[Paper Review] Probing quench dynamics across a quantum phase transition into a 2D Ising antiferromagnet

Elmer Guardado-Sanchez, Peter Brown+5 more|arXiv (Cornell University)|Nov 2, 2017

Quantum many-body systems68 references54 citations

TL;DR

The paper experimentally studies quench dynamics in a 2D quantum Ising model realized with a near defect-free Li-6 atomic array coupled to a low-lying Rydberg state, analyzing sudden and slow quenches across the paramagnet–antiferromagnet transition and comparing to NLCE and exact diagonalization.

ABSTRACT

Simulating the real-time evolution of quantum spin systems far out of equilibrium poses a major theoretical challenge, especially in more than one dimension. We experimentally explore the dynamics of a two-dimensional Ising spin system with transverse and longitudinal fields as we quench it across a quantum phase transition from a paramagnet to an antiferromagnet. We realize the system with a near unit-occupancy atomic array of over 200 atoms obtained by loading a spin-polarized band insulator of fermionic lithium into an optical lattice and induce short-range interactions by direct excitation to a low-lying Rydberg state. Using site-resolved microscopy, we probe the correlations in the system after a sudden quench from the paramagnetic state and compare our measurements to exact calculations in the regime where it is possible. We achieve many-body states with longer-range antiferromagnetic correlations by implementing a near-adiabatic quench and study the buildup of correlations as we cross the quantum phase transition at different rates.

Motivation & Objective

• Motivate understanding real-time dynamics of quantum spin systems beyond 1D and equilibrium.
• Realize a 2D Ising model with Rydberg-mediated nearest-neighbor interactions in a near-unity-occupancy atomic array.
• Investigate quench dynamics across the paramagnet to antiferromagnet transition using sudden and slow protocols.
• Measure site-resolved spin correlations and compare with state-of-the-art numerical methods.

Proposed method

• Implement a 2D quantum Ising model with transverse and longitudinal fields realized by coupling Li-6 atoms to a 23P Rydberg state."
• Use a near unit-occupancy 2D lattice loaded from a degenerate Li-6 gas to create a 6-site annulus with 95.7% occupancy.
• Model Hamiltonian H = Ω sum_i S_i^x + sum_i (I_i − Δ) S_i^z + sum_{i≠j} (V_ij/2) S_i^z S_j^z with V_ij = C6/|r_i−r_j|^6.
• Extract spin correlators C(r) = 4[⟨S_i^z S_{i+r}^z⟩ − ⟨S_i^z⟩⟨S_{i+r}^z⟩] from site-resolved images.
• Compare short-time dynamics to NLCE (11th order) and exact diagonalization on 4×4 lattices, fitting C6 and detection scaling α.
• Perform longer, near-adiabatic quenches to build longer-range antiferromagnetic correlations.

Experimental results

Research questions

• RQ1 How do quench dynamics across a 2D Ising transition manifest in nearest- and next-nearest-neighbor spin correlations?
• RQ2 To what extent do NLCE and exact diagonalization capture the observed dynamics in 2D with Rydberg-mediated interactions?
• RQ3 What is the impact of quench rate on the buildup and range of antiferromagnetic correlations?
• RQ4 Can near-adiabatic ramps generate longer-range correlations, and what limits decoherence imposes on slower quenches?

Key findings

• Sudden quenches show sign changes in nearest-neighbor correlations as detuning Δ is varied.
• NLCE (11th order) and exact diagonalization agree with short-time data, yielding C6/h ≈ −1.1(1) MHz μm^6 and α ≈ 0.89(1).
• Longer quenches reveal next-nearest-neighbor correlations with zero crossings, challenging beyond-12th-order NLCE convergence.
• Slower quenches build longer-range antiferromagnetic correlations but decoherence becomes significant, reducing peak correlations.
• Exponential decay of correlations with distance is observed near end of slow ramps, with correlation lengths ξ in the range ~0.74–1.9 a_l.
• Probabilities of 3×3 sub-system configurations show antiferromagnetic states becoming most probable toward ramp end.