%0 Journal Article
%T A Method for the Measurement of Photons Number and Squeezing Parameter in a Quantum Cavity
%A Ghasem Naeimi
%A Siamak Khademi
%A Ozra Heibati
%J ISRN Optics
%D 2013
%R 10.1155/2013/271951
%X Measurement of photons number in a quantum cavity is very difficult and the photons number is changed after each measurement. Recently, many efforts 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 field is filled 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 The formulation of quantum mechanics in phase space was proposed by Wigner [1]. This formulation is very useful in various fields of physics including quantum mechanics [2, 3], quantum optics [4¨C6], and condensate matter [7, 8]. The physical concepts are extractable from Wigner function. Wigner function may take negative value for a quantum state. The existence of negative or interference of Wigner function is a nonclassicality indicator for quantum systems [9¨C11]. On the other hand, Wigner function is a measurable quantity. Many authors introduced methods to measure Wigner function for trapped ions [12], photonic number states in quantum cavity [13¨C15], 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 Davidovich presented a method to measure the Wigner distribution function of photonic state in a quantum cavity field [18, 19]. They 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 fields in a cavity with the number states and at origin of phase space [20]. The Wigner distribution function at the origin of phase space is positive for and negative for . Therefore, 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
%U http://www.hindawi.com/journals/isrn.optics/2013/271951/