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Even and odd coherent states and tomographic representation of quantum mechanics and quantum optics VI. Man'ko
| Content Provider | Scilit |
|---|---|
| Author | Dodonov, V. V. Man'ko, V. I. |
| Copyright Year | 2003 |
| Description | Book Name: Theory of Nonclassical States of Light |
| Abstract | Even/odd coherent states can be generated from a vacuum in the following way \a±)=D(a±)\0), (9) where even/odd displacement operators read [1,7] D(a+) = cosh( ) , ( 1 3 ) |a_> - 7 V _ e - l a l 2 / 2 ^ 1 ^ 1 z l ^ Q n | n ) . ( 1 4 ) The even coherent state can only be expressed in terms of even number states and the odd coherent state can only be expressed in terms of odd number states. Consequently, the probability of finding an odd number of photons in the even coherent states equals zero, as does the probability of finding an even number of photons in the odd coherent states. Thus the probability distribution functions for these states strongly oscillate: \a\4k for n=2k P(+)(n) = \ coshH 2 (2 fc ) ! 0 for n=2k+l 0 for n=2k P ( _)(n) = ( | a | W L sinh|a:| 2(2£; + l ) ! for n=2k+l Expectation values of the first-order moments for the annihilation and creation operators in the even and odd coherent states are equal to zero ( a ± | a | a ± ) = 0 , (15) MULTIMODE EVEN AND ODD COHERENT STATES 223 due to Eqs. (11), (12), and the orthogonality property ( a ± | a T ) = 0. The expectation values of the second-order moments are (a±\a2\a±) = a2, (a+\a*a\a+) = \a\2 tanh | a | 2 , (a_|a + a|a_) = \a\2 coth | a | 2 . (16) Defining the quadratures of the electromagnetic field mode as Xx = (a + a f ) /2 , X2 = (a-a f ) /(2i), one obtains the following expressions for their variances in the even coherent state: 4 A X 2 = 2\a\2 tanh \a\2 + 2 |a | 2 cos 20 + 1, (17) 4 A X 2 = 2 |a | 2 tanh \a\2 - 2\a\2 cos 261 + 1. (18) We have introduced the modulus and phase of the complex coherent state amplitude as a=|a|e^. Eqs. (17) and (18) show that for 9=TT/2 the first quadrature has some amount of squeezing for small values of |a | , while for 0=0 the second quadrature is squeezed. There is a possibility of squeezing alternatively in both the quadratures depending upon the phase of the complex amplitude a. For odd coherent states we get the same expressions as in (17) and (18), but tanh \ a\2 should be replaced by coth \ a\2. Also, odd coherent states do not exhibit the property of second-order squeezing. |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2010-0-34620-0&isbn=9780429153051&doi=10.1201/9781482288223-9&format=pdf |
| Ending Page | 252 |
| Page Count | 22 |
| Starting Page | 231 |
| DOI | 10.1201/9781482288223-9 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2003-03-13 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Theory of Nonclassical States of Light Particles and Fields Physics Photons Amplitude Quantum Coherent States Squeezing Odd Coherent Even/odd |
| Content Type | Text |
| Resource Type | Chapter |
