bar code for .NET Generation of quadrature squeezed light in .NET Get Code 128C in .NET Generation of quadrature squeezed light

Generation of quadrature squeezed light using barcode implementation for none control to generate, create none image in none applications.generate barcode using Most schemes for generation none none of quadrature squeezed light are based on some sort of parametric process utilizing various types of nonlinear optical devices. Generally, one desires an interaction Hamiltonian quadratic in the annihilation and creation operators of the eld mode to be squeezed. We consider a device known as a degenerate parametric down-converter.

A certain kind of nonlinear medium is pumped by a eld of frequency P and some photons of that eld are converted into pairs of identical photons, of frequency = P /2 each, into the signal eld, the process known as degenerate parametric down-conversion. The Hamiltonian for this process is given by. About 2D Code H = h a a + h P b b + i h (2) (a 2 b a 2 b), (7.84). where b is the pump mode an none none d a is the signal mode. The object (2) is a secondorder nonlinear susceptibility. (For a discussion of nonlinear optics, the reader.

Nonclassical light Fig. 7.11. Q function for (a) the squeezed vacuum, and (b) the displaced squeezed vacuum. 0.2 0.15.

Q(x,y). 0.1 0.05 0 2 0 2.

0 2 2. 0.2 0.15.

Q(x,y). 0.1 0.05 0 2 0 2.

0 2 2. should consult, for example , the book by Boyd [11].) We now make the parametric approximation whereby we assume that the pump eld is in a strong coherent classical eld, which is strong enough to remain undepleted of photons over the relevant time scale. We assume that that eld is in a coherent state .

e i P t and approximat none none e the operators b and b by e i P t and ei P t , respectively. Dropping irrelevant constant terms, the parametric approximation to the Hamiltonian in Eq. (7.

84) is. H (PA) = h a a + i h a 2 ei P t a 2 e i P t , (7.85). 7.3 Detection of quadrature squeezed light where = (2) . Finally, transforming to the interaction picture, we obtain H I (t) = i h a 2 none none ei( P 2 )t a 2 e i( P 2 )t , (7.86). which is generally time dep endent. But if P is chosen such that P = 2 , we arrive at the time-independent interaction Hamiltonian. H I = i h( a 2 a none none 2 ). (7.87).

The associated evolution operator U I (t, 0) = exp( i none none H I t/ h) = exp( t a 2 t a 2 ) (7.88). obviously has the form of the squeeze operator of Eq. (7.10), U I (t, 0) = S( ), for = 2 t.

There is another nonlinear process that gives rise to squeezed light, namely degenerate four-wave mixing in which two pump photons are converted into two signal photons of the same frequency. The fully quantized Hamiltonian for this process is. H = h a none for none a + h b b + i h (3) (a 2 b 2 a 2 b2 ) (7.89). where (3) is a third-orde r nonlinear susceptibility. Going through similar arguments as above for the parametric down-converter, and once again assuming a strong classical pump eld we obtain the parametric approximation of Eq. (7.

87) but this time with = (3) 2 .. Detection of quadrature squeezed light It is, of course, not enoug h to generate squeezed light; one must be able to detect it. Several schemes for detection have been proposed and implemented. The general idea behind all proposed methods is to mix the signal eld, presumed to contain the squeezing, with a strong coherent eld, called the local oscillator .

Here we shall consider only one method, the one known as balanced homodyne detection. A schematic of the method is shown in Fig. 7.

12. Mode a contains the single eld that is possibly squeezed. Mode b contains a strong coherent classical eld which may be taken as a coherent state of amplitude .

The beam splitters are assumed to be 50:50 (hence the term balanced homodyne detection). Let us assume that the relation between the input (a, b) and output (c, d) operators is the same as in Eq. (6.

10):. 1 c = (a + i b) 2 1 none for none d = (b + i a). 2. (7.90).
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