Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1709.02202 · Europhysics Letters (EPL)

Entanglement dynamics following a sudden quench: An exact solution

Supriyo Ghosh, Kumar S. Gupta, Shashi C. L. Srivastava

Published Dec 1, 2017• 22 citations
arXivHTMLPDF

Abstract

We present an exact and fully analytical treatment of the entanglement dynamics for an isolated system of N coupled oscillators following a sudden quench of the system parameters. The system is analyzed using the solutions of the time-dependent Schrodinger's equation, which are obtained by solving the corresponding nonlinear Ermakov equations. The entanglement entropies exhibit a multi-oscillatory behaviour, where the number of dynamically generated time scales increases with N . The harmonic chains exhibit entanglement revival and for larger values of N (> 10), we find near-critical logarithmic scaling for the entanglement entropy, which is modulated by a time-dependent factor. The N = 2 case is equivalent to the two-site Bose-Hubbard model in the tunneling regime, which is amenable to empirical realization in cold-atom systems.

DOI
10.1209/0295-5075/120/50005

Related papers

Entanglement dynamics of coupled oscillators from Gaussian states

Cemal Dinc, Onur Oktay

In this work, we explore the dynamics of entanglement of an isolated quantum system consisting of two time-dependent, coupled harmonic oscillators. Through the use of a numerical method that relies on the estimation of the system's Wigner representation by a specific Gaussian function, we investigate the time evolution of the entanglement entropy after an instant quench in the inherent parameters of the system. Besides, from the comparison of the results obtained from the analytical expression for the time-dependent von Neumann entropy with the numerically computed entropy data, the effectiveness of the numerical method is tested for a variety of angular frequency combinations. Also, we analyze how the entropy of entanglement change as a function of time.

arXiv:2104.12332•Apr 26, 2021•1 citation

Entanglement dynamics after quantum quenches in generic integrable systems

Vincenzo Alba, Pasquale Calabrese

The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by combining a quasiparticle picture for the entanglement spreading with the exact knowledge of the stationary state provided by Bethe ansatz, it is possible to obtain an exact and analytic description of the evolution of the entanglement entropy. Here we discuss the application of these ideas to several integrable models. First we show that for non-interacting systems, both bosonic and fermionic, the exact time-dependence of the entanglement entropy can be derived by elementary techniques and without solving the dynamics. We then provide exact results for interacting spin chains that are carefully tested against numerical simulations. Finally, we apply this method to integrable one-dimensional Bose gases (Lieb-Liniger model) both in the attractive and repulsive regimes. We highlight a peculiar behaviour of the entanglement entropy due to the absence of a maximum velocity of excitations.

arXiv:1712.07529•SciPost Physics•Mar 27, 2018•307 citations

The Schmidt Decomposition for Entangled System and Nonadiabatic Berry Phases

Ahlem Abidi, A. Trabelsi

The time-dependent Hamiltonians are a very important portion in the modeling of real systems. In fact, the dynamic description of an entangled quantum systems is reflected in full coherence with the resolution of a wave function, solution of the Schrödinger equation throughout the entire study path. In this regard, we specify in this paper the system of two-site Bose-Hubbard model that obeys tunnel behavior, as two coupled harmonic oscillators, to examine quantum entanglement. The dynamics of such a system is described by the Schrödinger equation have introduced to the solution, the non-linear Ermakov equations as well as through a passage to the Heisenberg picture approach and the general Lewis and Riesenfeld invariant method compute between coupled harmonic oscillators and the coupled Caldirola Kanai oscillators. We prove that a time exponential increase in the mass of the system brings back to an exponential increase of entanglement and the Heisenberg picture approach is the most stable method to quantum entanglement because, this last has reached very large values. Also, we specify a cyclic time evolution, we find analytically the nonadiabatic Berry phases. In a particular case, such an entangled system acquired a nonadiabatic Berry phases that exhibits the same behavior as the Schmidt parameter.

American Journal of Physics and Applications•Oct 31, 2024•0 citations

Dynamics and redistribution of entanglement and coherence in three time-dependent coupled harmonic oscillators

Radouan Hab-Arrih, Ahmed Jellal, Abdeldjalil Merdaci

We study the dynamics and redistribution of entanglement and coherence in three time-dependent coupled harmonic oscillators. We resolve the Schrödinger equation by using time-dependent Euler rotation together with a linear quench model to obtain the state of vacuum solution. Such state can be translated to the phase space picture to determine the Wigner distribution. We show that its Gaussian matrix [Formula: see text] can be used to directly cast the covariance matrix [Formula: see text]. To quantify the mixedness and entanglement of the state, one uses respectively linear and von Neumann entropies for three cases: fully symmetric, bi-symmetric and fully nonsymmetric. Then we determine the coherence, tripartite entanglement and local uncertainties and derive their dynamics. We show that the dynamics of all quantum information quantities are driven by the Ermakov modes. Finally, we use an homodyne detection to redistribute both resources of entanglement and coherence.

arXiv:2007.14746•International Journal of Geometric Methods in Modern Physics•Apr 2, 2021•7 citations

Aging and coarsening in isolated quantum systems after a quench: Exact results for the quantum O(N) model with N → ∞

Anna Maraga, Alessio Chiocchetta, Aditi Mitra +1 more

The nonequilibrium dynamics of an isolated quantum system after a sudden quench to a dynamical critical point is expected to be characterized by scaling and universal exponents due to the absence of time scales. We explore these features for a quench of the parameters of a Hamiltonian with O(N) symmetry, starting from a ground state in the disordered phase. In the limit of infinite N, the exponents and scaling forms of the relevant two-time correlation functions can be calculated exactly. Our analytical predictions are confirmed by the numerical solution of the corresponding equations. Moreover, we find that the same scaling functions, yet with different exponents, also describe the coarsening dynamics for quenches below the dynamical critical point.

arXiv:1506.04528•Physical Review E•Oct 26, 2015•84 citations

Entanglement and correlation spreading in non-Hermitian spin chains

Xhek Turkeshi, Marco Schirò

Non-Hermitian quantum many-body systems are attracting widespread interest for their exotic properties, including unconventional quantum criticality and topology. Here, we study how quantum information and correlations spread under a quantum quench generated by a prototypical non-Hermitian spin chain. Using the mapping to fermions, we solve exactly the problem and compute the entanglement entropy and the correlation dynamics in the thermodynamic limit. Depending on the quench parameters, we identify two dynamical phases. One is characterized by rapidly saturating entanglement and correlations. The other presents a logarithmic entanglement growth in time and correlations spreading faster than the associated unitary system, with collapses and revivals giving rise to a modulated light-cone structure. Here, in the long-time limit, we analytically compute the entanglement entropy that follows a logarithmic law, with an effective central charge that we obtain in closed form. Our results provide an example of an exactly solvable non-Hermitian many-body problem that shows rich physics, including entanglement and spectral transitions.

arXiv:2201.09895•Physical review. B./Physical review. B•Jan 9, 2023•115 citations
We present an exact and fully analytical treatment of the entanglement dynamics for an isolated system of N coupled oscillators following a sudden quench of the system parameters. The system is analyzed using the solutions of the time-dependent Schrodinger's equation, which are obtained by solving the corresponding nonlinear Ermakov equations. The entanglement entropies exhibit a multi-oscillatory behaviour, where the number of dynamically generated time scales increases with N . The harmonic chains exhibit entanglement revival and for larger values of N (> 10), we find near-critical logarithmic scaling for the entanglement entropy, which is modulated by a time-dependent factor. The N = 2 case is equivalent to the two-site Bose-Hubbard model in the tunneling regime, which is amenable to empirical realization in cold-atom systems.
In this work, we explore the dynamics of entanglement of an isolated quantum system consisting of two time-dependent, coupled harmonic oscillators. Through the use of a numerical method that relies on the estimation of the system's Wigner representation by a specific Gaussian function, we investigate the time evolution of the entanglement entropy after an instant quench in the inherent parameters of the system. Besides, from the comparison of the results obtained from the analytical expression for the time-dependent von Neumann entropy with the numerically computed entropy data, the effectiveness of the numerical method is tested for a variety of angular frequency combinations. Also, we analyze how the entropy of entanglement change as a function of time.
The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by combining a quasiparticle picture for the entanglement spreading with the exact knowledge of the stationary state provided by Bethe ansatz, it is possible to obtain an exact and analytic description of the evolution of the entanglement entropy. Here we discuss the application of these ideas to several integrable models. First we show that for non-interacting systems, both bosonic and fermionic, the exact time-dependence of the entanglement entropy can be derived by elementary techniques and without solving the dynamics. We then provide exact results for interacting spin chains that are carefully tested against numerical simulations. Finally, we apply this method to integrable one-dimensional Bose gases (Lieb-Liniger model) both in the attractive and repulsive regimes. We highlight a peculiar behaviour of the entanglement entropy due to the absence of a maximum velocity of excitations.
The time-dependent Hamiltonians are a very important portion in the modeling of real systems. In fact, the dynamic description of an entangled quantum systems is reflected in full coherence with the resolution of a wave function, solution of the Schrödinger equation throughout the entire study path. In this regard, we specify in this paper the system of two-site Bose-Hubbard model that obeys tunnel behavior, as two coupled harmonic oscillators, to examine quantum entanglement. The dynamics of such a system is described by the Schrödinger equation have introduced to the solution, the non-linear Ermakov equations as well as through a passage to the Heisenberg picture approach and the general Lewis and Riesenfeld invariant method compute between coupled harmonic oscillators and the coupled Caldirola Kanai oscillators. We prove that a time exponential increase in the mass of the system brings back to an exponential increase of entanglement and the Heisenberg picture approach is the most stable method to quantum entanglement because, this last has reached very large values. Also, we specify a cyclic time evolution, we find analytically the nonadiabatic Berry phases. In a particular case, such an entangled system acquired a nonadiabatic Berry phases that exhibits the same behavior as the Schmidt parameter.
We study the dynamics and redistribution of entanglement and coherence in three time-dependent coupled harmonic oscillators. We resolve the Schrödinger equation by using time-dependent Euler rotation together with a linear quench model to obtain the state of vacuum solution. Such state can be translated to the phase space picture to determine the Wigner distribution. We show that its Gaussian matrix [Formula: see text] can be used to directly cast the covariance matrix [Formula: see text]. To quantify the mixedness and entanglement of the state, one uses respectively linear and von Neumann entropies for three cases: fully symmetric, bi-symmetric and fully nonsymmetric. Then we determine the coherence, tripartite entanglement and local uncertainties and derive their dynamics. We show that the dynamics of all quantum information quantities are driven by the Ermakov modes. Finally, we use an homodyne detection to redistribute both resources of entanglement and coherence.
The nonequilibrium dynamics of an isolated quantum system after a sudden quench to a dynamical critical point is expected to be characterized by scaling and universal exponents due to the absence of time scales. We explore these features for a quench of the parameters of a Hamiltonian with O(N) symmetry, starting from a ground state in the disordered phase. In the limit of infinite N, the exponents and scaling forms of the relevant two-time correlation functions can be calculated exactly. Our analytical predictions are confirmed by the numerical solution of the corresponding equations. Moreover, we find that the same scaling functions, yet with different exponents, also describe the coarsening dynamics for quenches below the dynamical critical point.
Non-Hermitian quantum many-body systems are attracting widespread interest for their exotic properties, including unconventional quantum criticality and topology. Here, we study how quantum information and correlations spread under a quantum quench generated by a prototypical non-Hermitian spin chain. Using the mapping to fermions, we solve exactly the problem and compute the entanglement entropy and the correlation dynamics in the thermodynamic limit. Depending on the quench parameters, we identify two dynamical phases. One is characterized by rapidly saturating entanglement and correlations. The other presents a logarithmic entanglement growth in time and correlations spreading faster than the associated unitary system, with collapses and revivals giving rise to a modulated light-cone structure. Here, in the long-time limit, we analytically compute the entanglement entropy that follows a logarithmic law, with an effective central charge that we obtain in closed form. Our results provide an example of an exactly solvable non-Hermitian many-body problem that shows rich physics, including entanglement and spectral transitions.