Optical realization of a quantum beam splitter

Mar-Sarao, R.; Moya‐Cessa, H.

doi:10.1364/ol.33.001966

Cited by 11 publications

(6 citation statements)

References 13 publications

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“…As commented in the introduction, waveguide arrays are a good testbed to simulate both classical and quantum phenomena [20][21][22][23][24]. We shall discuss in this section, to motivate physically the coherent states discussed in this paper, the model of equally spaced and homogeneous waveguide arrays, in the cases of an infinite, a semi-infinite and a finite number of waveguides.…”

Section: Equally Spaced Homogeneous Waveguide Arraysmentioning

confidence: 99%

Coherent states for equally spaced, homogeneous waveguide arrays

Guerrero¹,

Moya‐Cessa²

2021

Preprint

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Coherent states for equally spaced, homogeneous waveguide arrays are defined, in the infinite, semiinfinite and finite cases, and resolutions of the identity are constructed, using different methods. In the infinite case, which corresponds to Euclidean coherent states, a resolution of the identity with coherent states on the circle and involving a nonlocal inner product is reviewed. In the semiinfinite case, which corresponds to London coherent states, various construction are given (restricting to the circle with a non-local scalar product, rescaling the coherent states, modifying them, or using a non-tight frame). In the finite case, a construction in terms of coherent states on the circle is given, and this construction is shown to be a regularization of the infinite and semiinfinite cases.

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Section: Equally Spaced Homogeneous Waveguide Arraysmentioning

confidence: 99%

Coherent states for equally spaced, homogeneous waveguide arrays

Guerrero¹,

Moya‐Cessa²

2021

Preprint

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“…Waveguide arrays are a good testbed to simulate both classical and quantum phenomena [19][20][21][22][23], and in this case we shall use them to realize coherent states of the Euclidean E(2) group. We shall focus in the case of an infinite number of equally spaced and homogeneous parallel waveguide arrays.…”

Section: Equally Spaced Infinite Homogeneous Waveguide Arraysmentioning

confidence: 99%

Coherent States for infinite homogeneous waveguide arrays

Guerrero¹,

López-Ruiz²

2021

Preprint

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Perelomov coherent states for equally spaced, infinite homogeneous waveguide arrays with Euclidean E(2) symmetry are defined, and new resolutions of the identity are constructed in Cartesian and polar coordinates. The key point to construct these resolutions of the identity is the fact that coherent states satisfy Helmholtz equation (in coherent states labels) an thus a non-local scalar product with a convolution kernel can be introduced which is invariant under the Euclidean group. It is also shown that these coherent states for the Eucliean E(2) group have a simple and natural physical realization in these waveguide arrays.

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“…The Hamiltonian H int = k(â † A âB + h.c.) models a linear interaction between two quantum fields (e.g. a beam-splitter in quantum optics [19]). It is exactly solvable in the sense that it can be linearly transformed into decoupled harmonic oscillators.…”

Section: Bathmentioning

confidence: 99%