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The European Physical Journal D

Conditions for obtaining positronium Bose–Einstein condensation in a micron-sized cavity

Marcus X. Asaro, Steven A. Herrera, Melina Fuentes-Garcia, Gabriel G. Cecchini, Erick E. Membreno, Rod G. Greaves, Allen Paine Mills

Published Jun 1, 2022• 5 citations
Publisher

Abstract

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 $$10^7$$ 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

DOI
10.1140/epjd/s10053-022-00427-1

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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.

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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.

Physical Review A•Mar 6, 2014•19 citations
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 10710^7107 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
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.
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.
In this paper we consider the possibilities for producing a dense gas of N\ensuremath{\simeq}105{10}^{5}105 triplet positronium (Ps) atoms in vacuum contained in small cavity V\ensuremath{\simeq}${10}^{\mathrm{\ensuremath{-}}13}$ cm3{\mathrm{cm}}^{3}cm3. We then consider the scenario where this dense gas of polarized Ps atoms may cool through a weakly interacting Bose transition. The rates for thermalization with the wall, equilibrium in the bulk, and loss of polarization by exchange collisions are calculated. A method for observing the transition is also discussed.
Abstract A proposed new method of cooling positronium is to realize the Bose–Einstein condensation (BEC) of positronium. We perform detailed studies of three processes: (1) thermalization processes between positronium and the silica walls of a cavity, (2) Ps–Ps scattering and (3) laser cooling. The thermalization process is shown to be not sufficient for BEC. Ps–Ps collision is shown to have a big effect on the cooling performance. We combine both methods and establish an efficient cooling process for BEC. We also propose a new optical laser system for the cooling.
We have measured the kinetic energy of positronium (Ps) atoms emitted into a vacuum from a porous silica film subsequent to positron bombardment, via the Doppler spread of the linewidth of the Ps 13S{1}^{3}S13S-23P{2}^{3}P23P transition. We find that the deeper in the target film that positrons are implanted the colder is the emitted Ps, an effect we attribute to cooling via collisions in the pores as the atoms diffuse back to the film surface. We observed a lower limit to the mean Ps kinetic energy associated with motion in the direction of the laser, ${E}_{x}=42\ifmmode\pm\else\textpm\fi{}3$ meV, that is consistent with conversion of the confinement energy of Ps in the 2.7-nm-diameter pores to kinetic energy in vacuum. An implication is that a porous sample would need to be composed of pores greater than around 10 nm in diameter in order to produce thermal Ps in vacuum with temperatures of less than 100 K. By performing Doppler spectroscopy on intense pulses of Ps we have experimentally demonstrated the production of many excited-state Ps atoms simultaneously, which could have numerous applications, including laser cooling and fundamental spectroscopic studies of Ps and the production of antihydrogen.
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.