Bu e gas cooling o a con inuous CO molecula
1
beam2
AMAN GANGWAR,1TOMMASO VEDOVELLO,2FRANCESCO PIO3
MERAFINA,3GIACOMO INSERO,1,4,6 SIMONE BORRI,1,4 PAOLO DE4
NATALE,1,4 GABRIELE SANTAMBROGIO,1,4,5,* AND SAGAR5
SUTRADHAR1,4
6
1Eu opean Labo a o y o Nonlinea Spec oscopy, LENS, Via Nello Ca a a 1, 50014 Ses o Fio en ino,7
I aly8
2
Dipa imen o di Fisica e As onomia, Uni e si y o Flo ence, Via Sansone 1, 50014 Ses o Fio en ino, I aly
9
3Uni e si à di Ba i, Piazza Umbe o I, 1, 70121 Ba i, I aly10
4Is i u o Nazionale di O ica, CNR, La go E. Fe mi 6, 50125 Fi enze, I aly11
5Is i u o Nazionale di Rice ca Me ologica, INRIM, Via Nello Ca a a 1, 50019 Ses o Fio en ino, I aly12
6Depa men o Expe imen al and Clinical Biomedical Sciences “Ma io Se io”, Uni e si y o Flo ence,13
Viale G. Pie accini 6, 50139 Flo ence, I aly14
*san amb [email p o ec ed]15
Abs ac : We cha ac e ise a new con inuous bu e gas cooled sou ce using CO molecules. We
16
show esul s abou he sou ce pe o mance conside ing di e en pa ame e s, like gas low a e,
17
nozzle size, and in e nal cell olume. The beam con ains
2.5×1014
molecules/(s s ) a abou
18
160 m/s. Mo eo e , o wo o a ional s a es we obse e an unexpec ed popula ion dis ibu ion
19
ha we en a i ely a ibu e o a lowe empe a u e inside he cell. Conside ing he impo ance o
20
bu e -gas cooling o expe imen s on ul acold molecules p epa ed wi h di ec lase cooling,
21
we belie e ha ou wo k will imp o e his key i s -s age cooling, accele a ing he adop ion o
22
molecules in he amewo k o quan um echnologies.23
1. In oduc ion24
Ul acold molecules a e e y p omising candida es o ad ancing mode n physics, wi h applica-
25
ions anging om undamen al physics o on ie echnologies such as quan um simula ion and
26
quan um compu a ion [1,2]. This is due o hei ich in e nal s uc u e, symme y, and s ong
27
in amolecula ields, which make hem ideal sys ems o in es iga ing new physics. Howe e , his
28
same complexi y poses signi ican challenges o cooling and de ec ion, making hese p ocesses
29
much mo e di icul compa ed o a oms. To o e come hese di icul ies, a i s cooling s age is
30
usually applied o he molecula sample. Vi ually all cu en expe imen s wi h lase -cooled
31
molecules ely on a bu e gas sou ce [3,4]. In his sou ce, molecules a e injec ed o p oduced
32
inside he cell, whe e hey he malise wi h a cold a e bu e gas, ypically helium o neon. The
33
molecula beam exi ing he sou ce is usually in an in e media e egime be ween e usi e and
34
hyd odynamic, i.e. expe iencing almos no o a ew collisions, espec i ely, a he exi ape u e.35
Bu e gas cooling echniques ha e been success ully applied o a a ie y o species, spanning
36
a b oad spec um o chemical p ope ies, including alkali a oms [5, 6], alkaline ea hs [7],
37
me als [8], chemically eac i e pola molecules [9–11], and polya omic molecules [12].38
In his wo k, we p esen ou newly-de eloped bu e gas sou ce ha we cha ac e ize using
39
ca bon monoxide. Al hough CO is no a pa icula ly in e es ing species o lase cooling, i
40
has he ad an age o being easily a ailable in a bo le. Mo eo e , by exci ing CO o i s i s
41
exci ed, me as able, elec onic s a e, he
𝑎3Π
s a e, cha ac e isa ion o he beam is s aigh o wa d.
42
Wi h he p esen se up o a con inuously seeded bu e gas beam, we can calcula e he o e all
43
e iciency o he sou ce om he know amoun o gas ha we le in o he sys em and he numbe
44
o cold molecules in he beam. Such measu emen s a e ex emely ha d when he species o
45
in e es a e p oduced ia lase abla ion and/o chemical eac ion. In ense e usi e beams can be
46
p oduced wi h o he molecules, oo, [7] bu CO is pa icula ly ad an ageous gi en i s ela i ely
47
low eezing empe a u e.48
We op imized he sou ce o maximal lux and minimal eloci y o he molecula beam ying
49
a ious combina ions o nozzle sizes and cell leng hs. We also measu e molecules in wo di e en
50
o a ional s a es in o de o es ima e o a ional he maliza ion inside he cell and p o ide an
51
es ima ion o he beam empe a u e.52
2. Theo e ical desc ip ion o he dynamics wi hin a bu e gas cell53
Bu e -gas cooling o a oms o molecules elies on collisions wi h cold bu e gas a oms a
54
c yogenic empe a u es, b inging he a ge species o low empe a u es. The bu e gas dissipa es
55
he ansla ional and in e nal ene gy o he a ge species, ideally wi hou chemical eac ion o
56
clus e o ma ion. This me hod o ene gy dissipa ion is independen o any speci ic ene gy le el
57
s uc u e, making i applicable o a wide ange o a ge species [7].58
A comp ehensi e o e iew o he dynamics in a bu e gas cell can be ound in Re s. [4,9].
59
He e, we ocus on ou lining he key pa ame e s associa ed wi h ou se up.60
Conside a bu e gas cell wi h a olume de ined by
𝑉cell =𝐴cell ×𝐿𝑐
, whe e
𝐿𝑐
is he leng h
61
o he cell in e io and
𝐴cell
is he c oss-sec ional a ea. Typically,
𝐿𝑐
is o he o de o a ew
62
cen ime e s, and
𝐴cell
o a ew cm
2
. The cell is main ained a a ixed empe a u e
𝑇
by a c yogenic
63
e ige a o , ypically be ween 1 K and 20 K. We use helium as bu e gas.64
Bu e Gas Flow h ough he cell65
The bu e gas exi s he cell h ough a ound ape u e wi h diame e
𝑑ape u e
o a ew millime e s.
66
The low a e o he bu e gas, He in ou case, is ypically measu ed in s anda d cubic cen ime e s
67
pe minu e (SCCM), whe e 1 SCCM is app oxima ely equi alen o a low o
4.5×1017
gas
68
pa icles pe second. Unde s eady-s a e condi ions, he numbe densi y o helium a oms in he
69
bu e cell,
𝑛He
, can be es ima ed by conside ing he cons an low o helium in o he cell,
𝑓He
,
70
and he pumping speed h ough he ape u e [4],71
𝑛He =4𝑓He
𝐴ape u e ¯𝑣He
,(1)
whe e
¯𝑣He
is he mean he mal eloci y o he helium a oms nea he ape u e. Fo a ypical low
72
o 1 SCCM o helium h ough an ape u e wi h a diame e o 3 mm in a bu e cell main ained
73
a a empe a u e o a ound 4 K, he numbe densi y is
𝑛He ≈2×1015 cm−3
. The p ope ies o
74
he a ge species eme ging om he bu e cell a e solely de e mined by collisions wi h he
75
bu e gas, which can be quan i ied by he mean ee pa h. The mean ee pa h is de ined as
76
𝜆CO =1/(𝑛He𝜎CO-He√︁𝑚CO/𝑚He +1)
, whe e
𝜎
is a collisional c oss sec ion and
𝑚
a mass. To a
77
good app oxima ion [9], 𝜎CO-He ≈𝜎He-He and 𝜎He-He ∼10−14 𝑐𝑚2[13].78
The Reynolds numbe (Re) is an impo an igu e o me i o he desc ip ion o a gas low.
79
Fo he bu e gas lows h ough an ape u e o diame e
𝑑ape u e
, he Reynolds numbe can be
80
app oxima ed as,81
Re ≈2𝑑ape u e
𝜆He
,(2)
whe e
𝜆He
is he mean ee pa h o he collisions o bu e gas a oms and i is exp essed as,
82
𝜆He =1/(√2𝑛He 𝜎He-He). The e o e, he Reynolds numbe can be exp essed as,83
Re ≈8√2𝑓He 𝜎He-He
𝜋𝑑ape u e ¯𝑣He
.(3)
The low egimes can be ca ego ised in o h ee dis inc ypes based on he Reynolds numbe ,
84
which e lec s he ex en o collisional in e ac ions nea he cell ape u e. In he e usi e egime
85
(
Re ≲1
), ew o no collisions occu nea he ape u e, and he beam p ope ies align wi h he
86
he mal dis ibu ion inside he cell. Mo ing in o he in e media e o pa ially-hyd odynamic
87
egime (
1≲Re ≲100
), collisions begin o in luence he beam p ope ies, al hough he low does
88
no ye exhibi ully luid-like cha ac e is ics. Finally, in he hyd odynamic egime (
Re ≳100
),
89
he bu e gas beha es like a luid, and he beam p ope ies s a o esemble hose o a supe sonic
90
expansion, leading o a colde and less di e gen beam.91
Ex ac ion e iciency o he cell92
The pa icles o he a ge species can be deple ed om he cooling egion o he bu e cell
93
h ough wo p ima y p ocesses: di usion and en ainmen . In he di usion p ocess, a signi ican
94
ac ion o pa icles may collide wi h, and adhe e o, he walls o he cell, while only a e y small
95
ac ion di use ou h ough he ape u e. The e ec i eness o di usion h ough he ape u e is
96
go e ned by he a io o he ape u e a ea o he su ace a ea o he cooling egion, which is
97
ypically
≤1%
. Consequen ly, o he emainde o his discussion, we assume ha he di usion
98
p ocess p edominan ly esul s in pa icle losses, he eby limi ing he ex ac ion e iciency o
99
pa icles om he bu e gas cell. In con as , he second p ocess in ol es en ainmen , whe e
100
pa icles a e ex ac ed o “pumped ou ” by he helium low con inuously eme ging h ough he
101
ape u e.102
Conside ing he di usion and he en ainmen p ocesses, we de ine wo cha ac e is ic ime
103
scales o pa icle mo emen wi hin he cell. The di usion ime scale,
𝜏di
, ep esen s he ime
104
equi ed o pa icles o he a ge species o di use o he walls o he cooling egion. The
105
pump-ou ime scale,
𝜏pump
, ep esen s he ime i akes o hese pa icles o a e se he cell
106
unde he in luence o helium low. Following Re . [4], we can w i e107
𝜏di =16 𝐴cell 𝑛He 𝜎CO-He
9𝜋¯𝑣He
.(4)
and108
𝜏pump =4𝑉cell
¯𝑣He 𝐴ape u e
(5)
The di usion and pump-ou imes a e ypically a ound 1–10 ms. The e iciency o pa icle
109
ex ac ion om he cell is go e ned by he in e play be ween hese wo ime scales. The e o e, i
110
is ins uc i e o de ine a dimensionless pa ame e 111
𝛾cell ≡𝜏di
𝜏pump
=4
9𝜋
𝑛He𝜎CO-He 𝐴ape u e
𝐿cell ≈𝜎CO-He 𝑓He
𝐿cell ¯𝑣He
.(6)
The alue o
𝛾cell
de ines he egime o pa icle ex ac ion. Fo ins ance,
𝛾cell ≲1
co esponds o
112
he “di usion limi ", whe e pa icles di use o he wall as e han hey a e ex ac ed om he
113
cell. This egime esul s in a low ou pu lux o a ge pa icles. In con as , when
𝛾cell >1
, he
114
sys em ope a es in he “hyd odynamic egime", esul ing in a beam ich in a ge species.115
While
𝛾cell
can es ima e he ex ac ion e iciency well, he e a e ins ances whe e his simple
116
es ima e b eaks down. Fo example,
𝛾cell
has no explici dependence on he ape u e diame e ;
117
howe e , i has been obse ed expe imen ally ha dec easing he cell ape u e diame e can
118
educe he ex ac ion e iciency. [14, 15] These measu emen s sugges ha he cell ape u e
119
diame e should no be oo small (less han 3 mm) o achie e good ex ac ion. I is hus help ul o
120
de e mine empi ically he op imal cell geome y. The gas low egime, desc ibed by he Reynolds
121
numbe , Eq.
(3)
, and he ex ac ion pa ame e
𝛾cell
, Eq.
(6)
a e ela ed by a ac o ha depends on
122
geome y:123
𝛾cell
Re ∝𝑑ape u e
𝐿cell
.(7)
This means ha , a leas in p inciple, i is possible o sepa a ely con ol he ex ac ion e iciency
124
(go e ned by
𝛾cell
) and he low egime (go e ned by Re). Mos bu e gas sou ces ope a e in
125
ei he he e usi e o he in e media e low egimes, and i is expe imen ally challenging o design
126
a beam ha is comple ely e usi e, has good ex ac ion, and has su icien he maliza ion.127
The maliza ion o CO molecules128
As p e iously men ioned, he cha ac e is ics o he a ge pa icles eme ging om he bu e cell
129
a e de e mined by he collisions wi h bu e gas a oms. The ansla ional empe a u e o he CO
130
molecules,
𝑇CO
, a e unde going
𝑁
collisions wi h he bu e gas, can be es ima ed as ollows [4],
131
𝑇CO (𝑁)
𝑇He ≈1+𝑇CO (0)
𝑇He
𝑒−𝑁/𝜅,(8)
whe e
𝜅=(𝑚CO +𝑚He)2/(2𝑚CO 𝑚He)
,
𝑇He
is he empe a u e o he bu e gas a oms in he
132
cell,
∼4
K, and
𝑇CO (0)
is he empe a u e o he a ge pa icles when hey a e in oduced
133
in o he cell,
∼70
K (see below). Using his o mula, we es ima e ha o CO molecules in
134
he bu e cell, abou 30 collisions a e needed o ansla ionally cool he molecules om oom
135
empe a u e o wi hin 2.5% o he empe a u e o he bu e gas a oms. Fo ypical alues o
136
𝜎CO-He ≈10−14 cm2
and He numbe densi y o 10
15−16/cm3
, he mean ee pa h is
0.01−0.2mm
.
137
The e o e, he he maliza ion leng h o he species in he bu e gas cell is ypically no mo e
138
han 30 ×0.2mm =6mm.139
Apa om ansla ional cooling o he a ge species, bu e gas cooling is also e ec i e
140
a o a ional quenching which is d i en by he aniso opy o he helium in e ac ion wi h he
141
molecule [16]. Typical o a ional elaxa ion c oss sec ions o molecules wi h helium bu e gas
142
a e o he o de
𝜎 o ∼10−(15−16)cm2
[17], which means ha a ound
𝜎CO-He/𝜎 o ∼10 −100143
collisions a e equi ed o elax a o a ional s a e. Wi h he pa ame e s gi en abo e, we es ima e
144
ha a cell leng h o 9–90 mm is equi ed o ull o a ional quenching.145
Fo wa d Veloci y o he CO beam146
In he in e media e egime, he a e age eloci y o he Helium,
¯𝑣He
, is highe han ha o CO,
147
¯𝑣CO
, by a ac o o
√︁𝑚CO/𝑚He
. The collisions o he Helium a oms wi h he CO nea he ape u e
148
a e p edominan ly in he o wa d di ec ion. The e o e, he CO molecules a e accele a ed in he
149
o wa d di ec ion, which esul s in a eloci y la ge han he he mal eloci y o he CO molecules
150
in he cell.151
CO molecules unde go app oxima ely
Re
2
collisions nea he ape u e [14]. Fo a small numbe
152
o collisions, he esul ing o wa d eloci y is gi en by [4],153
𝑣CO ≈¯𝑣CO +0.6 ¯𝑣He Re 𝑚He
𝑚CO
(9)
This sugges s a linea inc ease o o wa d eloci y wi h Re
(1≲Re ≲10)
and he e o e wi h
154
bu e gas low. Howe e , as
𝑣CO
app oaches
¯𝑣He
, he abo e model b eaks down, as he maximum
155
possible o wa d eloci y o he CO molecules is
1.4¯𝑣He
as de e mined by he ully hyd odynamic
156
expansions o he helium a oms [4]. We he e o e expec ha he o wa d eloci y should sa u a e
157
o his alue a la ge enough
𝑅𝑒
. Fo
Re ≳10
, he o wa d eloci y is desc ibed by he “sudden
158
eeze” model,159
𝑣CO (Re) ≈ 1.4¯𝑣He 1−4
Re4/5(10)
The ansi ion o sudden- eeze model occu s a he low a e o which he e a e collisions a a
160
dis ance la ge han one ape u e diame e om he ape u e. This happens o
Re ≳10
[14]. Fo
161
su icien ly high Re (speci ically Re ≳100), species can achie e a o wa d eloci y o 162
𝑣CO ≈1.4¯𝑣He (11)
3. Expe imen al sys em163
A schema ic o he acuum sys em is shown in Fig. 1. The acuum sys em consis s o wo
164
chambe s. The i s chambe con ains he bu e gas cell, which is connec ed o a wo-s age
165
pulse ube c yos a (PT425, C yomech). The second chambe houses he de ec ion egion. Bo h
166
chambe s a e pumped by u bo-molecula pumps, HiPace 1200 and HiPace 300 (P ei e Vacuum),
167
o he i s and second chambe , espec i ely. The sys em ypically ope a es a a p essu e o
168
app oxima ely
∼10−7
mba , which limi s he numbe o collisions wi h backg ound gas, he eby
169
acili a ing he o ma ion o a molecula beam. The p essu e is measu ed in bo h chambe s a he
170
oom- empe a u e pa o he chambe s.171
x
y
z
40K s age
4K s age
Bu e gas cell
PMT
Aluminium
shield
206 nm
lase beam
Molecula
beam axis
(a)
Cha coal
ins
Bu e gas
cell
40K s age
4K s age
z
y
x(b)
Fig. 1. O e iew o he o e all acuum sys em (a) and a de ailed a angemen o
he bu e cell (b). Cha coal g ains a e glued o coppe ins (as desc ibed in he ex )
and a ached o a 4K cold head. Fo he isual cla i y, only one o he cha coal in
a angemen is shown, on wo di e en sides in he wo pic u es o a oid obs uc ing
he iew o he cell. The bo om o he adia ion shield is closed by a se ies o coppe
s ipes a anged in a che on shape.
An aluminum shield is moun ed in con ac wi h he 40-K s age o he c yos a , while he bu e
172
cell is a ached o he 4-K s age. The aluminum shield unc ions as a adia ion shield, e ec i ely
173
educing he he mal adia ion load on he bu e cell. A
∼
23 mm hole a he on o he adia ion
174
shield se es as an ape u e o he molecula beam o eme ge. Addi ionally, wo o hogonal
175
po s on he adia ion shield, posi ioned pe pendicula o he molecula beam, p o ide access o
176
he exci a ion lase . The exci a ion lase in e cep s he molecula beam app oxima ely 30 mm
177
a e he cell nozzle. To u he minimize he he mal load on he bu e cell, he adia ion shield
178
is w apped 10 laye s o polyes e oil, double-sided aluminized, pe o a ed and in e lea ed wi h
179
10 laye s o non-wo en polyes e space ma e ial.180
Cha coal a c yogenic empe a u es is well known o i s abili y o e icien ly abso b helium. [18]
181
In many c yogenic bu e gas beam sou ces, he cell is su ounded by a small me al enclosu e
182
main ained a 4K, wi h cha coal glued on i s in e io walls. Ins ead, we de eloped a skele al
183
like coppe s uc u e moun ed o he 4K head o he c yos a . Fine cha coal g ains a e glued
184
o he coppe ins using a hin laye o he mally conduc i e epoxy glue. These ins a e hen
185
in eg a ed in o he coppe amewo k, which is connec ed o he 4K cold head. This solu ion
186
subs an ially inc eases he a ea co e ed by cha coal, he eby enhancing helium pumping capaci y,
187
while main aining good conduc ance owa d he u bo pump. The la ge coppe su ace co e ed
188
by cha coals allows o con inuous pumping o 20 SCCM o Helium o o e 2 days wi hou
189
using he u bo pump be o e hea ing he sys em o elease he adso bed helium, a alue much
190
highe compa ed o o he sys ems.191
3.1. Design o he bu e gas cell192
The schema ic o he bu e gas cell is shown in Fig. 2. The op pa o he cell is a ached o he
193
4K cold head o he c yos a . The cell is machined om a coppe block and ea u es a cylind ical
194
egion, which we e e o as he “cooling egion”. The empe a u e measu ed a he cell unde
195
no mal ope a ion condi ions is o 3.7 K.196
To 4K s age
Helium ube
Ca idge hea e
CO ube
PEEK
B ass
Ape u e
diame e : 5mm
Cooling egion bo e
diame e : 15 mm
leng h: 20 mm
Cylind ical PEEK piece
z
y
x
Fig. 2. The c oss-sec ional iew o he bu e cell illus a es he a angemen o he
ape u e and he gas inle ubes o CO and helium. A polye he e he ke one (PEEK)
componen is employed o he mally isola e he CO inle ube om he cold bu e
cell, as desc ibed in he ex . Fu he mo e, a cylind ical PEEK piece is in eg a ed o
p ecisely con ol he leng h o he cooling egion. The empe a u e o he CO ube nea
he bu e cell is egula ed using a ca idge hea e moun ed on a coppe elemen .
The nozzle o he cell is machined om a sepa a e coppe piece and subsequen ly a ached o
197
he bu e cell wi h a speci ic h eading, acili a ing a sys ema ic s udy o how ape u e dimensions
198
de e mine he sys em pe o mance. The cooling egion is designed as a cylinde wi h a diame e
199
o 15 mm. The exi nozzle has a conical shape, as ou lined in [19]. The gas inle con igu a ion
200
o he bu e cell is depic ed in Fig. 2. To p ecisely con ol he cooling egion leng h, cylind ical
201
PEEK pieces a e a ached o he back end o he cell. These PEEK pieces ea u e app op ia ely
202
sized holes o allow helium low in o he cooling egion, as shown in Fig. 2. By inco po a ing
203
hese pieces, we educed he o e all leng h o he cell, allowing o con olled a ia ion o he
204
cooling egion leng h. In his s udy, we es ed nozzles wi h diame e s o 2, 3, 4, and 5 mm, and205
cooling egion leng hs o 2, 3, 4, and 5 cm.206
Helium and CO gases a e supplied o he bu e gas cell om hei espec i e bo les, wi h he
207
low a es o bo h gases con olled by lowme e s (MCE-20SCCM-D-6MMCOMP o helium
208
and MCE-1SCCM-D-6MMCOMP o CO, by Alica ). The helium line passes h ough a cooling
209
cell solde ed o he 4-K s age o he c yos a . The cold helium is injec ed in o he bu e cell
210
ia a s ainless s eel capilla y ube wi h an ou e diame e o 3.2 mm, as depic ed in Fig. 2. The
211
CO gas is in oduced om he back end o he cell h ough a 3.2-mm-ou e -diame e coppe
212
capilla y ube. This ube is he mally isola ed om he bu e cell by a PEEK piece, and ca idge
213
hea e s a e used o keep he CO line a 70 K by a PID con olle o p e en eezing. This hea ing
214
a angemen is illus a ed in Fig. 2. Unde s anda d p essu e, CO lique y a 81.15 K and eezes
215
a 74.15 K.216
3.2. Op ical ansi ions, de ec ion, and he lase sys em217
BGC
30 mm
70 mm
245 mm
Top iew
Molecula
beam axis
206 nm
lase beam
40-K shield
ape u e 23 mm
x
z
y
PMT
.
Side iew
Fig. 3. Scheme o he molecula beam and de ec ion sys em.
To de ec CO molecules eme ging om he bu e cell, we i s exci e hem o a me as able iple
218
s a e wi h a pulsed lase . 1 mJ o ligh a 206 nm sa u a es he spin- o bidden ansi ion
𝑎3Π1(𝑣=219
0, 𝐽 =1) ← 𝑋1Σ+(𝑣=0)
. The
𝑎3Π1(𝑣=0, 𝐽 =1)
has a li e ime o 2.63 ms. [20] Then,
220
we de ec hei phospho escence on a pho o-mul iplie ube (PMT) (9813BQ, ET En e p ises),
221
posi ioned app oxima ely 24.5 cm downs eam om he exci a ion egion. I has an e iciency o
222
30% a 206 nm and i is moun ed behind a qua z window wi h a ansmission o 90% a 206 nm.
223
The PMT is 117 mm om he axis o he molecula beam and has an e ec i e en ance ape u e
224
o 35 mm in diame e . Such geome y allows o he collec ion o phospho escence signal unde
225
0.07 s . All oge he hese pa ame e s yield a o al de ec ion e iciency o 0.135%. We show a
226
scheme o his se up in Figu e 3. We acqui e he phospho escence signal wi h 13
𝜇
s esolu ion.
227
Fo he ange o eloci ies s udied in his wo k (100–250 m/s), his se o pa ame e s yields a
228
eloci y esolu ion o abou
±
10 m/s and de ec ion e iciency is independen on eloci y in i s
229
app oxima ion. A i s ape u e in he 40-K shield educe he di e gence o he beam, bu he ield
230
o iew o he PMT u he educe he po ion o he beam ha is de ec ed, yielding an o e all
231
di e gence o 0.012 s . This alue is la ge bu we belie e ha i is a use ul measu e because wi h
232
high-powe lase s one can decele a e and ans e se-cool beams wi h such cha ac e is ics.233
The elec onic g ound s a e
𝑋1Σ+
is bes desc ibed in Hund’s case (b), whe e he o a ional
234
s a es a e ully cha ac e ized by he o a ional quan um numbe
𝑁
. The pa i y o he o a ional
235
s a es ollows
(−1)𝑁
. In con as , he o a ional s uc u e o he elec onically exci ed s a e
𝑎3Π1
236
is desc ibed by he o al angula momen um quan um numbe
𝐽
. We cha ac e ized he bu e gas
237
cell by exci ing he CO molecules om he o a ional le els
𝑁=0
o he lowe componen o he
238
Λ
double in he
𝑎3Π1
(
𝐽=1
) s a e. Only o he da a shown in Figu e 8, we exci e molecules
239
also om he
𝑁=1
le el o he uppe componen o he
Λ
double in he
𝑎3Π1
(
𝐽=1
) s a e. A
240
mo e de ailed desc ip ion o he ene gy le els can be ound in Re [21].241
We employed a lase sys em simila o ha desc ibed in Re [22], which gene a es a pulsed
242
beam wi h an ene gy o app oxima ely 1 mJ a 206 nm, a epe i ion a e o 10 Hz, a pulse du a ion
243
o a ound 6 ns and a linewid h o app oxima ely 200 MHz.244
4. Resul s and discussions245
480.0 240.0 160.0 120.0 96.0 80.0
Veloci y (m/s)
0.5 1.0 1.5 2.0 2.5 3.0
Time (ms)
0
1
2
3
4
5
Molecules / (s s) (×1013)
0 SCCM He
12 SCCM He
16 SCCM He
20 SCCM He
Fig. 4. A i al ime o CO molecules in on o he PMT wi h 1 SCCM o CO, and 0
and 12, 16, 20 SCCM o helium, a 3-cm cell leng h and 5-mm ape u e, solid lines.
The dashed lines a e he i o a Maxwell-Bol zmann dis ibu ion o he da a. On op,
he a i al ime is con e ed in o he co esponden molecula eloci y.
Figu e 4 shows he phospho escence signal de ec ed by he PMT, bo h in he p esence and
246
absence o helium low in he cell. We co ec o he exponen ial decay o he popula ion in he
247
exci ed s a es and ake he o e all de ec ion e iciency in o accoun o calcula e he numbe o
248
molecules/(s s ) ha ha e been p epa ed by he lase in a single quan um s a e.249
Knowing he CO exci a ion ime and he phospho escence ime, and he dis ance be ween
250
exci a ion lase and PMT, we calcula e he eloci y o he molecula beam, shown on he ho izon al
251
axis on op o he g aph. The shi in he o e all p o ile and in he o wa d eloci y in dependence
252
o he helium low clea ly indica e he cooling e ec on CO. We a ibu e his e ec o he
253
he maliza ion o CO molecules wi hin he bu e cell. Collisions wi h He a oms migh ans e
254
pa o he me as able popula ion o he lowe o a ional s a es o he
Ω = 0
mani old on he
𝑎3Π255
s a e. Howe e , he li e ime o hose s a es a e abou wo o de s o magni ude longe han om
256
he
Ω = 1
s a es. The e o e, we conside hei con ibu ion o he obse ed signal o be negligible.
257
Fi ing he ime o ligh p o iles in Figu e 4 o a Maxwell-Bol zmann dis ibu ion yields
258
empe a u es o
69.2±0.1K
and
6.9±0.2K
o helium low a es o 0 and 20 SCCM, espec i ely.
259
Two di e en e ec s a e esponsible o he obse ed da a. Collisions wi h helium lowe he CO
260
2 4 6 8 10 12 14 16 18 20
Helium Flow Ra e (SCCM)
0.0
0.2
0.4
0.6
0.8
1.0
In eg a ed signal (a. u.)
3 mm Ape u e, 2 cm Cell
4 mm Ape u e, 2 cm Cell
5 mm Ape u e, 2 cm Cell
3 mm Ape u e, 3 cm Cell
4 mm Ape u e, 3 cm Cell
5 mm Ape u e, 3 cm Cell
3 mm Ape u e, 4 cm Cell
4 mm Ape u e, 4 cm Cell
5 mm Ape u e, 4 cm Cell
3 mm Ape u e, 5 cm Cell
4 mm Ape u e, 5 cm Cell
5 mm Ape u e, 5 cm Cell
Fig. 5. In eg a ed phospho escence signal in dependence on He low a e, o all
ape u e diame e s and cell leng hs. In all cases, la ge He low yields la ge CO signal.
eloci y om he o e 250 m/s expec ed o CO a a ound 70 K ( empe a u e o he CO line) o
261
below 150 m/s. Howe e , by u he inc easing he He low, we inc ease he Reynolds numbe
262
and sligh ly accele a e CO molecules.263
Figu e 5 shows he CO phospho escence signal in dependence on he He low a e, o all
264
sou ce con igu a ions. We see a mono onic signal inc ease wi h inc easing low, up o 20 SCCM,
265
which is he limi o ou He lowme e . The same is ue o he CO low a e, which is limi ed o
266
1 SCCM by he CO lowme e . The e o e, all da a shown in he ollowing a e measu ed wi h 1
267
SCCM o CO and 20 SCCM o He.268
We es Eq.
(6)
by measu ing he phospho escence signal in dependence on he cell leng h o
269
a ious nozzle sizes, Figu e 6. A sho e cell minimizes he p obabili y o di usion o he walls
270
and hus inc eases he ex ac ion e iciency,
𝛾
. Measu ed da a show a quali a i e ag eemen wi h
271
heo y. Howe e , al hough we do no expec signi ican dependence on he nozzle sizes, we know
272
om he li e a u e ha lowe ou pu is expec ed when he nozzle is oo small, see Re . [14]. This
273
is in ac wha we obse e wi h a nozzle diame e o 3 mm.274
We hen in es iga e he dependency o he o wa d eloci y on he nozzle diame e , which
275
in luences he Reynolds numbe cha ac e izing he low a he sou ce exi . Da a a e shown in
276
Figu e 7. We i a Maxwell-Bol zmann cu e o he eco ded phospho escence signal and ex ac
277
a peak o wa d eloci y. Al hough we obse e an o e all eloci y educ ion upon nozzle diame e
278
enla gemen , we also see la ge di e ence depending on cell leng h. Wi h longe cells, CO
279
molecules unde go mo e collisions and a e hus mo e likely o di use o he walls. The e o e, we
280
