By P. L. Knight, L. Allen

ISBN-10: 0080291503

ISBN-13: 9780080291505

ISBN-10: 0080291600

ISBN-13: 9780080291604

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**Extra info for Concepts of Quantum Optics**

**Sample text**

D ^ . A / n T 7 = V* . 21) is still valid for the combined atom-plus-field system. The system is initially prepared in the state |i> and the interaction V turned on at t = 0. The probability amplitude for finding the atom in the excited state |b> irrespective of whether it reaches it from |a> by emission or absorption is CI) if* « { 1 }( t ) . - i | d f V f ie •to 1 it' i ft ^ 2 ^ ' -Mdt'V e . 56) where the first term is due to emission, the second to absorption. 56). Then the factor n^ can Absorption and Emission of Radiation 38 be combined with the factors outside the curly brackets.

27) 58 Coherent States Compared with other common eigenstates the coherent states behave improperly. For example, they are not orthogonal, and the scalar product is 2 2 = exp(aVi(|cx| + | 3 | ) ) . 28) 2 If (a-3) is2 large, then the states are "almost" orthogonal because || = exp-(|a-S| ). 16) and its conjugate. 30) as a|0> = 0. This simple and obvious formula will prove to be extraordinarily useful when we come to discuss the semi-classical limit in Chapter 6. In fact the coherent state expectation of any function of the operators a + and a can be written in terms of vacuum expectations if the operators are normally ordered + = <0(F(a+a, a + a*) |0> .

81) arises from the non+ commutability of a and a (or p and q). 82) and so, as noticed first by Born, Heisenberg and Jordan (1926), the zero-point energy and the particle fluctuation term in <(An)2> are closely related. 83) where the mode function F^(r) satisfies the wave-equation subject to the usual boundary conditions used in the classical theory. Interference effects are determined by the spatial mode functions F^(r) and are precisely those of classical theory. The size of the interference effects however depends on the expectation value of combinations of field mode annihilation and creation operators.

### Concepts of Quantum Optics by P. L. Knight, L. Allen

by Charles

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