Squeezing with Nonlinear Optics
The earliest experiments on nonclassical light sources were able to produce photon-antibunching, or sub-Poissonian light, from single-atom resonance fluorescence [1]. However, the most useful experimental techniques for generating squeezing [2,3] have rel
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Squeezing with Nonlinear Optics
P. D. Drummond
The earliest experiments on nonclassical light sources were able to produce photon-antibunching, or sub-Poissonian light, from single-atom resonance fluorescence [1]. However, the most useful experimental techniques for generating squeezing [2,3] have relied on nonlinear optical [4] techniques. There are a variety of possible methods [5], depending on the type of nonlinearity, and number of interacting modes involved. The choice of optical nonlinearity reduces to either three-wave or four-wave mixing, which correspond to quadratic or cubic nonlinear response functions respectively. Each of these has advantages and disadvantages. Three wave mixing requires a pump field at twice the frequency of the field-mode being squeezed. While this is a complication, it is also an advantage in some respects; any sidebands induced on the pump due to phase noise have a large frequency offset from the squeezed fields. On the other hand, four-wave mixing does not require any frequencydoubling step, which has advantages in terms of simplicity. This was also the first method [2], used to obtain squeezing with quadrature noise below the vacuum level. Most of the early experiments attempted to obtain squeezing initially in one or two cavity modes, with the squeezed fields being transferred to propagating external modes for measurement purposes, through a beam-splitter or mirror [6-8]. This procedure is typically rather narrow-band. In current practice, this technique is most commonly used for three-wave (parametric) squeezing. Later, it was realized that propagating modes in a waveguide could be squeezed directly, giving a relatively simple, broad-band implementation of quadrature squeezing [9,10]. Due to the ready availability of high-quality single-mode silica fiber, this is most often carried out via four-wave mixing with short pulses or solitons [11-13]. Finally, it is possible to obtain squeezing directly through propagation in a bulk crystal, although at signal levels too low to measure quadrature noise-reduction. For this reason, these bulk experiments are usually referred to as spontaneous down-conversion or correlated photon experiments. To understand the physics of these different techniques, and how they relate to each other, we start with an elementary model using reversible single mode theory in the un depleted pump approximation. These types of model P. D. Drummond et al. (eds.), Quantum Squeezing © Springer-Verlag Berlin Heidelberg 2004
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P. D. Drummond
describe idealized, lossless, single-mode interferometers, and are unrealistic for most practical purposes. However, they do show in principle how a nonlinear optical interaction can lead to quantum states which satisfy the fundamental definition of squeezed states. A central problem is that one must then 'extract' the squeezed state - or transfer the internal squeezing to a propagating external mode. This is achieved either using an output coupler, described by quantum input-output theory, or even more simply by the d
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