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Physical Review A

Positronium laser cooling in a magnetic field

Christian Zimmer, P. Yzombard, A. Camper, D. Comparat

Published Aug 18, 2021• 11 citations
Publisher

Abstract

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 $B⪆0.7\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{T}$. Near $100\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$ long laser pulses, spectrally broad enough to cover most of the Ps Doppler profile and with energy in the $\mathrm{mJ}$ 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 $300\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ down to below $50\phantom{\rule{0.16em}{0ex}}\mathrm{K}$) 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.

DOI
10.1103/physreva.104.023106

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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≲50mTB\ensuremath{\lesssim}50\phantom{\rule{0.16em}{0ex}}\mathrm{mT}B\ensuremath≲50mT 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.
Zeeman mixing of singlet and triplet 2P states of positronium (Ps) atoms, followed by decay back to the ground state, can effectively turn a long-lived triplet atom into a short-lived singlet state, which would seem to preclude laser cooling of Ps in a magnetic field. Here we report experiments which show that, in fact, because of the large splitting of the n=2 states in a high magnetic field (the Paschen-Back regime), the amount of such mixing diminishes approximately exponentially with an increasing magnetic field >0.01 T and is essentially eliminated above ∼2 T. Thus, laser cooling of Ps should be feasible at high fields, which will facilitate the production of a Ps Bose-Einstein condensate.
Antihydrogen production by charge exchange reaction between positronium (Ps) atoms and antiprotons requires an efficient excitation of Ps atoms up to high-nnn levels (Rydberg levels). In this study it is assumed that a Ps cloud is produced within a relatively strong uniform magnetic field (1T)(1\phantom{\rule{0.3em}{0ex}}\mathrm{T})(1T) and with a relatively high temperature (100K)(100\phantom{\rule{0.3em}{0ex}}\mathrm{K})(100K). Consequently, the structure of energy levels are deeply modified by Zeeman and motional Stark effects. A two-step laser light excitation, the first one from ground to n=3n=3n=3 and the second from this level to a Rydberg level, is proposed and the physics of the problem is discussed. We derive a simple formula giving the absorption probability with substantially incoherent laser pulses. A 30% population deposition in high-nnn states can be reached with feasible lasers suitably tailored in power and spectral bandwidth.
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.
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We report on laser cooling of a large fraction of positronium (Ps) in free flight by strongly saturating the 1^{3}S-2^{3}P transition with a broadband, long-pulsed 243 nm alexandrite laser. The ground state Ps cloud is produced in a magnetic and electric field-free environment. We observe two different laser-induced effects. The first effect is an increase in the number of atoms in the ground state after the time Ps has spent in the long-lived 2^{3}P states. The second effect is one-dimensional Doppler cooling of Ps, reducing the cloud's temperature from 380(20) to 170(20) K. We demonstrate a 58(9)% increase in the fraction of Ps atoms with v_{1D}<3.7×10^{4} ms^{-1}.
The theory of laser cooling assisted by transverse magnetic field Bt{\mathbf{B}}_{\mathbf{t}}Bt​ based on the (1+3)(1+3)(1+3)-level atomic system is presented. With the additional Bt{\mathbf{B}}_{\mathbf{t}}Bt​, atoms could be redistributed among the upper Zeeman sublevels via Larmor precession, and results in large stimulated radiation force and low temperature. Here we consider this cooling model both for broad transition line and narrow line. A Fokker-Planck-type kinetic equation is derived for a broad line. Numerical result shows that the final temperature could be lower than the Doppler limit. For a narrow line, the Monte Carlo approach is applied to simulate the distribution of atoms in the momentum regime and the result shows that most atoms are distributed around zero velocity with width about several $\ensuremath{\hbar}k∕m$.