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COOLING AND QUENCHING OF POSITRONIUM AND PROSPECT FOR A Ps BEC

Toshio Hyodo, Haruo Saito, Y. Nagashima, Fuminori Saito, Noriyuki Shinohara

Published Jan 1, 2002• 0 citations
OpenAlex

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.

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Challenges and advances of positronium Bose-Einstein condensation

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While scientists in the USA have accomplished Bose-Einstein Condensation (BEC) of inert gas and alkaline atoms successfully, a challenging question comes into the other’s mind why not BEC of Positronium (Ps), even though, its lowest lifetime (142 ns)? A few auspicious methods of having BEC were invented and successfully applied in the atoms of infinite lifetime. But in case of Ps-BEC laser cooling is considered to be the best method provided we can meet the requisite parameters. Using the medium range e+ beam intensity we explored some solid surfaces for the laser cooling of Ps but Ps-BEC could not be achieved. Because the intensity of pulsed beam was not enough to have the phase space density, outgoing Ps from the surface with thermal motion could not be controlled inside the scattering chamber and laser-Ps interaction was without synchronization. Hence, scientists of different laboratories have been searching materials of high density Ps production, intense pulsed e+ beam, advanced detector and image reconstruction techniques. Recently we have developed calumnious silicon nano-wires of various diameters and found the signature of a long-life component of Ps and estimated the Ps production density about 1015 Ps/cm3. It is an ideal case for the achievement of the Ps-BEC. The details of these systems are explained in the following sections.

AIP Advances•May 1, 2019•1 citation

Study on Bose-Einstein condensation of positronium

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A new method to realize Bose-Einstein condensation (BEC) of positronium (Ps) is proposed and a Monte-Carlo simulation was performed to evaluate the cooling efficiency of Ps atoms. Ps-BEC was found to be possible by a method including laser cooling of Ps. Laser specifications for Ps cooling are challenging and development is ongoing. A new temperature measurement method for cold Ps and development of an intense, pulsed, slow-positron microbeam are also necessary. They are under study as outlined in this contribution.

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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.

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

Marcus X. Asaro, Steven A. Herrera, Melina Fuentes-Garcia +4 more

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

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Possible experiments with high density positronium

Allen Paine Mills

Although it can probably only exist within a confining potential, a positronium (Ps) Bose-Einstein condensate (BEC) would be interesting because it could be viewed as the ultimate member of Wheeler’s polyelectron series, e+, Ps, Ps−, Ps+, Ps2, …, Ps-BEC [1], not counting high density neutral e+-e− plasmas. A Ps-BEC could be a source of very cold Ps atoms for precision spectroscopy, for gravitation experiments, and as the gain medium for an annihilation gamma ray laser [2]. It would also be interesting to look for other effects that are non-linear in the positron density, such as the production of Ps+ ions and highly polarized positrons at a metal surface. Specifically, a process in which one thermalized bulk positron passes into the vacuum accompanied by an electron and a surface positron (surface pseudo-Ps) to form a Ps+ ion in vacuum, e+solid + Pssurf → Ps+vac + □E, is energetically allowed for a Ni(100) remoderator surface, for which + □E = 1.00 eV. The positive ions could be used in an experiment in which one positron undergoes a process in a material and the other positron reports on the process via its subsequent Ps emission, etc. Since the two positrons involved in the formation of Ps+ and Ps2 must have opposite spins, at sufficiently high implanted positron densities the minority positron spins will be significantly depleted by these processes, resulting in the enhancement of the spin polarization of the reemitted positrons which might be useful for spin polarized angle-resolved positronium emission spectroscopy of the electronic structure of solids and surfaces.

AIP conference proceedings•Jan 1, 2019•10 citations

Positronium Laser Deceleration, Cooling and Trapping

Barna Mendei, Helmut Ritsch

We numerically study laser deceleration, cooling and trapping of host fast ortho-positronium (Ps) bunches as produced in silica microchannel targets using positron bunches from a Surko trap. While Doppler laser cooling routinely allows to cool neutral atom species below milli-Kelvin kinetic temperatures, the fast ground state annihilation and the high recoil shift to line-width ratio in Ps pose new challenging limitations on timing and the required laser power. Earlier theoretical work and first experiments already exhibit viable prospects for radiation pressure cooling to create unprecedented cold and dense Ps ensembles. Our extended numerical studies confirm very good prospects to simultaneously decelerate, cool and optically trap Ps atoms in a standard Doppler cooling geometry on the $1^3\mathrm{S}$--$2^3\mathrm{P}$ transition. Including the full Zeeman state manifolds and adding additional transverse lasers on the $2^3\mathrm{P}$--$3^3\mathrm{D}$ transition improves timing and final temperature to allow for optical trapping at the end. The required laser powers and geometry parameters to implement effective slowing and trapping within a time frame, where the majority of atoms is not annihilated, is in reach of current technology of $\mathrm{mJ}$ energy pulses of approximately $100\ \mathrm{ns}$ duration. Future extensions to collectively enhance cooling and trapping in optical cavities or hollow-core fibres should finally allow fast preparation of ultra-cold Ps systems as future basis of superradiant lasing and Bose--Einstein condensates.

quant-pharXiv:2609.35202•Sep 29, 2026•0 citations
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.
While scientists in the USA have accomplished Bose-Einstein Condensation (BEC) of inert gas and alkaline atoms successfully, a challenging question comes into the other’s mind why not BEC of Positronium (Ps), even though, its lowest lifetime (142 ns)? A few auspicious methods of having BEC were invented and successfully applied in the atoms of infinite lifetime. But in case of Ps-BEC laser cooling is considered to be the best method provided we can meet the requisite parameters. Using the medium range e+ beam intensity we explored some solid surfaces for the laser cooling of Ps but Ps-BEC could not be achieved. Because the intensity of pulsed beam was not enough to have the phase space density, outgoing Ps from the surface with thermal motion could not be controlled inside the scattering chamber and laser-Ps interaction was without synchronization. Hence, scientists of different laboratories have been searching materials of high density Ps production, intense pulsed e+ beam, advanced detector and image reconstruction techniques. Recently we have developed calumnious silicon nano-wires of various diameters and found the signature of a long-life component of Ps and estimated the Ps production density about 1015 Ps/cm3. It is an ideal case for the achievement of the Ps-BEC. The details of these systems are explained in the following sections.
A new method to realize Bose-Einstein condensation (BEC) of positronium (Ps) is proposed and a Monte-Carlo simulation was performed to evaluate the cooling efficiency of Ps atoms. Ps-BEC was found to be possible by a method including laser cooling of Ps. Laser specifications for Ps cooling are challenging and development is ongoing. A new temperature measurement method for cold Ps and development of an intense, pulsed, slow-positron microbeam are also necessary. They are under study as outlined in this contribution.
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.
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
Although it can probably only exist within a confining potential, a positronium (Ps) Bose-Einstein condensate (BEC) would be interesting because it could be viewed as the ultimate member of Wheeler’s polyelectron series, e+, Ps, Ps−, Ps+, Ps2, …, Ps-BEC [1], not counting high density neutral e+-e− plasmas. A Ps-BEC could be a source of very cold Ps atoms for precision spectroscopy, for gravitation experiments, and as the gain medium for an annihilation gamma ray laser [2]. It would also be interesting to look for other effects that are non-linear in the positron density, such as the production of Ps+ ions and highly polarized positrons at a metal surface. Specifically, a process in which one thermalized bulk positron passes into the vacuum accompanied by an electron and a surface positron (surface pseudo-Ps) to form a Ps+ ion in vacuum, e+solid + Pssurf → Ps+vac + □E, is energetically allowed for a Ni(100) remoderator surface, for which + □E = 1.00 eV. The positive ions could be used in an experiment in which one positron undergoes a process in a material and the other positron reports on the process via its subsequent Ps emission, etc. Since the two positrons involved in the formation of Ps+ and Ps2 must have opposite spins, at sufficiently high implanted positron densities the minority positron spins will be significantly depleted by these processes, resulting in the enhancement of the spin polarization of the reemitted positrons which might be useful for spin polarized angle-resolved positronium emission spectroscopy of the electronic structure of solids and surfaces.
We numerically study laser deceleration, cooling and trapping of host fast ortho-positronium (Ps) bunches as produced in silica microchannel targets using positron bunches from a Surko trap. While Doppler laser cooling routinely allows to cool neutral atom species below milli-Kelvin kinetic temperatures, the fast ground state annihilation and the high recoil shift to line-width ratio in Ps pose new challenging limitations on timing and the required laser power. Earlier theoretical work and first experiments already exhibit viable prospects for radiation pressure cooling to create unprecedented cold and dense Ps ensembles. Our extended numerical studies confirm very good prospects to simultaneously decelerate, cool and optically trap Ps atoms in a standard Doppler cooling geometry on the 13S1^3\mathrm{S}13S--23P2^3\mathrm{P}23P transition. Including the full Zeeman state manifolds and adding additional transverse lasers on the 23P2^3\mathrm{P}23P--33D3^3\mathrm{D}33D transition improves timing and final temperature to allow for optical trapping at the end. The required laser powers and geometry parameters to implement effective slowing and trapping within a time frame, where the majority of atoms is not annihilated, is in reach of current technology of mJ\mathrm{mJ}mJ energy pulses of approximately 100 ns100\ \mathrm{ns}100 ns duration. Future extensions to collectively enhance cooling and trapping in optical cavities or hollow-core fibres should finally allow fast preparation of ultra-cold Ps systems as future basis of superradiant lasing and Bose--Einstein condensates.