1 A. Iucci Spectroscopy of ultracold bosons

Mainz/München

1D 2D

Spectroscopy of ultracold bosons by periodic lattice modulations

Superfluid-Mott insulating transition

Bose-Fermi mixtures

Low-dimensional systems

A. Iucci, C.Kollath, T. Giamarchi, W. Hofstetter, and U. Schollwöck

disordered systems

LENS

ETHZ

2 A. Iucci Spectroscopy of ultracold bosons

Probing cold atoms

noise measurement:

-> density-density correlations

time-of-flight measurement

-> momentum distribution

periodic lattice modulation

-> energy spectrum

ETHZ

Mainz/München

Mainz

& (in)commensurability

3 A. Iucci Spectroscopy of ultracold bosons

Experimental resultsResponse to a periodic modulation

periodic modulation of optical lattice height

T. Stöferle et al. PRL 92, 130403

ab

sorb

ed

en

erg

y

4 A. Iucci Spectroscopy of ultracold bosons

Bosonic atoms in an optical lattice

kinetic energyinteraction energy

1

†1

11

( 1) .2

.M

jj

j

M

jjj

J b bH n hn cU

periodic modulation of lattice height

-> time dependent J(t) and U(t)

explicitly time-dependent Hamiltonian

experimental parameter -> J and U

Methods: - adaptive t-DMRG- linear response

5 A. Iucci Spectroscopy of ultracold bosons

two particle hole excitations -> energy 2U

Strong interaction

single particle hole excitation -> energy U

response to periodic modulation -> creation of excitations

-> expect peaks at multiples of U

U 2U 3U ħ abso

rbed e

nerg

y

6 A. Iucci Spectroscopy of ultracold bosons

Energy absorption

L=24

L=32 at resonance

ħ=U

away of resonance

abso

rbed

en

erg

y

C. Kollath et al. cond-mat 2006

7 A. Iucci Spectroscopy of ultracold bosons

Energy absorption at commensurate filling

experiment

• peak at U

• small peak at U/2

• no peak at higher frequencies

U/J =72

?

U/J =95

abso

rpti

on r

ate

linear response: A. Iucci et al. accepted by PRA

U 2U

8 A. Iucci Spectroscopy of ultracold bosons

Energy absorption at incommensurate filling

• peak at U

• peak at 2U

experiment

ab

sorp

tion

rate

U/J =95

n~1.2

experiment

U/J =72

9 A. Iucci Spectroscopy of ultracold bosons

2U peak

corresponding processes

two particle-hole excitations single particle-hole excitation

2U peak measure of incommensurability

10 A. Iucci Spectroscopy of ultracold bosons

Intermediate interaction strength

peaks at U, 1.9 U, and 2.6 U

abso

rbed e

nerg

y

experimental results:

peaks at approx. U, 1.9 U, and 2.6 U

U/J =28

U 1.9U

2.6U

T. Stöferle et al. PRL 92, 130403

11 A. Iucci Spectroscopy of ultracold bosons

Energy absorption at incommensurate filling

• peaks at U, 2.1 U, and 2.6 U

• shift of position of energy eigenvalues

at incommensurate filling

U/J =9

n~1.2

a

bso

rpti

on r

ate

12 A. Iucci Spectroscopy of ultracold bosons

Positions of peaks

small system at incommensurate filling:

• position shifts,

• splitting of peaks

0.1 0.2 0.3

J/U

13 A. Iucci Spectroscopy of ultracold bosons

20% perturbation -> beyond linear response

absorption rate, 1% modulation (scaled)

absorption rate, 20% modulation

integrated absorption, 20% modulation

saturation effects occur

in height and width

14 A. Iucci Spectroscopy of ultracold bosons

Summary

occurence of higher frequency peaks for incommensurate filling: confining potential, temperature

shift in peak position stem from shift in energy

20% perturbation -> saturation effects in width and height

not described by linear response

full time-dependent calculation: adaptive t-DMRGmany more applications possible