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Abstract
Errors in the recent article, "Quantum optics with particles of light," are discussed. "Dispersed states" resulting from linear optics are simply coherent states, and have no interesting quantum statistics.
... In conclusion, the above derivations show that the dispersed states are squeezed and non-classical. It is in contrast to Ref. [1] where the states were found to be coherent. We attribute the difference in the two conclusions to the fact that Ref. [1] deals with the photon creation and annihilation operators while the effect of squeezing shows up in the momentum-position observables Ref. [2]. ...
... It is in contrast to Ref. [1] where the states were found to be coherent. We attribute the difference in the two conclusions to the fact that Ref. [1] deals with the photon creation and annihilation operators while the effect of squeezing shows up in the momentum-position observables Ref. [2]. We recommend to an interested reader Ref. [5] where the derivations presented above will be given in great detail. ...
We prove formal identity of the dispersed states and the two-photon coherent states. As the last fall in the class of squeezed states and are non-classical, so are the dispersed states. A state which exhibits squeezing and/or non-classicality should not be called coherent as suggested in the Comment.
We prove formal identity of the dispersed states and the two-photon coherent states. As the last fall in the class of squeezed states and are non-classical, so are the dispersed states. A state which exhibits squeezing and/or non-classicality should not be called coherent as suggested in the Comment.
A linearized quantum theory of soliton squeezing and detection is presented. The linearization reduces the quantum problem to a classical one. The classical formulation provides physical insight. It is shown that a quantized soliton exhibits uncertainties in photon number and phase, position (time), and momentum (frequency). Detectors for the measurement of all four operators are discussed. The squeezing of the soliton in the fiber is analyzed. An optimal homodyne detector for detection of the squeezing is presented that suppresses the noise associated with the continuum and the uncertainties in position and momentum.
We propose a technique for generating momentum-squeezed states of optical pulses with a simple apparatus. An initial coherent state is launched into a dispersion-decreasing fiber, leading to pulse compression. The compressed pulse has a broader spectrum, but the average frequency of the pulse is fundamentally conserved by the Kerr effect. Although the momentum, or frequency, uncertainty of the pulse is not reduced, the final momentum uncertainty is below the coherent-state level with respect to the broadened output spectrum. The observable momentum uncertainty reflects photon correlations generated during the Kerr-effect scattering events. We discuss the basic characteristics of squeezing as well as the possibility of generating interesting quantum superposition states in an ideal lossless device.
We examine the effects of loss and gain on a quantum soliton using a configuration-space approach. A simple microscopic model of local photon-matter interaction is applied to solitons with arbitrary quantum superpositions of momentum. Such a theory is needed in the analysis and design of systems that manipulate the wave function of soliton center-of-mass coordinates. The formalism is tested by calculating the momentum noise induced by loss and gain, and by comparison with the well-known Gordon-Haus calculation [J. P. Gordon and H. A. Haus, Opt. Lett. 11, 665 (1986)]. The comparison provides physical insight and reproduces the old result as a special case.
The stochastic theory presented by Drummond, Gardiner, and Walls [Phys. Rev. A 24, 914 (1981)] is an interesting approach to problems in quantum optics. In this theory, an exact, quantum evolution is written in terms of classical functions (not operators) driven by explicit, quantum noise. We examine the origin of uncertainty in the formalism through the simple example of a single, nonlinear oscillator. We then test the stochastic theory applied to the problem of soliton propagation. We extend the linearized stochastic model by computing analytically quantum uncertainties in the four basic soliton parameters: photon number, momentum, phase, and position. Agreement with second-quantized and configuration-space soliton theories verifies the stochastic formalism.
The fiber Bragg gratings (FBGs) with Kerr nonlinearity exhibit optical soliton like phenomena known as the Bragg solitons. Due to the high dispersion of FBGs near the band edge, optical solitons in the anomalous dispersion side is produced when the input pulse has suitable pulse-width and peak intensity. The Bragg solitons belong to the class of bi-directional pulse propagation problems. In this paper, general quantum theory for bi-directional pulse propagation problems is developed and applied to the Bragg solitons. The output Bragg soliton pulses are quantum-mechanically squeezed and their squeezing ratios calculated.
The concept of particles of light is introduced by ascribing a mechanical degree of freedom to a radiational wave packet. Evolution of the position and momentum observables of such particle in a dispersive dielectric is studied. It is shown that an initial coherent state evolves into a dispersed state which is characterized by a reduction of quantum fluctuations below Standard Quantum Limit when a certain combination of the position and momentum observables is measured.
Lai and Haus [Phys. Rev. A 40, 854 (1989)] recently introduced the use of a photon configuration-space wave function to analyze optical soliton propagation in a fiber. This is of interest as photon wave functions have long been the source of controversy; the work of Lai and Haus was the first to demonstrate that they could be of use in quantum optics. The systematic reduction of photon configuration-space wave functions directly from QED was recently carried out, which puts the general approach on solid ground. Here we apply the photon configuration-space approach systematically to the dynamics of the soliton center of mass and phase spread, and to squeezing in optical fibers. The predictions of the configuration-space model agree with results from the quantum field theory linearization models, which provide an important benchmark for the new approach. The configuration-space model leads ultimately to a description of the soliton as a quantum object that obeys free particle dynamics in relative position and phase. Phase squeezing appears in the configuration-space model as a consequence of free particle dynamics following initial phase localization due to the use of an initial classical soliton state. © 1996 The American Physical Society.