento, 3-5 June 2009
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 starting
point
• Entropy control of species A exploiting species B
The Apparatus
The apparatus
The Apparatus
•
•
•
•
Triple Chamber system, 2 high pressure (10-9 mbar), 1 UHV (10-11 mbar)
Milli-Trap, low power, low inductance magnetic trapping device
High Power Fiber laser for Dipole Trap / Optical Lattice, 20W @ 1064 nm, <100KHz
Possibility to tune external magnetic fields (Feshbach resonances) up to 100 G
2D-MOT
Rb
2D-MOT
K
Sympathetic Cooling and
87Rb-41K
Double BEC
• Rb (K) atoms are precooled to 100 mK (1mK) by MOT
and MOLASSES
• m-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)
41K
87Rb
Tunability of interactions in 87Rb-41K
• The |1,1>|1,1> state has nice tunability of interactions in the 0-100 G range
Dipole trap loaded at ~ 1 mK
mwave transfers at 6.3 G
F=2
F=1
A. Simoni et al., Phys. Rev. A 77, 052705 (2008).
Interaction between K and Rb is tailored during final
evaporation to obtain two BECs with
tunable interspecies interactions
K
20 Katoms
Rb
40 Katoms
G. Thalhammer, G. Barontini, L. De Sarlo, J. C., F. Minardi, and M. Inguscio, PRL 100, 210402 (2008)
Association of Heteronuclear
87Rb-41K
Molecules
• We associate heterospecies Bose molecules by modulating the external magnetic field
S. T. Thompson, E. Hodby, and C. E.Wieman, PRL 95, 190404 (2005)
in proximity of a FR (B0)
•K-Rb molecules show permanent e-dipole in the ground state, ~Debye
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)
• The mixture is prepared at temperatures in the 200600 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
•
When n=Eb/h threshold atoms
are stimulated to association
• We detect ATOM LOSS after a certain RF time.
Molecules relax with lifetime 1/g into deeply bound
pairs
C. Weber, G. Barontini, J. C., G. Thalhammer, M. Inguscio, and F. Minardi, Phys. Rev. A 78, 061601(R) (2008)
Association of Heteronuclear
87Rb-41K
Molecules
• Binding energies of associated molecules are measured ( ) aside both FR for different
values of magnetic field -> comparison with theoretical model ( ) sourcing from
A. Simoni et al., Phys. Rev. A 77, 052705 (2008).
different isotopic K-Rb admixtures
• 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)
C. Weber, G. Barontini, J. C., G. Thalhammer, M. Inguscio, and F. Minardi, Phys. Rev. A 78, 061601(R) (2008)
Association of Heteronuclear
87Rb-41K
Molecules
• 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;
C. Weber, G. Barontini, J. C., G. Thalhammer, M. Inguscio, and F. Minardi, Phys. Rev. A 78, 061601(R) (2008)
Association of Heteronuclear
87Rb-41K
Molecules
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 employed
J. 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).
C. Weber, G. Barontini, J. C., G. Thalhammer, M. Inguscio, and F. Minardi, Phys. Rev. A 78, 061601(R) (2008)
Association of Heteronuclear
87Rb-41K
Molecules
• 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).
Thermally averaged
g
T
Estimation of molecules lifetime:
(left side of line) 20 ms<t<5 ms (no decay after RF pulse)
T. M. Hanna, T. Köhler, and K. Burnett, PRA 75, 013606 (2007).
C. Weber, G. Barontini, J. C., G. Thalhammer, M. Inguscio, and F. Minardi, Phys. Rev. A 78, 061601(R) (2008)
Association of Heteronuclear
87Rb-41K
Molecules
2) Molecular association signal is nonzero for fractional values of Eb: hn = 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.
C. Weber, G. Barontini, J. C., G. Thalhammer, M. Inguscio, and F. Minardi, Phys. Rev. A 78, 061601(R) (2008)
Association of Heteronuclear
87Rb-41K
Molecules
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
350 nK
15 ms
• 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 hDB2
Time average:
< E(t)>=hn
• In order to measure the “real” Eb we have to
extrapolate to zero-modulation the association signal.
130 mG ~ -6 KHz
C. Weber, G. Barontini, J. C., G. Thalhammer, M. Inguscio, and F. Minardi, Phys. Rev. A 78, 061601(R) (2008)
Association of Heteronuclear Efimov Trimers
• In the early ’70s, V. Efimov predicted the existence of trimer states leaning beyond the
V. Efimov, Phys. Lett. B 33B, 563 (1970); V. Efimov, Sov. J. Nucl. Phys. 12, 589 (1971),
range where dimers exist (a<0).
Yadern. Fiz. 12 (1970), 1080-1091.
• Original field: Nuclear Physics, but first evidence
in ultracold homonuclear atomic systems T. Kraemer et al., Nature 440, 315 (2006).
• Log-periodicity of resonances by a universal
scaling factor (ep/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
E. Nielsen, H. Suno, and B. D. Esry, PRA 66, 012705 (2002).
S. Knoop, et al., Nature Physics 5, 227 (2009)
• Values for s0 and a*/a_ has been predicted and measured for the homonuclear case
E. Braaten and H.-W. Hammer, Phys. Rep. 428, 259 (2006).
M. Zaccanti et al., arXiv:0904.4453 (2009)
• Scaling laws have been found to extract properties on heteronuclear systems.
J. P. D’Incao and B. D. Esry, PRA 73, 030702 (2006).
No experimental evidence for heteronuclear systems
Efimov resonances in a B-B mixture
• Efimov physics in a homonuclear system stems from the resonant character of
interactions among all three constituents in proximity of a common FR.
• Observation of Efimov effect in a heteronuclear system would grant that only two
resonant interactions are sufficient to Efimov Effect to take place.
Efimov resonances in a B-B mixture
• 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.
KRbRb
KKRb
So, two possible Efimov trimers families should
exist in a two species system, different
periodicity factors s0
V. Efimov, Nucl. Phys. A 210, 157 (1973)
Efimov resonances in a B-B mixture
• We observe two “candidate” atom loss peaks for a_ (a<0) , aside FR at 38 G
0.3 mK, 100 ms
0.4 mK, 500 ms
57.7(5) G
-246 a0
38.8(1) G, -22000 a0
KKRb
KRbRb
• Single species behaviors are useful for channel assignment (see insets&later)
G. Barontini, C. Weber, F. Rabatti, J. C., G. Thalhammer, M. Inguscio, and F. Minardi, arXiv:0901.4584v2 (2009)
Efimov resonances in a B-B mixture
KRbRb
KKRb
• 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).
in analogy to the homonuclear case
• Things go smoothly for the strongest KRbRb channel…
G. Barontini, C. Weber, F. Rabatti, J. C., G. Thalhammer, M. Inguscio, and F. Minardi, arXiv:0901.4584v2 (2009)
Efimov resonances in a B-B mixture
KRbRb
KKRb
• … the unitary limit should be taken into account to reproduce the KKRb channel data
• 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 aKRbRb (
)
• We assume the unitary limit to be T dependent and of the same order of
the homonuclear one
J. P. D’Incao, H. Suno, and B. D. Esry, PRL 93, 123201 (2004).
G. Barontini, C. Weber, F. Rabatti, J. C., G. Thalhammer, M. Inguscio, and F. Minardi, arXiv:0901.4584v2 (2009)
Efimov resonances in a B-B mixture
• Why should these data (a<0) be Efimov-related signatures?
1) Atom number combinations show loss peaks typical of ABB or AAB 3body processes
2) No features if only Rb or only K is present
3) No FR are predicted, nor measured even for higher momentum
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
B = 56.8 G
KRbRb channel
NRblost/NKlost ~ 1.7(3)
=
G. Barontini, C. Weber, F. Rabatti, J. C., G. Thalhammer, M. Inguscio, and F. Minardi, arXiv:0901.4584v2 (2009)
Mixtures in Optical Lattices
• MIXTURES in optical lattices
For high lattice heights atoms localize, but a
small finite tunneling can induce ORDER
• New exotic ordered phases are in principle engineerable (SS, Checkerboard, SCF)
when interactions and tunneling are adjusted
E. Altman et al., New J. Phys. 2003
A. Isacsson et al., PRB 2005
Mixtures in Optical Lattices
• Few experiments has been investigating properties of heteronuclear MIXTURES in OL:
• FERMI-BOSE mixtures
• BOSE-BOSE mixture
(K. Guenter et al. PRL 2006,
S. Ospelkaus et al. PRL 2006,
Th. Best et al. PRL 2009)
J. C. et al, PRA(R) 2008
Still no evidence for ordered
quantum phases (BB, FB and
FF mixtures) predicted by
recent works
QMC
S. G. Soyler et al., arXiv:0811.0397 (2008)
• 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 T
A. 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
Mixtures in Optical Lattices
• 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
S/N a ln(S/N )
A method to control the ENTROPY of the system at ultralow temperatures would be
desirable to ease the realization of ordered phases
…Preliminary results…
Entropy exchange in an ultracold atomic mixture
(collaboration with S. Stringari, University of Trento)
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 S 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 S decreases as before but
T increases less.
In the limit NRb >> NK Rb is a thermal bath, negligible T increase,
ISOTHERMAL transformation
Entropy exchange in a Bose-Bose Mixture
• ENTROPY EXCHANGE: we use a selective compression (SSDP) of K to reduce its
entropy by transferring it to Rb
M-trap
+
SSDP
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
with t=45 ms (adiabaticity is fulfilled)
M-trap freq. for K:
2π × (24, 297, 297)Hz
• Max. compression ratio on K frequencies: ~2
• Residual compression on Rb due to SSDP: VRb/VK =0.08
Entropy exchange in a Bose-Bose Mixture
• SELECTIVE COMPRESSION of K
Rb
K
Rb
K
• K entropy is transferred to Rb cloud, selective compression can induce BEC transition on 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 fc(T)
[3]
[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).
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
Entropy exchange in a Bose-Bose Mixture
• 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
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
• SSDP wawelenght: 789.85 nm
Rb
D1
794.8 nm
D2
780.0 nm
K
769.9 nm
• Max. Beam Power: 32 mW
Beam waist: 55 mm
Beam orthogonal to the weak M-trap axis.
766.5 nm
M-trap axis (x)
…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:
Postdocs:
PhD students:
Undergraduate students:
M. Inguscio, F. Minardi
J. Catani, G. Lamporesi,
G. Thalhammer (now in Innsbruck)
G. Barontini, C. Weber (now in Bonn)
F. Rabatti
Thank you
Jacopo Catani
FerMix ESF Meeting
Trento, 3-5 June 2009