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Concept
Optical phase space
Summary
In quantum optics, an optical phase space is a phase space in which all quantum states of an optical system are described. Each point in the optical phase space corresponds to a unique state of an optical system. For any such system, a plot of the quadratures against each other, possibly as functions of time, is called a phase diagram. If the quadratures are functions of time then the optical phase diagram can show the evolution of a quantum optical system with time.
An optical phase diagram can give insight into the properties and behaviors of the system that might otherwise not be obvious. This can allude to qualities of the system that can be of interest to an individual studying an optical system that would be very hard to deduce otherwise. Another use for an optical phase diagram is that it shows the evolution of the state of an optical system. This can be used to determine the state of the optical system at any point in time.
When discussing the quantum theory of light, it is very common to use an electromagnetic oscillator as a model. An electromagnetic oscillator describes an oscillation of the electric field. Since the magnetic field is proportional to the rate of change of the electric field, this too oscillates. Such oscillations describe light. Systems composed of such oscillators can be described by an optical phase space.
Let u(x,t) be a vector function describing a single mode of an electromagnetic oscillator. For simplicity, it is assumed that this electromagnetic oscillator is in vacuum. An example is the plane wave given by
where u0 is the polarization vector, k is the wave vector, the frequency, and AB denotes the dot product between the vectors A and B. This is the equation for a plane wave and is a simple example of such an electromagnetic oscillator. The oscillators being examined could either be free waves in space or some normal mode contained in some cavity.
A single mode of the electromagnetic oscillator is isolated from the rest of the system and examined.
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