We investigate the possibility to produce a Bose-Einstein condensate made of positronium atoms in a porous silica material containing isolated nanometric cavities. The evolution equation of a weakly interacting positronium system is presented. The model includes the interactions among the atoms in the condensate, the surrounding gas of noncondensed atoms, and the pore surface. The final system is expressed by the Boltzmann evolution equation for noncondensed particles coupled with the Gross-Pitaevskii equation for the condensate. In particular, we focus on the estimation of the time necessary to form a condensate containing a macroscopic fraction of the positronium atoms initially injected in the material. The numerical simulations reveal that the condensation process is compatible with the lifetime of ortho-positronium.
We investigate the possibility to produce a Bose-Einstein condensate made of positronium atoms in a porous silica material containing isolated nanometric cavities. The evolution equation of a weakly interacting positronium system is presented. The model includes the interactions among the atoms in the condensate, the surrounding gas of noncondensed atoms, and the pore surface. The final system is expressed by the Boltzmann evolution equation for noncondensed particles coupled with the Gross-Pitaevskii equation for the condensate. In particular, we focus on the estimation of the time necessary to form a condensate containing a macroscopic fraction of the positronium atoms initially injected in the material. The numerical simulations reveal that the condensation process is compatible with the lifetime of ortho-positronium.
The evolution equation of a weakly interacting boson system is derived. The model includes the interaction between the atoms in the condensate and the surrounding gas of noncondensed particles. The Bogoliubov transformation is introduced in a full quantum context and the scattering kernel between dressed particles and the condensate phase is obtained. The final system is expressed by the Boltzmann evolution equation for noncondensed particles coupled to the Gross-Pitaevskii equation for the condensate. We consider an out-of-equilibrium situation that induces a fast production of condensed particles. We apply our model to study the condensation dynamics of positronium atoms by evaporation.
Abstract The quest for making a triplet positronium (Ps) Bose–Einstein condensate confined in a micron-sized cavity in a material such as porous silica faces at least three interrelated problems: (1) About 107 10 7 spin polarized Ps atoms must be injected into a small cavity within a porous solid material without vaporizing it. (2) It is known that Ps atoms confined in 30–100 nm diameter cavities in porous silica do not remain in the gas phase, but become stuck to the cavity walls at room temperature (Cooper et al., Phys. Rev. B 97:205302, 2018). (3) Cooling a gas of Ps atoms to cryogenic temperatures by energy exchange with the walls would be a very slow process (Saito and Hyodo, in: Surko, Gianturco (eds) New Directions in Antimatter Chemistry and Physics, Springer Dordrecht, Netherlands, 2001) because of the relatively low collision rate with the walls and the large mismatch between the masses of the Ps and the wall atoms. A possible solution of these difficulties is presented, based on cooling the implanted positrons in an isotopically pure diamond single crystal target, subsequent saturating of the wall Ps coverage so that a substantial portion of the Ps will be in the gaseous state, and thermalizing the gas-phase Ps via collisions with the low effective mass wall Ps. A design process for the target material is outlined as well, including preliminary results in porous cavity fabrication using focused ion beam milling. Graphical abstract
Laser cooling of positronium (Ps) is an important technique to advance the frontier of science by, for instance, realizing the first Bose-Einstein condensation of antimatters. It was proposed that performing laser cooling on Ps trapped in a cryogenic porous material would be more efficient, but a recent study (Cooper, et al., Phys. Rev. B 97, 205302 (2018)) reported that Ps in the excited (2P) state inside nano pores of silica had a large decay rate into γ-rays, and the resonant spectrum of the transition was significantly broadened, both of which are critically problematic for the proposed cooling scheme. A possible cause of these unexplained results was proposed to be residual impurities which trapped Ps in the vicinity of the pore surface and then enhanced interactions between Ps and the material. This work reports fabrication and inspection of a new porous silica cavity without such impurities, and construction of an experimental system to induce the Lyman-α transition of Ps trapped in pores of the cavity.
Realization of Bose-Einstein Condensate (BEC) of positronium (Ps), a purely leptonic particle-antiparticle bound system, is a challenging subject [1, 2]. Recently, Ivanov et al. [3] theoretically investigated the Ps-Ps scattering and showed theoretically that the scattering length for the o-Ps atoms is positive, indicating that a stable o-Ps BEC is actually possible. The condition for the BEC of the ideal Bose gas is λth > (2.612/n)1/3, where λth = h/ √ 2πmkT is the thermal de Broglie wavelength of the atom and n is the number density. This gives the critical temperature for the Ps BEC as Tc = 1.46×10−15n2/3, where Tc is in K and n is in m−3. This condition is much less severe than for the usual alkali atom BEC because λth is longer by five orders of magnitude. However, Ps has a finite lifetime: the lifetime of singlet state, para-positronium (p-Ps), is 125 ps and that of triplet state, ortho-positronium (o-Ps), is 142 ns. Thus a many-Ps system must be cooled within the lifetime of o-Ps. The short lifetime of Ps demands quick cooling and high density. The laser cooling which is employed for the accomplishment of alkali atom BEC is likely to be impractical because it takes longer time. It is also subject to relatively large recoil of the Ps atom when hit by a photon. Moreover, unless an effective method for trapping Ps in free space is developed, the system of Ps atoms diffuses and lowers its density. Platzmann and Mills [1] suggested to confine Ps in a small cavity of insulating material and let the Ps atoms give away their kinetic energy to the walls of the cavity. If one injects an intense polarized positron beam onto a material which has a micro cavity near surface, some of the positrons form Ps and are emitted into the cavity and stay there. This is expected because the work function of most of the material for Ps is negative, i.e., Ps atoms emitted into the cavity after thermalization in the material will never penetrate back into the material. They just hit the cavity walls and approach thermal equilibrium by exciting phonons. The probability of the annihilation of o-Ps with a surface electron is small if there are no paramagnetic centers on the cavity walls. It is necessary to use a polarized positron beam to make Ps. Otherwise all the o-Ps atoms are lost through mutual spin conversion into p-Ps [1, 4]. In this report we would like to discuss prospect of a Ps BEC with special attention to the following aspects [4]: (1) use of 18F for a source of an intense spin-polarized positron beams [5], (2) development of high efficiency Wmesh positron moderator, (3) emission of Ps from solid surface (4) the cooling of Ps in a cavity, and (5) the detection of a Ps BEC.
Bose-Einstein condensates (BECs) of positronium (Ps) have been of experimental and theoretical interest due to their potential application as the gain medium of a $\ensuremath{\gamma}$-ray laser. Ps BECs are intrinsically spinor due to the presence of ortho-positronium (o-Ps) and para-positronium (p-Ps), whose annihilation lifetimes differ by three orders of magnitude. In this paper, we study the spinor dynamics and annihilation processes in the p-Ps/o-Ps system using both solutions of the time-dependent Gross-Pitaevskii equations and a semiclassical rate-equation approach. The spinor interactions have an O(4) symmetry which is broken to SO(3) by an internal energy difference between o-Ps and p-Ps. For an initially unpolarized condensate, there is a threshold density of $\ensuremath{\approx}{10}^{19}$ cm${}^{\ensuremath{-}3}$ at which spin mixing between o-Ps and p-Ps occurs. Beyond this threshold, there are unstable spatial modes accompanied by spin mixing. To ensure a high production yield above the critical density, a careful choice of external field must be made to avoid the spin mixing instability.
We review the proposal for Bose–Einstein condensation of positronium atoms. All of the ingredients necessary to achieve BEC of Ps atoms are currently available. Introduction In this volume several authors have discussed and described a variety of weakly interacting systems which might display BEC. In this short contribution we suggest that a dense gas of positronium (Ps) atoms in vacuum is a rather ideal but somewhat more exotic system that might be a very good candidate for observing a weakly interacting BEC. Recent investigations of the interactions of positrons ( e + ) and (Ps) with solids have led to extraordinary improvements in the kinds of low energy experiments we can do with the positron [1, 2]. All of the ingredients necessary to achieve BEC of Ps atoms are currently available. We envision a scenario where roughly N ≅ 10 5 Ps atoms are trapped in a volume v ≃ 10 −13 cm 3 and allowed to cool through the Bose transition temperature of 20 – 30K in a time of the order of nanoseconds. In the following we discuss the relevant interactions and describe how Ps BEC can be achieved. Single Positronium Physics Ps is comprised of an e + − e − bound in a hydrogenic orbit. Its mass, 2 m e , is extremely light compared to H, an important ingredient for achieving reasonable Bose condensation temperatures. Its binding energy (6.8 eV) is half that of H.