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Journal of the Physical Society of Japan

Monte Carlo Study of Ortho-Positronium Laser Cooling

Hokuto Iijima, T. Hirose, M. Irako, Masatoshi Kajita, Tetsuro Kumita, Hiroyuki Yabu, Kazuyuki Wada

Published Nov 1, 2001• 4 citations
Publisher

Abstract

On the basis of three dimensional (3-D) Monte Carlo simulation, we studied details of laser cooling (Doppler cooling) of ortho-Positronium ( o -Ps) which would be applied to the achievement of Bose–Einstein condensation of positronium. The cooling is carried out by an ultraviolet laser with a wavelength of 243 nm being equivalent to the 1 S –2 P transition energy of o -Ps. For this purpose, we have constructed a laser cooling apparatus which consists of a slow positron generator and a long pulse, wide linewidth laser. A 3-D Monte Carlo calculation, which incorporated various parameters of laser beam and positronium distributions expected in the current laser cooling apparatus, revealed that 7% of o -Ps was able to be cool down to 1 K and to be confined in a relatively small volume without employing a special trap.

DOI
10.1143/jpsj.70.3255

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On the basis of three dimensional (3-D) Monte Carlo simulation, we studied details of laser cooling (Doppler cooling) of ortho-Positronium ( o -Ps) which would be applied to the achievement of Bose–Einstein condensation of positronium. The cooling is carried out by an ultraviolet laser with a wavelength of 243 nm being equivalent to the 1 S –2 P transition energy of o -Ps. For this purpose, we have constructed a laser cooling apparatus which consists of a slow positron generator and a long pulse, wide linewidth laser. A 3-D Monte Carlo calculation, which incorporated various parameters of laser beam and positronium distributions expected in the current laser cooling apparatus, revealed that 7% of o -Ps was able to be cool down to 1 K and to be confined in a relatively small volume without employing a special trap.
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 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.
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.
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 study realistic 3D laser cooling of positronium (Ps) in the presence of a magnetic field. Triplet and singlet states mixing due to the magnetic field, and dynamical Stark effect, generally produce higher annihilation rates than in the zero-field case. 3D cooling is efficient only at very low field $B\ensuremath{\lesssim}50\phantom{\rule{0.16em}{0ex}}\mathrm{mT}$ and at high field values B⪆0.7TB⪆0.7\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{T}B⪆0.7T. Near 100ns100\phantom{\rule{0.16em}{0ex}}\mathrm{ns}100ns long laser pulses, spectrally broad enough to cover most of the Ps Doppler profile and with energy in the mJ\mathrm{mJ}mJ range, are required to cool Ps. Simulations based on full diagonalization of the Stark and Zeeman Hamiltonian and a kinetic Monte Carlo algorithm exactly solving the rate equations indicate that an efficient cooling (typically from 300K300\phantom{\rule{0.16em}{0ex}}\mathrm{K}300K down to below 50K50\phantom{\rule{0.16em}{0ex}}\mathrm{K}50K) is possible even in a magnetic field. We also propose 3D moving molasses cooling that can produce a well-defined monochromatic Ps beam useful for applications.
Our demonstration of multiple-photon resonant cycling between the 1/sup 3/S and 2/sup 3/P states of ortho-Positronium (oPs) makes possible the production of cold positronium (Ps) through the technique of laser cooling. A simplified analysis of magnetic mixing in excited-state Ps is given. This effect is important both as a diagnostic of resonant cycling and Ps cooling. The significance of cold Ps in fine structure measurements and the formation of a Bose-Einstein condensate is discussed. 13 refs., 3 figs.