The 2nd International symposium onClustering as a Window on the Hierarchical Structureof Quantum Systems--CLUSHIQ2022 (EMMI Workshop)-Sendai, Japan, Nov 2, 2022

Ultracold atom study of exotic phenomena
bridging different hierarchies
Kyoto University

Y. Takahashi

Quantum Optics Group @ Kyoto University

F. Schäfer

Y. Takasu

H. Konishi

S. Nakajima(→Osaka U.)

K. OnoD. Okuno(→OIST)YTT. TakanoY. Takata

S. Taie

K. Terakawa
Y. Nakamura

K. Honda

N. Kitamura

K. Isogai
T. Kusano

T. Ishiyama

M. Yasuhara

Y. Haruna

T. TsunoOutline1. Introduction: three-body problem for ultracold atoms
2. Three-body force for atoms in an optical latticeoccupancy-resolved high-resolution spectroscopy
prospects for non-perturbative regime

3. Efimov trimmer with unequal mass
creation of ultracold Er-Li mixture
Feshbach resonances between Er and Li

4. Summary

Outline
1. Introduction: three-body problem for ultracold atoms
2. Three-body force for atoms in an optical latticeoccupancy-resolved high-resolution spectroscopy
prospects for non-perturbative regime

3. Efimov trimmer with unequal mass
creation of ultracold Er-Li mixture
Feshbach resonances between Er and Li

4. Summary

Quantum Simulation
quantum systems in various
hierarchies and between them(quarks, hadron, nucleus,atom, molecules,…)Three-Body Forcetheoretical model

ultracold atoms“highly controllable”(Feshbach resonance, mass ratio,dimensionality, quantum statistics,…)

Three ultracold atoms in a harmonic trap
Eho= ℏ𝜔𝜔

S. Jonssel, et al., PRL, 89, 250401 (2002)
M. Stoll and T. Köller PRA 72, 022714 (2005)
F. Werner and Y. Castin, PRL 97, 150401 (2006)
D. Blume, et al., PRA 97, 033621 (2018)…

3-body pot. V0 =97700 Eho

s1=4.46529... “atomic state”“Fujita-Miyazawa type
3-body force”
s0=i1.00624 “Efimov state”

F. Werner and Y. Castin,
PRL 97, 150401 (2006)

unitarity(𝑎𝑎𝑠𝑠 = ∞)D. Blume, et al., PRA 97, 033621 (2018)

Outline
1. Introduction: three-body problem for ultracold atoms
2. Three-body force for atoms in an optical latticeoccupancy-resolved high-resolution spectroscopy
prospects for non-perturbative regime

3. Efimov trimmer with unequal mass
creation of ultracold Er-Li mixture
Feshbach resonances between Er and Li

4. Summary

Spectroscopy of Atoms in an Optical Lattice+Ueg

174Yb: 1S -3P spectroscopy
023P
2+Ugg
+2Ueg+Ugg+3Ugg
2(Ueg−Ugg) !?

Ueg−Ugg

1S0

“Effective 3-body interaction”
174Yb: 1S -3P spectroscopy
𝜈𝜈102
𝜈𝜈
2
𝜈𝜈
𝜈𝜈5

𝜈𝜈43

[Y. Nakamura, et al., PRA 99, 033609 (2019)]

𝜈𝜈𝑛𝑛 − 𝜈𝜈1 ≠ (𝑛𝑛 − 1)(𝜈𝜈2 − 𝜈𝜈1)

simple 2-body physics unapplicable

“Effective 3-body interaction”
P. R. Johnson, E. Tiesinga, J. V. Porto, and C. J. Williams, NJP 11, 093022 (2009)“Eﬀective three-body interactions of neutral bosons in optical lattices”

P. R. Johnson, D. Blume, X. Y. Yin, W. F. Flynn, and E. Tiesinga, NJP 14, 053037 (2012)“Eﬀective renormalized multi-body interactions of harmonically conﬁned ultracold neutral bosons”“interaction-inducedchange of Wannier function”
Small scattering length: as << 𝜎𝜎= aho

J. Fujita et al., Prog. Theor. Phys. 17, 360 (1957)．

Evaluated upto 2nd & 3rd order of as/ ahoEffective 3-body force in an
optical lattice

Fujita-Miyazawa-type 3body force

“Effective 3-body interaction”
174Yb: 1S -3P spectroscopy𝜈𝜈102𝜈𝜈2𝜈𝜈𝜈𝜈5𝜈𝜈43With high-controllability of cold atom system,
we can perform Quantum Simulation of 3-body force !
[Y. Nakamura, et al., PRA 99, 033609 (2019)]

Calculation:Y. Haruna, T. Ishiyama et al., (unpublished)𝜈𝜈3 − 𝜈𝜈1 = −20.2 2 kHz
𝜈𝜈4 − 𝜈𝜈1 = −28.1 2 kHz
𝜈𝜈5 − 𝜈𝜈1 = −34.6 4 kHz

Similar work: L. Franchi, et al., NJP 19, 103037 (2017)

Magnetic Feshbach Resonance (170Yb)
S. Kato et al., PRL 110, 173201 (2013)“1S03P (m= −2)”:170Yb
2a(B) = abg (1- Δ/(B−B0))

abg = 119 a0 Δ = 2.1G B0 = 1.1 G

Calculation of energies of 3 bosons with large Ueg(poster presentation by Y. Haruna)
𝜎𝜎 = ahoGreydashed line:
age=agg(V0=0)
𝜎𝜎𝑎𝑎𝑔𝑔𝑔𝑔

𝜎𝜎𝑎𝑎𝑔𝑔𝑔𝑔

Outline
1. Introduction: three-body problem for ultracold atoms
2. Three-body force for atoms in an optical latticeoccupancy-resolved high-resolution spectroscopyprospects for non-perturbative regime

3. Efimov trimmer with unequal mass
creation of ultracold Er-Li mixture
Feshbach resonances between Er and Li

4. Summary

Efimov Trimer
Identical Boson:
eπ s0 ≅ 22.7

[P. Naidon and S. Endo,Rep. Prog. Phys. 80, 056001 (2017)]

Introducing
Mass imbalance
two-identical bosons (blue)(2-resonant interaction)

two-identical
Fermions(orange)

LiErErtwo-identicalbosons (green)(3-resonantinteraction)𝑒𝑒 𝜋𝜋⁄𝑠𝑠0 ≅ 5𝑀𝑀𝐸𝐸𝐸𝐸≅ 28𝑀𝑀𝐿𝐿𝐿𝐿[P. Naidon and S. Endo, Rep. Prog. Phys. 80, 056001 (2017)]

Magnetically tunable Feshbach resonances in Li+Er[M. L. Gonzalez-Martinez and Piotr S. Zuchowski, PRA 92, 022708 (2015)]

166Er(b)+6Li(f)

166Er(b)+7Li(b)

Realization of ultracold Er-Li (& Yb) mixtures

Observation of 168Er-7Li(F=1, mF=−1) Feshbach resonances

F. Schäfer et al., PRA 105, 012816 (2022)

Observation of 168,166Er - 6,7Li Feshbach resonances
F. Schäfer et al., PRA 105, 012816 (2022)

167Er (m = −19/2) - 6Li (F=1/2, m = 1/2) Feshbach resonancesFF

T= 2~ 4 μK

2.4 G wide

Ultracold mixture of spin-polarized fermions
Suppression of atom loss due to Pauli exclusion
161Dy and 40K Feshbach resonances (R. Grimm group)

arXiv:2207.03407v3 & PRL 124, 203402 (2020)
loss spectroscopyinterspecies
thermalization

binding energy
measurement

Characterization of narrow Feshbach resonances
D. S. Petrov, PRL 93, 143201 (2004)

hydrodynamicexpansion

Summary
1. Three-body force for atoms in an optical latticeoccupancy-resolved spectroscopy doneinterpreted by effective 3-body force
prospects for quantum simulation

2. Feshbach resonances of Er-Li mixture

successful creation of ultracold Er-Li (&Yb) mixture
observation of many “narrow” Feshbach resonances
prospects for careful characterization

Thank you very much for attention

16 AugustMount Daimonji at Kyoto

p-wave Superfluidity
fermion attraction mediated via BEC in mixed dimension”PRL117,245302 (2016) , PRA 94, 063631(2016), NJP19, 115011 (2017), arXiv:1809.04812”

aBF

7Li

boson (3D)

polarizedfermion(2D)

SU(4) singlet:4-body entangled state
SU(4) in plaquette: 173Yb𝑡𝑡

𝑡𝑡𝑝𝑝𝑡𝑡/𝑡𝑡𝑝𝑝 = 0.043

HSU2 = Ji,j(Si�Sj-1/4)

4𝑡𝑡2Ji,j =, U≫t𝑈𝑈AC SU(4) singlet:BDi,j,k,l = A,B,C,D
1,2,3,4 =Alpha particle: 𝜶𝜶 (4He2+)
SU(4):SU(2)× SU(2)S(Spin)=0T(Isospin)=0p↑

p↓

Szn↑
Tzn↓

Robustness of SU(4)-Singlet State against Interaction

𝐼𝐼s−t

Spin correlation

J’ J

Isotope Shift and King Linear Relation

Delaunay et al., PRD 96 093001 (2017),
Berengut et al., PRL 120 091801 (2018)

Isotope shift between isotope pairs (A’, A) for the transition 𝜆𝜆Mass shift

Field shift

Higher-order Isotope shift
New Particle shift (beyond SM)

Higher-Order Field shift (within SM)
Next-leading-Order
Seltzer moment:
Quadratic Field Shift(QFS):

nonlinearity of King relation? signature of physics beyond SM

New Particle shift

Generalized 3D King Plot Analysis
W. H. King, J. Opt. Soc. Am 53, 638-639 (1963)

30

K. Mikami et al., Eur. Phys. J. C 77, 896 (2017)

×106

𝛼𝛼𝛽𝛽I. Counts, et al., PRL 125, 123002 (2020)

Uncertainty ~300 Hz(dof = 3)

Nonlinearity @ 3𝜎𝜎[arXiv:2110.13544, K. Ono, et al.,to appear in Phys. Rev. X]

Determine the upper-boundof new boson

Er-Li-Yb Oven
Er transverse coolingHigh-temperature
Ta crucible oven(about 1100℃)

total length ofoven assembly: 81 cm

to experiment
Yb & Li oven(about 350 ℃)

Ion pump

Quantum Gas Mixtures with Unequal Mass
Lithium(Li) : [He] 2s1 : light
Mass number
Abundance[%]
Bose or Fermi

67.5
F

792.5
B

Ytterbium(Yb) : [Xe]4f146s2 : heavy
4f14

Mass number 168 170 171 172 173 174 176
Abundance[%] 0.13 3.1 14.3 21.9 16.1 31.8 12.7
Bose or Fermi BBFBFB
B

Erbium(Er) : [Xe]4f126s2 : heavy
4f12

Mass number 162
Abundance[%] 0.1
Bose or FermiB164 166 167 168 170
1.6 33.5 22.9 27.0 14.9
BBFBB

Er: [Xe]4f126s2 (Yb: [Xe]4f146s2)

from
J. Schindler

M(Er)/m(Li)= 23.14 ~ 28.3

Er

401 nm[Xe]4f12(3H6)6s6p(1P1)[Xe]4f12(3H6)6s6p(3P1)

583 nm[Xe]4f126s2 3H6Yb

399 nm[Xe]4f146s6p(1P1)[Xe]4f146s6p(3P1)556 nm[Xe]4f126s2 1S0