Trio coherent states

Novel states called trio coherent states are introduced and studied. It is shown that these states possess inherent nonclassical properties such as sub-Poissonian number distributions and violation of Cauchy-Schwarz inequalities. Concerning squeezing, though the usual multimode squeezing is absent, a new type of higher-order multimode squeezing may occur in a trio coherent state. Finally, an experimental scheme is proposed to generate the introduced trio coherent state.

Nonclassical states are responsible for a wide class of intriguing physical phenomena that were unimaginable in classical physics. The properties of quantum mechanics allow for paradoxes such as uncertainties, uncontrollable disturbances caused by any measurements, etc. Only recently we have become aware that such ‘negative’ aspects in certain circumstances may become ‘positive’, to be exploited for applicable tasks that would be provably impossible in a classical world, such as quantum cryptography [1-3], quantum teleportation [4], quantum memory [5] necessary for quantum computation [6-8] and, in general, quantum networks. As an example, squeezed light, a kind of nonclassical state, was used to prepare the Einstein-Podolsky-Rosen beams to perform the first bona fide teleportation of an unknown quantum pure state [9]. Entangled quantum states can also be teleported with the use of squeezed light providing high fidelity [10]. Nonclassical states are however not automatically available in the natural world. Their theoretical discovery and experimental production prove to be very important.

Numerous nonclassical states have been found so far (see e.g. [11-32]). This does not mean that a search for newer nonclassical states is superfluous. Some time ago, for example, pair coherent states were considered [33], to which a number of papers [34-39] have been devoted. In this paper, as an extension of the pair coherent states, we introduce the so-called trio coherent states, whose definition is given in section 2. Section 3 shows that trio coherent states are nonclassical statesexhibiting clear sub-Poissonian number distributions, strong violation of Cauchy-Schwarz inequalities and a remarkable degree of a new-type squeezing. Finally, in section 4, we propose an experimental scheme to generate the introduced trio coherent states.

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