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Study on laser cooling of ortho-positronium
Nuclear Instruments and Methods in Physics Research B 192 (2002) 171–175 www.elsevier.com/locate/nimb
Study on laser cooling of ortho-positronium T. Kumita a
a,*
, T. Hirose a, M. Irako a, K. Kadoya a, B. Matsumoto a, K. Wada, N.N. Mondal a, H. Yabu, K. Kobayashi b,1, M. Kajita c
High Energy Physics Group, Department of Physics, Tokyo Metropolitan University, 1-1 Minami-Ohsawa, Hachioji-shi, Tokyo 192-0397, Japan b Sumitomo Heavy Industries USA Inc., 666 Fifth Avenue, 10th floor, New York, NY 10103-1999, USA c Communications Research Laboratory, 4-2-1 Nukui-Kitamachi, Koganei, Tokyo 184-8795, Japan
Abstract We have been theoretically and experimentally studying details of laser cooling of ortho-positronium. Experimental apparatus consists of a pulsed positron beam generator, a long pulse wide bandwidth ultraviolet laser and a time-offlight system to measure kinetic energy of positronium atoms is constructed and tested. Using this apparatus, production of thermally activated positronium is confirmed. Its production rate is larger as the target temperature increases and ratio of thermally activated ortho-positronium to all c-ray annihilation events is estimated to be 32:3 6:7% for the target temperature 1000 K. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 03.75.F; 32.80.P; 36.10.D; 52.55.L Keywords: Bose–Einstein condensation; Positronium; Laser cooling; Positron beam
1. Introduction The exotic atom positronium (Ps), bound state of an electron–positron pair, has extremely light mass (1=918 of a hydrogen atom) and short lifetime. The spin singlet ground state, para-Ps (p-Ps), dominantly decays into two c-rays with a lifetime of 0.125 ns, while the spin triplet ground state, ortho-Ps (o-Ps), dominantly decays into three crays with a lifetime of 142 ns. Laser cooling of Ps brings interesting physics to us, such as Bose– Einstein condensation of Ps [1]. * Corresponding author. Tel.: +81-426-77-3328; fax: +81426-77-2483. E-mail address: [email protected] (T. Kumita). 1 Aculight Corporation, 11805 North Creek Parkway South, Suite 113, Bothell, WA 98011, USA.
Possibility of the o-Ps laser cooling is theoretically studied by Liang et al. utilizing the 1S–2P transition whose energy interval is 5.1 eV corresponding to the photon wavelength of 243 nm [2]. Since lifetime of the spontaneous transition from 2P to 1S is 3.2 ns, Doppler cooling of p-Ps is not possible due to its extremely short lifetime. Therefore, only cooling of o-Ps is considered hereafter. A characteristic feature of the laser cooling of o-Ps is that the recoil energy is large owing to the small Ps mass, thus photon recoil limit (0.6 K) is higher than the Doppler limit (7.5 mK). The large recoil makes o-Ps atoms at room temperature cooled down to the photon recoil limit in 32 cycles of the 1S–2P stimulated absorption and the 2S–1P spontaneous emission. In a sufficiently strong laser field, spontaneous emission from an o-Ps atom occurs every 6.4 ns on
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T. Kumita et al. / Nucl. Instr. and Meth. in Phys. Res. B 192 (2002) 171–175
the average, which is two times longer than the lifetime of the 2P state because populations of 1S Ps and 2P Ps are same. Thus the total cooling time is estimated to be 6:4 ns 32 200 ns, which is comparable to the lifetime of o-Ps. Note that o-Ps lifetime is also doubled in the strong laser field because the direct decay time (100 ls) from the 2P state is much longer than that from the 1S state. Wavelength of the cooling laser is usually swept during the cooling process to compensate Doppler shift due to motion of atoms while ordinary atoms are cooled. However, this technique is not applicable for the o-Ps laser cooling because of the short cooling time. Thus, a laser with wide line width, which covers Doppler broadening of the 1S–2P resonance without sweeping its wavelength, is required. The pulse duration also has to be long enough to cover the cooling time 200 ns. In this report, we describe Monte Carlo studies on laser cooling of o-Ps, the experimental apparatus for the cooling experiment, and the experimental result of thermal Ps observation.
2. Monte Carlo simulation Details of the Monte Carlo simulation code are described elsewhere [3]. The coordinate system in the simulation is defined in the following way: the positive z-direction is opposite to the direction of the eþ beam, x- and y-axes cross the z-axis at right angles. Ps atoms are supposed to be produced by implanting an eþ beam at the time t ¼ 0 on a metallic target placed at z ¼ 0. Initial space and time distributions of the Ps cloud are set to 0.75 cm (1r) on the x–y plane and 2.5 ns (1r), corresponding to size and pulse width of our eþ beam, respectively. Initial kinetic energies of the o-Ps atoms obey the Maxwell–Boltzmann distribution at 300 K. The cooling laser is assumed to have pulse energy 60 lJ, time duration 68 ns (1r), line width 11 pm (1r) and radius 2.5 mm (1r). It is divided into six beams and irradiates the Ps cloud along the x-, y-, zdirections. Transition rate between the 1S and 2P states are given as
P¼
Z
X2 C dx; 2 x0 ~ k ~ v x þ C2
ð1Þ
k the wave where x0 is the resonance of the 1S–2P, ~ number vector, ~ v the velocity vector of the Ps and x the laser frequency. The Rabbi frequency X is defined as X ¼ le=h, where e is the laser field and l is the dipole moment of the 1S–2P transition whose magnitude is 1:26 1029 cm. The quantity C stands for the relaxation constant which is assumed only for the spontaneous emission from the 2P state, i.e. C ¼ 2p=3:2 109 s1 . A stimulated absorption or emission modulates the Ps velocity by d~ v h~ k ¼d P; dt 2pmPs
ð2Þ
where d ¼ þ1 ð1Þ denotes absorption (emission). Position, velocity and energy state of each Ps atom are calculated using Eq. (2) every 0.5 ns step in the simulation. In order to examine the cooling process quantitatively, we define two quantities R5mm and T5mm . R5mm is number of o-Ps atoms stay in a spherical volume with the radius 5 mm after a certain cooling time normalized to the number of Ps
Fig. 1. Plot of R5mm and T5mm as functions of the laser detune.
T. Kumita et al. / Nucl. Instr. and Meth. in Phys. Res. B 192 (2002) 171–175
173
atoms initially produced. T5mm is temperature of the Ps cloud in the 5 mm spherical volume. Fig. 1 shows R5mm and T5mm after 220 ns as functions of the laser detune. One can see that 7% of generated o-Ps are cooled down to 1 K in 220 ns for detune of 170 GHz.
3. Experimental apparatus We have developed an experimental apparatus of the laser cooling system, which consists of an eþ beam generator and a laser system [4]. The beam generator consists of an RI source (22 Na, 50mCi) and a beam bunching system. Slow mono-energetic positrons converted in a tungsten mesh moderator are guided into a positron accumulator through a magnetic beam transport system. Then positron beam is bunched with the positron accumulator for the synchronization with a laser pulse and injected on a target to produce Ps atoms [5]. Pulse width of the bunched beam is 15 ns (FWHM) with the intensity of 0.005 eþ ’s/pulse while it is operated with 100 kHz repetition. The laser light is also irradiated to the target in a cooling chamber through a quartz window which seals the vacuum from air. The laser system for the o-Ps cooling experiments, illustrated in Fig. 2, consists of a Cr:LiSAF crystal which create a laser light with the wavelength of 972 nm, a second harmonic generator and
Fig. 3. A schematic view of the TOF measurement system.
a forth harmonic generator. Cr:LiSAF is chosen because of its long lifetime of the excited state (67 ls) and low gain, which result long pulse duration. The second and forth harmonic generators provide required wavelength of 243 nm utilizing two BBO (b-Ba borate) crystals in each generator. Parameters of the 243 nm laser are measured as follows: time duration 280 ns, pulse energy 40 J and line width 17pm (1r), which is consistent with the line width used in the Monte Carlo simulation for compensation of the Doppler broadening. To confirm the laser cooling process, we constructed a time-of-flight (TOF) measurement system [6] illustrated in Fig. 3. The TOF system consists of a cylindrical-shape lead collimator with a gap size of 5 mm and ten modules of NaI(Tl) c-ray detectors. A metallic target, on which Ps atoms are produced is placed at typically 1 cm downstream the gap.
4. Observation of thermal positronium
Fig. 2. A schematic view of the cooling laser system.
There are two categories of Ps atoms produced on a metallic target by injecting eþ beam: the Ps
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T. Kumita et al. / Nucl. Instr. and Meth. in Phys. Res. B 192 (2002) 171–175
with eV kinetic energies due to the Ps work function for the target metal and thermally activated Ps (thermal Ps). Since the latter has lower kinetic energy (typically 39 meV at room temperature), high production rate of thermal Ps is required for the laser cooling experiment. By injecting the bunched eþ beams on a gold (Au) target, we observed decay time distributions of o-Ps for the target temperature of 300, 600 and 1000 K. As seen in Fig. 4, the o-Ps production becomes larger as the target temperature increases. The broad peak appearing around 300 ns is due to beam reflections at the target. Assuming contribution from the Ps with the work function energy is independent of temperature, increase of the o-Ps production is considered to be thermal Ps. A TOF measurement shows production of thermal Ps is negligibly small for the target temperature 300 K. Thus contribution of the thermal o-Ps can be extracted by subtracting the data for 300 K from that for 600 and 1000 K. Fig. 5 shows ratio of produced thermal o-Ps to all c-ray annihilation events, i.e. prompt decay, p-Ps and o-Ps. Production rate of thermal o-Ps, which is target of the laser cooling experiment, is evaluated to be 32:3 6:7% at the target temperature 1000 K. The TOF spectrum for the distance between the target and the gap of 1 cm is taken at 1000 K as
Fig. 5. Production rate of thermal o-Ps.
Fig. 6. TOF spectrum at 1000 K. A solid line shows a result of fitting of Eq. (1).
shown in Fig. 6. Energy spectrum of the thermal Ps is expected to obey the Maxwell–Boltzmann distribution. Considering correction for o-Ps velocity and lifetime, the TOF spectrum of thermal Ps is observed as 2 S0 S1 t S ¼ exp þ ; ð3Þ t t2 soPs-Ps where soPs-Ps is the lifetime of o-Ps and S0 and S1 are the fitting parameters. The quantity S1 is a function of T, temperature of the Ps cloud as Fig. 4. Decay curve of o-Ps produced on the Au target at the temperature of 300, 600 and 1000 K.
S1 ¼ ml2 =2pkB T ;
ð4Þ
T. Kumita et al. / Nucl. Instr. and Meth. in Phys. Res. B 192 (2002) 171–175
where kB is Boltzmann constant. By fitting the data to Eq. (3), the o-Ps temperature T is obtained to be 962 189 K. Therefore, temperature of the Ps cloud obtained from the fit is consistent with the target temperature 1000 K and thus, production of thermal o-Ps is confirmed.
5. Summary Using our bunched eþ beam, we observed production of thermal o-Ps on the Au target and estimated its production rate as 32:3 6:7% for the target temperature of 1000 K. We are pursuing the improvement of the eþ beam intensity and the TOF resolution in order to reduce systematic and statistic uncertainty of the experiment. As for the laser system, final adjustment of the resonator is carried out to suppress a instability of the output wavelength. Line width of the laser currently obtained (17 pm) can compensate Doppler shift of thermal Ps resonance up to
175
300 K. Therefore, further study is necessary to produce sufficient number of thermal Ps at room temperature.
Acknowledgements This research is partially supported by Grantin-Aid for Scientific Research 09304034, 10354004, 10740126 and 12640286 from the Ministry of Education, Culture, Sports, Science and Technology of Japan.
References [1] P.M. Platzman, A.P. Mills Jr., et al., Phys. Rev. B 49 (1994) 454. [2] E.P. Liang, C.D. Dermer, Opt. Commun. 65 (1988) 419. [3] H. Iijima et al., J. Phys. Soc. Jpn. 70 (2001) 3255. [4] H. Iijima et al., Nucl. Instr. and Meth. A 455 (2000) 104. [5] T. Kumita et al., Appl. Surf. Sci. 149 (1999) 16. [6] N.N. Mondal et al., Appl. Surf. Sci. 149 (1999) 269.
Study on laser cooling of ortho-positronium T. Kumita a
a,*
, T. Hirose a, M. Irako a, K. Kadoya a, B. Matsumoto a, K. Wada, N.N. Mondal a, H. Yabu, K. Kobayashi b,1, M. Kajita c
High Energy Physics Group, Department of Physics, Tokyo Metropolitan University, 1-1 Minami-Ohsawa, Hachioji-shi, Tokyo 192-0397, Japan b Sumitomo Heavy Industries USA Inc., 666 Fifth Avenue, 10th floor, New York, NY 10103-1999, USA c Communications Research Laboratory, 4-2-1 Nukui-Kitamachi, Koganei, Tokyo 184-8795, Japan
Abstract We have been theoretically and experimentally studying details of laser cooling of ortho-positronium. Experimental apparatus consists of a pulsed positron beam generator, a long pulse wide bandwidth ultraviolet laser and a time-offlight system to measure kinetic energy of positronium atoms is constructed and tested. Using this apparatus, production of thermally activated positronium is confirmed. Its production rate is larger as the target temperature increases and ratio of thermally activated ortho-positronium to all c-ray annihilation events is estimated to be 32:3 6:7% for the target temperature 1000 K. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 03.75.F; 32.80.P; 36.10.D; 52.55.L Keywords: Bose–Einstein condensation; Positronium; Laser cooling; Positron beam
1. Introduction The exotic atom positronium (Ps), bound state of an electron–positron pair, has extremely light mass (1=918 of a hydrogen atom) and short lifetime. The spin singlet ground state, para-Ps (p-Ps), dominantly decays into two c-rays with a lifetime of 0.125 ns, while the spin triplet ground state, ortho-Ps (o-Ps), dominantly decays into three crays with a lifetime of 142 ns. Laser cooling of Ps brings interesting physics to us, such as Bose– Einstein condensation of Ps [1]. * Corresponding author. Tel.: +81-426-77-3328; fax: +81426-77-2483. E-mail address: [email protected] (T. Kumita). 1 Aculight Corporation, 11805 North Creek Parkway South, Suite 113, Bothell, WA 98011, USA.
Possibility of the o-Ps laser cooling is theoretically studied by Liang et al. utilizing the 1S–2P transition whose energy interval is 5.1 eV corresponding to the photon wavelength of 243 nm [2]. Since lifetime of the spontaneous transition from 2P to 1S is 3.2 ns, Doppler cooling of p-Ps is not possible due to its extremely short lifetime. Therefore, only cooling of o-Ps is considered hereafter. A characteristic feature of the laser cooling of o-Ps is that the recoil energy is large owing to the small Ps mass, thus photon recoil limit (0.6 K) is higher than the Doppler limit (7.5 mK). The large recoil makes o-Ps atoms at room temperature cooled down to the photon recoil limit in 32 cycles of the 1S–2P stimulated absorption and the 2S–1P spontaneous emission. In a sufficiently strong laser field, spontaneous emission from an o-Ps atom occurs every 6.4 ns on
0168-583X/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 2 ) 0 0 8 6 3 - 7
172
T. Kumita et al. / Nucl. Instr. and Meth. in Phys. Res. B 192 (2002) 171–175
the average, which is two times longer than the lifetime of the 2P state because populations of 1S Ps and 2P Ps are same. Thus the total cooling time is estimated to be 6:4 ns 32 200 ns, which is comparable to the lifetime of o-Ps. Note that o-Ps lifetime is also doubled in the strong laser field because the direct decay time (100 ls) from the 2P state is much longer than that from the 1S state. Wavelength of the cooling laser is usually swept during the cooling process to compensate Doppler shift due to motion of atoms while ordinary atoms are cooled. However, this technique is not applicable for the o-Ps laser cooling because of the short cooling time. Thus, a laser with wide line width, which covers Doppler broadening of the 1S–2P resonance without sweeping its wavelength, is required. The pulse duration also has to be long enough to cover the cooling time 200 ns. In this report, we describe Monte Carlo studies on laser cooling of o-Ps, the experimental apparatus for the cooling experiment, and the experimental result of thermal Ps observation.
2. Monte Carlo simulation Details of the Monte Carlo simulation code are described elsewhere [3]. The coordinate system in the simulation is defined in the following way: the positive z-direction is opposite to the direction of the eþ beam, x- and y-axes cross the z-axis at right angles. Ps atoms are supposed to be produced by implanting an eþ beam at the time t ¼ 0 on a metallic target placed at z ¼ 0. Initial space and time distributions of the Ps cloud are set to 0.75 cm (1r) on the x–y plane and 2.5 ns (1r), corresponding to size and pulse width of our eþ beam, respectively. Initial kinetic energies of the o-Ps atoms obey the Maxwell–Boltzmann distribution at 300 K. The cooling laser is assumed to have pulse energy 60 lJ, time duration 68 ns (1r), line width 11 pm (1r) and radius 2.5 mm (1r). It is divided into six beams and irradiates the Ps cloud along the x-, y-, zdirections. Transition rate between the 1S and 2P states are given as
P¼
Z
X2 C dx; 2 x0 ~ k ~ v x þ C2
ð1Þ
k the wave where x0 is the resonance of the 1S–2P, ~ number vector, ~ v the velocity vector of the Ps and x the laser frequency. The Rabbi frequency X is defined as X ¼ le=h, where e is the laser field and l is the dipole moment of the 1S–2P transition whose magnitude is 1:26 1029 cm. The quantity C stands for the relaxation constant which is assumed only for the spontaneous emission from the 2P state, i.e. C ¼ 2p=3:2 109 s1 . A stimulated absorption or emission modulates the Ps velocity by d~ v h~ k ¼d P; dt 2pmPs
ð2Þ
where d ¼ þ1 ð1Þ denotes absorption (emission). Position, velocity and energy state of each Ps atom are calculated using Eq. (2) every 0.5 ns step in the simulation. In order to examine the cooling process quantitatively, we define two quantities R5mm and T5mm . R5mm is number of o-Ps atoms stay in a spherical volume with the radius 5 mm after a certain cooling time normalized to the number of Ps
Fig. 1. Plot of R5mm and T5mm as functions of the laser detune.
T. Kumita et al. / Nucl. Instr. and Meth. in Phys. Res. B 192 (2002) 171–175
173
atoms initially produced. T5mm is temperature of the Ps cloud in the 5 mm spherical volume. Fig. 1 shows R5mm and T5mm after 220 ns as functions of the laser detune. One can see that 7% of generated o-Ps are cooled down to 1 K in 220 ns for detune of 170 GHz.
3. Experimental apparatus We have developed an experimental apparatus of the laser cooling system, which consists of an eþ beam generator and a laser system [4]. The beam generator consists of an RI source (22 Na, 50mCi) and a beam bunching system. Slow mono-energetic positrons converted in a tungsten mesh moderator are guided into a positron accumulator through a magnetic beam transport system. Then positron beam is bunched with the positron accumulator for the synchronization with a laser pulse and injected on a target to produce Ps atoms [5]. Pulse width of the bunched beam is 15 ns (FWHM) with the intensity of 0.005 eþ ’s/pulse while it is operated with 100 kHz repetition. The laser light is also irradiated to the target in a cooling chamber through a quartz window which seals the vacuum from air. The laser system for the o-Ps cooling experiments, illustrated in Fig. 2, consists of a Cr:LiSAF crystal which create a laser light with the wavelength of 972 nm, a second harmonic generator and
Fig. 3. A schematic view of the TOF measurement system.
a forth harmonic generator. Cr:LiSAF is chosen because of its long lifetime of the excited state (67 ls) and low gain, which result long pulse duration. The second and forth harmonic generators provide required wavelength of 243 nm utilizing two BBO (b-Ba borate) crystals in each generator. Parameters of the 243 nm laser are measured as follows: time duration 280 ns, pulse energy 40 J and line width 17pm (1r), which is consistent with the line width used in the Monte Carlo simulation for compensation of the Doppler broadening. To confirm the laser cooling process, we constructed a time-of-flight (TOF) measurement system [6] illustrated in Fig. 3. The TOF system consists of a cylindrical-shape lead collimator with a gap size of 5 mm and ten modules of NaI(Tl) c-ray detectors. A metallic target, on which Ps atoms are produced is placed at typically 1 cm downstream the gap.
4. Observation of thermal positronium
Fig. 2. A schematic view of the cooling laser system.
There are two categories of Ps atoms produced on a metallic target by injecting eþ beam: the Ps
174
T. Kumita et al. / Nucl. Instr. and Meth. in Phys. Res. B 192 (2002) 171–175
with eV kinetic energies due to the Ps work function for the target metal and thermally activated Ps (thermal Ps). Since the latter has lower kinetic energy (typically 39 meV at room temperature), high production rate of thermal Ps is required for the laser cooling experiment. By injecting the bunched eþ beams on a gold (Au) target, we observed decay time distributions of o-Ps for the target temperature of 300, 600 and 1000 K. As seen in Fig. 4, the o-Ps production becomes larger as the target temperature increases. The broad peak appearing around 300 ns is due to beam reflections at the target. Assuming contribution from the Ps with the work function energy is independent of temperature, increase of the o-Ps production is considered to be thermal Ps. A TOF measurement shows production of thermal Ps is negligibly small for the target temperature 300 K. Thus contribution of the thermal o-Ps can be extracted by subtracting the data for 300 K from that for 600 and 1000 K. Fig. 5 shows ratio of produced thermal o-Ps to all c-ray annihilation events, i.e. prompt decay, p-Ps and o-Ps. Production rate of thermal o-Ps, which is target of the laser cooling experiment, is evaluated to be 32:3 6:7% at the target temperature 1000 K. The TOF spectrum for the distance between the target and the gap of 1 cm is taken at 1000 K as
Fig. 5. Production rate of thermal o-Ps.
Fig. 6. TOF spectrum at 1000 K. A solid line shows a result of fitting of Eq. (1).
shown in Fig. 6. Energy spectrum of the thermal Ps is expected to obey the Maxwell–Boltzmann distribution. Considering correction for o-Ps velocity and lifetime, the TOF spectrum of thermal Ps is observed as 2 S0 S1 t S ¼ exp þ ; ð3Þ t t2 soPs-Ps where soPs-Ps is the lifetime of o-Ps and S0 and S1 are the fitting parameters. The quantity S1 is a function of T, temperature of the Ps cloud as Fig. 4. Decay curve of o-Ps produced on the Au target at the temperature of 300, 600 and 1000 K.
S1 ¼ ml2 =2pkB T ;
ð4Þ
T. Kumita et al. / Nucl. Instr. and Meth. in Phys. Res. B 192 (2002) 171–175
where kB is Boltzmann constant. By fitting the data to Eq. (3), the o-Ps temperature T is obtained to be 962 189 K. Therefore, temperature of the Ps cloud obtained from the fit is consistent with the target temperature 1000 K and thus, production of thermal o-Ps is confirmed.
5. Summary Using our bunched eþ beam, we observed production of thermal o-Ps on the Au target and estimated its production rate as 32:3 6:7% for the target temperature of 1000 K. We are pursuing the improvement of the eþ beam intensity and the TOF resolution in order to reduce systematic and statistic uncertainty of the experiment. As for the laser system, final adjustment of the resonator is carried out to suppress a instability of the output wavelength. Line width of the laser currently obtained (17 pm) can compensate Doppler shift of thermal Ps resonance up to
175
300 K. Therefore, further study is necessary to produce sufficient number of thermal Ps at room temperature.
Acknowledgements This research is partially supported by Grantin-Aid for Scientific Research 09304034, 10354004, 10740126 and 12640286 from the Ministry of Education, Culture, Sports, Science and Technology of Japan.
References [1] P.M. Platzman, A.P. Mills Jr., et al., Phys. Rev. B 49 (1994) 454. [2] E.P. Liang, C.D. Dermer, Opt. Commun. 65 (1988) 419. [3] H. Iijima et al., J. Phys. Soc. Jpn. 70 (2001) 3255. [4] H. Iijima et al., Nucl. Instr. and Meth. A 455 (2000) 104. [5] T. Kumita et al., Appl. Surf. Sci. 149 (1999) 16. [6] N.N. Mondal et al., Appl. Surf. Sci. 149 (1999) 269.