Probing the Quench Dynamics of Antiferromagnetic Correlations in a 2D Quantum Ising Spin System

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 quench dynamics in a two-dimensional Ising spin system with transverse and longitudinal fields. 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 lowlying Rydberg state. Using site-resolved microscopy, we probe antiferromagnetic correlations in the system after a sudden quench from a paramagnetic state and compare our measurements to numerical calculations using state-of-the-art techniques. We achieve many-body states with longer-range antiferromagnetic correlations by implementing a near-adiabatic quench of the longitudinal field and study the buildup of correlations as we vary the rate with which we change the field. Lattice quantum spin models serve as a paradigm for exploring a range of many-body phenomena, including quantum phase transitions [1,2], equilibration and thermalization [3,4], and quench dynamics [5][6][7][8][9][10]. While there exists a variety of well-developed theoretical techniques to study the equilibrium properties of quantum spin systems [11][12][13][14][15][16][17], the toolkit for simulating real-time dynamics of these systems is rather limited and can only capture the evolution accurately for short times, especially for systems in more than one dimension [11,[18][19][20]. Recent advances in the field of quantum simulation have introduced several experimental platforms where the dynamics of quantum spin systems can be measured over long evolution times, providing much needed benchmarks for testing uncontrolled theoretical approximations. Examples of such platforms include trapped ions [21-23], polar molecules [24], Rydberg atoms [25][26][27][28][29], magnetic atoms [30,31], and atoms interacting through superexchange in optical lattices [32][33][34][35][36][37].In this work, we explore the dynamics of a two-dimensional quantum Ising model using a nearly defect-free array of neutral atoms which are coupled with laser light to a lowlying Rydberg state in an optical lattice [38]. The spin coupling in the model arises due to a van der Waals interaction between atoms in the Rydberg state. If one atom is in a Rydberg state, the excitation of another atom to a Rydberg state is strongly suppressed within a blockade radius R b [39][40][41][42][43]. This is because the interaction between the Rydberg atoms within this radius is much larger than the laser coupling strength. Previous experiments in 2D arrays have studied the regime R b ≫ a l , where a l is the lattice spacing [25,28]. In this regime, the Rydberg blockade makes it difficult to access many-body states with a large Rydberg fraction. This significantly reduces the size of the relevant Hilbert space of the system from the maximum possible size of 2 N , where N is the numb...

Many-body physics with individually controlled Rydberg atoms

“…The slope gives access to critical exponents characterizing the quantum phase transition. d: Antiferromagnetic spin-spin correlation function in two dimensional arrays of atoms after adiabatic preparation for the experiment of [83] (left) and [84] (right). obtained from an adiabatic preparation detailed below.…”

“…In their case, they varied the ratio R b /a between 2 and 4, so that they could access several Z n phases. The Institut d'Optique group [83] and the group of W. Bakr in Princeton [84] explored the two-dimensional case using respectively atoms in arrays of tweezers and in optical lattices. Both groups observed the appearance of antiferromagnetic correlations in their system.…”

A generalized phase space approach for solving quantum spin dynamics

“…In particular, models of coupled spin-particles with long-range interactions have become a topic of intensive research because of important experimental progress. While models with spin S=1/2 have been implemented with many different setups, e.g.using polar molecules [15,17], Rydberg atoms [16,[18][19][20][21][22][23], trapped ions [24][25][26] and cavity QED systems [27,28], recently also models with larger spins S>1/2 have become a research focus in particular for experiments with magnetic atoms [29][30][31][32][33][34]. The large spin degrees of freedom in S>1/2 systems poses a much more stringent requirement for numerical treatment compared to S=1/2 systems.…”

Dynamics of an itinerant spin-3 atomic dipolar gas in an optical lattice

“…Ultra-cold gases provide an excellent platform to study strongly correlated out-of-equilibrium quantum matter. So far, a broad range of atomic, molecular, and optical systems [1][2][3] including trapped-ions [4][5][6][7] polar molecules [8,9], Rydberg atoms [10][11][12][13][14], magnetic atoms [15][16][17][18][19][20][21][22], and cavity QED arrays [23,24] have been used to realize quantum many-body systems with long-range interactions and to probe equilibrium properties and outof-equilibrium dynamics both in pinned and itinerant systems.…”