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Journal of Modern Optics

A simple scheme with coupled down converters with type-I phase matching as resource for conditional preparation of macroscopic entangled states

Sergey A. Podoshvedov, Nguyen Ba An, Jaewan Kim

Published Jun 23, 2006• 2 citations
Publisher

Abstract

It is shown that macroscopic entangled states can be generated using an experimental arrangement consisting of coupled spontaneous parametric down-converters with type-I phase matching (SPDCI) pumped simultaneously by optical fields in coherent state and two beam splitters. Two beam splitters in auxiliary generated modes are used to conditionally prepare macroscopic entangled states in output pumping modes of the studied system. Identification of two macroscopic entangled states is produced by use of photon number resolving detection. In contrast to all previous schemes, our scheme does not need Kerr-type nonlinear interaction and is purely based on second-order susceptibility of the crystal which is stronger for the Kerr nonlinearity. We calculate concurrence of the states as a measure of the amount of entanglement stored in the states and present analysis concerning ‘separation’ between components forming studied entangled states.

DOI
10.1080/09500340600654889

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It is shown that macroscopic entangled states can be generated using an experimental arrangement consisting of coupled spontaneous parametric down-converters with type-I phase matching (SPDCI) pumped simultaneously by optical fields in coherent state and two beam splitters. Two beam splitters in auxiliary generated modes are used to conditionally prepare macroscopic entangled states in output pumping modes of the studied system. Identification of two macroscopic entangled states is produced by use of photon number resolving detection. In contrast to all previous schemes, our scheme does not need Kerr-type nonlinear interaction and is purely based on second-order susceptibility of the crystal which is stronger for the Kerr nonlinearity. We calculate concurrence of the states as a measure of the amount of entanglement stored in the states and present analysis concerning ‘separation’ between components forming studied entangled states.
Two experimental arrangements consisting of coupled spontaneous parametric down-converters with type-I phase matching pumped simultaneously by a powerful optical field in a coherent state through a balanced beam splitter and linear optical elements are proposed for conditional preparation of macroscopic entangled states in output pumping modes of the studied system. Successful generation of the macroscopic entangled state in the pumping modes is unambiguously heralded by coincident detection of two photons in the generated signal and idler modes of the system. We calculate the amount of entanglement and probabilities of successfully observing the X (2) macroscopic entangled states in the total wavefunction. We show that the proposed schemes can be used to obtain a new type of macroscopic entangled states.
We generalize the scheme of conditional preparation of x (2) macroscopic entangled states [S.A. Podoshvedov, JETP 129 (2006)]. The studied system consists of a system of coupled down converters with type-I phase matching pumped simultaneously by powerful optical fields in coherent states with one auxiliary photon in the superposition state of two input modes and a projective measurement system. The projective measurement system involves two Hadamard gates introduced to generated output modes followed by photodetectors. Identification of macroscopic entangled states is produced by registration of one photon. No photon number resolving detection is required for the studied scheme.
We suggest an all-optical scheme to generate entangled superposition of a single photon with macroscopic entangled states for testing macroscopic realism. The scheme consists of source of single photons, a Mach-Zehnder interferometer in routes of which a system of coupled-down converters with type-I phase matching is inserted, and a beam splitter for the other auxiliary modes of the scheme. We use quantization of the pumping modes, depletion of the coherent states passing through the system, and interference effect in the pumping modes in the process of erasing which-path information of the single-photon on exit from the Mach-Zehnder interferometer. We show the macroscopic fields of the output superposition are distinguishable states. This scheme generates macroscopic entangled state that violates Bell's inequality. Moreover, the detailed analysis concerning change of amplitudes of entangled superposition by means of repeating this process many times is accomplished. We show our scheme works without photon number resolving detection and it is robust to detector inefficiency.
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.
It is shown that a linear superposition of two macroscopically distinguishable optical coherent states can be generated using a single photon source and simple all-optical operations. Weak squeezing on a single photon, beam mixing with an auxiliary coherent state, and photon detecting with imperfect threshold detectors are enough to generate a coherent state superposition in a free propagating optical field with a large coherent amplitude $(\ensuremath{\alpha}>2)$ and high fidelity (F>0.99)(F>0.99)(F>0.99). In contrast to all previous schemes to generate such a state, our scheme does not need photon number resolving measurements nor Kerr-type nonlinear interactions. Furthermore, it is robust to detection inefficiency and exhibits some resilience to photon production inefficiency.
Summary form only given. We have experimentally demonstrated that the two-photon probability amplitudes of photon pairs generated using spontaneous parametric down conversion from separate nonlinear crystals, under the conditions outlined above, remain independent and cannot be used to engineer more complex quantum states. The spontaneous nature of the down-conversion process prevents pairs of photons generated in unconnected regions of interaction from having a stable phase relationship between components of their probability amplitudes. The experiment has been performed using two BaB/sub 2/O/sub 4/ nonlinear crystals, of lengths 0.5 mm and 1.5 mm respectively. They have been cut to generate phase-matched type-II collinear down conversion.