Towards a Theory of Metastability in Open Quantum Dynamics

Macieszczak, Katarzyna; Guţǎ, Mădălin; Lesanovsky, Igor; Garrahan, Juan P.

doi:10.1103/physrevlett.116.240404

Cited by 187 publications

(281 citation statements)

References 48 publications

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“…We find c i → c L i 2κ λi , and σ = i c L i 2κ λi M i . Now, putting the expressions of c L i and M i , we find the covariance matrix (11). Finally, we estimate the time needed to reach the steady-state.…”

Section: + ω0γmentioning

confidence: 99%

Critical Quantum Metrology with a Finite-Component Quantum Phase Transition

et al. 2020

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Physical systems close to a quantum phase transition exhibit a divergent susceptibility, suggesting that an arbitrarily-high precision may be achieved by exploiting quantum critical systems as probes to estimate a physical parameter. However, such an improvement in sensitivity is counterbalanced by the closing of the energy gap, which implies a critical slowing down and an inevitable growth of the protocol duration. Here, we design different metrological protocols that make use of the superradiant phase transition of the quantum Rabi model, a finite-component system composed of a single two-level atom interacting with a single bosonic mode. We show that, in spite of the critical slowing down, critical quantum optical systems can lead to a quantum-enhanced time-scaling of the quantum Fisher information, and so of the measurement sensitivity.In a system close to a critical point, small variations of physical parameters may lead to dramatic changes in the equilibrium state properties. The possibility of exploiting this sensitivity for metrological purposes is well known, and it has already been applied in classical devices, e.g. in superconducting transition-edge sensor [1]. Besides, the development of quantum metrology has extensively shown that quantum states can outperform their classical counterparts for sensing tasks [2]. Therefore, a question naturally arises: what sensitivity can be achieved using interacting systems close to a quantum-critical point? In the last few years, this question has attracted growing interest and it has been addressed by different methods [3][4][5][6][7][8][9]. These studies may be roughly divided in two classes.The first approach, which we will call the "dynamical" paradigm [5,7], focus on the time evolution induced by a Hamiltonian close to a critical point. In this approach, one prepares a probe system in a suitably chosen state, lets it evolve according to the critical Hamiltonian, and finally measures it. This bear close similarity to the standard interferometric paradigm of quantum metrology [2]. On the other hand, the "static" approach [3, 6] is based on the equilibrium properties of the system. It consists in preparing and measuring the system ground state in the unitary case, or the system steady-state when open quantum systems are considered. In proximity of the phase transition the susceptibility of the equilibrium state diverges, and so it does the achievable measurement precision. Unfortunately, the time required to prepare the equilibrium state diverges as well, both in the unitary [10] and in the driven-dissipative case [11,12], a behavior called critical slowing down. Only very re-cently, it has been demonstrated that for a large class of spin models these two approaches are formally equivalent [9], and that they both make it possible to achieve the optimal scaling limit of precision with respect to system size and to measurement time. These results were obtained considering spin systems that undergo quantum phase transitions in the thermodynamic limit, where the numb...

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Section: + ω0γmentioning

confidence: 99%

Critical Quantum Metrology with a Finite-Component Quantum Phase Transition

et al. 2020

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“…At the HEP, the NHHĤ eff becomes non-diagonazible, i.e., it attains a Jordan form. Hence, the generalized eigenspace of the NHHĤ eff consists of the the eigenvectors |ψ 0 = |00 , |ψ 1 = |11 , |ψ HEP ≡ |10 + |01 , (46) and the singlet-type pseudo-eigenvector [59]:…”

Section: A Non-hermitian Hamiltonian Exceptional Pointsmentioning

confidence: 99%

“…[43,44]. The study of the spectrum of a Liouvillian provides a framework for the investigation of the properties of non-Hermitian systems and their EPs in a rigorous quantum approach [44][45][46][47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

Quantum and semiclassical exceptional points of a linear system of coupled cavities with losses and gain within the Scully-Lamb laser theory

et al. 2020

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In the past few decades, many works have been devoted to the study of exceptional points (EPs), i.e., exotic degeneracies of non-Hermitian systems. The usual approach in those studies involves the introduction of a phenomenological effective non-Hermitian Hamiltonian (NHH), where the gain and losses are incorporated as the imaginary frequencies of fields, and from which the Hamiltonian EPs (HEPs) are derived. Although this approach can provide valid equations of motion for the fields in the classical limit, its application in the derivation of EPs in the quantum regime is questionable.Recently, a framework [Minganti et al., arXiv:1909.11619], which allows to determine quantum EPs from a Liouvillian (LEPs), rather than from an NHH, has been proposed. Compared to the NHHs, a Liouvillian naturally includes quantum noise effects via quantum-jump terms, thus, allowing to consistently determine its EPs purely in the quantum regime. In this work, we study a non-Hermitian system consisting of coupled cavities with unbalanced gain and losses, and where the gain is far from saturation, i.e, the system is assumed to be linear. We apply both formalisms, based on an NHH and a Liouvillian within the Scully-Lamb laser theory, to determine and compare the corresponding HEPs and LEPs in the semiclassical and quantum regimes. Our results indicate that, although the overall spectral properties of the NHH and the corresponding Liouvillian for a given system can differ substantially, their LEPs and HEPs occur for the same combination of system parameters.

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“…where N is the number of spins and |Ψ(t) is the many-body wavefunction given in equation (2). In our particular case, N = 2, we can write the following code to compute the average magnetization M z down = [0 1]'; Psi_0 = kron(down,down); T = 2*pi/(2*B); Nt = 1000; ti = 0; tf = 2*T; dt = (tf-ti)/(Nt-1); t = ti:dt:tf; U = expm(-1i*H*dt); Psi = Psi_0; SSz = (kron(Sz,I)+kron(I,Sz))/2; Mz = zeros(size(t)); for n=1:length(t) Psi = U*Psi; Mz(n) = Psi'*SSz*Psi; end plot(t/T,real(Mz),'r-','LineWidth',3) xlabel('$t/T$','Interpreter','LaTex','Fontsize', 30) ylabel('$\langle M_z \rangle$','Interpreter','LaTex','Fontsize', 30) set(gca,'fontsize', 21) In figure 1 we plotted the expected average magnetization M z for the two-spin system. Initially, the system has a magnetization M z = −1 due to the condition |Ψ(0) = |↓ 1 ⊗ |↓ 2 , and then two characteristic oscillations are observed.…”

Section: Closed Quantum Systemsmentioning

confidence: 99%

“…By choosing the initial condition ρ(0) = |Ψ(0) Ψ(0)|, with |Ψ(0) = |↓ 1 ⊗ |↓ 2 , we can compute the average magnetization M z = Tr(M z ρ(t)). The code read as down = [0 1]'; Psi_0 = kron(down,down); rho_0 = Psi_0*Psi_0'; Nt = 1000; T = 2*pi/(2*B); ti = 0; tf = 4*T; dt = (tf-ti)/(Nt-1); t = ti:dt:tf; Mz = zeros(size(t)); SSz = (kron(Sz,I)+kron(I,Sz))/2; for n=1:length(t) % general solution rho = zeros(dim,dim); for k=1:length(lambda) Lk = LM{k}; Rk = RM{k}; ck = trace(rho_0*Lk); rho = rho + ck*exp(lambda(k)*t(n))*Rk; end Mz(n) = trace(SSz*rho); end figure() hold on plot(t/T,real(Mz),'r-','LineWidth',3) plot(t/T, exp(real(lambda(end))*t),'k--','LineWidth',2) plot(t/T,-exp(real(lambda(end))*t),'k--','LineWidth',2) hold off xlabel('$Bt$','Interpreter','LaTex','Fontsize', 30) ylabel('$\langle M_z \rangle$','Interpreter','LaTex','Fontsize', 30) set(gca,'fontsize',21)…”

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confidence: 99%

Coding closed and open quantum systems in MATLAB: applications in quantum optics and condensed matter

Norambuena¹,

Tancara²,

Coto³

2020

Eur. J. Phys.

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We present optimized and easy to follow numerical simulations for complex many-body quantum systems implemented in MATLAB. The examples include the calculation of the magnetization dynamics for the closed and open Ising model, dynamical quantum phase transition in cavity QED arrays, Markovian dynamics for interacting two-level systems, and the non-Markovian dynamics of the pure-dephasing spin-boson model. This tutorial will be a useful toolbox for undergraduate and graduate students with an interest in numerical simulations with applications in quantum optics and condensed matter problems.

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Towards a Theory of Metastability in Open Quantum Dynamics

Cited by 187 publications

References 48 publications

Critical Quantum Metrology with a Finite-Component Quantum Phase Transition

Critical Quantum Metrology with a Finite-Component Quantum Phase Transition

Quantum and semiclassical exceptional points of a linear system of coupled cavities with losses and gain within the Scully-Lamb laser theory

Coding closed and open quantum systems in MATLAB: applications in quantum optics and condensed matter

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