Mechanisms for the emergence of Gaussian correlations

Marek Gluza

presenting based on collaboration with

T. Schweigler, M. Tajik, J. Sabino, F. Cataldini, S-C. Ji, F. Moller, B. Rauer, J. Schmiedmayer, J. Eisert, S. Sotiriadis

https://arxiv.org/abs/2108.07829

NTU Singapore

2108.07829

Join in for a science popularization experiment:

 

 

archiving our temporal thoughts about time

Today will be about

Using quantum simulator read-out

 

to better understand observed physics

The physical system

Can we 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

Amin Tajik on Friday

van Nieuwkerk, Schmiedmayer, Essler, arXiv:1806.02626

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

\Delta z

Interferometry

measures velocities

van Nieuwkerk, Schmiedmayer, Essler, arXiv:1806.02626

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

\Delta z

Initial non-Gaussianity decays

Why does it decay?

The system is isolated

Schweigler, ..., Schmiedmayer, arxiv:2003.01808

Initial non-Gaussianity decays

Why does it revive?

The system is isolated

Then it revives

Schweigler, ..., Schmiedmayer, arxiv:2003.01808

Cramer, Dawson, Eisert,  Osborne, arXiv:cond-mat/0703314

Cramer, Eisert, arXiv:0911.2475

Sotiriadis, Calabrese, arXiv:1403.7431

Calabrese, Essler, Fagotti, arXiv:1104.0154

Haag, Kadison, Kastler, '73 (Paywall link)

Murthy, Srednicki, arXiv:1809.03681

Gluza, Eisert, Farelly, arXiv:1809.08268

See persistence of non-Gaussianity in Rydberg arrays: Deger, Daniel, Papić, Pachos arxiv:2306.12210

Schweigler, Schmiedmayer et al. arxiv:2003.01808

Gluza, Sotiriadis et al. arxiv:2108.07829

X = \frac 1 {\sqrt n} \sum_{i=1}^n X^{(i)}
\hat a_x(t) \approx \frac 1 {\sqrt {vt}} \sum_{y=1}^{vt} e^{i\phi_{x,y}(t)} \hat a_y(0)

Single-particle Green's functions that behave like this: Gaussify

(Think: Central limit theorem)

Phase fluctuations

Phase derivative correlations

increase with distance

decay but sizeable

Effective light cone

not dispersive

Conclusion: Spatial scrambling unlikely in this experiment

\langle \hat x^4\rangle \neq \langle \hat x^2\rangle^2
\langle \hat p^4\rangle = \langle \hat p^2\rangle^2

but

\langle \hat x^2\rangle \ll \langle \hat p^2\rangle
\hat x(t) = \cos(\omega t) \hat x(0) +\sin(\omega t)\hat p(0)
\langle \hat x(t)^4\rangle \approx (\omega t)^4 \langle \hat p^2\rangle^2
\langle \hat x(\pi / 2 \omega)^4\rangle = \langle \hat p^2\rangle^2

Think: transmuting the cumulant

Canonical decoupling:

Dominant Gaussian sector:

Quadrature rotation:

Gaussification by transmutation:

Classical field approximation conjecture: general at high temperature?

Schweigler, ..., Schmiedmayer, arxiv:2003.01808

Conclusion: Canonical transmutation likely in this experiment

Conclusion: Canonical transmutation likely in this experiment

Conclusion: Spatial scrambling unlikely in this experiment

https://arxiv.org/abs/2108.07829

T. Schweigler, M. Tajik, J. Sabino, F. Cataldini, S-C. Ji, F. Moller, B. Rauer, J. Schmiedmayer, J. Eisert, S. Sotiriadis

Join in for a science popularization experiment:

 

 

archiving our temporal thoughts about time

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?

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!

Made with Slides.com