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EPJ Web of Conferences

Quantum Tomography of Microwave Region

George P. Miroshnichenko

Published Jan 1, 2015• 2 citations
Publisher

Abstract

An alternative method of reconstruction of the density matrix of microwave range created in the maser cavity is proposed. Here a technique for measuring the probability density of the quadrature field for different phases is presented. The measured quantity is the probability of difference between the numbers of atoms emitted in the excited and ground states in a sample of N atoms passing sequentially through the cavity. Numerical simulations performed for the numerical values of the typical parameters setting show the effectiveness of the proposed method.

DOI
10.1051/epjconf/201510302006

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An alternative method of reconstruction of the density matrix of microwave range created in the maser cavity is proposed. Here a technique for measuring the probability density of the quadrature field for different phases is presented. The measured quantity is the probability of difference between the numbers of atoms emitted in the excited and ground states in a sample of N atoms passing sequentially through the cavity. Numerical simulations performed for the numerical values of the typical parameters setting show the effectiveness of the proposed method.
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.
We perform state tomography of an itinerant squeezed state of the microwave field prepared by a Josephson parametric amplifier (JPA). We use a second JPA as a preamplifier to improve the quantum efficiency of the field quadrature measurement from 2% to 36%±4%. Without correcting for the detection inefficiency we observe a minimum quadrature variance which is 68(-7)(+9)% of the variance of the vacuum. We reconstruct the state's density matrix by a maximum likelihood method and infer that the squeezed state has a minimum variance less than 40% of the vacuum, with uncertainty mostly caused by calibration systematics.
We propose an alternative method for detecting the density matrix of a radiation field via optical homodyne tomography. The method needs no assumption on the state, and the density matrix is recovered directly from averages on data. The tomographic reconstruction is very fast and provides very reliable statistics on line with detection. As a test of the method we present numericla results for a set of computer-simulated experiments, corresponding to different quantum states of the radiation source. Then a tomographic reconstruction is given for experimental data provided by Smithey etal. [Phys. Rev. Lett. 70, 1244 (1993)].