marco polini- luther-emery phase and atomic-density waves in a trapped fermion gas

8/3/2019 Marco Polini- Luther-Emery phase and atomic-density waves in a trapped fermion gas

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Luther-Emery phase and atomic-density waves in a

trapped fermion gas

Marco Polini(NEST-CNR-INFM and Scuola Normale Superiore)

Collaborators:Rosario Fazio, Xianlong Gao, Matteo Rizzi, and Mario Tosi (Italy)

Vivaldo Campo Jr. and Klaus Capelle (Brasil)

Jairo Sinova and Allan MacDonald (Texas)

Pisa (Pisa (TuscanyTuscany,, ItalyItaly))

October 2006October 2006



Outline

!Introduction and motivationsUltracold atoms and optical lattices

Why are cold gases interesting?

Bloch Oscillations, Vortices, Tonks-Girardeau limit,

Quantum Phase Transitions

!Rotating optical lattices, effective magnetic fields, and frustration

!A reminder of density-functional theory

(the Hohenberg-Kohn theorem and the Kohn-Sham mapping)

!One-dimensional two-component attractive fermions on a lattice

(…and very brief intro to the Luther-Emery liquid)

!Spin-pairing and atomic-density waves in the presence of confinement

!Conclusions and Future Perspectives



thanks to Markus Greiner

Optical lattices: artificial crystals of light for cold atoms

I. Bloch, Nature Physics 1, 23 (2005)

M.P.A. Fisher et al., Phys. Rev. B 40, 546 (1989)



cold cesium atoms87

Rb BEC

40K Fermi gas

Bloch oscillations in cold atom systems

M.B. Dahan et al., Phys. Rev. Lett. 76, 4508 (1996) B.P. Anderson and M.A. Kasevich, Science 282, 1686 (1998)

G. Roati et al., Phys. Rev. Lett. 92, 230402 (2004)



Superfluid-to-Mott insulator quantum phase transition

M. Greiner et al., Nature 415, 39 (2002)

D. Jaksch et al., Phys. Rev. Lett. 81, 3108 (1998)

complete tunability of interactions



Vortices and Abrikosov vortex arrays

K.W. Madison et al., Phys. Rev. Lett. 84, 806 (2000)

16 32 80 130J.R. Abo-Shaeer et al., Science 292, 476 (2001)



Superfluidity in spin polarized gases

M.W. Zwierlein et al., Science 311, 492 (2006)

Polarization increases in this direction



Phase separation and exotic

superfluid states (FFLO, et cetera)

Y. Shin et al., Phys. Rev. Lett. 97, 030401 (2006)



Outline

!Rotating optical lattices, effective magnetic fields, and frustration



Rotating optical lattices and effective magnetic fields

z

!

d

M. Polini et al., Laser Physics 14, 603 (2004)

C. Wu et al., Phys. Rev. A 69, 043609 (2004)Other ways:

D. Jaksch and P. Zoller, New J. Phys. 5, 56 (2003)

E.J. Mueller, Phys. Rev. A 70, 041603 (2004)

A.S. Sorensen et al., Phys. Rev. Lett. 94, 086803 (2005)

R. Fazio and H. van der Zant, Phys. Rep. 355, 235 (2001)

rotating hologram



Fully Frustrated Cold Bosons: U(1) and Ising order

M. Polini, R. Fazio, A.H. MacDonald, and M.P. Tosi, Phys. Rev. Lett. 95, 010401 (2005)



Outline

!A reminder of density-functional theory

(the Hohenberg-Kohn theorem and the Kohn-Sham mapping)



Density-functional theory: The Hohenberg-Kohn theorem

3. The GS total energy functional can be written as

“universaluniversal”

2. The GS density minimizesminimizes the total energy functional

1. The GS expectation value of every observable

is a unique functionalfunctional of the GS density

“basicbasic variablevariable”



Density-functional theory: The Kohn-Sham mapping

For any interacting system there exists a local single-particle potential

such that the exact GS density of the interacting system

equals the GS density of the auxiliary noninteracting system

we need to approximate “ONLY” the XC potential!



The local density approximation for the xc potential

n1

n2

V xc taken from

the homogeneous

electron liquid

at that density

V xc taken from

the homogeneous

electron liquidat that density

approximated, exactly known (e.g. 1D),

or known from QMC



Outline




Density-functional theory for trapped Fermi gases

Two-component Fermi gases in a 1D optical lattice +trapping potential

exactly solvable by Bethe-Ansatz E.H. Lieb and F.Y. Wu, Phys. Rev. Lett. 20, 1445 (1968)

U

=

t

t

t

t



Generic phase diagram for a 1D quantum fluid

Charge gapless

Spin gapless(Luttinger liquid)

Charge gapless

Spin gapful(Luther-Emery liquid)

T. Giamarchi, Quantum Physics in One Dimension (Clarendon Press, Oxford, 2004)



Spin-density and charge-density waves



Outline




Tendency to spin pairing

thermodynamic limit in the presence of an harmonic trapK. Damle et al., Europhys. Lett. 36, 7 (1996)

N N+2

N+1 N+1



Ground-state site occupation for a 1D

attractive Fermi gases



Ground-state site occupation in a strong

harmonic potential

filled symbols LDA

x DMRG data



Crossover from weak to strong coupling

(emergence of atomic-density waves…)



Crossover from weak to strong coupling

(…and their disappearance)



Observability of the atomic-density waves



Conclusions

References:

Phys. Rev. Lett. 95, 010401 (2005)

Phys. Rev. A 73, 033609 (2006)

Phys. Rev. B 73, 165120 (2006)

Phys. Rev. B 73, 161103 (R) (2006)

cond-mat/0609346

1. Ultracold atomic gases in low-dimensional geometries are of momentous experimental

and theoretical interest (quest for the FFLO superfluid state…)

2. Quoting J.I. Cirac and P. Zoller, Science 301, 176 (2003),

"in the strong interaction regime, atomic experiments may help us to understand several

physical phenomena that have been predicted or observed in solid-state systems"

3. Many cold atom systems constitute, already at this time, an ideal, highly-tunable, and

controllable laboratory realization of many one-dimensional exactly-solvable modelsof condensed matter physics

4. Density-functional theory and density-matrix renormalization-group techniques are ideal

theoretical tools to study the interplay between interactions and inhomogeous

external potentials in one-dimensional systems of interacting fermions

marco polini- luther-emery phase and atomic-density waves in a trapped fermion gas

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