Hindawi Publishing Corporation ISRN Optics Volume 2013, Article ID 271951, 9 pages http://dx.doi.org/10.1155/2013/271951 Research Article A Method for the Measurement of Photons Number and Squeezing Parameter in a Quantum Cavity Ghasem Naeimi, Siamak Khademi, and Ozra Heibati Department of Physics, University of Zanjan, P.O. Box 45196-313, Zanjan, Iran Correspondence should be addressed to Siamak Khademi; khademi@znu.ac.ir Received 20 September 2013; Accepted 7 November 2013 Academic Editors: Y. S. Kivshar, X. Shu, and Y. Tsuji Copyright © 2013 Ghasem Naeimi et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Measurement of photons number in a quantum cavity is very difcult and the photons number is changed afer each measurement. Recently, many eforts have been done for the nondemolition measurement methods. Haroche et al. succeed in recognizing existence or nonexistence of one photon in a quantum cavity. In this paper, we employ their experimental setup for a quantum nondemolition measurement and pump a coherent state in their quantum cavity. In this case, we could detect more photons in the quantum cavity by a measurement of a displaced Wigner function. It is also shown that the measurement of more than one photon is possible by the Haroche method by measuring just one point of displaced Wigner function. Furthermore, if the cavity feld is flled by a superposition of two number states, the average number of photons within the cavity would be measurable. We show that their setup is also suitable to apply for the measurement of the squeezing parameter for the squeezed state of photons number in the quantum cavity successfully. 1. Introduction Te formulation of quantum mechanics in phase space was proposed by Wigner [1]. Tis formulation is very useful in various felds of physics including quantum mechanics [2, 3], quantum optics [4–6], and condensate matter [7, 8]. Te physical concepts are extractable from Wigner function. Wigner function may take negative value for a quantum state. Te existence of negative or interference of Wigner function is a nonclassicality indicator for quantum systems [9–11]. On the other hand, Wigner function is a measurable quantity. Many authors introduced methods to measure Wigner func- tion for trapped ions [12], photonic number states in quantum cavity [13–15], Schrodinger cat state, and coherent state [16]. Bertet et al. measure a complete Wigner function for the vacuum and a single photon state [17]. Lutterbach and David- ovich presented a method to measure the Wigner distribution function of photonic state in a quantum cavity feld [18, 19]. Tey used an experimental ingenious setup which was made by one high Q-factor and two low Q-factor cavities. Nogues et al. (members of Haroche group) measured the Wigner distribution functions of electromagnetic felds in a cavity with the number states =0 and =1 at origin of phase space [20]. Te Wigner distribution function at the origin of phase space is positive for =0 and negative for =1. Terefore, the sign of measured Wigner distribution function, itself, gives us the number of photons in the cavity and its value is not important [20]. So, if there are more than one photon, it would not be possible to recognize the number of photons. In this paper we used the Haroche method to measure the larger number of photons by measuring just one point of the displaced Wigner distribution function in a quantum cavity. We use an experimental setup for the meas- urement of displaced Wigner function proposed by Del´ eglise et al. [16] (Haroche group). It is shown that their experimental setup is useful for the measurement of number of photons, even for >1. Tis method is also suitable to measure the average number of superpositions of two number states. Te development of method to an arbitrary superposition of states needs more measurement for many more points of Wigner function which is not discussed in this paper. Fur- thermore this method is also applied to measure the squeez- ing parameter for squeezed number state of photons. In the next section, the Wigner distribution function is calculated for four values of  and their plot in phase space is illustrated. It would be shown that Wigner functions at