Dynamics of a harmonic oscillator coupled with a Glauber amplifier

Grimaudo, Roberto; Man’ko, Vladimir I.; Man’ko, Margarita A.; Messina, A.

doi:10.1088/1402-4896/ab4305

Cited by 20 publications

(15 citation statements)

References 42 publications

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“…The exact solution of the dynamical problem has been simplified by analyzing the different dynamically invariant subspaces emerging from the symmetry possessed by the effective Hamiltonian. This symmetry-based approach turned out to be useful to study and solve dynamical problems related to more complex interacting spin systems subjected to time-dependent fields [ 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 ]. By focusing our attention on the sub-dynamics involving the two-qubit states

and

, we brought to light the possibility of generating maximally entangled states of the two qubits.…”

Section: Conclusive Remarksmentioning

confidence: 99%

Two-Qubit Entanglement Generation through Non-Hermitian Hamiltonians Induced by Repeated Measurements on an Ancilla

Grimaudo

Messina

Sergi

et al. 2020

Entropy

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In contrast to classical systems, actual implementation of non-Hermitian Hamiltonian dynamics for quantum systems is a challenge because the processes of energy gain and dissipation are based on the underlying Hermitian system–environment dynamics, which are trace preserving. Recently, a scheme for engineering non-Hermitian Hamiltonians as a result of repetitive measurements on an ancillary qubit has been proposed. The induced conditional dynamics of the main system is described by the effective non-Hermitian Hamiltonian arising from the procedure. In this paper, we demonstrate the effectiveness of such a protocol by applying it to physically relevant multi-spin models, showing that the effective non-Hermitian Hamiltonian drives the system to a maximally entangled stationary state. In addition, we report a new recipe to construct a physical scenario where the quantum dynamics of a physical system represented by a given non-Hermitian Hamiltonian model may be simulated. The physical implications and the broad scope potential applications of such a scheme are highlighted.

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and

, we brought to light the possibility of generating maximally entangled states of the two qubits.…”

Section: Conclusive Remarksmentioning

confidence: 99%

Two-Qubit Entanglement Generation through Non-Hermitian Hamiltonians Induced by Repeated Measurements on an Ancilla

Grimaudo

Messina

Sergi

et al. 2020

Entropy

Self Cite

View full text Add to dashboard Cite

show abstract

“…There exist different representations of quantum states [ 39 , 40 , 41 , 42 , 43 , 44 ], and among them, the probability tomographic representation is of particular interest. In this representation, e.g., one-mode photon states are identified with symplectic tomograms [ 45 ], which correspond to the conditional probability distribution

of the photon quadrature

, to be measured in a reference frame with parameters

and

.…”

Section: Gaussian States and Their Evolution In The Tomographic-prmentioning

confidence: 99%

Differential Parametric Formalism for the Evolution of Gaussian States: Nonunitary Evolution and Invariant States

López-Saldívar

Man’ko

2020

Entropy

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In the differential approach elaborated, we study the evolution of the parameters of Gaussian, mixed, continuous variable density matrices, whose dynamics are given by Hermitian Hamiltonians expressed as quadratic forms of the position and momentum operators or quadrature components. Specifically, we obtain in generic form the differential equations for the covariance matrix, the mean values, and the density matrix parameters of a multipartite Gaussian state, unitarily evolving according to a Hamiltonian H ^ . We also present the corresponding differential equations, which describe the nonunitary evolution of the subsystems. The resulting nonlinear equations are used to solve the dynamics of the system instead of the Schrödinger equation. The formalism elaborated allows us to define new specific invariant and quasi-invariant states, as well as states with invariant covariance matrices, i.e., states were only the mean values evolve according to the classical Hamilton equations. By using density matrices in the position and in the tomographic-probability representations, we study examples of these properties. As examples, we present novel invariant states for the two-mode frequency converter and quasi-invariant states for the bipartite parametric amplifier.

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“…In case of two qubits we end up with two two-dimensional subspaces and then we can solve the two-spin dynamics by solving separately the two two-level dynamical problems. This dynamical decomposition approach was used to find other remarkable features of the two-qubit system [55] and to study the exact dynamics of more complex systems like two qudits [56], Nqubit chain [57] and pairs of interacting quantum harmonic oscillators [58]. Moreover, it is important to underline that the dynamical decomposition method is independent of the specific time-dependent scenario we take into account.…”

Section: Conclusive Remarksmentioning

confidence: 99%

Dzyaloshinskii-Moriya and dipole-dipole interactions affect coupling-based Landau-Majorana-Stückelberg-Zener transitions

Grimaudo,

Nakazato,

Messina

et al. 2020

Preprint

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It has been theoretically demonstrated that two spins (qubits or qutrits), coupled by exchange interaction only, undergo a coupling-based joint Landau-Majorana-Stückelberg-Zener (LMSZ) transition when a linear ramp acts upon one of the two spins. Such a transition, under appropriate conditions on the parameters, drives the twospin system toward a maximally entangled state. In this paper, effects on the quantum dynamics of the two qudits, stemming from the Dzyaloshinskii-Moriya (DM) and dipole-dipole (d-d) interactions, are investigated qualitatively and quantitatively. The enriched Hamiltonian model of the two spins, shares with the previous microscopic one the same C2-symmetry which once more brings about an exact treatment of the new quantum dynamical problem. This paper transparently reveals that the DM and d-d interactions generate independent, enhancing or hindering, modifications in the dynamical behaviour predicted for the two spins coupled exclusively by the exchange interaction. It is worthy noticing that, on the basis of the theory here developed, the measurement of the time evolution of the magnetization in a controlled LMSZ scenario, can furnish information on the relative weights of the three kinds of couplings describing the spin system. This possibility is very important since it allows in principle to legitimate the choice of the microscopic model to be adopted in a given physical scenario.

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Dynamics of a harmonic oscillator coupled with a Glauber amplifier

Cited by 20 publications

References 42 publications

Two-Qubit Entanglement Generation through Non-Hermitian Hamiltonians Induced by Repeated Measurements on an Ancilla

Two-Qubit Entanglement Generation through Non-Hermitian Hamiltonians Induced by Repeated Measurements on an Ancilla

Differential Parametric Formalism for the Evolution of Gaussian States: Nonunitary Evolution and Invariant States

Dzyaloshinskii-Moriya and dipole-dipole interactions affect coupling-based Landau-Majorana-Stückelberg-Zener transitions

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