Simulating Anyonic Statistics in Few-Body Dynamics Philipp Prei - - PowerPoint PPT Presentation

▶
simulating anyonic statistics in few body dynamics
SMART_READER_LITE
LIVE PREVIEW

Simulating Anyonic Statistics in Few-Body Dynamics Philipp Prei - - PowerPoint PPT Presentation

Jan 12, 2024 111 likes •533 views

Simulating Anyonic Statistics in Few-Body Dynamics Philipp Prei Physikalisches Institut Universitt Heidelberg Anyon Physics of Ultracold Atomic Gases 14.12.2018 Anyonic quasiparticles with ultracold atoms Fractional Statistics 2D

slide-1
SLIDE 1

Simulating Anyonic Statistics in Few-Body Dynamics

Philipp Preiß Physikalisches Institut Universität Heidelberg Anyon Physics of Ultracold Atomic Gases 14.12.2018

slide-2
SLIDE 2

Anyonic quasiparticles with ultracold atoms

Fractional Statistics See also the next talk by Christof Weitenberg

Dai et al. Nature Physics 13,1195 (2017)

2D topologically ordered systems

slide-3
SLIDE 3

What are the phases and dynamics of anyonic particles in one dimension?

Keilmann et al., Nature Communications 2, 361(2011)

One-dimensional anyon models

Fractional statistics bosons pseudo-fermions

slide-4
SLIDE 4

Keilmann et al., Nature Communications 2, 361(2011)

Engineering anyonic statistics

bosons fermions Engineering of effective anyonic statistics:

???

Sebastian Greschner, Luis Santos, Thassilo Keilmann, Marco Roncaglia, Axel Pelster, André Eckardt, Yunbo Zhang, and many others …

  • Raman-assisted tunneling
  • Lattice shaking
  • Lattice depth modulation
slide-5
SLIDE 5

I. Engineering occupation-dependent tunneling Lattice modulation in Mott insulators

  • II. Identify a suitable experimental setting

Quantum walks of two bosons

Outline

Simulation of Anyons with one-dimensional Bosons

Ask anything any time!

slide-6
SLIDE 6

Markus Greiner Ruichao Ma Eric Tai Matthew Rispoli Jon Simon Rajibul Islam

  • R. Ma et al.: Photon-Assisted Tunneling in a Biased Strongly Correlated Bose Gas PRL 107, 095301 (2011)
  • P. M. Preiss et al.: Strongly Correlated Quantum Walks in Optical Lattices Science 347 1229 (2015)

The team

Greiner group Harvard University

slide-7
SLIDE 7

Anyon-Boson Mapping

  • L. Cardarelli et al., PRA 94, 023615 (2016)
  • C. Sträter et al., PRL 117, 205303 (2016)

Lattice amplitude modulation

slide-8
SLIDE 8

Bose-Hubbard Model

Mott insulator Initialize one particle per site tunneling J interaction U bias E

slide-9
SLIDE 9

Anyon-Boson Mapping

  • L. Cardarelli et al., PRA 94, 023615 (2016)
  • C. Sträter et al., PRL 117, 205303 (2016)

Strong tilt: suppress direct tunneling

slide-10
SLIDE 10

Anyon-Boson Mapping

  • L. Cardarelli et al., PRA 94, 023615 (2016)
  • C. Sträter et al., PRL 117, 205303 (2016)

Restore individual processes

slide-11
SLIDE 11
  • Rubidium 87 in 2D square lattice
  • Site-resolved imaging
  • Initialize one particle per site

Experiment

Bosonic quantum gas microscope

slide-12
SLIDE 12
  • R. Ma et al. PRL 107, 095301 (2011)

Photon-assisted tunneling

slide-13
SLIDE 13
  • R. Ma et al. PRL 107, 095301 (2011)

Photon-assisted Tunneling

slide-14
SLIDE 14
  • R. Ma et al. PRL 107, 095301 (2011)

Photon-assisted tunneling

slide-15
SLIDE 15

Photon-assisted many-body dynamics

Coherent oscillations Prepare Drive

slide-16
SLIDE 16

Photon-assisted tunneling

Summary

✔ ✔

All ingredients demonstrated

  • Suppression of free tunneling
  • Selective assisted tunneling
  • Coherent many-body dynamics
  • Combine for multi-chromatic drive
slide-17
SLIDE 17

I. Engineering occupation-dependent tunneling Lattice modulation in Mott insulators

  • II. Identify a suitable experimental setting

Quantum walks of two bosons

Outline

Simulation of Anyons with one-dimensional Bosons

slide-18
SLIDE 18

Keilmann et al., Nature Communications 2, 361(2011)

Experimental settings

Picking the right scenario

  • L. Cardarelli et al., PRA 94, 023615 (2016)

Focus on few-body dynamics

+

Experiment Numerics

slide-19
SLIDE 19

Control over individual Bosons

slide-20
SLIDE 20

Single-Particle Quantum Walk

Free quantum walks of individual particles Single realiza+on

Quantum faster than classical!

slide-21
SLIDE 21

Single-Particle Quantum Walk

slide-22
SLIDE 22

Single-Particle Quantum Walk

Free quantum walks of individual particles Single realization Average density evolution

Quantum faster than classical!

  • P. M. Preiss et al., Science 347 1229 (2015)
slide-23
SLIDE 23

How do we know it is really quantum motion?

slide-24
SLIDE 24

Tilt: Bloch Oscillations

α

Refocusing of matter wave: absolutely impossible for classical motion

slide-25
SLIDE 25

Single-Particle Bloch Oscillations

slide-26
SLIDE 26

Single-Particle Bloch Oscillations

slide-27
SLIDE 27

Single-Particle Bloch Oscillations

  • Temporal period

, spatial width

  • Delocalized over ~14 sites = 10μm.
  • Revival probability 96(3)%

See also:

  • E. Haller et al., PRL104, 200403 (2010)
  • M. Genske et al., PRL 110, 190601 (2013)
slide-28
SLIDE 28

Hanbury Brown-Twiss Interference

Bunching of non-interacting bosons

Single realization Histogram of many runs

Very strong signature of bosonic statistics

slide-29
SLIDE 29

Each tunneling step = phase i

Sensitivity to quantum statistics

Time evolution of two free bosons Correlation properties from microscopic tunneling phases

slide-30
SLIDE 30

Fermionization of Bosons

Bosons with strong repulsive interactions

u=U/J

Weak interactions u<1 Strong interactions u>>1 In 1D, hard-core bosons free spinless fermions

Experiments on Tonks-Girardeau gas: Weiss group, Bloch group

  • T. Kinoshita et al., Science 305 (2004), B. Paredes et al., Nature 429 (2004)

Proposal: Y. Lahini et al., PRA 86 011603 (2012)

slide-31
SLIDE 31

Repulsively Bound Pairs

  • No HBT interference terms
  • Independent quantum walk

Weak interaction Strong interaction

  • Pairs bound by repulsive interaction
  • Quantum walk of the pair

See also: K.Winkler et al., Nature 441 853 (2006)

  • A. Ahlbrecht et al., New J. Phys. 14, 073050 (2012)
slide-32
SLIDE 32

Bloch Oscillations of Two Bosons

  • Independent oscillations
  • Clean revival
  • Complex dynamics
  • Asymmetry
  • Bloch oscillations of pairs
  • Frequency-doubled BO

Weak interaction Strong interaction

See also: R. Khomeriki et al., PRA 81 065601 (2010), G. Corrielli et al., Nature Comm. 41556 (2013)

slide-33
SLIDE 33

Summary

Bound Pairs Quantum Walk Fermionization Bloch Oscillation

Quantum Walks Coherent dynamics Sensitivity to statistics Formation of bound state Numerical calculations

Strong overlap with other proposals: L.Wang et al., PRA 90, 063618 (2014)

  • S. Greschner et al., PRA 97, 053605 (2018)
  • L. Cardarelli et al., PRA 94, 023615 (2016)
slide-34
SLIDE 34

Bosons with photon-assisted tunneling U’ = 0; E’=0

Bound state formation

Partially paired phase

  • S. Greschner et al., PRA 97, 053605 (2018)

See also: Wang et al., PRA 90, 063618 (2014)

slide-35
SLIDE 35

Bosons with photon-assisted tunneling U’ = 0; E’=0

Bound state formation

Partially paired phase

  • S. Greschner et al., PRA 97, 053605 (2018)

Mapping out the bound state with different initial placements

slide-36
SLIDE 36

Quantum walk asymmety

Re-introduce interactions

See also: Wang et al., PRA 90, 063618 (2014)

Interaction- and statistics-induced asymmetry

U’ = 2; δ=0

slide-37
SLIDE 37

Bloch oscillations

Non-interacting walkers with gradient

U’ = 0; δ=1

Destruction and frequency tripling of Bloch oscillations

~ωmod = E − δ

slide-38
SLIDE 38

Summary

Boson dynamics and engineered tunneling

  • Occupation-dependent tunneling demonstrated
  • Fully controlled two-particle dynamics
  • Signatures with available systems sizes & scales
slide-39
SLIDE 39

Group of Selim Jochim @ Heidelberg University

Acknowledgements

Few-fermion systems in optical tweezers

Thank you for your a?en@on!

slide-40
SLIDE 40