Research of the conditions under which the Bose-Einstein condensate (BEC) , new aggregate state of matter is obtained led to the new interesting results in the physics of condensed mediums. This new (fifth) state of substance opens the door to obtaining of mediums in new aggregate states, prospective technologies and design of new equipment with new technical and functional characteristics and experimental capabilities. Requirements to the meeting of these conditions for carrying out of the experimental study of BEC are peculiar: low concentration of atoms in the subjects under study, ultralow temperatures, maintaining of high vacuum in magneto-optical cell where the study of medium is performed; these requirements make experiments complicated and set up the considerable financial expenditures for their performance. The results of BEC observations which have been obtained over the last ten years showed that accumulated experience of such research carrying out is not sufficient as of yet. However, we can forecast high potential of theoretical and practical importance of BEC research for the solution of different scientific-technical and theoretical tasks.
Analysis of the physical basis of this phenomenon and experimental experience accumulated over the time will make it possible to substantiate and find more acceptable conditions for the experimental study of BEC. The messages have occurred where the results of obtaining of BEC with the involvement of chemical substances are given . Search of new mediums in order to obtain BEC state makes progress quite fast: if in the initial experiments the amount of used atomic mediums was only few elements, perhaps their amount will increase soon. Occurrence of the paper on study of BEC with the involvement of photon condensate  became interesting and unexpected, although theorists rejected these conditions for a variety of physical reasons. Nevertheless, researchers-experimenters from the University of Bonn showed that it is not quite so. Their experiments with photon condenser carried out in 2010 were published in NATURE magazine . Authors published the results of experimental study of BEC obtained with the involvement of laser photons and solution of R6G organic dye as the cooling agent. They showed that there is no substantial difference between mediums containing atoms and mediums containing photons for the implementation of BEC states. The fundamental difference lies only in the fact that the temperature at which BEC state is achieved with the use of photons does not require the generation of ultralow temperatures and application of magneto-optical traps. It turned out that BEC state can be achieved and observed at the room temperature under laboratory conditions!!! In the whole world (as well as in Russia particularly) the research connected with the condensation of radiation spectrum of tunable broad-band lasers has been carried out for several decades already [3, 5-14]. These lasers are used when analyzing gases and plasma mediums by the method of intracavity laser spectroscopy (ILS). Gases and poorly-ionized medium with the involvement of dope additives of metal atoms (sodium, cesium etc.) were used as the subjects under study. Therefore, plasma subjects (heterogeneous plasma where the metal atoms were transferred into the poorly-excited state) were submitted to the experimental research. These subjects were usually located in the resonator of IL-spectrum analyzer. Construction of the experimental facility has a number of peculiarities: resonator mirrors are made on the basis of peculiar geometry and laser active mediums have broad homogeneously-broadened luminescence band. Such construction excludes the potential occurrence of spurious interference on external edges of optical elements located in the optical path of laser resonator. Simultaneously with the publication of papers on the study of matter in BEC state, the papers similar in content started to occur; authors of these papers took into account the influence of such state (quasi-state) of medium  on the occurrence of coherent radiation. It opened up possibilities to use the new phenomena in the solution of some applied tasks. So, the paper  was devoted to the obtaining of coherent surface radiation and laser generation on carbon nanomaterials with the involvement of heterogeneous plasma where the procedure of thermal synthesis of metal-carbon nanotubes (MCNTs) was performed. Conditions of obtaining of the process of induced coherent radiation were achieved in a number of published papers [3, 6, 7]. Implementation of new applied and functional capabilities of laser equipment using the high-resolution probe microscopes and IL-spectrum analyzers expanded the opportunities to obtain and observe new mediums [3, 7]. The results of study of micro- and macrostructure of new laser mediums created under the conditions which differ from the traditional ones are given in these papers. The study of photon BEC has many aspects in common with the issues of study of gases and heterogeneous plasma under the conditions of IL-spectroscopy. Metal-carbon nanomaterials which are prospective for a number of practical applications are thermally synthesized in such plasma. Let us try to examine the peculiarities of these experiments and compare them with the conditions of implementation of the photon BEC . Data published in the papers [3, 5-14] are adequate to the data obtained in the experiments which were carried out in the University of Bonn in many aspects . Let us qualitatively compare the conditions of carrying out of the experiments on obtaining of photon BEC under laboratory conditions at the room temperature  with the conditions of carrying out of the experiments with heterogeneous plasma in resonator of IL-spectrum analyzer [3, 5-14]. Let us also compare optical elements of the constructions of experimental facilities on which these experiments were carried out. We used the facility flow diagram of which is shown in Fig. 1 for the observation of photon BEC. Interaction of the broad-band laser luminous flux of radiation from MCNT thermally synthesized in the carbon heterogeneous plasma [3, 5-14] is illustrated in Fig. 2. Research carried out on the used facility made it possible to record interesting data which is analogous to the results given in the paper . The difference between these experiments lies only in the fact that in [5-14] we used the crystal of gadolinium-scandium-gallium garnet with chrome ions (or other laser mediums) which performs the generation of broad-band radiation and authors of the paper  used the dye solution. Configuration of the mirrors (R≈0.5 m) in resonators is close to the confocal geometry with the locating distance of about 0.5 m between them. Two diaphragms with the diameter ≤ 1–2 mm were located between the mirrors on each side of the laser crystal. They were used in order to mark out one or several axial modes of laser radiation. Besides the fact that the diaphragms were installed inside of IL-spectrum analyzer, also the process of thermal synthesis of carbon nanotubes (CNTs) in heterogeneous plasma was performed inside of it. And as the subsequent measurements showed, the linear dimensions of the synthesized CNTs turned out to be commensurable with the wavelength of laser light falling on them. Then, in the course of the experiment the localization and concentration of the falling photon flux take place in the volume of synthesized CNTs. Let us compare this condition with the similar condition emphasized by authors of the paper  as one of the main conditions of the experiment carrying out (reaching of photon BEC at the room temperature). Spectral reflectivity of the resonator spherical mirrors in the experiments [5-14] in the generation bands Δλ≈0.6-1.3 µm was about 99.9%. When the necessity to broaden or shift this band occurred other resonator mirrors with high spectral reflectivity of radiation set by the used tunable lasers were used. Back edges of the facility mirrors had angles of bevel within the range 5-15° to the optical axis of resonator. Such construction excludes the potential occurrence of radiation spurious interference on the optical element edges. It is the standard condition for the performance of IL-spectroscopy used in order to obtain the "smooth" radiation spectrum and achievement of high spectral resolution upon the detection of absorption (or emission) spectrums of gas or plasma subjects. Laser quantron together with optical elements and xenon pump lamp was cooled down to the room temperature. Although, in case of use of alexandrite crystal doped by chrome ions as the laser medium we had to heat it up to the temperatures of about 100 °C and higher. Heating up of alexandrite crystal increased the efficiency of crystal laser generation and influenced on the broadening of generation spectral band. Then for the cooling of elements the thermostat with flow-through movement of cooling agent and accurate adjustment of temperature conditions was used in the facility. Researchers of the University of Bonn used the resonator with spherical mirrors (R≈1 m) and spectral reflectivity close to 100% (as well as in the papers [5-14]) located at the distance L≈1.5 µm from each other in the experimental facility. It made it possible for them to mark out several (about 7) longitudinal radiation modes and perform the local concentration of photons in the resonator assigned volume. Rhodamine 6G organic dye solution was poured out between the mirrors, its molecules were excited by the radiation of argon laser (Р ≤ 2.0 W). Heat energy which was released upon the spectral conversion and transformation of radiation from the green region to the yellow spectrum interval was decreased and cooled down to the room temperature upon the pumping of dye solution using the hydraulic pump. In other words, it was the standard scheme of pumping laser radiation transformation upon the obtaining of tunable radiation spectrum on organic dyes dissolved in ethylene glycol or other liquid matrix. The detecting system which makes it possible to register the change of dynamic characteristics of radiation pulses and their spectrums after passing the high-resolution polychromator (resolution R≈106 and dispersion D≈0.01-1 nm/mm) was used in the experiments [3, 5-14]. Indication system of luminous fluxes had PC output and spectrophotometer. Upon the interaction of the flux of broad-band tunable radiation with heterogeneous plasma the process of thermal synthesis of metal-carbon nanomaterials (metal-carbon nanotubes – MCNT) took place. Their occurrence in the resonator of IL-spectrum analyzer resulted in various optical phenomena (the dynamics of detected pulse changed, the occurrence of coherent generation on carbon nanotubes was observed , the occurrence of coherent laser Dicke superradiance was detected , the transformation of laser radiation with the occurrence of photon BEC conditions was observed (as we believe), the non-linear character of observed optical phenomena was detected etc.). The typical changes of generation spectrums observed in the course of thermal synthesis of CNTs in heterogeneous plasma are given below (Fig. 3). Generation spectral regions are caused by the coherent radiation occurring in Förster region (MCNT-target) upon its irradiation by the external laser source tunable by frequency. We observe the competitiveness of two effects in Fig. 3b and Fig. 3c: occurrence of the radiation with wavelength of 783.3 nm and wavelength of 785.3 nm. The occurrence of described competitive effects in two experiments carried out at different times under different conditions is illustrated in Fig. 3c, Fig. 3d. The results which we obtained (Fig. 3) are analogous to the data published in the paper in NATURE magazine . Fragments of the spectrums given in Fig. 3 characterize the change of spectral intensity upon the study of heterogeneous plasma doped by the additions of cerium atoms thermally synthesized into the walls of CNTs and potentially influencing on the development of photon BEC state. The results obtained in this paper were characterized by the change of spectral intensity, radiation spectrums  and change of the dynamics of generation pulse stream . The dependence of change of the radiation spectral intensity recorded from the area of detection of optical signal from near-field region (or region which is adjacent to the near-field scanning microscope probe [3, 6, 7]) which is situated between the microscope probe (CNT played the role of probe) and metal-carbon target is displayed in Fig.4 as the example . This area was irradiated by the luminous flux of tunable laser and the probe scanning was accomplished in fold intervals δl (Fig. 4) using the adjusting screw of micropillar. Such dependence was detected by the quick-response photodetector for the interval between probe and target: curve 1 corresponds to the results obtained for the initial radiation flux, curve 2 – for the increased distance, curve 4 – for the decreased distance, curve 3 corresponds to the optimal distance. Selection of the optimal distance was determined experimentally (qualitatively). Detector was installed after the high-resolution polychromator and the signal was detected on the screen of storage oscilloscope which then was photographed and obtained data was processed. Analysis of the known papers and experimental results obtained in this paper allows making the following assumptions on the observed phenomenon of BEC: Experimental facility which was used by the researchers from Bonn  for the detection of photon BEC state is close to IL-spectrum analyzer which was used for the study of absorption (emission) spectrums of heterogeneous plasma doped by cerium atoms thermally synthesized into MCNT walls. Tunable lasers with homogeneously broadened amplification loop which were excited by the optical radiation sources at the room temperature were used as the coherent radiation sources in considered cases. Apparently, all observed and detected phenomena are connected with each other by one basic condition – provision of the coherence of radiation flux and non-linear change of dynamics of radiation fluxes. Further study of these phenomena will expand the knowledge of photon BEC state (if it exists or mechanism of its occurrence corresponds to the description in the paper ) and make it possible to observe other effects occurring upon the laser broad-band irradiation of heterogeneous plasma doped by metal atoms. There are no exhausting characteristics of radiation fluxes which characterize the dynamic and spectral parameters of radiation in BEC state and potential non-linear developments in the paper . The results of research carried out and planned in future will make it possible to find and develop the conditions of creation of the new class of laser active mediums. Perhaps, they will be applied within the broad spectral interval (including UV and X-ray ranges) with different temporary characteristics in solution of various tasks.