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Physical Review A

Nonlinear χ(2) Mach-Zehnder interferometer: Conditional preparation of maximal microscopic entanglement

Sergey A. Podoshvedov, Jaewan Kim

Published Mar 29, 2007• 5 citations
Publisher

Abstract

A nonlinear ${\ensuremath{\chi}}^{(2)}$ Mach-Zehnder interferometer is proposed as a simple device for conditional preparation of a two-photon maximally entangled state. Successful generation is unambiguously heralded by detection of a single photon in one of the routes of the nonlinear ${\ensuremath{\chi}}^{(2)}$ Mach-Zehnder interferometer. The mechanism of the conditional preparation is based on interference of the pumping modes. The scheme works without photon-number-resolving detection with a high fidelity.

DOI
10.1103/physreva.75.032346

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A nonlinear \ensuremathχ(2){\ensuremath{\chi}}^{(2)}\ensuremathχ(2) Mach-Zehnder interferometer is proposed as a simple device for conditional preparation of a two-photon maximally entangled state. Successful generation is unambiguously heralded by detection of a single photon in one of the routes of the nonlinear \ensuremathχ(2){\ensuremath{\chi}}^{(2)}\ensuremathχ(2) Mach-Zehnder interferometer. The mechanism of the conditional preparation is based on interference of the pumping modes. The scheme works without photon-number-resolving detection with a high fidelity.
The nonlinear χ (2) Mach-Zehnder interferometer is proposed as a device for conditional generation of a modified coherent nonclassical state. We show that the generated macroscopic state exhibits nonclassical effects, such as squeezing, photon antibunching, and sub-Poissonian statistics. The modified coherent state generates a macroscopic entangled state. The scheme works without the photon number resolving detection but requires high-efficiency photodetectors. We explain the mechanism of generation of the modified coherent non-classical state.
Nonlinear interferometers are Mach-Zehnder interferometers with Kerr media in either one or both arms. We refer to these devices, respectively, as the asymmetric and symmetric nonlinear interferometers. In the asymmetric case, with one input mode in the vacuum, it is possible to generate maximally entangled photonic states or superpositions of such states. We consider the device as a resource of entangled states for applications to Heisenberg-limited interferometry. Interferometry with the maximally entangled states cannot be performed by simply subtracting the output photocounts as in standard interferometry. Instead, one must perform parity measurements on only one of the output beams. We show that the symmetric nonlinear interferometer, with one input mode in the vacuum, may be used to perform such parity measurements. The same device is shown to produce, with an input coherent state and upon projective measurements, even or odd coherent states, examples of the Schr\"odinger-cat states.
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.
A simple experimental setup consisting of a spontaneous parametric down-conversion source and passive linear optics is proposed for conditional preparation of a maximally entangled polarization state of two photons. Successful preparation is unambiguously heralded by coincident detection of four auxiliary photons. The proposed scheme utilizes the down-conversion term corresponding to the generation of three pairs of photons. We analyze imperfect detection of the auxiliary photons and demonstrate that its deleterious effect on the fidelity of the prepared state can be suppressed at the cost of decreasing the efficiency of the scheme.
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.
A new system for entangled photon-pair generation using an all-fiber optic scheme consists of a fiber optic Mach-Zehnder interferometer (MZI) incorporating a fiber optic ring resonator. The Kerr nonlinearity effect in the fiber ring resonator is exploited for the generation of two independent squeezed beams. The advantage of such a system is that it requires a simple arrangement without any optical pumping parts or bulky optical components. Polarized light pulse trains are launched randomly into a MZI, and one part of the light is delayed in the longer path. The output pulses from both arms of the MZI enter a fiber optic ring resonator. A polarization controller controls the polarization states of the light pulses while they circulate in the ring resonator. The superposition of the nonlinear light pulses in a fiber optic ring resonator randomly occur. These forms are seen on an avalanche photodetector. The results are in good agreement with previous work.