Challenges and advances of positronium Bose-Einstein condensation Open Access

A few methods which are playing crucial roles for obtaining BEC are: (i) Laser cooling (Steven Chu), (ii) Magneto-Optical trapping (MOT, Carl Wieman), (iii) Sisyphus cooling, first proposed by Claude Cohen-Tannoudji in 1989. The three dimensional laser cooling of atoms was validated by Chu, et al., in 1985¹ for the first time. In case of Positronium Bose-Einstein Condensation (Ps-BEC) laser cooling is the best,² provided (i) high intensity slow positron (≥10¹² e⁺/s) beam, (ii) efficient material target for the production of high density Ps, (iii) laser-Ps scattering chamber without any loss to achieve required number of phase space density ∼10¹⁵ Ps atoms/cm³ at a few tenth of Kelvin temperature, and (iv) an advanced detection and imaging system to visualize the Ps-BEC are available. Using the medium range slow e⁺ beam intensity we explored some material surfaces (Mo, W, Au, Cu) for a high density Ps production^2,3 and achieved the laser (Cr:LiSAF) cooling of ortho-Ps. A deficit slow e⁺ beam did not permit us to attain the required number of phase space density of Ps which is defined by,

Where $λDB$⁠, m and T respectively are De Broglie wavelength, rest mass and temperature (measured in Kelvin) of the Ps atom. If mili Kelvin (mK) temperature can be attained then Ps-BEC will be achieved at lower density of ∼10¹² Ps/cm³, hence THz slow e⁺ beam is suitable to obtain Ps-BEC. Recently accelerator physicists have been commissioning highest intense slow e⁺ beams.⁴ One of the highest intense e⁺ beams (10⁷e⁺/sec) is commissioned at AIST, Tsukuba, Japan.⁵ Instead of conventional time-of-flight (TOF) data accumulating system an advanced TOF data taking and an image reconstruction technique were taken into account in order to visualize the Ps-BEC.⁶ 

In order to achieve the Ps-BEC at mK temperature a high density mono-energetic e⁺ beam is required, because the production rate of thermal ortho-Ps on clean metal surface is only 20 – 30% of the beam incident on it. Up to the last decade only 10⁹ e⁺/sec was attained in the accelerator based e⁺ beam. Many groups have studied 1S-2S, 2S-3S, 1S-2P transitions of Ps for laser cooling using different types of laser, e.g., CO₂, Nd:YAG, Cr:LiSAF etc. Most efficient cooling process is outlined as 1S-2P transition where 243 nm wavelength of laser beam is ideal for the stimulated absorption and emission of thermal ortho-Ps. Lifetime of para-Ps (125 ps) is shorter than 1S-2P transition time, so that it can’t be the subject of laser cooling. On the other hand lifetime of ortho-Ps (142 ns) is higher than the transition interval (3.2 ns), and it is possible to cool down after several synchronized collisions (∼28) with the incident laser. In this case conventional TOF detectors system can detect those annihilation γ-rays in the field of view region only and many cooled ortho-Ps decay beyond the slit-gap. Separation of thermal ortho-Ps (1 few meV) from the work function Ps (1 few eV) and then cooling down is another challenge.

An intense pulsed e⁺ source has been developed at AIST, Tsukuba, Japan using a buffer gas trap to accumulate large numbers of e⁺s and created a denser e⁺ plasma, which may then be bunched and spatially focused. Areal densities > 3×10¹⁰ e⁺/cm² have been estimated in a sub-nanosecond pulse that produces an instantaneous e⁺ current of 10 μA with a beam diameter ∼ 1 cm.⁷ Slow e⁺ beam facility at High Energy Accelerator Research Organization (KEK) has an energy-tunable (0.1 – 35 keV) that is created by a dedicated ∼ 50 MeV LINAC. High energy e⁺s from pair creation are moderated by reemission after thermalization in W foils.⁸ It operates in a short pulse (width 1-12 ns, variable, 5×10⁶ e⁺/s) and a long pulse (width 1.2 µs, 5×10⁷e⁺/s) mode of 50 Hz.

The intense e⁺ beam at the PULSTAR reactor at NCSU has achieved an intensity of nearly 10⁹ e⁺/sec with a beam diameter of 1 inch. With magnetic guidance, the main e⁺ beam can be steered away from the reactor core region to drive the two different e⁺ spectrometers. One of those is e⁺-PALS spectrometer, is a magnetically guided bunching system that has less than 300 ps timing resolution and is capable of studying the fast e⁺ annihilation events. The second spectrometer, namely, the Ps-PALS spectrometer, has a 1000 ps timing resolution and is more specific for Ps related materials characterization.⁹ 

In order to accomplish the Ps-BEC we have been paying a lot of attention to improve our laboratory based experiments. In TMU we had developed a high intense pulsed slow e⁺ beam, Cr:LiSAF laser system, advanced TOF detector and Ps-Laser interaction chamber for this purpose. We had studied the production mechanisms of work function Ps and thermal Ps respectively inside and outside of the clean metal surfaces of W, Mo, Cu and Semiconductor using this beam and distinctly measured the work function Ps and thermal ortho-Ps. We incorporated extensive Monte Carlo Simulation based on GEANT for these precision measurements. Later on we developed a e⁺ trapping and pulsing system and studied the laser cooling of ortho-Ps on Mo surface at various temperatures by using Cr:LiSAF laser.

Recently we have studied high density Si-nano-wires (Si-NWs) samples (Table I, Fig. 1) in order to find the ortho-Ps production. Using the PAS technique we confirm the production of ortho-Ps inside the calumnious spikes of the samples and results are summarized in the following Table I.

Results show that the third component of ortho-Ps lifetime and its yield increase with decreasing the pore sizes of the samples. It infers that thermal Ps remain intact inside the bigger pores and immediately annihilate via pick-off annihilation that decreases the lifetime. Hence, the production rate of other Ps increases. We estimated the density of pores per area and Ps density per volume of each samples and results are shown respectively in the third and last columns. It shows that required number of phase-space density of Ps-BEC is possible to accommodate inside these samples.

In TMU we had developed an advanced TOF system by using YAP:Ce scintillator with position sensitive photomultipliers tubes [PSPMT model: Hamamatsu Photonics, H6568; see Table I of Ref. 6(b)]. We also investigated the spatial and energy resolution coupling with other scintillators and found that YAP:Ce with H6568 is better than others for imaging the Ps-BEC. Important feature of the YAP:Ce scintillator is that the response function is independent of temperature that makes it reliable in thermal Ps measurement when target is required to be heated more than room temperature. The detail of this system can be found elsewhere.⁶ In Table II, a few useful scintillators and their properties with energy and spatial resolutions are displayed and some of them are yet undone for these verifications. It should be noted out that the results of the last three columns are case sensitive: shape, size, properties of the scintillators and PMTs which are used. An extensive Monte Carlo Simulation (MCS) based on GEANT was performed in order to construct an advanced PS-PMT γ-rays detection and imaging system for the Ps-BEC. Spatial and energy resolutions and detection efficiency of PS-PMT are better than those of conventional TOF system can be found elsewhere.⁶ More than one pair of three detector modules will provide better detection efficiency and reduce time of the experiment. We should also investigate other types of high density nanoporous materials for thermal Ps production rate and optimize one for the Ps-BEC. It is our prime requirement to construct and utilize this system in any high intense slow e⁺ beam facility in order to accomplish the Ps-BEC, a long lusting charismatic problem.

Almost two decades have been passed away from our research dilemma, but we are still far behind of the achievement of Ps-BEC. Up to now our successes are: (i) high intense slow e⁺ beam (10⁴ → 10¹³e⁺/sec), (ii) efficient targets (various shapes and sizes of nano-materials) for Ps production, (iii) laser cooling systems for 1S – 2P transitions, (iv) conventional and advanced TOF detectors system, (v) data taking and analysis system, (vi) image reconstruction algorithms etc. Many of those are performed systematically but in scattered laboratories and some of them are unattended. Hence we need a common platform in the form of international collaboration so that we can give our best efforts for the triumph of Ps-BEC.

Author is pleased to acknowledge the financial support from the MONBUSHO, NEDO and JSPS from the Govt. of Japan. He is thankful to Professor T. Hirose and Professor R. Hamatsu for their sincere guidance of these research projects and accomplishments. He is pleased to his colleagues Prof. P.M.G. Nambissan and Dr. N.S. Das for attending PALS and Si-NWs projects respectively.