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Abstract. This work presents an exactly soluble scheme to address the problem of optimal transfer of quantum states through a set of s harmonic oscillators composing a network with connected ends as a closed quantum circuit. For this purpose we start from a general quadratic Hamiltonian form. The relationship between the parameters of the Hamiltonian, the network size, and the time interval required for such transfer are explicitly shown. Particular physical realizations of this Hamiltonian, transfer of entangled states, including transfer of states at the expense of a quantum entanglement, are also considered.

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“…This transformation is defined by V = 0 and the unitary matrix W that diagonalizes C, given explicitly by [14],…”

Section: The Hamiltonian For Perfect State Transfermentioning

confidence: 99%

Perfect transfer of quantum states in a network of harmonic oscillators

Portes¹,

Rodrigues²,

Duarte

et al. 2013

Eur. Phys. J. D

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“…nonzero entries only on the diagonal, the subdiagonal and the superdiagonal). We shall refer to M h as the "interaction matrix" [11,21]. Let us for a while consider quantum systems described by a Hamiltonian with a more general interaction matrix M :…”

Section: General Methodsmentioning

confidence: 99%

“…One paper dealing with this problem (and closely related ones) is [21]. In that paper, some examples of analytically solvable Hamiltonians are given.…”

Section: General Methodsmentioning

confidence: 99%

Analytically solvable Hamiltonians for quantum systems with a nearest-neighbour interaction

Regniers¹,

Jeugt²

2009

J. Phys. A: Math. Theor.

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We consider quantum systems consisting of a linear chain of n harmonic oscillators coupled by a nearest neighbour interaction of the form −q rqr+1 (q r refers to the position of the rth oscillator). In principle, such systems are always numerically solvable and involve the eigenvalues of the interaction matrix. In this paper, we investigate when such a system is analytically solvable, i.e. when the eigenvalues and eigenvectors of the interaction matrix have analytically closed expressions. This is the case when the interaction matrix coincides with the Jacobi matrix of a system of discrete orthogonal polynomials. Our study of possible systems leads to three new analytically solvable Hamiltonians: with a Krawtchouk interaction, a Hahn interaction or a q-Krawtchouk interaction. For each of these cases, we give the spectrum of the Hamiltonian (in analytic form) and discuss some typical properties of the spectra.

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“…These properties were first noticed by Nierenberg [31] for lines and further exploited and generalized for lines and rings in Refs. [29,32]. The basic property is that the Majorana matrix on a line M L with matrix elements…”

Section: The Fundamental Vibration V=1mentioning

confidence: 99%

“…(19), with in total two quanta, in terms of the four parameters, A, A ′ , λ (I) , λ (II) and the anharmonicity parameter N . Analytic solutions can be obtained only in the weak coupling (λ/A ≪ 1) and strong coupling limit (λ/A ≫ 1) [29,32].…”

Section: The Overtone V=2mentioning

confidence: 99%

Algebraic theory of crystal vibrations: Singularities and zeros in vibrations of one- and two-dimensional lattices

et al. 2015

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A novel method for the calculation of the energy dispersion relation (EDR) and density of states (DOS) in one (1D) and two (2D) dimensions is introduced and applied to linear lattices (1D) and square and hexagonal lattices (2D). The (van Hove) singularities and (Dirac) zeros of the DOS are discussed. Results for the 2D hexagonal lattice (graphene-like materials) are compared with experimental data in microwave photonic crystals.

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Cited by 13 publications

References 10 publications

Perfect transfer of quantum states in a network of harmonic oscillators

Perfect transfer of quantum states in a network of harmonic oscillators

Analytically solvable Hamiltonians for quantum systems with a nearest-neighbour interaction

Algebraic theory of crystal vibrations: Singularities and zeros in vibrations of one- and two-dimensional lattices

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