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Journal of Experimental and Theoretical Physics

Modified nonclassical coherent state: Squeezing, antibunching, sub-Poissonian photon statistics, realization scheme with the χ(2)-nonlinearity, and generation of a macroscopic entangled state

Sergey A. Podoshvedov

Published Apr 1, 2007• 0 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776107040048

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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.
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.
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.
In this paper, after a brief review on the entangled coherent state, a general form of the entangled nonlinear coherent state has been introduced based on the nonlinear coherent states approach. By choosing particular f-deformation functions, theoretical schemes for generation of two distinct classes of such states associated with SU(1,1) and SU(2) groups are presented. The entanglement characteristic of the corresponding entangled coherent states has been studied by evaluating the concurrence. In the continuation, other nonclassical behaviors of the produced states have been analyzed by investigating sub-Poissonian photon statistics, the oscillatory photon number distribution, one- and two-mode quadrature squeezing, and sum and difference squeezing. Accordingly, in addition to their entanglement property, other nonclassicality features of the introduced states are well established in detail.
Abstract Two-mode nonlinear semi-coherent states and their even and odd superpositions are defined. Their non-classical properties, including photon statistics and squeezing, are then evaluated. We use the Mandel parameter and the second-order coherence function to study sub-Poissonian photon statistics and the photon antibunching effect. By calculating the variance of two-mode quadrature operators, we evaluate the squeezing effect for the introduced states. Next, we examine entanglement using concurrence. We have found that all states display non-classical properties within certain ranges of the parameters involved. The calculation of concurrence demonstrates that all states are entangled within specific ranges of parameters.
Photon statistics effects are analyzed for Mach-Zehnder and Michelson interferometers in which a strong coherent state is inserted into one input port and a squeezed vacuum is inserted in the other input port. We study the effects related to entanglement, for the general case, by using Zassenhaus's perturbation theory as a function of the squeezing parameter. For the special case in which the strong coherent state exits fully through one output port while the squeezed vacuum exits through the other “dark” output port, the Lie group disentangling method is used. For this case we show that the signal can be amplified with sub-Poissonian photon statistics.
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.