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Journal of Modern Optics

Two-mode Squeezed Gaussons

Gordon Yeoman, Stephen Mark Barnett

Published Aug 1, 1993• 50 citations
Publisher

Abstract

Two-mode squeezed Gaussons are non-classical states of light which are intermediate between single-mode and two-mode squeezed states. They may be prepared by coherently mixing two single-mode squeezed states at a beam-splitter or via a frequency converter. When equally squeezed single-mode squeezed states are incident on a 50/50 beam-splitter the output will range between a two-mode squeezed state and two single-mode squeezed states as the phase of the input squeezed light is varied. This behaviour is reflected when the properties of such states are investigated.

DOI
10.1080/09500349314551561

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Two-mode squeezed Gaussons are non-classical states of light which are intermediate between single-mode and two-mode squeezed states. They may be prepared by coherently mixing two single-mode squeezed states at a beam-splitter or via a frequency converter. When equally squeezed single-mode squeezed states are incident on a 50/50 beam-splitter the output will range between a two-mode squeezed state and two single-mode squeezed states as the phase of the input squeezed light is varied. This behaviour is reflected when the properties of such states are investigated.
Two-mode squeezed light is a macroscopic quantum entangled state of electro-magnetic fields and shows non-classical correlation between quadrature phase amplitudes in each optical mode. In this work the author is developing a high-quality two-mode squeezed light source for exploring the possibility of a quantum radar system based on a quantum illumination method and also expecting to apply it to quantum imaging. Two-mode squeezed light can be generated by combining two independent single-mode squeezed light beams using a beam splitter with a relative optical phase of 90 degrees between them. In current experimental progress the author developed two sub-threshold optical parametric oscillators to generate single-mode squeezed light beams. In the actual quantum radar or quantum imaging system, a turbulent atmosphere degrades quantum entanglement of a light source and affects performance of target detection. An optical loss is one of the simplest and most probable examples of environmental factors. In this work an evaluation method for quantum entanglement of two-mode squeezed light source is developed with consideration for the optical loss based on Duan's inseparability criteria.
Nonclassicality of optical fields are the key resources in quantum information processing.Recently, Agarwal [New J. Phys., 13, 073008(2011)] proposed a method for engineering of a two-mode vortex state, a non-Gaussian state, by subtracting a photon from a two-mode squeezed state produced by down-converter from idler mode via a beam splitter with low reflectivity and detection of one photon by the avalanche photo diode (APD), or even better by a single-photon detector.We study the nonclassicalities of this state in terms of squeezing, antibunching, photon number correlation and distribution of photon number.In addition, we study higher-order nonclassical properties, viz., sum squeezing.We find that the non-Gaussian state shows strong nonclassical effects.
Photon catalysis is a technique by which a readily available Gaussian state of light prepared in one mode is incident upon a beam splitter with a discrete number of photons, q, prepared in another mode; the resulting two-mode state is then subjected to single-photon resolving detection for q photons on one of the output modes. By employing beam splitters of different transmissivities and reflectivities, the subsequent single-mode state is shown to possess nonclassical properties such as quadrature squeezing and sub-Poissonian statistics. We consider the case in which the input state is the most general of pure single-mode Gaussian states: a squeezed coherent state. Noting the Gaussianity of the initial state, we demonstrate non-Gaussianity of the photon-catalyzed state by analyzing the quadrature uncertainty product and explicitly illustrate it through the Wigner quasi-probability distribution. We extend this technique to the two-mode squeezed states, whereby we perform photon catalysis on one mode of a two-mode squeezed vacuum state. The resulting correlated two-mode state may have applications in fundamental tests of quantum mechanics, such as violations of Bell’s inequalities, as the detection loophole can be closed due to the non-Gaussianity of the photon-catalyzed state. We also generalize our method to include state projective measurements for l≠q photons.
The properties of states generated by the application of the two-mode squeeze operator to the pair coherent states are studied. These states are the two-mode analogues of the single-mode squeezed states generated by the application of the single-mode squeeze operator to an ordinary coherent state. In the present case there are correlations between the modes and strong non-classical properties are to be expected. We study the statistical properties of the photon number distributions, squeezing, violations of the Cauchy-Schwartz inequality, quasiprobability distributions and the phase distributions.
A new generalized two-mode squeezed state which has less fluctuation in one quadrature phase then the usual two-mode squeezed state at the expense of increased fluctuation in the other quadrature is proposed. The coordinate representations and normally ordered expansions of the generalized two-mode squeeze operators and are given. The wavefunction of the generalized two-mode squeezed coherent state is obtained. The non-classical properties of the state such as squeezing and sub-Poissionian statistics are discussed.
We study the squeezing of light beams in a system combining beam splitters and time-varying media. First, we derive the input-output operator transformations for time-varying media. Integrating these with the input-output operator transformations of beam splitters allows describing arbitrary sequences of beam splitters and time-varying media. We show that a specific configuration—beam splitter, time-varying medium, beam splitter, time-varying medium—enables simultaneous single- and two-mode squeezing. This dual squeezing mechanism leverages the benefits of both types of squeezing, offering potential advantages for high-precision, non-demolition measurements.