phase separation of exotic superfluids in a chain of high spin …eszirmai/bilbao2015.pdf · 2016....
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![Page 1: Phase separation of exotic superfluids in a chain of high spin …eszirmai/bilbao2015.pdf · 2016. 1. 4. · Phase separation of exotic superfluids in a chain of high spin ultracold](https://reader035.vdocument.in/reader035/viewer/2022071517/613b577bf8f21c0c8268f1c2/html5/thumbnails/1.jpg)
Phase separation of exotic superfluids in a chain ofhigh spin ultracold atoms
Edina Szirmai
International Workshopon Cold Gases in Quantum Information
June 30 - July 1, 2015, Bilbao
In collaboration with:
G. BarczaJ. SólyomÖ. Legeza
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Homogeneous vs. inhomogeneous pairing
Bardeen, Cooper, Schrieffer (1957)
BCS pairing
k
k'
k
k'
2 species of fermionic particles.
QCOM = 0→ homogeneous op.
Spin singlet S = 0.
Particles close to the Fermi surface.
Fulde, Ferrell (1964), Larkin, Ovchinnikov (1964)
FFLO pairing
k1
22
2
1k'
k
k'
2 species offermionic particles.
QCOM 6= 0→inhomogeneous op.
Spin singlet S = 0.
Particles close to theFermi surface.
Experimental studies withultracold atomic systems:
Zwierlein, et al. (2006);Partridge, et al. (2006);Schunck, et al. (2007);Liao, et al. (2010);
and more...
Small Zeeman fieldno effect on the BCS pairs
1st order phase transition.
Intermediate Zeeman fielddepairing state
2nd order phase transition.
Large enough Zeeman field
ferromagnetic normal state
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Homogeneous vs. inhomogeneous pairing
Bardeen, Cooper, Schrieffer (1957)
BCS pairing
k
k'
k
k'
2 species of fermionic particles.
QCOM = 0→ homogeneous op.
Spin singlet S = 0.
Particles close to the Fermi surface.
Effect of applied/generated magnetic field:
Small Zeeman fieldno effect on the BCS pairs
1st orderphase
transition.
Large enough Zeeman field
ferromagnetic normal stateChandrasekhar (1962), Clogston (1962)
Fulde, Ferrell (1964), Larkin, Ovchinnikov (1964)
FFLO pairing
k1
22
2
1k'
k
k'
2 species offermionic particles.
QCOM 6= 0→inhomogeneous op.
Spin singlet S = 0.
Particles close to theFermi surface.
Experimental studies withultracold atomic systems:
Zwierlein, et al. (2006);Partridge, et al. (2006);Schunck, et al. (2007);Liao, et al. (2010);
and more...
Small Zeeman fieldno effect on the BCS pairs
1st order phase transition.
Intermediate Zeeman fielddepairing state
2nd order phase transition.
Large enough Zeeman field
ferromagnetic normal state
![Page 4: Phase separation of exotic superfluids in a chain of high spin …eszirmai/bilbao2015.pdf · 2016. 1. 4. · Phase separation of exotic superfluids in a chain of high spin ultracold](https://reader035.vdocument.in/reader035/viewer/2022071517/613b577bf8f21c0c8268f1c2/html5/thumbnails/4.jpg)
Homogeneous vs. inhomogeneous pairing
Fulde, Ferrell (1964), Larkin, Ovchinnikov (1964)
FFLO pairing
k1
22
2
1k'
k
k'
2 species offermionic particles.
QCOM 6= 0→inhomogeneous op.
Spin singlet S = 0.
Particles close to theFermi surface.
Experimental studies withultracold atomic systems:
Zwierlein, et al. (2006);Partridge, et al. (2006);Schunck, et al. (2007);Liao, et al. (2010);
and more...
Small Zeeman fieldno effect on the BCS pairs
1st order phase transition.
Intermediate Zeeman fielddepairing state
2nd order phase transition.
Large enough Zeeman field
ferromagnetic normal state
![Page 5: Phase separation of exotic superfluids in a chain of high spin …eszirmai/bilbao2015.pdf · 2016. 1. 4. · Phase separation of exotic superfluids in a chain of high spin ultracold](https://reader035.vdocument.in/reader035/viewer/2022071517/613b577bf8f21c0c8268f1c2/html5/thumbnails/5.jpg)
Homogeneous vs. inhomogeneous pairing
Fulde, Ferrell (1964), Larkin, Ovchinnikov (1964)
FFLO pairing
k1
22
2
1k'
k
k'
2 species offermionic particles.
QCOM 6= 0→inhomogeneous op.
Spin singlet S = 0.
Particles close to theFermi surface.
Experimental studies withultracold atomic systems:
Zwierlein, et al. (2006);Partridge, et al. (2006);Schunck, et al. (2007);Liao, et al. (2010);
and more...
Small Zeeman fieldno effect on the BCS pairs
1st order phase transition.
Intermediate Zeeman fielddepairing state
2nd order phase transition.
Large enough Zeeman field
ferromagnetic normal state
![Page 6: Phase separation of exotic superfluids in a chain of high spin …eszirmai/bilbao2015.pdf · 2016. 1. 4. · Phase separation of exotic superfluids in a chain of high spin ultracold](https://reader035.vdocument.in/reader035/viewer/2022071517/613b577bf8f21c0c8268f1c2/html5/thumbnails/6.jpg)
Homogeneous vs. inhomogeneous pairing
Fulde, Ferrell (1964), Larkin, Ovchinnikov (1964)
FFLO pairing
k1
22
2
1k'
k
k'
2 species offermionic particles.
QCOM 6= 0→inhomogeneous op.
Spin singlet S = 0.
Particles close to theFermi surface.
Experimental studies withultracold atomic systems:
Zwierlein, et al. (2006);Partridge, et al. (2006);Schunck, et al. (2007);Liao, et al. (2010);
and more...
Small Zeeman fieldno effect on the BCS pairs
1st order phase transition.
Intermediate Zeeman fielddepairing state
2nd order phase transition.
Large enough Zeeman field
ferromagnetic normal state
![Page 7: Phase separation of exotic superfluids in a chain of high spin …eszirmai/bilbao2015.pdf · 2016. 1. 4. · Phase separation of exotic superfluids in a chain of high spin ultracold](https://reader035.vdocument.in/reader035/viewer/2022071517/613b577bf8f21c0c8268f1c2/html5/thumbnails/7.jpg)
Simulation of orbital degree of freedom with fermionicultracold atoms1D systems – confinement induced resonance
Chain of two-orbital Yb-173 atoms[E. Sz. PRB (2013), and in preparation]
Spin polarized 4-component fermionic chain[Barcza, E. Sz., Solyom, Legeza, PRA (2012), EPJ ST (2015), and in preparation]
Summary
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Simulation of orbital degree of freedom with fermionicultracold atoms
Spin-F atoms in an optical lattice.
Electronic ground state and metastable excited state.
Charge neutral atoms→ SU(N=2F+1) symmetric interaction.
S (g)01
gg
pl. F=1/2:
P (e)3 0
eg ge_g+gge
S=0 S=0 S=1S=0
[Gorshkov, et al. (2010); Scazza, et al. (2014); Cappellini, et al. (2014); Zhang, et al. (2014)]
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Simulation of orbital degree of freedom with fermionicultracold atoms
Spin-orbit coupled system
Eg. transition metals: Kugel-Kohmskii model
Various mixtures of light and heavy particles, impurity modelsheavy fermion systems
Periodic Anderson model, Kondo lattice model
One orbit systems
SU(N) Hubbard and
Heisenberg models
Source: jila.colorado.edu
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One-dimensional systems
a3D87Sr 173Yb
ag 96.2 aB 199.4 aBae 176 aB 306.7 aBa+
ge 169 aB 219.5 aB
a−ge 68 aB 3300 aB
Confinement induced resonance:
Coupling constant in a1D optical lattice:
g =2h̄2
m1
a2⊥
a3D
1− c a3Da⊥
,
Tuning of the confining potential(a⊥ =
√h̄/mω⊥).
2-orbital system→ 4 resonances.Typical confining:
ω⊥ ≈ 100 kHz→ aYb⊥ ≈ 680 aB .
ω⊥ to be changed up to 0.5-1 MHz.
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Low energy behavior of Yb-173 atoms: F=5/2, SU(6)
Field theoretical RG treatment, and bosonizationAsymptotic behavior of the correlation functions→ dominant order
Phase diagram as a function of population and the confining potential:
Competing orders:
OADW ∼ |r |−∆κ−−∆κ
+
OpFFLO ∼ |r |−∆σ−−∆σ
+
OSDW ∼ |r |−∆κ−−∆κ
+−∆σ ′− −∆σ ′
+
E. Szirmai, PRB (2013), and in preparation
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Low energy behavior of Yb-173 atoms: F=5/2, SU(6)
Field theoretical RG treatment, and bosonizationAsymptotic behavior of the correlation functions→ dominant order
Phase diagram as a function of population and the confining potential:
Competing orders:
OADW ∼ |r |−∆κ−−∆κ
+
OpFFLO ∼ |r |−∆σ−−∆σ
+
OSDW ∼ |r |−∆κ−−∆κ
+−∆σ ′− −∆σ ′
+
E. Szirmai, PRB (2013), and in preparation
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Phase separation - preliminary results
Phase separation:presence of heavy and light particles + strong repulsive interaction.
Close to each resonances.
Properties of the segregatedphase depend on the populationsand a⊥.
1st order transition with divergentcompressibility.√
1±ggec√
κgκe = 0.
E. Szirmai, PRB (2013), and in preparation
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Polarized 4-component fermions on a 1D chain
1 orbital state→ 1 scattering length – tuned to the attractiveregime by transverse confinement.
Spin imbalance: nonzero total magnetization Sztot .
Phase diagram predicted by weak coupling analysis:
Barcza, E. Sz., Solyom, Legeza, PRA (2012), EPJ ST (2015), and in preparation
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Polarized 4-component fermions on a 1D chain
1 orbital state→ 1 scattering length – tuned to the attractiveregime by transverse confinement.
Spin imbalance: nonzero total magnetization Sztot .
Phase diagram predicted by weak coupling analysis:
Barcza, E. Sz., Solyom, Legeza, PRA (2012), EPJ ST (2015), and in preparation
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Polarized 4-component system – DMRG analysis
Density distribution along the chain:
0 10 20 30 40 500
0.1
0.2
0.3
0.4
i
S3/2
S1/2
P2,2
Q
0 10 20 30 40 500
0.2
0.4
0.6
0.8
1
i
S3/2
T3/2
Q
Density-density correlations→ static structure factor
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
k/π
χ n(k)
06121524293947
m̃
0 0.2 0.4 0.6 0.8 10
2
4
6
8
k/π
0612151821 m̃
x10-1
Barcza, E. Sz., Solyom, Legeza, PRA (2012), EPJ ST (2015), and in preparation
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Polarized 4-component system – DMRG analysis
Density distribution along the chain:
0 10 20 30 40 500
0.1
0.2
0.3
0.4
i
S3/2
S1/2
P2,2
Q
0 10 20 30 40 500
0.2
0.4
0.6
0.8
1
i
S3/2
T3/2
Q
Density-density correlations→ static structure factor
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
k/π
χ n(k)
06121524293947
m̃
0 0.2 0.4 0.6 0.8 10
2
4
6
8
k/π
0612151821 m̃
x10-1
Barcza, E. Sz., Solyom, Legeza, PRA (2012), EPJ ST (2015), and in preparation
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Summary
High spin fermionic chains where the interactions are tuned viachanging the transverse confinement.Two-orbital Yb-173 isotopes:
The system can be driven into an orbital-FFLO state.Phase separation is expected close to the resonances.
Spin polarized 4-component fermions:Formation of SU(4) quartets in a ferromagnetic background.Phase separation of the composite (spin neutral) particles and thespin carrier particles for strong enough attractive interaction.