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arXiv:1510.03155

CQED quantum tomography of a microwave range

George P. Miroshnichenko

Published Oct 12, 2015• 3 citations
arXivHTMLPDF

Abstract

The protocol of measurement the probability density of a rotated quadrature of microwave mode in an arbitrary quantum state is presented and numerically investigated. The protocol is adapted to the measuring procedure used in the CQED experiments. The method is based on measurement of integrated probability of detection of atoms - probes in the top working state from atoms flying via the cavity. Connection of random variables and is found, when is a qudrature phase. Connection of the tomogram and the tomogram is found. The protocol prescribes the rule of choice of problem parameters, such as interaction time, and the number of atoms in series . The method contains a single fitting parameter that is selected in the process of numerical simulation of the quadrature distribution in a coherent state. Quality selection is determined by the Kolmogorov test. The result of the calculation protocol is a convolution with the instrumental function of the method. The parameters of the instrumental function are shown. Numerical simulations performed for typical numerical values of parameters of the experimental setup, shows the effectiveness of the proposed method.

DOI
10.48550/arxiv.1510.03155

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A new type of tomogram, squeeze tomograms, of quantum states of light, is introduced, which is based on measuring photon statistics after the action of a squeeze operator on the states' density matrix. The introduced tomograms are photon number probability functions depending on two real parameters which are a scaling factor and a rotation angle. The rotation angle and scaling factor label the reference frame in the phase space of field quadratures in which the photon statistics is measured. The expressions of the squeeze tomogram in terms of the Wigner function and density matrix in quadrature representation are obtained. The examples of squeezed states, even and odd coherent states and thermal states are considered in detail. The multimode generalization is discussed.
Experiments have been performed to determine the Wigner distribution and the density matrix (and for pure states the wave function) of a light mode, by using tomographic inversion of a set of measured probability distributions for quadrature amplitudes.From these measurements the quantum distributions of optical phase and photon number have been obtained.The measurements of quadrature-amplitude distributions for a temporal mode of the electromagnetic field are carried out using balanced homodyne detection.We refer to this new method as optical homodyne tomography.Given the measured density matrix, one can experimentally infer any of the various quantum distributions of optical phase, in particular the Pegg-Barnett (or, equivalently, Shapiro-Shepard) phase distribution, the marginal Wigner distribution, and the Vogel-Schleich operational phase distribntion.We have used this approach to make measurements of the number-plase uncertainty relation for coherent-state fields.The coherent states do not attain the minimum value for the number-phase uncertainty product, as set by the expectation value of the commutator of the number and phase operators; this is true theoretically and experimentally.
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