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arXiv:2004.11945 · Journal of Physics B Atomic Molecular and Optical Physics

Nonlinear effects on the dynamics of quantum harmonic modes coupled through angular momentum

N. Canosa, R. Rossignoli, Javier Gonzalo Garcia, Swapan Mandal, Kartick Chandra Saha

Published Aug 28, 2020• 6 citations
arXivHTMLPDF

Abstract

Abstract We investigate nonlinear effects on the dynamics of entanglement and other quantum observables in a system of two harmonic modes coupled through angular momentum. The nonlinearity arises from a Kerr-type anharmonic term in each mode. The emergence and evolution of entanglement, non-Gaussianity, photon number, photon antibunching and squeezing are examined for different initial coherent product states and couplings, through exact diagonalization in a truncated basis. It is shown that the anharmonic terms, even if weak, can lead to very significant effects for such initial states, considerably enhancing and stabilizing entanglement and leading to a non negligible non-Gaussianity of the evolved states. They also affect other observables, stabilizing the dynamics after an initial transient regime, for not too small initial average populations of each mode. Analytic short-time approximate expressions are also provided.

DOI
10.1088/1361-6455/abb3ad

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Abstract We investigate nonlinear effects on the dynamics of entanglement and other quantum observables in a system of two harmonic modes coupled through angular momentum. The nonlinearity arises from a Kerr-type anharmonic term in each mode. The emergence and evolution of entanglement, non-Gaussianity, photon number, photon antibunching and squeezing are examined for different initial coherent product states and couplings, through exact diagonalization in a truncated basis. It is shown that the anharmonic terms, even if weak, can lead to very significant effects for such initial states, considerably enhancing and stabilizing entanglement and leading to a non negligible non-Gaussianity of the evolved states. They also affect other observables, stabilizing the dynamics after an initial transient regime, for not too small initial average populations of each mode. Analytic short-time approximate expressions are also provided.
Abstract We investigate the exact dynamics of a system of two independent harmonic oscillators coupled through their angular momentum. The exact analytic solution of the equations of motion for the field operators is derived, and the conditions for dynamical stability are obtained. As for the application, we examine the emergence of squeezing and mode entanglement for an arbitrary separable coherent initial state. It is shown that close to instability, the system develops considerable entanglement, which is accompanied with simultaneous squeezing in the coordinate of one oscillator and the momentum of the other oscillator. In contrast, for weak coupling away from instability, the generated entanglement is small, with weak alternating squeezing in the coordinate and momentum of each oscillator. Approximate expressions describing these regimes are also provided.
The exact dynamics of the entanglement between two harmonic modes generated by an angular momentum coupling is examined. Such a system arises when considering a particle in a rotating anisotropic harmonic trap or a charged particle in a fixed harmonic potential in a magnetic field, and it exhibits a rich dynamical structure, with stable, unstable, and critical regimes according to the values of the rotational frequency or field and trap parameters. Consequently, it is shown that the entanglement generated from an initially separable Gaussian state can exhibit quite distinct evolutions, ranging from quasiperiodic behavior in stable sectors to different types of unbounded increase in critical and unstable regions. The latter lead, respectively, to logarithmic and linear growth of the entanglement entropy with time. It is also shown that entanglement can be controlled by tuning the frequency, such that it can be increased, kept constant, or returned to a vanishing value with just stepwise frequency variations. Exact asymptotic expressions for the entanglement entropy in the different dynamical regimes are provided.
An analytical solution for a master equation describing the dynamics of a qubit interacting with a nonlinear Kerr-like cavity through intensity-dependent coupling is established. A superposition of squeezed coherent states is propped as the initial cavity field. The dynamics of the entangled qubit-cavity states are explored by negativity for different deformed function of the intensity-dependent coupling. We have examined the effects of the Kerr-like nonlinearity and the qubit-cavity detuning as well as the phase cavity damping on the generated entanglement. The intensity-dependent coupling increases the sensitivity of the generated entanglement to the phase-damping. The stability and the strength of the entanglement are controlled by the Kerr-like nonlinearity, the qubit-cavity detuning, and the initial cavity non-classicality. These physical parameters enhance the robustness of the qubit-cavity entanglement against the cavity phase-damping. The high initial cavity non-classicality enhances the robustness of the qubit-cavity entanglement against the phase-damping effect.
Gravitational generation of quantum entanglement on squeezed coherent states in a system of two quantum mechanical particles is explored. The particles are modeled as harmonic oscillators, and their gravitational interaction is described by an interaction potential. Dynamics of the gravi- tationally induced entanglement is explored using the linear entropy of entanglement. An analytical expression for the linear entropy is obtained via Gaussian integration and covariance method. In the short-time weakly coupled regime, it is observed that the entanglement is proportional to the square of the time interval, square of the interaction strength, and proportional to the squeezing parameters of the modes. These results provide insights into the effects of quantum squeezing on entanglement generation in systems with gravitational interactions. Analytically and numerically it is shown that momentum squeezing can enhance gravitationally induced quantum entanglement.
We examine the entanglement induced by an angular momentum coupling between two harmonic systems. The Hamiltonian corresponds to that of a charged particle in a uniform magnetic field in an anisotropic quadratic potential or, equivalently, to that of a particle in a rotating quadratic potential. We analyze both the vacuum and thermal entanglement, thereby obtaining analytic expressions for the entanglement entropy and negativity through the Gaussian state formalism. It is shown that vacuum entanglement diverges at the edges of the dynamically stable sectors, increasing with the angular momentum and saturating for strong fields, whereas at finite temperature entanglement is nonzero just within a finite field or frequency window and no longer diverges. Moreover, the limit temperature for entanglement is finite in the whole stable domain. The thermal behavior of the Gaussian quantum discord and its difference from the negativity is also discussed.
Abstract In the present paper, we study the influence of non-commutativity on entanglement in a system of two oscillators-modes in interaction with its environment. The considered system is a two-dimensional harmonic oscillator in non-commuting spatial coordinates coupled to its environment. The dynamics of the covariance matrix, the separability criteria for two Gaussian states in non-commutative space coordinates, and the logarithmic negativity are used to evaluate the quantum entanglement in the system, which is compared to the commutative space coordinates case. The result is applied for two initially entangled states, namely the squeezed vacuum and squeezed thermal states. It can be observed that the phenomenon of entanglement sudden death appears more early in the system for the case of squeezed vacuum state than in the case of squeezed thermal state. Thereafter, it is also observed that non-commutativity effects lead to an increasing of entanglement of initially entangled quantum states, and reduce the separability in the open quantum system. It turns out that a separable state in the usual commutative quantum mechanics might be entangled in non-commutative extension.