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Chinese Journal of Quantum Electronics

Excited circular states and their propertities

Zhongjie Wang

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

The excited circular states are introduced by repeated application of photon creation operator on the circular states.The sub-Poissonian distribution and squeezing effect are discussed.The results indicate that photon creation operator can enhance sub-Poissonian distribution but supress squeezing effects.The Wigner function is studied,which obviously displays its nonclassical feature.The results obtained using the numerical method indicate that the interference effects change alterantly when the exited number m takes odd and even number respectively.

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The excited circular states are introduced by repeated application of photon creation operator on the circular states.The sub-Poissonian distribution and squeezing effect are discussed.The results indicate that photon creation operator can enhance sub-Poissonian distribution but supress squeezing effects.The Wigner function is studied,which obviously displays its nonclassical feature.The results obtained using the numerical method indicate that the interference effects change alterantly when the exited number m takes odd and even number respectively.
Two new classes of nonclassical states are defined by exciting Hillery's even and odd coherent states. Their physical properties are investigated numerically. It is found that they do not exhibit the squeezing effect but exhibit remarkable characteristics of sub-Poissonian distribution and antibunching. In sharp contrast to the case of excited Glauber coherent states, it is observed that the uncertainty of the field quadrature in excited even and odd coherent states increases with the degree of excitation. It is also seen that the Wigner functions associated with them take negative values for wider regions of parameters compared to those of Hillery's even and odd coherent states.
We investigate theoretically the nonclassical properties, such as cross correlation function and sub- Poisson distribution effect, for the nonlocal coherent photon-added two-mode circular state. The results show the superposition number and excitation number have significant effect on these properties. When the superposition number , the value of cross correlation function decreases monotonously with the increasing of the average photon number of single-mode and the nonlocal coherent photon-added two-mode circular state has the cross correlation effect. Increasing the superposition number , the cross correlation effect will be reduced. When the superposition number , sub-Poissonian distribution effect of the nonlocal coherent two-mode photon-added circular state can be observed only when single-mode average photon number is greater than a certain threshold value.
Multi-photon-added cat states are constructed by repeatedly applying the creation operator to a cat state. We study in detail their photon-number distribution, QQQ parameter, squeezing properties, and Wigner function. We show that photon addition induces a πππ phase shift in the original parity configuration whenever an odd number of photons is added, reflected as swapped vanishing probabilities and phase space displacements at the origin. Remarkably, the same process drives these states into a sub-Poissonian regime regardless of the relative phase between their coherent state components, making them valuable resources for quantum imaging, at the cost of losing quadrature squeezing, but gaining amplitude-squared one. We also discuss how these states can be generated using existing hardware.
Laguerre polynomial’s photon-added squeezing vacuum state is constructed by operation of Laguerre polynomial’s photon-added operator on squeezing vacuum state. By making use of the technique of integration within an ordered product of operators, we derive the normalization coefficient and the calculation expression of 〈ala †〉. Its statistical properties, such as squeezing, the anti-bunching effect, the sub-Poissonian distribution property, the negativity of Wigner function, etc., are investigated. The influences of the squeezing parameter on quantum properties are discussed. Numerical results show that, firstly, the squeezing effect of the 1-order Laguerre polynomial’s photon-added operator exciting squeezing vacuum state is strengthened, but its anti-bunching effect and sub-Poissonian statistical property are weakened with increasing squeezing parameter; secondly, its squeezing effect is similar to that of squeezing vacuum state, but its anti-bunching effect and sub-Poissonian distribution property are stronger than that of squeezing vacuum state. These results show that the operation of Laguerre polynomial’s photon-added operator on squeezing vacuum state can enhance its non-classical properties.
We introduce the states D(z)a\+\{+\+m\}S(r)|0〉 and examine their properties . Such states are checked to be complete vectors via the IWOP (Integration W ithin an Ordered Product of operators) technique. We find larger－scale macrosco pic oscillations of photon distribution after the squeezed vacuum states being e xcited and displaced. On contrary to the bunching photons of the squeezed vacuum states as the displacing parameter |z| and the excitation number m are both small photons coherence can exhibit antibunching effect. The quasi－proba bility distribution functions (Husimi Q( 醆+*) function and Wigner W(q p) function) are derived and their dependences on the three parameters (z m r) are discussed. The Wigner function obviously displays their nonclassical fe ature.