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Propagation of Squeezing of the Electromagnetic Field

Iwo Białynicki‐Birula

Published Jan 1, 1998• 1 citation
OpenAlex

Abstract

Quantum field theoretic approach is used to describe the of the electromagnetic field in its most complete form that takes into account tem- poral and spatial characteristics of the squeezed state. This approach enables one to study the propagation of the squeezing wave in space-time. A simple exam- ple of a weak squeezing, that allows for all calculations to be done analytically, is discussed in detail.

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Introduction . The purpose of this chapter is to present the quantum theory of the electromagnetic field in the absence of charges and currents. Thus the classical field discussed in the previous chapter is subjected to canonical quantization in Section 2.1, where creation and annihilation operators for plane-wave and spherical wave modes, as well as their commutation relations, are derived along with various field-field commutators related to field propagators. In the next section we introduce the concept of the photon as an elementary excitation of the electromagnetic field. The attention is focused on the ground state of the quantized electromagnetic field in the absence of sources, which is the photon vacuum. The amplitude fluctuations, or zero-point fluctuations of this vacuum, are evaluated. Excited states of the field are examined in the next sections. In particular, Section 2.3 is concerned with number states and coherent states, the latter being obtained by a Glauber transformation of the vacuum, and with their statistical properties. Squeezed states of the field are introduced in Section 2.4 by a unitary transformation leading from the normal to the squeezed vacuum, whose statistical properties are compared with those of a coherent state. Section 2.5 is devoted to a brief discussion of thermal states. The final section of this chapter is dedicated to a discussion of the nonlocalizability of the photon.

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Squeezed-state effect on bound–continuum transitions

W. Leoński

An atomic model is discussed that contains one structured continuum interacting with an electromagnetic field of quantum nature. It is assumed that the field is initially in a squeezed state. Three kinds of squeezed state are discussed: (1) the squeezed vacuum state, (2) the squeezed state with a strong coherent component, and (3) the Holstein–Primakoff SU(1, 1) coherent state. A derivation is given of a fully analytical formula for the probability of finding the system in the continuum in a long-time regime. This result is obtained by a nonperturbative method and hence is valid for arbitrary field strengths. The result is discussed for various values of the parameters describing the electromagnetic field and its interaction with the atomic model and exhibits a strong dependence of the probability on the type and the squeezing parameters of the squeezed state.

Journal of the Optical Society of America B•Feb 1, 1993•18 citations
Quantum field theoretic approach is used to describe the of the electromagnetic field in its most complete form that takes into account tem- poral and spatial characteristics of the squeezed state. This approach enables one to study the propagation of the squeezing wave in space-time. A simple exam- ple of a weak squeezing, that allows for all calculations to be done analytically, is discussed in detail.
This article contains a review of an alternative theory of squeezing, based entirely on the wave function description of the squeezed states. Quantum field theoretic approach is used to describe the squeezing of the electromagnetic field in its most complete form that takes into account temporal and spatial characteristics of the squeezed state. An analog of the Wigner function for the full electromagnetic field is introduced and expressed in terms of second order correlation functions. The field-theoretic approach enables one to study the propagation of the ``squeezing wave'' in space-time. A simple example of weak squeezing, that allows for all calculations to be done analytically, is discussed in detail.
The propagation of quantized electromagnetic fields through optically isotropic media with cubic optical nonlinearity is considered. Analytical solutions are presented in closed form showing that the light field can emerge from the medium in a squeezed quantum state. A detailed numerical analysis of the results is performed and presented graphically. Over 90 per cent of the squeezing permitted by quantum-mechanical theory is achieved in this way. The dependence of the squeezing effect on the polarization state of the field and the nonlinear molecular parameters is also discussed.
Starting with the canonical quantization procedure for the electromagnetic field inside an effective (linear or nonlinear) medium, we present a direct-space formulation of the theory of quantum optics. This approach does not use the conventional modal decomposition of the field, but relies on the electromagnetic momentum operator defined in terms of local electric- and magnetic-field operators. The momentum operator contains all the information on the spatial characteristics of the field, and can describe the translation of a short light pulse in a nonlinear medium, without a modal analysis of the pulse. Propagation is described through an operatorial wave equation that relates the temporal evolution of an electromagnetic pulse to its spatial progression. Through this equation, the direct-space approach to quantum optics can treat traveling-wave nonlinear-optical phenomena and, at the same time, account for their quantum statistics. The theory is applied to squeezed-light generation by the parametric down-conversion of a short laser pulse, as an illustration.
Introduction . The purpose of this chapter is to present the quantum theory of the electromagnetic field in the absence of charges and currents. Thus the classical field discussed in the previous chapter is subjected to canonical quantization in Section 2.1, where creation and annihilation operators for plane-wave and spherical wave modes, as well as their commutation relations, are derived along with various field-field commutators related to field propagators. In the next section we introduce the concept of the photon as an elementary excitation of the electromagnetic field. The attention is focused on the ground state of the quantized electromagnetic field in the absence of sources, which is the photon vacuum. The amplitude fluctuations, or zero-point fluctuations of this vacuum, are evaluated. Excited states of the field are examined in the next sections. In particular, Section 2.3 is concerned with number states and coherent states, the latter being obtained by a Glauber transformation of the vacuum, and with their statistical properties. Squeezed states of the field are introduced in Section 2.4 by a unitary transformation leading from the normal to the squeezed vacuum, whose statistical properties are compared with those of a coherent state. Section 2.5 is devoted to a brief discussion of thermal states. The final section of this chapter is dedicated to a discussion of the nonlocalizability of the photon.
An atomic model is discussed that contains one structured continuum interacting with an electromagnetic field of quantum nature. It is assumed that the field is initially in a squeezed state. Three kinds of squeezed state are discussed: (1) the squeezed vacuum state, (2) the squeezed state with a strong coherent component, and (3) the Holstein–Primakoff SU(1, 1) coherent state. A derivation is given of a fully analytical formula for the probability of finding the system in the continuum in a long-time regime. This result is obtained by a nonperturbative method and hence is valid for arbitrary field strengths. The result is discussed for various values of the parameters describing the electromagnetic field and its interaction with the atomic model and exhibits a strong dependence of the probability on the type and the squeezing parameters of the squeezed state.