102 Squeezed States in Quantum Optics

QR Code JIS X 0510 Reader In Visual Studio .NETUsing Barcode Control SDK for Visual Studio .NET Control to generate, create, read, scan barcode image in .NET applications.

Encode QR Code 2d Barcode In .NET FrameworkUsing Barcode generation for Visual Studio .NET Control to generate, create QR-Code image in .NET framework applications.

Fig 103 Phase-squeezed light in the plane of phase quadratures The uncertainty ellipse is stretched in the radial direction

QR Code Recognizer In VS .NETUsing Barcode decoder for VS .NET Control to read, scan read, scan image in Visual Studio .NET applications.

not the average photon number) is zero For example, an optical parametric ampli er with a vacuum input can generate a squeezed vacuum with a reduction in the noise of one quadrature components on the order of 10 dB In summary, the main feature of the squeezed states lies in the fact that they offer the opportunity of deforming (squeezing!) in a certain direction the circle of quantum uncertainty that so becomes an uncertainty ellipse Hence, they provide a way of reducing the quantum noise for one of the two quadratures

Paint Barcode In VS .NETUsing Barcode generation for .NET framework Control to generate, create barcode image in VS .NET applications.

1022 Algebraic (su(1, 1)) Content of Squeezed States

Decode Bar Code In .NET FrameworkUsing Barcode decoder for Visual Studio .NET Control to read, scan read, scan image in .NET applications.

We have seen that squeezed states are obtained by forcing two-photon processes with time-dependent classical sources (from this the appellation two-photon coherent

Create QR In C#Using Barcode printer for VS .NET Control to generate, create QR Code ISO/IEC18004 image in VS .NET applications.

Fig 102 Amplitude-squeezed light in the plane of phase quadratures The uncertainty ellipse is stretched in the angular direction

Drawing Quick Response Code In Visual Studio .NETUsing Barcode drawer for ASP.NET Control to generate, create QR Code 2d barcode image in ASP.NET applications.

QR Code Drawer In VB.NETUsing Barcode printer for .NET framework Control to generate, create QR Code JIS X 0510 image in .NET framework applications.

10 Squeezed States and Their SU (1, 1) Content

Paint Code 128 Code Set C In Visual Studio .NETUsing Barcode drawer for VS .NET Control to generate, create Code 128B image in .NET framework applications.

states) The most general form of the corresponding Hamiltonian reads H = a a + 1 2 + f 2 (t) a + f 2 (t) a 2 + f 1 (t) a + f 1 (t) a

Make GS1 - 12 In Visual Studio .NETUsing Barcode generation for VS .NET Control to generate, create UPC Code image in Visual Studio .NET applications.

(1020)

Code 3/9 Generation In Visual Studio .NETUsing Barcode encoder for VS .NET Control to generate, create USS Code 39 image in Visual Studio .NET applications.

The production of coherent states or of squeezed states will depend on the respective importance granted to the factors f 1 (t) and f 2 (t) Now, the Hamiltonian in (1020) has clearly the form of an element in the two-photon Lie algebra, denot2 ed by h6 , generated by the set of operators {a, a , I d , N = a a, a 2 , a }, and already mentioned in Section 224 From the (nontrivial) commutation rules, [a, a ] = I d , [a 2 , a ] = 2a , [a, N ] = a ,

Create ISSN - 13 In .NET FrameworkUsing Barcode generation for .NET framework Control to generate, create ISSN - 13 image in .NET framework applications.

[a , N ] = a , [a , N ] = 2a ,

ECC200 Encoder In .NETUsing Barcode drawer for ASP.NET Control to generate, create Data Matrix image in ASP.NET applications.

[a , a] = 2a , [a 2 , N ] = 2a 2 ,

Draw Code 128 In Visual C#Using Barcode printer for .NET framework Control to generate, create Code 128B image in Visual Studio .NET applications.

(1021)

Generate Barcode In Visual C#Using Barcode printer for Visual Studio .NET Control to generate, create barcode image in .NET applications.

we see that h6 is a representation of the semidirect sum of su(1, 1) with the Weyl Heisenberg algebra The corresponding group, denoted by H 6 , is the semidirect product H 6 = W SU (1, 1) The existence of such an algebraic tool in the construction of squeezed states is very useful in solving problems involving Hamiltonians such as (1020) Suppose we have to deal with an evolution equation of the type i U (t, t 0 ) = H(t) U (t, t 0 ) , t U (t 0 , t 0 ) = I d , (1022)

Bar Code Generation In .NETUsing Barcode maker for ASP.NET Control to generate, create bar code image in ASP.NET applications.

where the mathematical objects have a h6 nature: the time-dependent Hamiltonian H is an element of the Lie algebra h6 , whereas the evolution operator U (t, t 0 ), as a solution to (1022), should be an element of a unitary representation of the Lie group H6 The trick is of disentangling nature [9], like in (874) It amounts to solving the equation by choosing among linear faithful representations of H6 or h6 the simplest one, namely, the four-dimensional one in which group and algebra elements are realized as 4 ~ 4 matrices Let us associate with a generic element X in h6 , written as X = N+

Barcode Maker In JavaUsing Barcode creation for Java Control to generate, create barcode image in Java applications.

+ I d + Ra + La 2 + ra + la ,

Creating USS Code 39 In VS .NETUsing Barcode generator for ASP.NET Control to generate, create Code 3/9 image in ASP.NET applications.

, , R, L, r, l C ,

Paint EAN-13 In VS .NETUsing Barcode printer for ASP.NET Control to generate, create EAN / UCC - 13 image in ASP.NET applications.

(1023)

GTIN - 12 Scanner In .NETUsing Barcode decoder for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications.

the following matrix in M(4, C): 0 r M(X ) = l 2

0 2L l

0 2R r

0 0 0 0

(1024)

This representation of X is made possible because of the Lie algebra isomorphism between basic operators de ning h6 and elementary projectors E i j with matrix elements E i j kl = ik j l generating the Lie algebra M(4, C): N+

1 E 22 E 33 , 2

I d 2E 41 , (1025)

a 2E 23 , a 2 2E 32 ,