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arXiv:2102.08350 · Physical Review A

Statistical parameter estimation of multimode multiphoton-subtracted thermal states of light

G. V. Avosopiants, B. I. Bantysh, Konstantin G. Katamadze, Nadezhda A. Bogdanova, Yu. I. Bogdanov, S. P. Kulik

Published Jul 12, 2021• 7 citations
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Abstract

Thermal states of light are widely used in quantum optics for testing of various quantum phenomena. Particularly, they can be utilized for characterization of photon creation and photon annihilation operations. During the last decade the problem of photon subtraction from multimode quantum states has become of much significance. Therefore in this paper we present a technique for statistical parameter estimation of multimode multiphoton-subtracted thermal states of light, which can be used for the multimode photon annihilation test.

DOI
10.1103/physreva.104.013710

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Thermal states of light are widely used in quantum optics for testing of various quantum phenomena. Particularly, they can be utilized for characterization of photon creation and photon annihilation operations. During the last decade the problem of photon subtraction from multimode quantum states has become of much significance. Therefore in this paper we present a technique for statistical parameter estimation of multimode multiphoton-subtracted thermal states of light, which can be used for the multimode photon annihilation test.
Photon creation and annihilation are two basic operators in quantum optics. Their experimental implementation provides a perfect toolbox for quantum state engineering. The simplest quantum states, which can be modified both by photon creation and annihilation are thermal states of light. Therefore, the multiphoton subtracted thermal states (MPSTS) draw attention of quantum optics experimentalists last decade. Despite its simplicity they serve as a good testing area for study of a number of quantum phenomena. In the current work we give a review of the recent works related to MPSTS: their theoretical description, preparation and measurement technique and their utilization as a testing area for studying some quantum phenomena like non-Gaussianity, Photonic Maxwell‟s Demon, Quantum Vampire and so on.
Thermal states of light are widely used in quantum optics due to their correlation properties. As is well known, their correlation properties and the photon-number distribution as a whole are strongly dependent on the mode number selected by the detection scheme. The same changes can be caused by photon subtraction. Therefore, we describe the general case of the multimode thermal state after a multiphoton subtraction, when the photon-number statistics is registered by the detector selecting a part of the initial modes. We present an analytical form of the obtained photon-number distribution and its general properties and check them in the experiment.
This work is devoted to the theoretical and experimental study of quantum states of light conditionally prepared by subtraction of a random number of photons from the initial multimode thermal state. A fixed number of photons is subtracted from a multimode quantum state, but only a subsystem of a lower number of modes is registered, in which the number of subtracted photons turns out to be a non-fixed random variable. It is shown that the investigation of multiphoton subtracted multimode thermal states provides a direct study of the fundamental quantum-statistical properties of bosons using a simple experimental implementation. The developed experimental setup plays a role of a specific boson lototron, which is based on the fundamental link between the statistics of boson systems and the Polya distribution. It is shown that the calculation of the photon number distribution based on the Polya‟s urn scheme is equivalent to a calculation using statistical weights for boson systems. A mathematical model based on the composition of the Polya distribution and thermal state is developed and verified. The experimental results are in a good agreement with the developed theory.
The estimation of high order correlation function values is an important problem in the field of quantum computation. We show that the problem can be reduced to preparation and measurement of optical quantum states resulting after annihilation of a set number of quanta from the original beam. We apply this approach to explore various photon bunching regimes in optical states with gamma-compounded Poisson photon number statistics. We prepare and perform measurement of the thermal quantum state as well as states produced by subtracting one to ten photons from it. Maximum likelihood estimation is employed for parameter estimation. The goal of this research is the development of highly accurate procedures for generation and quality control of optical quantum states.
Photon number resolving detectors can be highly useful for studying the statistics of multiphoton quantum states of light. In this work we study the counts statistics of different states of light measured on multiplexed on–off detectors. We put special emphasis on artificial nonclassical features of the statistics obtained. We show new ways to derive analytical formulas for counts statistics and their moments. Using our approach we are the first, to the best of our knowledge, to derive statistics moments for multimode thermal states measured on multiplexed on–off detectors. We use them to determine empirical Mandel parameters and recently proposed sub-binomial parameters suitable for tests of nonclassicality of the measured states. Additionally, we investigate sub-Poissonian and superbunching properties of the two-mode squeezed state measured on a pair of multiplexed detectors, and we present results of the Fano factor and second-order correlation function for these states.