Examples of Squeezed Coherent States
Depending on at which phase the state's quantum noise is reduced, one can distinguish amplitude-squeezed and phase-squeezed states or general quadrature squeezed states. If no coherent excitation exists the state is called a squeezed vacuum. The figures below give a nice visual demonstration of the close connection between squeezed states and Heisenberg's uncertainty relation: Diminishing the quantum noise at a specific quadrature (phase) of the wave has as a direct consequence an enhancement of the noise of the complementary quadrature, that is, the field at the phase shifted by .
From the top:
- Vacuum state
- Squeezed vacuum state
- Phase-squeezed state
- arbitrary squeezed state
- Amplitude-squeezed state
As can be seen at once, in contrast to the coherent state the quantum noise is not independent of the phase of the light wave anymore. A characteristic broadening and narrowing of the noise during one oscillation period can be observed. The wave packet of a squeezed state is defined by the square of the wave function introduced in the last paragraph. They correspond to the probability distribution of the electric field strength of the light wave. The moving wave packets display an oscillatory motion combined with the widening and narrowing of their distribution: the "breathing" of the wave packet. For an amplitude-squeezed state, the most narrow distribution of the wave packet is reached at the field maximum, resulting in an amplitude that is defined more precisely than the one of a coherent state. For a phase-squeezed state, the most narrow distribution is reached at field zero, resulting in an average phase value that is better defined than the one of a coherent state.
In phase space, quantum mechanical uncertainties can be depicted by Wigner distribution Wigner quasi-probability distribution. The intensity of the light wave, its coherent excitation, is given by the displacement of the Wigner distribution from the origin. A change in the phase of the squeezed quadrature results in a rotation of the distribution.
Read more about this topic: Squeezed Coherent State
Famous quotes containing the words examples of, examples, squeezed, coherent and/or states:
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)
““Tonight,
I must go to that lucky man
and in the blinding dark.”
Thinking that,
a respectable woman,
eyes squeezed shut,
practices walking in her house.”
—Hla Stavhana (c. 50 A.D.)
“We have good reason to believe that memories of early childhood do not persist in consciousness because of the absence or fragmentary character of language covering this period. Words serve as fixatives for mental images. . . . Even at the end of the second year of life when word tags exist for a number of objects in the child’s life, these words are discrete and do not yet bind together the parts of an experience or organize them in a way that can produce a coherent memory.”
—Selma H. Fraiberg (20th century)
“... no young colored person in the United States today can truthfully offer as an excuse for lack of ambition or aspiration that members of his race have accomplished so little, he is discouraged from attempting anything himself. For there is scarcely a field of human endeavor which colored people have been allowed to enter in which there is not at least one worthy representative.”
—Mary Church Terrell (1863–1954)