Abstract
We report a scheme for generation of high-order quadrature vortex states using two-mode photon-number squeezed states, generated via the non-linear process of Spontaneous Parametric Down Conversion. By applying a parametric rotation in the quadratures (X^,Y^), using a ϕ converter, the Gaussian profile of the photon-number squeezed input state can be mapped into a superposition of Laguerre-Gauss modes in the quadratures with N vortices or singularities, for an input state containing 2N photons, thus mapping photon-number fluctuations to interference effects in the quadratures. Our scheme has the potential to improve measurement sensitivity beyond the Standard uantum Limit (SQL ∝N), by exploiting the advantages of optical vortices, such as high dimensionality or topological properties, for applications requiring reduced uncertainty, such as quantum cryptography, quantum metrology and sensing.
Highlights
In quantum optics, a beam of light is in a squeezed state if its electric field amplitude has a reduced uncertainty, in relation to that of a coherent state
There is a broad range of applications of optical vortices in diverse areas, such as in astronomy for detection of extra-solar planets, in optical tweezers for manipulation of cells and micro-particles, in optical communication to improve the spectral efficiency, in Orbital Angular Momentum (OAM) multiplexing, and in quantum cryptography to increase communication bandwidth [11–20]
Our scheme has the potential of exploiting the advantages of optical vortices, such as high dimensionality or topological properties,√ for applications requiring precision beyond the SQL ∝ N, such as quantum cryptography, quantum metrology and sensing
Summary
A beam of light is in a squeezed state if its electric field amplitude has a reduced uncertainty, in relation to that of a coherent state. We report a scheme for generation of high-order quadrature vortex states using two-mode photon-number squeezed states generated via the non-linear process of Spontaneous. The article is structured as follows: First, in Section 2 we review the properties of two-mode photon-number squeezed states such as their quadrature representation and photonnumber distribution, second in Section 3 we introduce the concept of quadrature rotation. Consider a truncated two-mode photon-number squeezed state, produced by SPDC, in the Fock state representation of the form [21]: ψ〉. And (a, b) are annihilation operators for the two modes (a, b) [24] In this notation, the two-mode photon-number states nx, ny〉 can be written in the quadrature representation as 〈x, y nx, ny〉. Photon-number distributions for different values of the squeezing parameter r 1, 0.5, 0.1 are displayed in Figure 1D, revealing thermal statistics when tracing over one mode, while the overall photon-number statistics for the 2-mode squeezed states is sub-Poissonian
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