Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele....

Hanns-Christoph NägerlInstitut für Experimentalphysik, Universität Innsbruck

Dresden, July 5th 2019

Quantum dynamics in strongly correlated one-dimensional Bose gases

2012-2016

2019-2023Wittgenstein

Three quantum gas projects in my group in Innsbruck

CsIIICs and Cs2 in optical lattices:

1D physicsRb-CsRb-Cs mixtures

and bosonic RbCs dipolar molecules

K-CsK-Cs mixtures,

quantum gas microscopy,fermionic dipoles, topological states

Innsbruck Cesium-Team

FlorianMeinert

Manfred Mark

EmilKirilov

KatharinaLauber Philipp

Weinmann

Michael Gröbner

Andrew Daley

HCN

Theory support

The Team & Collaborators…

Michael KnapEugene Demler Mikhail Zvonarev

Jean-Sébastien Caux

Dirk-Sören Lühmann

Milosz Panfil

Ole Jürgensen

Team Members now

Milena Horvath,

PhD-Student

AnamikaNair,

Intern

BeatrixMair

(Rb-Cs)ManueleLandini,

Senior Scientist

BodhaSantra,

Postdoc

Spring 2019

Moore’s law

Gordon Moore

Oct. 2018: Samsung announced that it has started commercialproduction of 7-nm scale technology (~13 Si atoms)

Source: Intel

... approaching the ultimate limitof single-atom wires

B. Weber et al., Science 335, 64 (2012)

Electronic motion at the nano-scale

STM image of an atomic wire in Si,4 atoms wide and 1 atom tall

Quantum phenomenain 1D single-atom wires:

• many-body quantumdynamics and transport

• role of particle interactionsand correlations

• specifically in 1D-systems

• time-resolved observations

ultracold atomsconfined to 1D

„quantum tubes“

50 nm

Strongly interacting atoms in 1D

force F

Many-body dynamicson a lattice

Bose-Hubbard Hamiltonian

Nearest-neighbortunneling

on-siteinteraction

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


force F




on-siteinteraction


scattering length in cesium

strongly interacting 1D quantum fluid

Beyond static latticepotentials

„quantum wire“ withtunable interactions

E. Haller et al., Science 325, 1224 (2009)


force F




on-siteinteraction


• crystal-like properties

• collective excitations

• low-energy sector:

Luttinger liquidphonons!





force F




on-siteinteraction









Example: 1D Mott insulator

J. Simon et al., Nature 472, 307 (2011) S. Sachdev et al., Phys. Rev. B 66, 075128 (2002)

J«UMott insulator

long-range correlatedtunnel transport

correlated tunneling motionin strong fields

E=U/2 E=U/3E=U

E

doublons produced after 200 ms

F. Meinert, M. Mark, E. Kirilov, K. Lauber, P. Weinmann, M. Gröbner,A.J. Daley, and H.-C. Nägerl, Science 344, 1259 (2014)

Resonant long-range transport

Long-range tunneling

E=UE=U/2

E=U/3

V=10ER



E=U/2

J J

virtual state

analogue at the nano-scale

electron transport in quantum dot arrays

F. Braakman et al., Nat. Nanotech. 8, 432 (2013)




long-distance atom transport

without occupying intermediatelattice sites

analogues at the nano-scale

electron transport in quantum dot arrays

F. Braakman et al., Nat. Nanotech. 8, 432 (2013)

E=U/2

E=U/3

E=U/4

E=U/5

V=7ER


E=1.038 kHz

E=0.973 kHz

E=0.865 kHz

F. Meinert, M. Mark, E. Kirilov, K. Lauber, P. Weinmann, A.J. Daley,and H.-C. Nägerl, Phys. Rev. Lett. 111, 053003 (2013)

U=1.019(20) kHz

Time-resolved tunneling

E≈U

Coherent many-body tunneling dynamics

Coherent tunnel coupling

V=10ER

Dynamics driven by higher-order tunneling

Second- and third-order tunneling

E=U/37 ER, 253 a09 ER, 253 a09 ER, 175 a0

E=U/2

Growth rate 1/τDepends onJ and U.

10 ER, 253 a012 ER, 253 a010 ER, 400 a0

F. Meinert et al., Science 344, 1259 (2014)

Bloch oscillations in a latticeen

ergy

(ar

b. u

.)

quasi-momentum q (hkl)

single particle band structure

coherentBloch oscillations

J»USuperfluid

F. Meinert et al., Phys. Rev. Lett. 112, 193003 (2014)

BOs in momentum space

F

Tilting a 1D superfluid

non-interacting (U=0)

Bloch oscillations

th= 0 TB th= 7 TB th= 14 TB

Vz=7ER (J=52.3 Hz)

TB≈0.57 ms F. Meinert, M.J. Mark, E. Kirilov, K. Lauber, P. Weinmann, M. Gröbner,and H.-C. Nägerl, Phys. Rev. Lett. 112, 193003 (2014)


th= 0 TB th= 7 TB th= 14 TB

Collapse and revivals

Vz=7ER (J=52.3 Hz)

TB≈0.57 ms

weakly-interacting (U=110 Hz)


Period of the phase revival

frev = U/hDirect measure of U

in the superfluid regime

revi

val f

requ

ency

fre

v(H

z)

Blo

ch fre

quen

cy f

B(k

Hz)

Bloch oscillations in a lattice

dampedBloch oscillations

J≈U≈ESuperfluid

Superfluid sample in true 1D

Irreversible damping!

E = 266 Hz (squares)

E = 855 Hz (triangles)

Vz = 4 ER (i.e. J = 114.2 Hz)U = 106 Hz

Superfluid sample in true 1D

as = 4.5 a0 (squares), as = 20.8 a0 (triangles), as = 83.4a0 (circles) at E = 346(10)Hz and Vz = 4 ER (i.e. J = 114.2 Hz)

Irreversible damping as a fct of interaction strength

Superfluid sample in true 1D: Energy spectrum

E ≈ J ≈ U E >> J ≈ U

Theory:exact diagonali-zationfor 5 particleson 5 sites

Superfluid sample in true 1D: Damping rate

E = 346 Hz and Vz = 4 ER (J = 114.2 Hz) F. Meinert et al., PRL 2014


F




on-siteinteraction







„quantum wire“ withtuneable interactions


Can there be Bloch oscillations without a

lattice?

quasi-momentum q (hkl)

ener

gy (

arb.

u.)

Bloch oscillations without a lattice

Theory proposal

Bloch oscillations without a lattice

short-range crystal-likeproperties via strong repulsion

E. Lieb and W. Liniger, Phys. Rev. 130, 1616 (1963)

D. M. Gangardt et al., Phys. Rev. Lett. 102, 070402 (2009)M. Knap et al., Phys. Rev. Lett. 112, 015302 (2014)

ImpurityBloch oscillations

Tonks-Girardeau gas (TG)

low-energyspectral edge

Impurity

Model: E. Lieb and W. Liniger, Phys. Rev. 130, 1605 (1963)

bosons in uniform 1D systemrepulsive contact potential

Hamilton operator:

γ − parameter

Tonks-Girardeau gas (TG)( non-interacting fermions )( hard spheres )

kinetic energy interaction energy

Ideal gas(non-interacting bosons)

Lieb - Liniger model: Fermionization

c - constant γ - interaction strength

sketch: wave functions for two particles in harmonic trap

bosons

repulsiveinteraction

attractiveinteraction

fermions

Bose-Fermi mapping

Bose-Fermi mapping: bosons and fermions in 1D show similar density distributions

Bose-Fermi mapping

non-interactingstrongly attractive

fermionsbosons



Bose-Fermi mapping

strongly repulsive

non-interacting

fermionsbosons



Consequence for the Mott-insulator transition

Mott – insulator phase transition“metal - insulator transition”

deep lattice, tight-binding approximationconnects ground states of the

Bose-Hubbard modelsuperfluid Mott insulator

Mott-Hubbard transition

lattice

Pinning transition

add shallow lattice (perturbation) connects ground states of the

sine-Gordon modelTonks gas Mott insulator

My naïve intuition

pair correlation function

position0

Impurity performs Bloch oscillationson the g(2) -function!!!

Tuning interactions

Interaction control for impurity

Notation: for the bath-bath interaction

for the impurity-bath interactionscatterering length data by P. Julienne

host gas: F=3, mF=3

impurity: F=3, mF=2

Impurity transport: Experiment

Impurity momentum distribution n(k) for no interactions: Free fall

dashed line: free fall with g/3

Impurity momentum distribution: Experiment vs. theory

experimental resolution

Fermi k-vector, Fermi time


Impurity transport: Experiment vs. theoryMean impurity momentum green solid line: theory, no free parameters


Impurity transport: Comparision with theory

Bloch frequency drift momentum

Force in dimensionless units


Impurity transport: Can one do better?

Yes, use a weaker force!

Impurity transport: Many more questions

Where does the energy go? (origin of the damping)

What happens for even stronger interactions?

What happens for attractive interactions?(either within the bath and/or between impurity and bath)

What happens for more than one impurity per tube?

...

What happens for mass-unbalanced systems?Can one use the impurity as a probe for phasetransitions? (e.g. „pinning“ transition)

see E. Haller et al., Nature 466, 597 (2010)

What happens for uniformly moving impurities?see proposal by C. Mathey, M. Zvonarev, and E. Demler, Nature Physics 8, 881 (2012)

see E. Haller et al., Science 325, 1224 (2009)

Impurity transport: “quantum flutter” proposal

free Fermi gas

Impurity transport: “quantum flutter” proposal

Thank you!

One-dimensional systems are special!

Kinematics: Scattering in D=1 is special

Scattering in dimensions

?Scattering in dimension

Kinematics determines out-states in D=1 uniquely

Single-particledispersion:

Single particle-holepair spectrum:

Fermi momentum

Density

Particle branch

Hole branchhole

particle

Single particle-hole pair: some excitations are kinematically forbidden

Example: The D=1 non-interacting Fermi gas

πn

n

Example: Excitations in the D=1 Bose gas

Dynamic structure factor

free fermionsWealy-interactingbosons

J.-S. Caux and P. Calabrese,Phys. Rev. A 74, 031605(R) (2006)

increase interactions

Here: Quantum wires of bosons

Array of 1D tubes

Quantum wires of bosons

Lieb-Liniger model (1D gas of bosons, repulsive contact potential, T=0)

Lieb-Liniger γ−parameter

Tonks-Girardeau gas (TG)(fermionization)

kinetic term interaction term

ideal gas(non-interacting bosons)

c - constant γ - interaction strength

gas in 1D geometry


Quantum wires of bosons: Important parameters

Lieb-Liningerinteraction parameter Fermi k-vector

Ways to characterize the strongly-interacting D=1 Bose gas

How to characterize the strongly-interacting 1D gas?

Measure local correlations

Example: The D=1 Bose gas, local g(3) correlations

NIST group2004


PennStategroup2004


Innsbruckgroup2011

Other ways to characterize the D=1 Bose gas

Measure global properties

The strongly-interacting D=1 Bose gas

PennStategroup2004

saturation of samplelength as interactionsare increased

Characterization of the Tonks-Girardeau gas

Regimes

Noninteracting (thermal) 41D mean field 3Fermionized bosons (TG) 4... ...

Probe: Measure collective oscillation frequencies

Theory: C. Menotti and S. Stringari, PRA 66, 043610 (2002)

compression dipole

Characterization of the crossover to the Tonks-Girardeau gas...

E. Haller et al.,Science 325, 1224 (2009)

... and to the super Tonks-Girardeau gas


A2 ~ 1/γ2 interaction parameter

hard rods

Monte Carlo

red data:

blue data:

Another method: Measurement of the excitation spectrum

Our new method: Bragg spectroscopy

Direct measurement of the dynamic structure factor

Elementary excitations of the 1D Bose gasE. Lieb and W. Liniger, Phys. Rev. 130, 1616 (1963)Dynamic structure factor

free fermionsWeakly-interacting bosons

J.-S. Caux and P. Calabrese,Phys. Rev. A 74, 031605(R) (2006)

Interesting regime

= 1 to 10

finite temperature

and

Probing excitations via Bragg spectroscopyFlorence group: N. Fabbri et al., Phys. Rev. A 91, 043617 (2015)

Bragg spectroscopy in 1D

1D Bose gas with tuneable interactions

repulsive

attractive

confinement + Cs Feshbach structure

Time of flight---------

mapping tomomentum space

measure energy transfer

confinement-inducedresonance (CIR)

allows us to tune


Bragg spectroscopy in 1D:Theory expectation

zero temperature expectation insets: thick solid curves arewith inhomomgenous density


fixed momentum transfer


Excitation spectrum at finite temperatures

Theory: Y. Cherny and J. Brand,Phys. Rev. A 73, 023612(R) (2006)

Comparison with theory tells us that we see a collective excitation!

Details: F. Meinert et al., Phys. Rev. Lett. 115, 085301 (2015)

¼ 11 ¼ 22 ¼ 45

M. Panfil and J.-S. Caux,Phys. Rev. A 89, 033605 (2014)

Theory prediction: Momentum space images (for comparatively weak interactions)

Interaction control for impurity: Theory

Force in dimensionless units

Interaction control for impurity: Theory

Calc. based onmatrixproductstates

PublicationsQuantum Quench in an Atomic One-Dimensional Ising ChainF. Meinert, M. Mark, E. Kirilov, K. Lauber, P. Weinmann, A.J. Daley, and H.-C. Nägerl, Phys. Rev. Lett. 111, 053003 (2013)

F. Meinert, M.J. Mark, E. Kirilov, K. Lauber, P. Weinmann, M. Gröbner, and H.-C. Nägerl, Phys. Rev. Lett. 112, 193003 (2014)

Interaction-Induced Quantum Phase Revivals and Evidence for the Transition to the Quantum Chaotic Regime in 1D Atomic Bloch Oscillations

F. Meinert, M. Panfil, M. J. Mark, K. Lauber, J.-S. Caux, and H.-C. Nägerl, Phys. Rev. Lett. 115, 085301 (2015)

Probing the Excitations of a Lieb-Liniger Gas from Weak to Strong Coupling

F. Meinert, M. J. Mark, K. Lauber, A. J. Daley, and H.-C. Nägerl, Phys. Rev. Lett. 116, 205301 (2016)

Floquet Engineering of Correlated Tunneling in the Bose-Hubbard Model with Ultracold Atoms

O. Jürgensen, F. Meinert, M. Mark, H.-C. Nägerl, and D.-S. Lühmann,Phys. Rev. Lett. 113, 193003 (2014)

Observation of Density-Induced Tunneling

F. Meinert, M. Mark, E. Kirilov, K. Lauber, P. Weinmann, M. Gröbner, A.J. Daley, and H.-C. Nägerl, Science 344, 1259 (2014)

Observation of many-body dynamics in long-range tunneling after a quantum quench

F. Meinert, M. Knap, E. Kirilov, K. Jag-Lauber, M. B. Zvonarev, E. Demler, and H.-C. Nägerl, Science (2017)

Bloch oscillations in the absence of a lattice

Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele....

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