Dynamical properties of dissipative XYZ Heisenberg lattices

Rota, Riccardo; Minganti, Fabrizio; Biella, Alberto; Ciuti, Cristiano

doi:10.1088/1367-2630/aab703

Cited by 50 publications

(48 citation statements)

References 74 publications

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“…Indeed, there exist other possible choices of jump operators which result in the same master equation once the average over many quantum trajectories is taken [19,21]. Different unraveling can result in extremely different dynamics at a single trajectory level [19,56,57]. In this sense, the use of a Lindblad master equation allows to capture those properties which do not depend on the details of the systemenvironment exchange.…”

Section: B Quantum Trajectoriesmentioning

confidence: 99%

Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps

et al. 2019

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Exceptional points (EPs) are degeneracies of classical and quantum open systems, which are studied in many areas of physics including optics, optoelectronics, plasmonics, and condensed matter physics. In the semiclassical regime, open systems can be described by phenomenological effective non-Hermitian Hamiltonians (NHHs) capturing the effects of gain and loss in terms of imaginary fields. The EPs that characterize the spectra of such Hamiltonians (HEPs) describe the time evolution of a system without quantum jumps. It is well known that a full quantum treatment describing more generic dynamics must crucially take into account such quantum jumps. In a recent paper [Minganti et al., Phys. Rev. A 100, 062131 (2019)], we generalized the notion of EPs to the spectra of Liouvillian superoperators governing open system dynamics described by Linblad master equations. Intriguingly, we found that in situations where a classical to quantum correspondence exists, the two types of dynamics can yield different EPs. In a recent experimental work [Naghiloo et al. Nat. Phys. 15, 1232(2019], it was shown that one can engineer a non-Hermitian Hamiltonian in the quantum limit by postselecting on certain quantum jump trajectories. This raises an interesting question concerning the relation between Hamiltonian and Lindbladian EPs, and quantum trajectories. We discuss these connections by introducing a hybrid-Liouvillian superoperator, capable of describing the passage from an NHH (when one postselects only those trajectories without quantum jumps) to a true Liouvillian including quantum jumps (without postselection). Beyond its fundamental interest, our approach allows to efficiently discuss and analyze postselection on finite-efficiency detectors. CONTENTS

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Section: B Quantum Trajectoriesmentioning

confidence: 99%

Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps

et al. 2019

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“…whereσ x j ,σ y j ,σ z j are the Pauli matrices, σ ± j = (σ x j ± iσ y j )/2, J α are the coupling constants between nearest neighbour spins and γ is the dissipation rate. The excitations in the system -induced by the anisotropic spin coupling -compete with the isotropic dissipative process, and this competition is at the origin of the dissipative phase transition [19][20][21][22][23]. The effectiveness of the neural network ansatz is demonstrated by studying the system observables across a phase boundary.…”

Section: Arxiv:190209483v2 [Quant-ph] 29 Jun 2019mentioning

confidence: 99%

Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems

2019

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The possibility to simulate the properties of many-body open quantum systems with a large number of degrees of freedom is the premise to the solution of several outstanding problems in quantum science and quantum information. The challenge posed by this task lies in the complexity of the density matrix increasing exponentially with the system size. Here, we develop a variational method to efficiently simulate the non-equilibrium steady state of Markovian open quantum systems based on variational Monte Carlo and on a neural network representation of the density matrix. Thanks to the stochastic reconfiguration scheme, the application of the variational principle is translated into the actual integration of the quantum master equation. We test the effectiveness of the method by modeling the two-dimensional dissipative XYZ spin model on a lattice.Open quantum systems have evolved into a major field of studies in recent years. Focus of these studies are the characterization of emergent phenomena and dissipative phase transitions [1-23], as well as the ongoing debate about whether quantum computing schemes are still hard to simulate classically -and thus achieve quantum supremacy -when in presence of some degree of noise-induced decoherence [24][25][26][27].Assuming a Markovian interaction with the environment, the dynamics of open quantum systems is governed by the quantum master equation in Lindblad form [28]. Only few models within this description admit an analytical solution [29,30]. The quest for efficient numerical methods to simulate the dynamics and the asymptotic steady state resulting from the Lindblad master equation, is a research field that is still in its infancy. Many recent tools have been developed following in the footsteps of well established numerical methods for the simulations of closed, Hamiltonian quantum systems. In particular, matrix-product state and tensor network schemes [31][32][33][34], a real-space renormalization approach [35], cluster mean-field [19], and other ad-hoc approximation schemes [23,36] have recently emerged.A groundbreaking progress in the numerical simulation of both the ground state and the dynamics of closed quantum systems has recently been made with the introduction of the neural-network variational ansatz [37][38][39][40][41][42][43], which efficiently represents highly correlated quantum states and whose parameters are easily optimized by means of the variational Monte Carlo (VMC) method. Recently, a self-adjoint and positive semidefinite parametrization of the density matrix, in terms of a neural network has been introduced [44].The steady state of an open quantum system can be characterized by a variational principle [31,33,45,46], whereby the dissipative part of the real-time dynamics, under quite general conditions, drives the system towards a unique steady state, in analogy to the imaginary-time Schrödinger equation that leads to the ground state of Hamiltonian systems.In this Letter, we present a VMC approach to simulate the non-equilibrium steady state (NESS)...

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“…Near a critical point, the correlation time diverges, leading to the occurrence of critical slowing down. Some current works have addressed the latter effect in a dissipative context for optical bistability (a first-order dissipative phase transition) [33][34][35], fermionic lattices [36], optical lattice clocks [37] and miscellaneous spin lattices [38,39].…”

Section: Introductionmentioning

confidence: 99%

Classical critical dynamics in quadratically driven Kerr resonators

Verstraelen

Wouters

2020

Phys. Rev. A

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Driven-dissipative kerr lattices with two-photon driving are experimentally relevant systems known to exhibit a symmetry-breaking phase transition, which belongs to the universality class of the thermal Ising model for the parameter regime studied here. In this work, we perform finitesize scaling of this system as it is quenched to the transition and the dynamical critical exponent is found to be compatible with z ≈ 2.18 corresponding with metropolis dynamics in classical simulations. Furthermore, we show that the Liouvillian gap scales with the same exponent, similar to scaling of the Hamiltonian gap at quantum phase transitions in closed systems.

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Dynamical properties of dissipative XYZ Heisenberg lattices

Cited by 50 publications

References 74 publications

Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps

Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps

Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems

Classical critical dynamics in quadratically driven Kerr resonators

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