Tomography slides for Jörg
Marek Gluza
NTU Singapore
slides.com/marekgluza
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Gaussian quantum simulators
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How?
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Ultra-cold 1d gases
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Inside: atoms
Outside: wavepackets
hydrodynamics
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Energy of phonons
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Tomonaga-Luttinger liquid
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Interferometry measures velocities
van Nieuwkerk, Schmiedmayer, Essler, arXiv:1806.02626
Schumm, Schmiedmayer, Kruger, et al., arXiv:quant-ph/0507047
Quantum field refrigerators in the TLL model:
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System
Piston
Bath
Bath with excitations
System cooled down
Breaking of the Huygens-Fresnel principle
in the inhomogenous TLL model:
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Why?
Why develop continuous field
quantum simulators?
- Representation theory: Quantum information?
- Continuum limits: BQP and QMA or more?
- Are nanowires computationally hard to simulate?
What do we know is difficult?
SM
Fundamental
Universal
Effective
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Why develop continuous field
quantum simulators?
- Representation theory: Quantum information?
- Continuum limits: BQP and QMA or more?
- Are nanowires computationally hard to simulate?
What do we know is difficult?
SM
Fundamental
Universal
Effective
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/8692248/g1424.png)
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Non-thermal
steady states
Sine-Gordon
thermal states
Atomtronics
Generalized hydrodynamics
Recurrences
Some highlights:
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Interferometry measures velocities
van Nieuwkerk, Schmiedmayer, Essler, arXiv:1806.02626
Schumm, Schmiedmayer, Kruger, et al., arXiv:quant-ph/0507047
Tomography
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Tomography for phonons
Tomography for phonons
What are eigenmodes?
Transmutation
Tomography
(This formalism: Tomography for many modes)
Tomography Klein-Gordon thermal state after quench
Extracting physical properties
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Extracting physical properties
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Extracting physical properties
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Tomography for optical lattices
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What about quantum correlations?
Tomography Klein-Gordon thermal state after quench
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Data by M. Tajik, J. Schmiedmayer
Towards entanglement
Issue #1: Gibbs phenomenon
10 eigen-modes:
20 eigen-modes:
Issue #2: Zero mode missing in tomography
Towards entanglement
Role of the zero mode in entanglement
Squeezing criterion needs:
Not available in tomography
What?
What about correlations?
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Velocity correlations:
Velocity correlations
Anti-correlation:
Left moves opposite to right
And with anti-correlation:
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New data by M. Tajik, J. Schmiedmayer
Time step: 1ms
Simplicity arising from a quench:
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Data by M. Tajik, J. Schmiedmayer
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Mechanisms for the emergence of Gaussian correlations
Marek Gluza
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presenting based on collaboration with
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T. Schweigler, M. Tajik, J. Sabino, F. Cataldini, S-C. Ji, F. Moller, B. Rauer, J. Schmiedmayer, J. Eisert, S. Sotiriadis
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NTU Singapore
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Initial non-Gaussianity decays
Why does it decay?
The system is isolated
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Initial non-Gaussianity decays
Why does it revive?
The system is isolated
Then it revives
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Phase fluctuations
Phase derivative correlations
increase with distance
decay but sizeable
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Effective light cone
not dispersive
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Tomonaga-Luttinger liquid
Inhomogeneous
Breaking of Huygens-Fresnel principle in inhomogeneous Tomonaga-Luttinger liquids
Huygens-Fresnel principle
Tomonaga-Luttinger liquid
Tomonaga-Luttinger liquid
Cold atoms as
an inhomogeneous
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Huygens-Fresnel principle
Huygens-Fresnel principle broken
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The factor 2 is the source of leakage into the light-cone
Breaking of Huygens-Fresnel principle in inhomogeneous Tomonaga-Luttinger liquids
Marek Gluza
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Spyros Sotiriadis
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Per Moosavi
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NTU Singapore
Tomography overview
By Marek Gluza
Tomography overview
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