On the road to dynamical gauge fields in cold atoms Fred - - PowerPoint PPT Presentation

Fred Jendrzejewski

On the road to dynamical gauge fields in cold atoms

SynQS

Synthetic Quantum Systems

Torsten Valentin Florian Jürgen Philipp Markus Fabián Alexander M Kai Apoorva Jan Kerim Alexander H Lilo

Ω

Ωc(x)

geometric scalar potential

Goldman et al. RPP 77 126401 (2014) Jendrzejewski et al. PRA 94 063422 (2016) Lacki et al. PRL 117 233001 (2016)

|g⟩ |r⟩ |e⟩

̂ H = − t∑

i

( ̂ a†

j+1eiaeAj ̂

aj + ̂ a†

j e−iaeAj ̂

aj+1)

Particle Gauge field Dean et al.Nature 497, 598 (2013)

• M. Aidelsburger et al. PRL 111, 185301 (2013)

add a picture of CERN and the definition of charge

ℒQED = ¯ ψ (iγμDμ − m) ψ − 1 4 FμνFμν ℒQCD = ∑

fi

¯ ψfi (iγμDμij − mf) ψfi − 1 2g2Tr (GμνGμν)

Simulation of Higgs decay from CMS

Conserved local charges

=

Conserved local gauge symmetry

div E(r) = eρ(r)

E

eA

Quantum link approach

Wiese, Ann. Phys. 525 777 (2013)

• S. Chandrasekharan and U.-J. Wiese, Nucl. Phys. B 492, 455 (1997).

̂ L

E ∝ Lz L+ ∝ eieaA

Stern-Gerlach

E

eA

E

eA

E

eA

mF = 0 mF = − 1

mf = 0

Fraction of

mF = 0 mF = − 1 mF = 0 mF = − 1

Kasper et al. NJP 19 023030 (2017)

ℒQED = ¯ ψ (iγμDμ − m) ψ − 1 4 FμνFμν

One-axis twisting Hamiltonian

• nian

−J∑

n

(a†

n+1L+ n an + a† nL− n an+1) + M∑ n

(−1)na†

nan +χ∑ n

L2

z,n

HKS =

@Oberthaler group, Heidelberg

ℒQED = ¯ ψ (iγμDμ − m) ψ − 1 4 FμνFμν

−J∑

n

(a†

n+1L+ n an + a† nL− n an+1)

+χ∑

n

L2

z,n

HKS = +M∑

n

(−1)na†

nan

filled Dirac sea Particle Anti-Particle

Kasper et al. NJP 19 023030 (2017)

ℒQED = ¯ ψ (iγμDμ − m) ψ − 1 4 FμνFμν

−J∑

n

(a†

n+1L+ n an + a† nL− n an+1)

+χ∑

n

L2

z,n

HWilson = +M∑

n

(a†

n,↑an,↓ + h . c.)

Zache et al. Quantum Sci. Technol. 3 034010 (2018)

see the talks by Nigel Cooper, Xiong-Jun Liu, Christoph Weitenberg, … more from the Hauke group in weeks !

|0⟩ + ⋯ + |n⟩

ℒQED = ¯ ψ (iγμDμ − m) ψ − 1 4 FμνFμν

−J∑

n

(a†

n+1L+ n an + a† nL− n an+1)

+χ∑

n

L2

z,n

HKS = +M∑

n

(−1)na†

nan

Spin-changing collisions:

2 4 6 0.1 0.05

time fraction of Li up PhD of Arno Trautmann

Kasper et al. NJP 19 023030 (2017)

−J∑

n

(a†

n+1L+ n an + a† nL− n an+1)

+χ∑

n

L2

z,n

HKS = +M∑

n

(−1)na†

nan

χL2

z,n > 2M + χ (Lz,n − 1) 2

χLz,n > M

Spontaneous (Schwinger) pair production for large electric fields

Kasper et al. NJP 19 023030 (2017)

e+ e− E

Kasper et al. NJP 19 023030 (2017)

|g |e |g |e

Fermions Bosons

Zache et al. QST 3 034010 (2018)

Staggered fermions Wilson fermions

ℒQED = ¯ ψ (iγμDμ − m) ψ − 1 4 FμνFμν

[G. Eisner]

Supplemental slides

Platform Refrigeration Dyn Gauge Fields

e- e+ e- e+

Electric vacuum instability

16

Wiese, Ann. Phys. 525 777 (2013) Zohar et al.,Rep. Prog. Phys. 79 014401 (2016) [G. Eisner]