Observing the Space- and Time-Dependent Growth of Correlations in Dynamically Tuned Synthetic Ising Models with Antiferromagnetic Interactions

Lienhard, Vincent; Léséleuc, Sylvain de; Barredo, Daniel; Lahaye, Thierry; Browaeys, Antoine; Schuler, Michael; Henry, Louis-Paul; Läuchli, Andreas M.

doi:10.1103/physrevx.8.021070

Cited by 211 publications

(224 citation statements)

References 72 publications

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“…Despite the recent experimental progress in probing the emergent behaviour of out-of-equilibrium ensembles of cold atoms or trapped ions, [1][2][3][4][5][6], a clear understanding of these quantum non-equilibrium systems remains a major challenge. While in classical settings the study of such systems-of their phases and critical phenomena -are well developed, options for going beyond semi-classical treatments or the physics of exactly solvable quantum models are rather limited.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of critical dissipative non-equilibrium quantum systems with an absorbing state

2019

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The simulation of out-of-equilibrium dissipative quantum many body systems is a problem of fundamental interest to a number of fields in physics, ranging from condensed matter to cosmology. For unitary systems, tensor network methods have proved successful and extending these to open systems is a natural avenue for study. In particular, an important question concerns the possibility of approximating the critical dynamics of non-equilibrium systems with tensor networks. Here, we investigate this by performing numerical simulations of a paradigmatic quantum non-equilibrium system with an absorbing state: the quantum contact process. We consider the application of matrix product states and the time-evolving block decimation algorithm to simulate the time-evolution of the quantum contact process at criticality. In the Lindblad formalism, we find that the Heisenberg picture can be used to improve the accuracy of simulations over the Schrödinger approach, which can be understood by considering the evolution of operator-space entanglement. Furthermore, we also consider a quantum trajectories approach, which we find can reproduce the expected universal behaviour of key observables for a significantly longer time than direct simulation of the average state. These improved results provide further evidence that the universality class of the quantum contact process is not directed percolation, which is the class of the classical contact process.Schrödinger picture and Heisenberg picture. In the QCP, this asymmetry is particularly pronounced, and the Heisenberg picture does not display an absorbing state. It is then of interest to investigate any difference in performance between simulations in the two.Finally, the critical physics of the 1d QCP is similar to that of the CCP, in the sense that key observables display power-law behaviour but with different exponents. This means that, at criticality, different numerical methods or approaches to the dynamics can be compared by their ability to reproduce the expected power-laws. Furthermore, since the universality class of the QCP is currently debated, [7,9,11], it is of considerable interest in its own right to make estimates of critical exponents, comparing these with previous estimates and known cases.To simulate the non-equilibrium dynamics of the QCP, we apply matrix product states (MPSs) and the timeevolving block-decimation (TEBD) algorithm [13][14][15]. This algorithm belongs to a more general class of tensor network (TN) methods, well established for the simulation of closed quantum systems in 1d, which have also been applied to dissipative quantum systems previously in a number of cases [16][17][18][19][20][21][22][23][24]. In the context of studying dissipative quantum dynamics, a key question for TN methods is whether different approaches, such as quantum trajectories (QTs) as opposed to the Lindblad master equation, can lead to substantially different accuracies. This question has been explored previously in [16,17] and it has been suggested that in highentanglement ...

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Section: Introductionmentioning

confidence: 99%

Numerical simulation of critical dissipative non-equilibrium quantum systems with an absorbing state

2019

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“…Another possible direction is the use of Rydberg dressing techniques to realize a dipolar Fermi gas, taking advantage of the fast tunneling of lithium in an optical lattice to go beyond the frozen gas regime [27,[70][71][72]. [73].…”

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confidence: 99%

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

et al. 2018

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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...

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“…Recently, a large body of work has be devoted to investigate the properties of the dissipative quantum many-body systems including the dynamics [2][3][4][5][6], transport properties [7][8][9][10][11], steady-state phases [12][13][14][15]16] and phase transitions [17][18][19][20][21], quantum states engineering [22][23][24], as well as the possible applications in quantum sensing [25,26]. Thanks to the experiment progress, dissipative phase transitions have been observed in circuit QED arrays [27] and ensembles of Rydberg atoms [28,29].…”

Section: Introductionmentioning

confidence: 99%

Numerical linked-cluster expansion for the dissipative XYZ model on a triangular lattice

Qiao

Chang

et al. 2020

J. Phys. Commun.

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We generalize the numerical linked-cluster expansion (NLCE) method to study the dissipative quantum many-body system. We apply the NLCE to the triangular strip and two-dimensional lattice system. We investigate the dynamics and steady-state properties of the dissipative XYZ model where the coherent dynamics is governed by the anisotropic Heisenberg Hamiltonian while the nonunitary process is induced by the incoherent spin flips. By comparing with the quantum trajectory simulations, the NLCE results show good performance in capturing the dynamics of system with short-range correlations. For strong and long-range correlated system, the larger size clusters in the series should be included. The NLCE study for the magnetic susceptibility also signals the steady-state paramagnetic-ferromagnetic phase transition in the two-dimensional case.

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Observing the Space- and Time-Dependent Growth of Correlations in Dynamically Tuned Synthetic Ising Models with Antiferromagnetic Interactions

Cited by 211 publications

References 72 publications

Numerical simulation of critical dissipative non-equilibrium quantum systems with an absorbing state

Numerical simulation of critical dissipative non-equilibrium quantum systems with an absorbing state

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

Numerical linked-cluster expansion for the dissipative XYZ model on a triangular lattice

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