Generating superposition and entanglement of squeezed vacuum states

We propose a scheme for generating the superposition and the entanglement of squeezed vacuum states of electromagnetical fields. The scheme involves single-photon source, single photon detector, and cross Kerr nonlinearity. The Kerr nonlinearity required for generating the superposition of squeezed vacuum states is 1/2 of that required for generating the superposition of coherent states. The proposal can also be extended to generate the entanglement states between two coherent states and that between one coherent state and one squeezed vacuum state. Superposition and entanglement are characteristic features of quantum states and have important applications in quantum science and technology, for example, in quantum computation and quantum information [1]. The superpositions and entanglements of coherent states have been studied extensively[2]. Especially, there have been experimental demonstrations of generating the superpositions of coherent states in a cavity [3] and in an ion trap [4]. However, few attention has been paid on the study of superposition and entanglement of squeezed states[5]. Recently, Chen et al.[6] proposed a scheme for generating superposition and entanglement of squeezed states, and their scheme was based on cavity quantum electrodynamics (cavity QED). In this paper, we propose a simple scheme for generating superposition and entanglement of squeezed vacuum states. Our work was inspired by Gerry’s idea[7], and involves single photon source, single photon detector, beam splitter, phase-shifter, and cross Kerr nonlinearity. The scheme is shown in Fig.1. A photon in mode b is incident on the beam splitter BS1. One of the output modes of BS1 interacts with mode a (in a squeezed state) via a cross Kerr nonlinearity in the Kerr medium KM, and the other output mode of BS1 passes through the phase-shifter θ, then the two modes combine at the beam splitter BS2. By detecting output photons from the beam splitter BS2, the states of mode a will be projected into a superposition of squeezed states. By changing the configuration of Fig.1 to that of Fig.2, we can obtain entanglement of squeezed states. Now we discuss the schemes in more details. We assume the beam splitters are of the type of 50:50, as shown in Fig.3, then we have bout = 1 √ 2 (bin + icin) , cout = 1 √ 2 (cin + ibin) , (1) or b+in = 1 √ 2 ( bout + ic + out ) , c+in = 1 √ 2 ( cout + ib + out ) , (2) [email protected]