Experimental observation of curved light-cones in a quantum field simulator
Marek Gluza
Experiment
Theory
presenting based on new data by M. Tajik, J. Schmiedmayer
N. Sebe, S. Erne, G. Guarnieri, S. Sotiriadis, J. Eisert
P. Schüttelkopf, F. Cataldini, J. Sabino, S-C. Ji, F. Moller
new data by M. Tajik, J. Schmiedmayer
How?
Ultra-cold 1d gases
Inside: atoms
Outside: wavepackets
hydrodynamics
Energy of phonons
E
E
E
E
E
E
E
E
H^TLL=∫dz[2mℏ2nGP∂zφ^2+gδϱ^2]
\hat H_\text{TLL} = \int \text{d}z\left[ \frac{\hbar^2n_{GP}}{2m}\partial_z\hat\varphi^2+g\delta\hat\varrho^2\right]
δϱ
\delta\varrho
∂zφ
\partial_z\varphi
∂zφ
\partial_z\varphi
≪
\ll
δϱ
\delta\varrho
≪
\ll
Tomonaga-Luttinger liquid
Quantum field refrigerators in the TLL model:
System
Piston
Bath
Bath with excitations
System cooled down
Breaking of the Huygens-Fresnel principle
in the inhomogenous TLL model:
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
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
Non-thermal
steady states
Sine-Gordon
thermal states
Atomtronics
Generalized hydrodynamics
Recurrences
Some highlights:
clickeable links at slides.com/marekgluza
Interferometry measures velocities
van Nieuwkerk, Schmiedmayer, Essler, arXiv:1806.02626
Schumm, Schmiedmayer, Kruger, et al., arXiv:quant-ph/0507047
Interferometry measures velocities
van Nieuwkerk, Schmiedmayer, Essler, arXiv:1806.02626
Schumm, Schmiedmayer, Kruger, et al., arXiv:quant-ph/0507047
∂zφ^(z)≈Δzφ^(z)−φ^(z+Δz)≡ΔzΔφ^(z)
\partial_z\hat \varphi(z) \approx\frac{\hat \varphi(z)-\hat \varphi(z+\Delta z)}{\Delta z} \equiv \frac{\Delta \hat \varphi(z)}{\Delta z}
Δz
\Delta z
Interferometry measures velocities
van Nieuwkerk, Schmiedmayer, Essler, arXiv:1806.02626
Schumm, Schmiedmayer, Kruger, et al., arXiv:quant-ph/0507047
∂zφ^(z)
\partial_z\hat \varphi(z)
Δz
\Delta z
Idea by
S. Sotiriadis
ΔzΔφ^(z)
\frac{\Delta\hat\varphi(z)}{\Delta z}
is essentially the velocity
let's look at finite differences!
What is the meaning of velocity correlations?
z
z
z′
z'
⟨Δφ^(z)Δφ^(z′)⟩/Δz2≈⟨∂zφ^(z)∂zφ^(z′)⟩
\langle \Delta\hat\varphi(z)\Delta\hat\varphi(z')\rangle/ \Delta z^2 \approx \langle \partial_z\hat\varphi(z)\partial_z\hat\varphi(z')\rangle
Velocity correlations:
⟨Δφ^(z)Δφ^(z′)⟩/Δz2<0
\langle \Delta\hat\varphi(z)\Delta\hat\varphi(z')\rangle/ \Delta z^2 <0
Anti-correlation:
Left moves opposite to right
z
z
z′
z'
Velocity correlations
z
z
z′
z'
C(z,z′)≈Δz2⟨Δφ^(z)Δφ^(z′)⟩
C(z,z') \approx \frac{\langle \Delta\hat\varphi(z)\Delta\hat\varphi(z')\rangle}{ \Delta z^2 }
And with anti-correlation:
C(z,z′)≈Δz2⟨Δφ^(z)Δφ^(z′)⟩
C(z,z') \approx \frac{\langle \Delta\hat\varphi(z)\Delta\hat\varphi(z')\rangle}{ \Delta z^2 }
What are the measured velocity correlations?
Derivatives = relative velocities!
C(z,z′,t)≈Δz2⟨Δφ^(z,t)Δφ^(z′,t)⟩
C(z,z',t) \approx \frac{\langle \Delta\hat\varphi(z,t)\Delta\hat\varphi(z',t)\rangle}{ \Delta z^2 }
New data by M. Tajik, J. Schmiedmayer
u
C(z,z′,t)≈Δz2⟨Δφ^(z,t)Δφ^(z′,t)⟩
C(z,z',t) \approx \frac{\langle \Delta\hat\varphi(z,t)\Delta\hat\varphi(z',t)\rangle}{ \Delta z^2 }
New data by M. Tajik, J. Schmiedmayer
u
C(z,z′,t)≈Δz2⟨Δφ^(z,t)Δφ^(z′,t)⟩
C(z,z',t) \approx \frac{\langle \Delta\hat\varphi(z,t)\Delta\hat\varphi(z',t)\rangle}{ \Delta z^2 }
New data by M. Tajik, J. Schmiedmayer
u
u
u
u
u
u
C(z,z′,t)≈Δz2⟨Δφ^(z,t)Δφ^(z′,t)⟩
C(z,z',t) \approx \frac{\langle \Delta\hat\varphi(z,t)\Delta\hat\varphi(z',t)\rangle}{ \Delta z^2 }
New data by M. Tajik, J. Schmiedmayer
Simplicity arising from a quench:
Data by M. Tajik, J. Schmiedmayer
Reflections & recurrences
Speed of sound varies in space
Experimental observation of curved light-cones in a quantum field simulator
Marek Gluza
Experiment
Theory
presenting based on new data by M. Tajik, J. Schmiedmayer
N. Sebe, S. Erne, G. Guarnieri, S. Sotiriadis, J. Eisert
P. Schüttelkopf, F. Cataldini, J. Sabino, S-C. Ji, F. Moller
new data by M. Tajik, J. Schmiedmayer
Experimental observation of curved light-cones in a quantum field simulator Marek Gluza Experiment Theory presenting based on new data by M. Tajik, J. Schmiedmayer N. Sebe, S. Erne, G. Guarnieri, S. Sotiriadis, J. Eisert P. Schüttelkopf, F. Cataldini, J. Sabino, S-C. Ji, F. Moller new data by M. Tajik, J. Schmiedmayer
Observation of curved light cones in a quantum field simulator
By Marek Gluza
Observation of curved light cones in a quantum field simulator
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