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Physical Review A

Amplification of higher-order squeezing

Mark S. Hillery, Daoqi Yu

Published Feb 1, 1992• 16 citations
Publisher

Abstract

We examine the phase-insensitive amplification of three different kinds of higher-order squeezing. In particular, we consider fourth-order squeezing, intrinsic fourth-order squeezing, and amplitude-squared squeezing. It is found that for any input state both fourth-order squeezing and intrinsic fourth-order squeezing disappear at the output if the intensity gain is greater than 2. Amplitude-squared squeezing, on the other hand, can survive amplification at gains slightly greater than 2. Therefore the photon-cloning limit (intensity gain equals 2) is not a fundamental limit to nonclassical behavior.

DOI
10.1103/physreva.45.1860

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Exception to the cloning limit—amplification of amplitude-squared squeezed states

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arXiv:1009.2306•New Journal of Physics•Oct 5, 2010•24 citations
We examine the phase-insensitive amplification of three different kinds of higher-order squeezing. In particular, we consider fourth-order squeezing, intrinsic fourth-order squeezing, and amplitude-squared squeezing. It is found that for any input state both fourth-order squeezing and intrinsic fourth-order squeezing disappear at the output if the intensity gain is greater than 2. Amplitude-squared squeezing, on the other hand, can survive amplification at gains slightly greater than 2. Therefore the photon-cloning limit (intensity gain equals 2) is not a fundamental limit to nonclassical behavior.
An amplifier consists of a collection of inverted two-level atoms. It can be used to amplify a light signal but in the process the fluctuation behavior of the lights will be modified. In particular, for sufficiently large gains, nonclassical input states will become classical at the output. Hong, Friberg, and Mandel examined the effect of amplification on sub-Poissonian photon statistics and normal squeezing. They found that both of these effects disappear at the output if the intensity gain |G|2 > 2. The gain |G|2 = 2 is known as the photon cloning limit because one gets two photons out for every one that goes in. This gain has stood as an upper limit for the amplification of nonclassical behavior.
The real and imaginary parts of the square of the field amplitude obey an uncertainty relation. If the uncertainty in either of these variables is less than it would be in a minimum uncertainty state with equal uncertainties in both variables, the state is amplitude-squared squeezed. This is a nonclassical effect which can be produced by second harmonic generation, two-photon absorption, and degenerate parametric amplification, as well as by higher-order processes. Amplitude-squared squeezing can be converted into normal squeezing by interactions in which the square of the amplitude of one field is coupled to the amplitude of another. Second harmonic generation and some forms of four-wave mixing provide examples of such processes.
We investigate theoretically the generation of squeezed states in spontaneous and stimulated six-wave mixing process quantum mechanically. It has been found that squeezing occurs in field amplitude, amplitude-squared, amplitude-cubed, and fourth power of field amplitude of fundamental mode in the process. It is found to be dependent on coupling parameter “g” (characteristics of higher-order susceptibility tensor) and phase values of the field amplitude under short-time approximation. Six-wave mixing is a process which involves absorption of three pump photons and emission of two probe photons of the same frequency and a signal photon of different frequency. It is shown that squeezing is greater in a stimulated interaction than the corresponding squeezing in spontaneous process. The degree of squeezing depends upon the photon number in first and higher orders of field amplitude. We study the statistical behaviour of quantum field in the fundamental mode and found it to be sub-Poissonian in nature. The signal-to-noise ratio has been studied in different orders. It is found that signal-to-noise ratio is higher in lower orders. This study when supplemented with experimental observations offers possibility of improving performance of many optical devices and optical communication networks.
In this thesis we examine linear amplification of squeezed light, the phase properties of squeezed light and the effect on the phase of light from linear amplification. Previous studies of linear amplifiers of light have shown that (i) when amplifying squeezed light the power gain must be less than 2 to preserve some squeezing in the output light; and (ii) a squeezed output cannot be generated from a non-squeezed input. However, these studies were restricted to a class of linear amplifier that can now be identified as not being squeezed. In this thesis we show how to breach the gain limit with a squeezed linear amplifier, and how to generate squeezed light using a squeezed linear attenuator.
Kth-power amplitude squeezing (KPAS) is introduced and examined in the nonlinear-harmonic-oscillator model and the Jaynes-Cummings model with an intensity coupling. We discover that, in these two cases, the long-time behavior of KPAS (k\ensuremath{\le}4) for the strong initial field periodically displays a collapse-revival-valley and squeezed collapse-revival phenomenon, respectively. For a nonclassical state, the relation between KPAS and ordinary squeezing, Hong-Mandel squeezing, and antibunching is investigated. The results show that KPAS is another intrinsic and independent nonclassical effect inequivalent to the last three.