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Journal of the Korean Physical Society

Engineering vacuum-evacuated photonic states with three input beams and two detectors

Sun-Hyun Youn

Published Oct 1, 2013• 4 citations
Publisher

Abstract

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.

DOI
10.3938/jkps.63.1559

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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.
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.
By analyzing the action of a beam splitter on squeezed vacuum states (SVSs), it is found that, if the two input light beams of the beam splitter have the same squeezing amplitude and phase, the output state is a two-mode SVS. If the two input light beams of the beam splitter have the same squeezing amplitude but a phase difference of π, the output state is a direct product state of two single-mode SVSs. In the two-mode SVS, each mode has the same photon number with both even and odd photons, while the single-mode SVS which contains only even-number photon in the photon number-state representation. Based on these results, a scheme to divert the entanglement of entangled SVS from its initial locations to another location is suggested. In this scheme, the two SVSs are utilized as the quantum channel. The process of the entanglement diversion is achieved by using the 50/50 symmetric beam splitters and the photon detectors with the help of classical information.
Properties of the entanglement at the outputs of a cascade beam-splitter are investigated for two single-mode squeezed vacuum state inputs. It is shown that the entanglement depends on the squeezing amplitudes of the input states and the reflection coefficients of the cascade beam-splitter and the composite phase shift Δ between the cascade beam-splitter and the input fields has a great effect on the entanglement. In particular, the properties of the entanglement of a cascade beam-splitter differ from those of only one beam-splitter. A further method for manipulating entanglement by adjusting the parameters of the cascade beam-splitter and the input fields is proposed.
Photon subtraction is useful to produce nonclassical states of light addressed to applications in photonic quantum technologies. After a very accelerated development, this technique makes possible obtaining either single photons or optical cats on demand. However, it lacks theoretical formulation enabling precise predictions for the produced fields. Based on the representation generated by the two-mode SU(2) coherent states, we introduce a model of entangled light beams leading to the subtraction of photons in one of the modes, conditioned to the detection of any photon in the other mode. We show that photon subtraction does not produce nonclassical fields from classical fields. It is also derived a compact expression for the output field from which the calculation of conditional probabilities is straightforward for any input state. Examples include the analysis of squeezed-vacuum and odd-squeezed states. We also show that injecting optical cats into a beam splitter gives rise to entangled states in the Bell representation.
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.
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.