Spin Squeezing and Bell Correlations in a - Model with Occupation Defects

Tanausú Hernández-Yanes

Thank you

Y. Baamara
A. Niezgoda
A. Sinatra
E. Witkowska

T. Hernández-Yanes et al, Phys. Rev. B 109, 214310 (2024)
T. Hernández-Yanes et al, Phys. Rev. A 111, 023312 (2025)

Spin-squeezing

Jian Ma et al, Physics Reports 509, 2–3, (2011)

One-Axis Twisting (OAT)

Details of our models

  • 1D Lattice
  • Open Boundary Conditions
  • Mott insulating phase
  • M: lattice size, N: number of particles

Second-Order Perturbation Theory

K. A. Chao, J. Spałek, and A. M. Oleś. J. Phys. C 10 L271 (1977)

Heisenberg XXZ model

From Bose-Hubbard model when and

Effective Model for Anisotropy

Perturbation generates two-magnon excitations

Effective Model for Anisotropy

Effective Model for Inhomogeneous Magnetic Field

Single magnon excitations
cite PRL and PRA

Effective Model for Inhomogeneous Magnetic Field

Effective Model for Inhomogeneous Magnetic Field

Experimental Imperfections Affecting Squeezing

  • Temperature: strong, but manageable for finite systems
  • Harmonic trap: usually weak, even beneficial
  • Occupation defects

Occupation Defects at the Preparation Stage

  • - model
  • Limiting cases: and

- model

Additional tunnelling term since first-order terms survive the Schieffer-Wolff transformation

K. A. Chao, J. Spałek, and A. M. Oleś. J. Phys. C 10 L271 (1977)

Occupation Defects at the Preparation Stage

  • : Microscopic model of independent partial chains
  • : Effective model for

Mag. Field Model under Occupation Defects

Mag. Field Model under Occupation Defects

Density Matrix with Occupation Defects

Averaging over many realizations:

From density matrix to statistical ensemble of pure states results

Spin-Squeezing under Occupation Defects

Quantum Correlations under Occupation Defects

M. Płodzień et al, Phys. Rev. Lett. 129, 250402 (2022)
G. Müller-Rigat et al, PRX Quantum 2, 030329 (2021)

Toy Model for Lower Bound

M-Site Bell Correlator for GHZ State

Two-Site Bell Correlator for Squeezed States

  • Collective measurements only
  • Higher moments can increase accuracy
  • Data-driven procedure

G. Müller-Rigat et al, PRX Quantum 2, 030329 (2021)

Two-Site Bell Correlator for Squeezed states

For spin-squeezed states data we get

Summary

  • Two ways to simulate OAT: anisotropy and mag. field
  • Analyzed effective models for spatially fixed holes
  • Local dephasing is strongly detrimental
  • For anisotropy, tunneling immediately optimizes correlations
  • For mag. field, tunneling only provides tiny improvement
  • M-site Bell correlations limited by
  • 2-site Bell correlations limited by

Second Application: Occupation Defects at Measurement Stage

Single occupancies are not guaranteed, but .

M-site Bell Correlator

Bogoliubov + continuous limit at

Two-site Bell Correlator

Assume Entropy conservation

Effect of Harmonic Trap in eff. model

Typically

Effect of Temperature in eff. model

Initial state: Gibbs state (temperature T) of magnon excitations.

–