Multimode difference squeezing

We define a type of multimode difference-squeezed states and show explicitly that these states are entirely embedded within the non-classical domain. We then contrast multimode difference squeezing with normal squeezing. We further analyse its delicate dependence on the modal states. All these studies emphasize the role of the concept of difference squeezing as a helpful theoretical tool for how to prepare the input modes to generate a squeezed output mode in a proper multiwave nonlinear process. Finally, we also discuss the possible connection between difference squeezing and a symmetry group.

Information transmission is most important in communication networks.Coherentbeams from laser sources are widely utilized in optical fibres to attain a high signal-to-noise ratio. However, the information precision is always bounded by the shot noise limit set intrinsically by quantum mechanics through the Heisenberg uncertainty principle. The discovery of squeezed states [1-4] has opened the way to beat the shot noise limit in a number of applications. In [5] a proposition was made to use squeezed instead of coherent light in optical systems to essentially reduce the noise in a signal. Very weak forces such as gravitational waves would also be detected by injecting a squeezed source into the unused input port of an interferometer [6]. Optical data bus technology was suggested in [7]: a squeezed state is to be applied in an optical waveguide to tap a signal-carrying waveguide and a very-low-energy-loss signal may reach many user sites without repeaters over a long distance. In principle, a noise-free signal might be achieved if it is carried by the field component which is perfectly squeezed. The quantum-mechanical nature of light is also manifested directly in higher-order squeezed states. Of a single-mode type are those introduced by Hong and Mandel [8] and by Hillery [9] (see also [10-12]). Multimode versions of higher-order squeezing were first suggested by Hillery [13] in terms of so-called sum and difference squeezing. Yet, only the simplest case of two modes was treated in [13]. The concept of Hillery’s sum squeezing has been generalized to the situation of three modes by Kumar and Gupta [14] and, of an arbitrary number of modes by Nguyen and Vo [15]. Concerning the difference squeezing, Kumar and Gupta have recently considered the case of three modes [16]. In this paper we make a further generalization of [13, 16] to include any mode number. The results of [13, 16] are thus particular cases of the results we have given. In addition, some important issues (e.g. the boundaries between difference squeezed and classical states, the conditions imposed on the initial modal populations, the connection to symmetry groups, etc) omitted in [16] for three modes are clarified in detail here for an arbitrary number of modes.

This paper is organized as follows. In the next section we define a type of multimode difference-squeezed state and show that such states, in contrast to the sum-squeezed states [13-15], which are non-classical and have a common border with the classical states, are entirely embedded within the non-classical domain. Section 3 determines, within the shorttime approximation, the conditions under which the multimode difference squeezing is related to normal squeezing. We then examine, in section 4, all the possible situations of modal states on which the system multimode difference squeezing depends. In section 5 we show that the connection, found in [13] for two modes, of the operators characterizing the multimode difference squeezing to the generators of the su(2) Lie algebra is violated for a mode number greater than two. Finally, we give our conclusions.

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