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arXiv:1410.1398 · Journal of the Korean Physical Society

Conditional generation scheme for a high-purity superposed state of single and two-photon states by mixing two coherent beams with squeezed vacuum states

Sun-Hyun Youn

Published Jan 1, 2014• 2 citations
arXivHTMLPDF

Abstract

The numerical conditions to generate high-purity |1 >, |2 >, and |1 > + re iψ |2 > states were found from the explicit form of the probability amplitudes for two cascade-placed beam splitters with one squeezed state input and two coherent state inputs. The expected theoretical signal-tonoise ratio is more than 1000. Controlling the amplitudes and the phases of two coherent beams, as well as the transmittances of two beam splitters, allow various quantum states to be manipulated with a high signal-to-noise ratio. High-purity nonclassical states are expected to be a key element in quantum information science.

DOI
10.3938/jkps.64.217

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The numerical conditions to generate high-purity |1 >, |2 >, and |1 > + re iψ |2 > states were found from the explicit form of the probability amplitudes for two cascade-placed beam splitters with one squeezed state input and two coherent state inputs. The expected theoretical signal-tonoise ratio is more than 1000. Controlling the amplitudes and the phases of two coherent beams, as well as the transmittances of two beam splitters, allow various quantum states to be manipulated with a high signal-to-noise ratio. High-purity nonclassical states are expected to be a key element in quantum information science.
From the explicit form of the probability amplitude for two cascade-placed beam splitters (with one squeezed state input and two coherent state inputs), we calculated the probability amplitude of the output beam as a function of the transmittance of the two beam splitters and the amplitude and the relative phase of the three input states. At a certain condition, the output beam had no vacuum and was in a highly nonclassical state that contained more than one photon. Armed with explicit probability amplitude for two beam splitters and two coherent states, the squeezed vacuum state might be a very useful tool for generating highly nonclassical light.
In the two-cascade-placed beam splitter system, controllable entangled states can be conditionally generated with one squeezed light and two coherent lights. By measuring one photon in one of three output ports, an entangled quantum state can be generated in the remaining two ports. Using the Schmidt decomposition technique, we calculate the degree of entanglement, and maximize the degree of entanglement by adjusting the three input beams and the transmittances of the two beam splitters. The degree of entanglement can be easily adjusted by changing the relative phase angle of the input states.
Entangled coherent states are shown to emerge, with high fidelity, when mixing coherent and squeezed vacuum states of light on a beam-splitter. These maximally entangled states, where photons bunch at the exit of a beamsplitter, are measured experimentally by Fock-state projections. Entanglement is examined theoretically using a Bell-type nonlocality test and compared with ideal entangled coherent states. We experimentally show nearly perfect similarity with entangled coherent states for an optimal ratio of coherent and squeezed vacuum light. In our scheme, entangled coherent states are generated deterministically with small amplitudes, which could be beneficial, for example, in deterministic distribution of entanglement over long distances.
In this work, the basic idea of the quantum scissors (QS) device is slightly modified to generate finite-dimensional quantum states by means of conditional measurements on beam splitters (BSs). It turns out that a QS device with two single-photon inputs and two single-photon detections is just a projection operator composed of the vacuum state, one-photon state, and two-photon state, depending upon the transmission coefficients of BSs. As the most general example, we consider the squeezed coherent state as the input state and derive the analytical expression of the output state. Its nonclassical characteristics are analyzed in detail by means of the average photon number, intensity gain, and Wigner function. In addition, we extend this technique to the two-mode squeezed vacuum state (TMSVS). The resulting state is just the generalized Bell state, containing only the twin vacuum, twin one-photon, and twin two-photon components, whose entanglement properties are quantified by the von Neumann entropy and Einstein–Podolsky–Rosen correlation. The results show that the entanglement of the truncated TMSVS is stronger than that of TMSVS within a certain range of squeezing parameter and transmissivity.
We present an optical scheme to conditionally generate even or odd squeezed superpositions of coherent states (SSCSs). The optical setup consists of an unbalanced beam splitter whose transmittance tends to unity, and additional balanced beam splitters and photodetectors in auxiliary modes. Squeezed coherent states with different amplitudes are the input states in the optical scheme. The single-qubit operations are probabilistic and employ two- and three-photon subtractions from initial beams as the driving force. Generation of the even or odd SSCSs is observed in a wide diapason of values of used parameters. We consider a possibility to realize a one-way Hadamard gate for the squeezed coherent states when the base states are transformed into superposition states. States approximating the output states of a Hadamard gate with high fidelity can be realized by imposing restrictions on the values of used parameters. Higher-order subtractions from input beams are necessary to generate the SSCSs with larger amplitudes and higher fidelities. The problem is resolved in a Wigner representation to take into account imperfections of the optical devices.