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
\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]
\delta\varrho
\partial_z\varphi
\partial_z\varphi
\ll
\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:

https://arxiv.org/abs/2104.07751

https://arxiv.org/abs/2006.01177

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:

Schweigler, Schmiedmayer,

et. al, arxiv:1505.03126

Langen, Schmiedmayer,

et. al, arxiv:1411.7185

Rauer, Schmiedmayer,

et. al, arxiv:1705.08231

Schweigler, Schmiedmayer,

et. al, arxiv:2003.01808

Aidelsburger, Beugnon,

et. al, arXiv:1705.02650

Eckel, Campbell,

et. al, arXiv:1406.1095

Møller, Schmiedmayer,

et. al,  arXiv:2006.08577

Malvania, Weiss,

et. al, arxiv:2009.06651

Schemmer, Bouchoule,

et. al, arxiv:1810.07170

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

\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}
\Delta z

Interferometry measures velocities

van Nieuwkerk, Schmiedmayer, Essler, arXiv:1806.02626

Schumm, Schmiedmayer, Kruger, et al., arXiv:quant-ph/0507047

\partial_z\hat \varphi(z)
\Delta z

Idea by

S. Sotiriadis

\frac{\Delta\hat\varphi(z)}{\Delta z}

is essentially the velocity

let's look at finite differences!

https://arxiv.org/abs/2108.07829

What is the meaning of velocity correlations?

z
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:

\langle \Delta\hat\varphi(z)\Delta\hat\varphi(z')\rangle/ \Delta z^2 <0

Anti-correlation:

Left moves opposite to right

z
z'

Velocity correlations

z
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') \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) \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) \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) \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) \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

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