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

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Hanns - Christoph Nägerl Institut für Experimentalphysik, Universität Innsbruck Dresden, July 5 th 2019 Quantum dynamics in strongly correlated one - dimensional Bose gases 2012-2016 2019-2023 Wittgenstein

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

Page 1: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Hanns-Christoph NägerlInstitut für Experimentalphysik, Universität Innsbruck

Dresden, July 5th 2019

Quantum dynamics in strongly correlated one-dimensional Bose gases

2012-2016

2019-2023Wittgenstein

Page 2: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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

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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

Page 4: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Team Members now

Milena Horvath,

PhD-Student

AnamikaNair,

Intern

BeatrixMair

(Rb-Cs)ManueleLandini,

Senior Scientist

BodhaSantra,

Postdoc

Spring 2019

Page 5: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Moore’s law

Gordon Moore

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

Source: Intel

Page 6: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

... 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

Page 7: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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)

Page 8: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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)

scattering length in cesium

strongly interacting 1D quantum fluid

Beyond static latticepotentials

„quantum wire“ withtunable interactions

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

Page 9: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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)

• crystal-like properties

• collective excitations

• low-energy sector:

Luttinger liquidphonons!

Beyond static latticepotentials

„quantum wire“ withtunable interactions

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

Page 10: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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)

Beyond static latticepotentials

„quantum wire“ withtunable interactions

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

• crystal-like properties

• collective excitations

• low-energy sector:

Luttinger liquidphonons!

Page 11: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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

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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

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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

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-range tunneling

Page 14: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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-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

Long-range tunneling

Page 15: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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

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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)

Page 17: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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

Page 18: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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)

Page 19: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Tilting a 1D superfluid

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)

Page 20: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Tilting a 1D superfluid

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)

Page 21: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Bloch oscillations in a lattice

dampedBloch oscillations

J≈U≈ESuperfluid

Page 22: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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

Page 23: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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

Page 24: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Superfluid sample in true 1D: Energy spectrum

E ≈ J ≈ U E >> J ≈ U

Theory:exact diagonali-zationfor 5 particleson 5 sites

Page 25: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Superfluid sample in true 1D: Damping rate

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

Page 26: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Strongly interacting atoms in 1D

F

Many-body dynamicson a lattice

Bose-Hubbard Hamiltonian

Nearest-neighbortunneling

on-siteinteraction

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

• crystal-like properties

• collective excitations

• low-energy sector:

Luttinger liquidphonons!

Beyond static latticepotentials

„quantum wire“ withtuneable interactions

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

Page 27: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Can there be Bloch oscillations without a

lattice?

quasi-momentum q (hkl)

ener

gy (

arb.

u.)

Bloch oscillations without a lattice

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Theory proposal

Page 29: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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

Page 30: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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

Page 31: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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

Page 32: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Bose-Fermi mapping

non-interactingstrongly attractive

fermionsbosons

sketch: wave functions for two particles in harmonic trap

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

Page 33: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Bose-Fermi mapping

strongly repulsive

non-interacting

fermionsbosons

sketch: wave functions for two particles in harmonic trap

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

Page 34: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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

Page 35: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

My naïve intuition

pair correlation function

position0

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

Page 36: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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

Page 37: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Impurity transport: Experiment

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

dashed line: free fall with g/3

Page 38: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Impurity momentum distribution: Experiment vs. theory

experimental resolution

Fermi k-vector, Fermi time

F. Meinert et al., Science 356, 945 (2017)

Page 39: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Impurity momentum distribution: Experiment vs. theory

experimental resolution

Fermi k-vector, Fermi time

F. Meinert et al., Science 356, 945 (2017)

Page 40: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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

F. Meinert et al., Science 356, 945 (2017)

Page 41: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Impurity transport: Comparision with theory

Bloch frequency drift momentum

Force in dimensionless units

F. Meinert et al., Science 356, 945 (2017)

Page 42: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Impurity transport: Comparision with theory

Bloch frequency drift momentum

Force in dimensionless units

F. Meinert et al., Science 356, 945 (2017)

Page 43: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Impurity transport: Can one do better?

Yes, use a weaker force!

Page 44: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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)

Page 45: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Impurity transport: “quantum flutter” proposal

free Fermi gas

Page 46: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Impurity transport: “quantum flutter” proposal

Page 47: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Impurity transport: “quantum flutter” proposal

Page 48: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Thank you!

Page 49: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

One-dimensional systems are special!

Page 50: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Kinematics: Scattering in D=1 is special

Scattering in dimensions

?Scattering in dimension

Kinematics determines out-states in D=1 uniquely

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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

Page 52: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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

Page 53: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Here: Quantum wires of bosons

Page 54: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Array of 1D tubes

Page 55: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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

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

Page 56: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Quantum wires of bosons: Important parameters

Lieb-Liningerinteraction parameter Fermi k-vector

Page 57: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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

How to characterize the strongly-interacting 1D gas?

Measure local correlations

Page 58: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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

NIST group2004

Page 59: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Example: The D=1 Bose gas, local g(2) correlations

PennStategroup2004

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

Innsbruckgroup2011

Page 61: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Other ways to characterize the D=1 Bose gas

Measure global properties

Page 62: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

The strongly-interacting D=1 Bose gas

PennStategroup2004

saturation of samplelength as interactionsare increased

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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

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

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

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... and to the super Tonks-Girardeau gas

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

A2 ~ 1/γ2 interaction parameter

hard rods

Monte Carlo

red data:

blue data:

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Another method: Measurement of the excitation spectrum

Our new method: Bragg spectroscopy

Direct measurement of the dynamic structure factor

Page 67: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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)

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Interesting regime

= 1 to 10

finite temperature

and

Page 69: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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

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

Page 70: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Bragg spectroscopy in 1D:Theory expectation

zero temperature expectation insets: thick solid curves arewith inhomomgenous density

Page 71: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Bragg spectroscopy in 1D

fixed momentum transfer

Page 72: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Bragg spectroscopy in 1D

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)

Page 73: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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

Interaction control for impurity: Theory

Force in dimensionless units

Page 74: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Interaction control for impurity: Theory

Calc. based onmatrixproductstates

Page 75: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

Interaction control for impurity: Theory

Calc. based onmatrixproductstates

Page 76: Quantum dynamics in strongly correlated one- dimensional ...€¦ · Beatrix. Mair (Rb-Cs) Manuele. Landini, Senior Scientist. Bodha Santra, Postdoc Spring 2019. Moore’s law. Gordon

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