Tomography

and non-equilibrium dynamics

in continuous field quantum simulators

Marek Gluza

Experiment

Theory

presenting based on new data by M. Tajik, J. Schmiedmayer

S. Sotiriadis, J. Eisert

T. Schweigler, J. Sabino, F. Cataldini, S-C. Ji, F. Moller

Simplicity

in continuous field quantum simulators

Simplicity

 

new data by M. Tajik, J. Schmiedmayer

S. Sotiriadis

Based on new data by M. Tajik, J. Schmiedmayer

Simplicity

from a quench

How?

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

Gluza&Sabino&Vitaliagno&Ng, Huber&Schmiedmayer&Eisert, arixv:2006.01177

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:

Gluza, Moosavi, Sotiriadis, arxiv:2104.07751

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

Non-thermal

steady states

Sine-Gordon

thermal states

Atomtronics

Generalized hydrodynamics

Recurrences

Some highlights:

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

What?

What about 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 }
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

Time step: 1ms

Simplicity arising from a quench:

Data by M. Tajik, J. Schmiedmayer

What?

What about quantum correlations?

Tomography for phonons

\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]
\hat H_\text{TLL} = \sum_{k>0} \frac {\hbar \omega_k}2 (\phi_k^2+\delta\hat\rho_k^2) + g\rho_0^2
\langle\hat \phi_k^2(t)\rangle= \cos^2(\omega_k t) \langle \phi_k^2(0)\rangle \\ \quad\quad\quad\quad\quad+\sin^2(\omega_k t) \langle \delta\hat \rho_k^2(0)\rangle
\delta \hat\rho
\langle\hat \phi^2(t)\rangle
\langle\delta\hat \rho^2(0)\rangle =0?
\langle \hat \phi^2(0)\rangle
\hat \phi

 

Gluza, Schmiedmayer&Eisert, et al, arxiv:1807.04567

 

Gluza, Eisert,  arxiv:2005.09000

Tomography Klein-Gordon thermal state after quench

\hat H_\text{KG}=\hat H_\text{TLL}+J\int \mathrm{d}z \,n_{GP} \hat \varphi^2

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

\hat H_\text{TLL} = \sum_{k>0} \frac {\hbar \omega_k}2 (\phi_k^2+\delta\hat\rho_k^2) + g\hat\rho_0^2
\langle\hat \phi_0^2(t)\rangle= \langle\hat \phi_0^2(0)\rangle +g^2t^2 \langle \delta\hat \rho_0^2(0)\rangle

Towards entanglement

Role of the zero mode in entanglement

Squeezing  criterion needs:

\hat\phi_L+ \hat\phi_R = \hat\phi_0 = \int \mathrm{d}z \hat \varphi(z)
\hat\phi_L = \int_L \mathrm{d}z \hat \varphi(z)
\hat\phi_R = \int_R \mathrm{d}z \hat \varphi(z)
\hat\phi_L- \hat\phi_R \approx \hat\phi_1 = \int \mathrm{d}z \hat \varphi(z) \cos(2\pi z)

Not available in tomography

Conclusions

The atom chip experiment in Vienna:

M. Tajik, J. Schmiedmayer

S. Sotiriadis, J. Eisert

T. Schweigler, J. Sabino, F. Cataldini, S-C. Ji, F. Moller

Exciting simplicity!

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