Simulations of Abelian lattice gauge theories with optical lattices - - PowerPoint PPT Presentation

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Simulations of Abelian lattice gauge theories with optical lattices - - PowerPoint PPT Presentation

May 08, 2023 342 likes •1.69k views

Simulations of Abelian lattice gauge theories with optical lattices Luca Tagliacozzo Alessio Celi ICFO Maciej Lewenstein Maciej Lewenstein ICFO ICFO Alejandro Zamora ICFO Outlook Why simulations with optical lattices Why lattice

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Simulations of Abelian lattice gauge theories with optical lattices Luca Tagliacozzo

Alessio Celi ICFO Maciej Lewenstein ICFO Maciej Lewenstein ICFO Alejandro Zamora ICFO

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Outlook

  • Why simulations with optical lattices
  • Why lattice gauge theories
  • Describe the specific work on Abelian LGT
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Many body quantum systems

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Many body quantum systems

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Many body quantum systems

H = H1 ­ H2 ¢ ¢ ¢ HN

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Many body quantum systems

jÃi = ci1¢¢¢iNji1i ­ ¢¢ ¢jiNi

H = H1 ­ H2 ¢ ¢ ¢ HN

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Many body quantum systems

jÃi = ci1¢¢¢iNji1i ­ ¢¢ ¢jiNi

H = H1 ­ H2 ¢ ¢ ¢ HN

dN

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Many body quantum systems

jÃi = ci1¢¢¢iNji1i ­ ¢¢ ¢jiNi

H = H1 ­ H2 ¢ ¢ ¢ HN

dN

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What would we like to know

  • “More is different”
  • Equilibrium, phases: strong interaction

produces macroscopic phases very different from constituents (confinement, fractionalization, topological order) .

  • Short time out of Equilibrium dynamic?
  • Equilibration
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Classical simulations

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Classical simulations

  • Density functional theory (small interaction)
  • Monte Carlo (positive Hamiltonians)
  • Tensor Networks (generic)
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Controversial results

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Time evolution

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Time evolution

EXPONENTIALLY HARD PROBLEM

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Quantum simulators

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Quantum simulators

COLD ATOMS

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Quantum simulators

COLD ATOMS IONS TRAPS

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Quantum simulators

COLD ATOMS IONS TRAPS MICROWAVE ION CHIPS

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Quantum simulators

COLD ATOMS IONS TRAPS MICROWAVE ION CHIPS

IS it the way To dynamic?

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Gauge theories

  • Specific class of QMBS
  • They are very important ingredients for the

description of both high and low energies physics (QCD... antiferromagnets...)

  • They typically involve more than 2 bodies

interactions

  • Their strongly coupled regime is still under debate
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Natural interactions on optical lattices

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Natural interactions on optical lattices

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Natural interactions on optical lattices

Difficult to engineer interactions different from

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Natural interactions on optical lattices

Difficult to engineer interactions different from

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Natural interactions on optical lattices

Difficult to engineer interactions different from

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Natural interactions on optical lattices

Difficult to engineer interactions different from How do we get four body interactions ?

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Four body interactions via the Rydberg gate

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Four body interactions via the Rydberg gate

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Four body interactions via the Rydberg gate

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Four body interactions via the Rydberg gate

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Four body interactions via the Rydberg gate

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Four body interactions via the Rydberg gate We need a two dimensional Hilbert space

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x y t Lattice gauge theories

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x y t Lattice gauge theories

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x y t Lattice gauge theories

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x y t Lattice gauge theories

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x y t Lattice gauge theories

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x y t Lattice gauge theories

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Hamiltonian formulation of LGT, Hilbert space

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Hamiltonian formulation of LGT, Hilbert space

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Hamiltonian formulation of LGT, Hilbert space

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Hamiltonian formulation of LGT, Hilbert space

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Hamiltonian formulation of LGT, Hilbert space

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Hamiltonian formulation of LGT, Hilbert space

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Hamiltonian formulation of LGT, Hilbert space

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Hamiltonian formulation of LGT, Hilbert space

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Hamiltonian formulation of LGT, Hilbert space

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Hamiltonian formulation of LGT, operators

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Hamiltonian formulation of LGT, operators

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Hamiltonian formulation of LGT, operators

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Hamiltonian formulation of LGT, operators

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Hamiltonian formulation of LGT, operators

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Hamiltonian formulation of LGT, operators

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The deformed toric code in parallel field

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The deformed toric code in parallel field

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The deformed toric code in parallel field

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The deformed toric code in parallel field

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The deformed toric code in parallel field

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The deformed toric code in parallel field

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The deformed toric code in parallel field

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The deformed toric code in parallel field

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The deformed toric code in parallel field

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Pure Z2 lattice gauge theory as low energy of the deformed toric code

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Pure Z2 lattice gauge theory as low energy of the deformed toric code

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Pure Z2 lattice gauge theory as low energy of the deformed toric code

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Pure Z2 lattice gauge theory as low energy of the deformed toric code

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Pure Z2 lattice gauge theory as low energy of the deformed toric code

Deconfined/ T

  • pological

Confined Wegner 71, Kogut 79

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U(1) LGT with local Hilbert space of dim 2

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U(1) LGT with local Hilbert space of dim 2

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U(1) LGT with local Hilbert space of dim 2

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U(1) LGT with local Hilbert space of dim 2

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U(1) LGT with local Hilbert space of dim 2

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U(1) LGT with local Hilbert space of dim 2

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U(1) LGT with local Hilbert space of dim 2

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U(1) LGT with local Hilbert space of dim 2

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U(1) LGT with local Hilbert space of dim 2

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Link models and gauge magnets

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Link models and gauge magnets

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Link models and gauge magnets

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Link models and gauge magnets

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The U(1) gauge magnets

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The U(1) gauge magnets

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The U(1) gauge magnets

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The U(1) gauge magnets

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The U(1) gauge magnets Local Gaped Confined

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The U(1) gauge magnets Local Gaped Confined

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The U(1) gauge magnets T

  • pological

Gapless Confined Local Gaped Confined

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Can we really simulate it with Rydberg?

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Can we really simulate it with Rydberg?

We can perform time evolution

two level system which dynamic can be implemented via Rydberg

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Can we really simulate it with Rydberg?

Hamiltonian is not frustration free We do not know GS locally

We cannot make dissipative state preparation We can perform time evolution

two level system which dynamic can be implemented via Rydberg

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Can we really simulate it with Rydberg?

Hamiltonian is not frustration free We do not know GS locally

We cannot make dissipative state preparation We can perform time evolution

two level system which dynamic can be implemented via Rydberg

We cannot make adiabatic preparation

Gapless interesting phase no easy state Level crossing with other phase where easy state

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U(1) gauge magnet Rydberg state preparation

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U(1) gauge magnet Rydberg state preparation Adiabatic

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U(1) gauge magnet Rydberg state preparation Adiabatic We need an easy state

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U(1) gauge magnet Rydberg state preparation Adiabatic We need an easy state Slowly change H

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U(1) gauge magnet Rydberg state preparation Adiabatic We need an easy state Slowly change H but

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U(1) gauge magnet Rydberg state preparation Adiabatic We need an easy state Slowly change H but Dissipative

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U(1) gauge magnet Rydberg state preparation Adiabatic We need an easy state Slowly change H Engenier L(t) but Dissipative

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U(1) gauge magnet Rydberg state preparation Adiabatic We need an easy state Slowly change H Engenier L(t) Need to locally know GS but but Dissipative

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State preparation, mixed strategy

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State preparation, mixed strategy

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State preparation, mixed strategy

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State preparation, mixed strategy

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State preparation, mixed strategy

i) DISSIPATIVE

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State preparation, mixed strategy

i) DISSIPATIVE

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State preparation, mixed strategy

i) DISSIPATIVE

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State preparation, mixed strategy

i) DISSIPATIVE ii) ADIABATIC

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State preparation, mixed strategy

i) DISSIPATIVE ii) ADIABATIC

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State preparation, mixed strategy

0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 2.5 cw
  • i) DISSIPATIVE

ii) ADIABATIC

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State preparation, mixed strategy

0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 2.5 cw
  • 1

2 3 4 −8.5 −8 −7.5 −7 −6.5 −6 −5.5 t Energy CRAB Adiabatic linear ramp E0 E1

i) DISSIPATIVE ii) ADIABATIC

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U(1) gauge magnet Rydberg time evolution

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U(1) gauge magnet Rydberg time evolution

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U(1) gauge magnet Rydberg time evolution Trotter

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U(1) gauge magnet Rydberg time evolution Trotter

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U(1) gauge magnet Rydberg time evolution Trotter

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U(1) gauge magnet Rydberg time evolution Trotter

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U(1) gauge magnet Rydberg time evolution Trotter

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U(1) gauge magnet Rydberg time evolution Trotter

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U(1) gauge magnet Rydberg time evolution Trotter

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U(1) gauge magnet Rydberg time evolution Trotter

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Conclusions Intersting historical phase for MBQP First quantum simulations (QS) We propose a possible candidate for U(1) LGT QS Now should be possible to perform

  • ut of equilibrium time-evolution.

Further step towards complete QS LGT... (need matter).