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arXiv:0912.1552 · Optics Express

A bridge between the single-photon and squeezed-vacuum states

Nitin Jain, S.R. Huisman, Erwan Bimbard, Alexander I. Lvovsky

Published Aug 10, 2010• 8 citations
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Abstract

The two modes of the Einstein-Podolsky-Rosen quadrature entangled state generated by parametric down-conversion interfere on a beam splitter of variable splitting ratio. Detection of a photon in one of the beam splitter output channels heralds preparation of a signal state in the other, which is characterized using homodyne tomography. By controlling the beam splitting ratio, the signal state can be chosen anywhere between the single-photon and squeezed state.

DOI
10.1364/oe.18.018254

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The two modes of the Einstein-Podolsky-Rosen quadrature entangled state generated by parametric down-conversion interfere on a beam splitter of variable splitting ratio. Detection of a photon in one of the beam splitter output channels heralds preparation of a signal state in the other, which is characterized using homodyne tomography. By controlling the beam splitting ratio, the signal state can be chosen anywhere between the single-photon and squeezed state.
It is theoretically proved that the two output light beams can be used as a pair of EPR(Einstin-Podolsky-Rosen) entangled beams when the incident light upon a beam splitter is a single mode quadrature-squeezed coherent state or a squeezed quantum soliton. It is the simplest scheme for preparing entangled states to our knowledge. The formulas explicitly show the correlation between the two nonclassical optical fields: squeezed states and entangled states. The affection of squeezing degree on entanglement is also investigated.
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.
We propose and implement a new scheme of generating the optical Einstein-Podolsky-Rosen entangled state. Parametric down-conversion in two nonlinear crystals, positioned back-to-back in the waist of a pump beam, produces single-mode squeezed vacuum states in orthogonal polarization modes; a subsequent beam splitting entangles them and generates the Einstein-Podolsky-Rosen state. The technique takes advantage of the strong nonlinearity associated with type-0 phase-matching configuration while, at the same time, eliminating the need for actively stabilizing the optical phase between the two single-mode squeezers. We demonstrate our method, preparing a 1.4 dB two-mode squeezed state and characterizing it via two-mode homodyne tomography.
Quantum states of light, such as single photons, pairs of entangled photons, and squeezed light are a key resource for photonic quantum technologies. All these states can be obtained via the nonlinear optical effect of spontaneous parametric down-conversion (SPDC). In SPDC, a higher-energy photon of a coherent beam (pump) splits in two lower-energy daughter photons, called signal and idler. The photons of such a pair can be entangled in polarization, time/frequency, and position/momentum. Efficient generation of photon pairs requires a high second-order susceptibilityχ(2)\chi^{(2)}χ(2)of the material where it occurs, and the phase matching between the pump and the down-converted photons.
Two Kerr-squeezed optical beams can be combined in a beam splitter to produce non-Gaussian continuous-variable entangled states. We characterize the non-Gaussian nature of the output by calculating the third-order cumulant of quadrature variables and predict the level of entanglement that could be generated by evaluating the Duan-Simon and Reid Einstein-Podolsky-Rosen criteria. These states have the advantage over Gaussian states and non-Gaussian measurement schemes in that the well known, efficient, and proven technology of homodyne detection may be used for their characterization. A physical demonstration maintaining the important features of the model could be realized using optical fibers, beam splitters, and homodyne detection.