Dmitrii Kouznetsov and Daniel Rohrlich

Name: Quantum noise at the nonlinear mapping of phase space
Author: Dmitrii Kouznetsov and Daniel Rohrlich

Quantum noise at the nonlinear mapping of phase space

Summary

“Quantum noise at the nonlinear mapping of phase space”, is a work by Dmitrii Kouznetsov and Daniel Rohrlich. It explores elements such as amplifier, quadrature and quadrature components.

Quotes from Quantum noise at the nonlinear mapping of phase space (Dmitrii Kouznetsov and Daniel Rohrlich)

Dmitrii Kouznetsov and Daniel Rohrlich, Quantum noise at the nonlinear mapping of phase space

“ Quadrature components of a single-mode field are interpreted as coordinates of the phase space. It is assumed that a quantum amplifier transforms the state of a single mode and the initial state of the field in this mode is a coherent squeezed one. The transfer function relating the average values of the field in the initial and final states determines mapping of the phase state. In the case of amplification, the field uncertainty in the final state is usually greater than in the initial state. ”

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Dmitrii Kouznetsov and Daniel Rohrlich, Quantum noise at the nonlinear mapping of phase space

“ By setting the squeezing parameter and assuming that depends only on , we obtain conditions for a nonlinear phase-invariant amplifier. In this case, the output mean value of the field is , and Theorem 1 reproduces the lower estimate of the noise of such an amplifier [6] . In a still more special case, we set and obtain the lower bound [1-4] for a linear phase-invariant amplifier. Let us turn now to the dispersions and of the quadrature components. For a linear parametric amplifier, the noise in one component may be as small as desired. ”

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Dmitrii Kouznetsov and Daniel Rohrlich, Quantum noise at the nonlinear mapping of phase space

“ A degenerate parametric amplifier with pumping depletion is considered to be an illustration. Transformation of an initially orthogonal rectangular net in the phase space and deformation of the body of uncertainty given by the Wigner function are constructed for such an amplifier.
Introduction A classical field in a certain mode can be amplified without introducing additional noise, whereas a quantum field cannot, even if prepared in a coherent state. Field amplification in a quantum mode produces quantum noise, i.e., increases the total uncertainty of quadrature field components. ”

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Dmitrii Kouznetsov and Daniel Rohrlich, Quantum noise at the nonlinear mapping of phase space

“ Amplification, coherent states and squeezing Quantum mechanics of amplifiers suggests that an amplifier converts an input field a into an output field through a unitary transformation: ; we are using lower-case letters for the input field and uppercase letters for the output field. For simplicity, we restrict ourselves to the case of a single-mode amplifier. In terms of the operators of the input field and its Hermite conjugation , the input quadrature components may be represented as
These components are coordinates of the phase space and do not commute. ”

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Dmitrii Kouznetsov and Daniel Rohrlich, Quantum noise at the nonlinear mapping of phase space

“ The net in Fig.1c is condensed to the right, whereas the body of uncertainty becomes wider. Only the mean position of the body of uncertainty follows the mapping of the transfer function of the initial position. The nonlinear behavior of the body of uncertainty demonstrates how the second and higher derivatives of the transfer function increase the noise of an amplifier. ”

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Dmitrii Kouznetsov and Daniel Rohrlich, Quantum noise at the nonlinear mapping of phase space

“ The gain factor , the dispersion , and its lower bound decrease as the amplitude grows, which corresponds ot the squeezing; remains greater than its lower bound, as must happen. At moderate input amplitude, the compression of the profile of uncertainty in the region of net compression can be interpreted semiclassically. The mapping corresponding to degenerate parametric amplification does not change an element of the phase volume , so it can be carried out without additional degrees of freedom [equation (23) with a C-number instead of describes a parametric amplifier with classical pumping] . ”

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Dmitrii Kouznetsov and Daniel Rohrlich, Quantum noise at the nonlinear mapping of phase space

“ Multimode states may also be important in practice. The lower bounds given by Theorems 1 and 2 are not the best possible, because the projector introduced in (13) is only one of a set of orthogonal projectors in the multimode space. The consideration of additional projectors may improve the lower bounds. ”

Dmitrii Kouznetsov and Daniel Rohrlich

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