dorsal/arxiv
View SchemaQuadrature-dependent Bogoliubov transformations and multiphoton squeezed states
| Authors | Silvio De Siena, Antonio Di Lisi, Fabrizio Illuminati |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0105070 |
| URL | https://arxiv.org/abs/quant-ph/0105070 |
| DOI | 10.1103/PhysRevA.64.063803 |
| Journal | Phys. Rev. A 64, 063803 (2001) |
Abstract
We introduce a linear, canonical transformation of the fundamental single--mode field operators $a$ and $a^{\dagger}$ that generalizes the linear Bogoliubov transformation familiar in the construction of the harmonic oscillator squeezed states. This generalization is obtained by adding to the linear transformation a nonlinear function of any of the fundamental quadrature operators $X_{1}$ and $X_{2}$, making the original Bogoliubov transformation quadrature--dependent. Remarkably, the conditions of canonicity do not impose any constraint on the form of the nonlinear function, and lead to a set of nontrivial algebraic relations between the $c$--number coefficients of the transformation. We examine in detail the structure and the properties of the new quantum states defined as eigenvectors of the transformed annihilation operator $b$. These eigenvectors define a class of multiphoton squeezed states. The structure of the uncertainty products and of the quasiprobability distributions in phase space shows that besides coherence properties, these states exhibit a squeezing and a deformation (cooling) of the phase--space trajectories, both of which strongly depend on the form of the nonlinear function. The presence of the extra nonlinear term in the phase of the wave functions has also relevant consequences on photon statistics and correlation properties. The non quadratic structure of the associated Hamiltonians suggests that these states be generated in connection with multiphoton processes in media with higher nonlinearities.
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"abstract": "We introduce a linear, canonical transformation of the fundamental\nsingle--mode field operators $a$ and $a^{\\dagger}$ that generalizes the linear\nBogoliubov transformation familiar in the construction of the harmonic\noscillator squeezed states. This generalization is obtained by adding to the\nlinear transformation a nonlinear function of any of the fundamental quadrature\noperators $X_{1}$ and $X_{2}$, making the original Bogoliubov transformation\nquadrature--dependent. Remarkably, the conditions of canonicity do not impose\nany constraint on the form of the nonlinear function, and lead to a set of\nnontrivial algebraic relations between the $c$--number coefficients of the\ntransformation. We examine in detail the structure and the properties of the\nnew quantum states defined as eigenvectors of the transformed annihilation\noperator $b$. These eigenvectors define a class of multiphoton squeezed states.\nThe structure of the uncertainty products and of the quasiprobability\ndistributions in phase space shows that besides coherence properties, these\nstates exhibit a squeezing and a deformation (cooling) of the phase--space\ntrajectories, both of which strongly depend on the form of the nonlinear\nfunction. The presence of the extra nonlinear term in the phase of the wave\nfunctions has also relevant consequences on photon statistics and correlation\nproperties. The non quadratic structure of the associated Hamiltonians suggests\nthat these states be generated in connection with multiphoton processes in\nmedia with higher nonlinearities.",
"arxiv_id": "quant-ph/0105070",
"authors": [
"Silvio De Siena",
"Antonio Di Lisi",
"Fabrizio Illuminati"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.64.063803",
"journal_ref": "Phys. Rev. A 64, 063803 (2001)",
"title": "Quadrature-dependent Bogoliubov transformations and multiphoton squeezed states",
"url": "https://arxiv.org/abs/quant-ph/0105070"
},
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