Quantum State Measurement

Abstract

In twentieth century the quantum theory of physics has been a fascinating playground to study the nature of electromagnetic radiations and matter. In this subject, the forces on atom by light have received much theoretical and experimental attention during past many years, not only because of interest in the basic atom field interaction, but also for the measurement of an unknown state of eieciwiliaglictiC field which poses an interesting question in it. The measurement' of the cavity field had gained a very high attention because of the possibility of the quantum computers, quantum teleportation, quantum cryptography, dense coding and many more. A project of Pakistan Science Foundation entitled "Quantum State Measurement" is taken to keep our research in this area. There are many schemes presented for the quantum state measurement. One of the most widely used ways is the reconstruction of Wigner function. We worked in this area and presented new schemes for the reconstruction of Wigner function of the field from the recovered-photon statistics of the field. Photon statistics can be recovered in no of ways. In this report we present five different new schemes for the measurement of photon statistics of the field. These are based on Deflection of atomic beam from the cavity field in Raman-Nath regime, Electromagnatically induced transparency, Resonance florescence, Ramsey interferometry, Autler-Towns time dependent spectroscopy, and Deflection of atomic beam in Bragg's regime. In the atomic beam deflection in Raman-Nath regime the momentum distribution 'Am of the atoms after their interaction during the passage through the quantized cavity field is used for its reconstruction. We displace the photon statistics of the cavity field and reconstruct the Wigner function of the Schrodinger-cat state. In the Electromagnatically induced transparency we use a three level atom, the upper two levels were driven by the quantized field. The absorption spectrum of the probe beam gives the information about the photon statistics while in Resonance Florescence, instead of three level atoms we use two level atoms driven by the field. If the driving field is.position dependent then we find the position of the atoms passing through the cavity in Sub wavelength domain. In Ramsey interferometry we proposed to measure the joint photon statistics in two cavities containing entangled field. The cavities are placed in between the two Ramsey fields and two level atoms pass through these cavities and two Ramsey zone. In this setup the atoms goes under a dispersive phase shift while their passage through the off resonant entangled cavities. By measuring the internal states of the atoms we can reconstruct the photon statistics and then the Wigner function. The Autler-Towns spectroscopy is the reverse of EIT where the upper two levels of a three level atoms are driven by the field. Instead of measuring absorption spectrum we measure the spontaneous emission spectrum. In another scheme of atomic beam deflection in Bragg regime we measure the momentum distribution of atoms after passing through the two cavities containing entangled field. The momentum states contain the information about . the joint photon statistics. Apart from these schemes we also proposed another schemes for the reconstruction of Wigner function using tomography by phase sensitive amplification of the field. Three level atoms of two photon processes are passed through the cavity amplifying the field to be measured. The two cases are discussed here. One in which thephase of the atoms are controlled outside the cavity and the other in which the phase is controlled inside the cavity. The complete quadrature distribution is obtained by measuring the quadrature for the different phases. The inverse Radon transformation is then employed to reconstruct the original quantum state. Most of these schemes are based on the atom field interaction and the role of phase and intensity of the field. In one of our study we consider spontaneous emission in a four-level atomic system driven by three fields. It is shown that, by controlling the phase and the amplitude of the driving fields, a wide variety of spectral behavior can be obtained ranging from a very narrow single spectral line to six spectral lines of varying widths. We also present an exciting application of new emerging field of Quantum Informatics i.e., Quantum Teleportation. We consider the teleportation of entangled twoparticle and multiparticle states and present a scheme for the teleportation that may be suitable for both entangled atomic states or field states inside high Q cavities.