Slow and velocity-tunable beams of metastable He$_2$ by multistage Zeeman deceleration

1.2 MB·

by  Michael Motsch

Slow and velocity-tunable beams of metastable He by multistage Zeeman deceleration
2
Michael Motsch, Paul Jansen, Josef A. Agner, Hansju¨rg Schmutz, and Fr´ed´eric Merkt
Laboratorium fu¨r Physikalische Chemie, ETH Zu¨rich, CH-8093, Switzerland
He molecules in the metastable a3Σ+ state have been generated by striking a discharge in
2 u
a supersonic expansion of helium gas from a pulsed valve. When operating the pulsed valve at
room temperature, 77K, and 10K, the mean velocity of the supersonic beam was measured to be
1900m/s, 980m/s, and 530m/s, with longitudinal velocity distributions corresponding to temper-
atures of 4K, 1.9K, and 1.8K, respectively. The characterization of the population distribution
among the different rotational levels of the a3Σ+ state by high-resolution photoelectron and pho-
u
toionizationspectroscopyindicatedarotationaltemperatureofabout150Kforthebeamformedby
expansionfromtheroom-temperaturevalveandabimodaldistributionforthebeamproducedwith
the valve held at 10K, with rotational levels up to N(cid:48)(cid:48) =21 being populated. A 55-stage Zeeman
decelerator operated in a phase-stable manner in the longitudinal and transverse dimensions was
used to further reduce the beam velocity and tune it in the range between 100 and 150 m/s. The
internal-statedistributionofthedeceleratedsamplewasdeterminedbyrecordingandanalyzingthe
4 photoionizationspectrumintheregionofthelowestionizationthreshold,whereitisdominatedby
1 resonances corresponding to autoionizing np Rydberg states belonging to series converging to the
0 differentrotationallevelsoftheX2Σ+ groundstateofHe+. Thedecelerationprocessdidnotreveal
u 2
2 anyrotationalstateselectivity,buteliminatedmoleculesinspin-rotationalsublevelswithJ(cid:48)(cid:48) =N(cid:48)(cid:48)
n fromthebeam,J(cid:48)(cid:48) andN(cid:48)(cid:48) beingthetotalandtherotationalangularmomentumquantumnumber,
a respectively. ThelackofrotationalstateselectivityisattributedtothefactthatthePaschen-Back
J regime of the Zeeman effect in the rotational levels of the a3Σ+ state of He is already reached at
u 2
0 fields of only 0.1T.
3

] I. INTRODUCTION possibilitytousethecoldmolecularsamplestostudythe
h rovibrational energy-level structure of the a3Σ+ state of
p He and the X2Σ+ ground state of He+ by uphotoion-
- Inthelastdecade,severalmethodshavebecomeavail- 2 u 2
m ization and photoelectron spectroscopic methods. Be-
able to prepare molecules in the gas phase at low tem-
ing three- and four-electron systems, respectively, He
e peratures[1–4]. Goingbeyondthermalizationwithacold 2
h environment,thesemethodsallowforaprecisecontrolof and He+2 represent attractive systems to test the accu-
c racyofab-initio quantum-chemicalmethods. Inthetwo-
theexternalandinternaldegreesoffreedominmolecular
. electronsystemsH , HD,andD , theresultsofab-initio
s samples. Coldmoleculeswithtranslationaltemperatures 2 2
c calculationsofdissociationenergiesandrovibrationalen-
i in the range 100mK–1K may then find applications in ergylevelswhichincludeadiabaticandnonadiabaticcor-
s
precision spectroscopy [5, 6] and in the study of chemi-
y rectionstotheBorn-Oppenheimerapproximationaswell
h calreactivityatverylowcollisionenergiesandveryhigh as quantum-electrodynamics corrections up to the lead-
p energyresolution[7,8]. Alternatively,theymayalsorep-
ing (one-loop) contribution to the term proportional to
[ resent the starting point for further cooling steps toward
α4 were found to be in agreement with experimental re-
theultracoldregimebelow1mK[9–13]. Thechoiceofthe
1 sultswithinthecombineduncertaintiesoftheexperimen-
cooling method depends on the properties of the species
v tal and theoretical determinations [27–34]. Such calcu-
4 of interest [2, 14, 15]. In the case of paramagnetic atoms lations become increasingly challenging as the number
7 and molecules which can be entrained in a supersonic
of electrons increases, and the magnitudes of the rela-
7 beam, multistage Zeeman deceleration [16] and related
tivisticandquantum-electrodynamicscorrectionsarenot
7 techniques[17,18]arethemethodsofchoice: Thephase-
1. spacedensityofatomsandmoleculesinsupersonicbeams accurately known for He+2. In a recent high-resolution
spectroscopic study of the threshold ionization spectrum
0 is high and is preserved by a phase-stable operation of
of He∗, the level spacings between the lowest four rota-
4 the decelerator [19, 20], the method can be quantum- 2
tional levels of He+ could be determined at an accuracy
1 state selective [21], the final velocity of the particles can 2
: of 100MHz [35]. Comparison with the latest ab-initio
v be controlled and tuned over a wide range [22–24], and
calculations neglecting quantum-electrodynamics correc-
i the decelerated particles can be loaded into a magnetic
X tions [36] did not reveal significant deviations from the
trap [25, 26] for observation of slow decay processes or
experimentalresultsatthislevelofaccuracy,exceptper-
r
spectroscopic measurements requiring long observation
a hapsforthehighestrotationallevelobservedexperimen-
times.
tally. Infuture,wewouldliketoimprovetheaccuracyof
We describe here the use of multistage Zeeman decel- these measurements by using a slow beam of metastable
eration to generate slow and velocity-tunable beams of He , which motivated us to develop a He∗ source better
2 2
He2 molecules in the metastable a3Σ+u state (referred to suited to precision spectroscopic experiments.
as He∗ hereafter) in a setup tailored for future applica-
2
tionsinprecisionspectroscopy. Wealsodemonstratethe Asastartingpoint,asupersonicbeamofHe∗ waspro-
2
2
ducedwithapulsedsourceoperatedatcryogenictemper-
atures. The velocity of the molecules was subsequently
reduced to ≈100m/s by coupling the cryogenic beam
sourcetoamultistageZeemandecelerator. Frompulsed-
field-ionization zero-kinetic-energy (PFI-ZEKE) photo-
electron spectra of the X+2Σ+ ←a3Σ+ transition, we
u u
have determined the internal-state distribution of the
cold molecules in the beam and found rotational states
up to N(cid:48)(cid:48) = 21 to be populated. Deceleration experi-
ments with these molecules enabled the study of the ro-
tational state selectivity of the deceleration process and
a comparison with the deceleration of molecular oxy-
gen (O ) in the X3Σ− state, for which full selectivity
2 g
of the spin-rotational state |N =1,J =2,M =2(cid:105) was
J
achieved [21].
II. EXPERIMENT FIG. 1. (a) Schematic representation of the experimental
setup (not to scale). 1: Pulsed valve body and orifice, 2:
Discharge electrodes, 3: Cryogenic-liquid container, 4: skim-
He∗ isformedinagasofpureheliumunderconditions
2 mer, 5: multistage Zeeman decelerator, 6: UV laser beam, 7:
where the density allows for three-body collisions on the extraction electrodes, 8: MCP. The supersonic beam propa-
relevant time scales and collision partners of sufficiently gation direction, the UV laser beam, and the ion extraction
high energy are available to excite helium atoms to their direction are mutually orthogonal. (b) Zeeman effect in the
metastable states. Such conditions typically prevail in N(cid:48)(cid:48) = 1 rotational ground state of He2 (a3Σ+u). The low-
plasmas, such as those generated by striking an electric field-seekingstates,forwhichthedecelerationpulsesequence
discharge through helium gas [37, 38]. The large ratio is optimized, are indicated in red.
of magnetic moment to mass makes He∗ particularly at-
2
tractive for multistage Zeeman deceleration. Moreover,
the predicted radiative lifetime of 18s of He∗ [37] is suf- tector. The Zeeman decelerator was described in detail
2
in Ref. [23]. Consequently, only the beam source is pre-
ficiently long that no decay takes place on the millisec-
sented in detail in the following description of the exper-
ond timescale of the deceleration process. However, the
imental setup and procedure.
highvelocity(about2000m/s)ofasupersonicexpansion
of pure He from a reservoir held at room temperature
poses a problem. For the multistage Zeeman decelerator
usedinourexperiments,thedeceleration-solenoidgeom- A. The cryogenic discharge source
etry and the 8µs switching times of the pulsed decelera-
tion magnetic fields limit the maximal initial velocity of The pulsed supersonic beam is created by expand-
the particles to be decelerated to about 700m/s [2, 20]. ing helium gas into vacuum from a reservoir held at
The common approach to produce low-velocity super- high stagnation pressure (typically 2–6bar) through the
sonic beams consisting of seeding the species of interest 250µm-diameterceramicorificeofamodifiedEven-Lavie
inaheavyraregasisnotanoptioninthecaseofHe∗ and valve[40]. Toefficientlycoolthevalve,itsentirehousing,
He∗ because these metastable species carry sufficient in- originallymadeofstainlesssteel,wasreplacedbycopper
2
ternalenergytocausethePenningionizationofallother components. The valve assembly is mounted onto the
raregases[39]. Theoperationofthepulsed-valveassem- copper baseplate of a ≈0.7l cylindrical container which
bly, including discharge electrodes, at cryogenic temper- can be filled with cryogenic liquids, either liquid nitro-
atures is therefore the only viable option to reduce the gen for operation at 77K, or liquid helium for operation
initial velocity of the supersonic beam to below 700m/s. down to 4K. The temperature of the valve assembly is
To produce slow and velocity-tunable beams of monitored with a silicon diode (Lakeshore DT-670) di-
metastable helium molecules at low speed, we have com- rectly attached to it. Throughout this paper, we refer to
bined a pulsed cryogenic supersonic beam source with a thetemperaturemeasuredwiththissensorasthe“source
multistageZeemandeceleratorintheexperimentalsetup temperature”.
depicted schematically in FIG. 1 (a). The setup consists Startingwiththevalveassemblyatroomtemperature,
of the pulsed-valve assembly with discharge electrodes, it takes about two hours until the valve and discharge
the actual multistage Zeeman decelerator, and a detec- operatestablyatabout10K.Oncethedesiredfinaltem-
tionregionwherethemetastablemoleculesarephotoion- perature is reached, the nozzle-assembly temperature is
ized with UV laser radiation and the ions or electrons actively stabilizedwitha resistiveheater attachedto the
are extracted in the direction perpendicular to the beam valve. With feedback from a closed-loop proportional-
propagationaxistowardamicrochannel-plate(MCP)de- integral-derivative (PID) controller (Lakeshore 336), the
3
sourcetemperaturefluctuatesbylessthan0.1Kandcon- 2mm-diameter hole of a skimmer, which separates the
ditions remain stable for several hours. source chamber from the multistage Zeeman decelerator
The metastable helium molecules are generated by or the photoelectron spectrometer used to characterize
striking a discharge and forming a plasma in the ex- the beam properties and guarantees efficient differential
pansion region. For this purpose, the expanding gas pumping.
passes through a 10mm-long, 1.6mm-diameter channel
definedbytwocylindricalelectrodesdirectlyattachedto
the front plate of the valve and separated by an elec- B. The multistage Zeeman decelerator
trically insulating sapphire spacer (2mm length, inner
diameter of cylindrical channel 2mm). The discharge is ThemultistageZeemandeceleratorusedinthepresent
ignited by applying a typically 5µs long, −600V pulse work consists of an array of deceleration solenoids to
to the front electrode as soon as the density of the he- which current pulses are applied and was described in
lium beam in the channel is sufficiently high. In the Ref. [23]. The deceleration results from the force
discharge, the metastable (1s)(2s) 1S and 3S states
0 1 f(cid:126) =−∇E =∇(µ(cid:126) ·B(cid:126)) (1)
of atomic helium are populated, and the metastable he- Z Z mag
liumdimermoleculesareformed. Tofacilitateignitionof that acts on a paramagnetic atom or molecule with
the discharge during the short duration of the gas pulse magnetic moment µ(cid:126) and Zeeman energy shift E
mag Z
(typically a few tens of microseconds), the discharge is in the presence of an inhomogeneous magnetic field B(cid:126).
seeded with electrons emitted from a hot tungsten fil-
Particle-trajectorysimulationsindicatedthat55deceler-
ament [23, 41] and attracted toward the channel by a
ationstagesoperatedatacurrentof300Asufficetofully
+200V bias on the front electrode. Without the fil-
decelerateabeamofHe∗ withaninitialvelocityofabout
ament, ignition of the discharge required much higher 2
500m/s. The 55 solenoids (length 7.2mm, 64 windings
electric tensions, which unnecessarily heated the beam.
in four layers, 7.0mm inner diameter) used as decelera-
The discharge and nozzle operation parameters (electric
tion stages were grouped in two modules of each twelve
tension, timing, stagnation pressure) were optimized by
stagesandonemoduleof31stages. Thesemoduleswere
monitoring the yield of He∗ with the methods described
2 separated by pumping towers, as depicted in Fig. 2 of
in Section IIC.
Ref. [23].
We have also tested other discharge-electrode designs TheZeemaneffectinthelowestrotationallevel(N(cid:48)(cid:48) =
(e.g., high electric tension applied to a sharp tip in the 1) of the metastable a3Σ+ state of He is depicted in
u 2
expansionregion[23,41],cylindricalelectrodessurround-
FIG. 1 (b), where the low-field-seeking magnetic sub-
ingaglasscapillary)andfoundthebestyieldofHe∗ with
2 levels (mS = 1, drawn in red) suitable for deceleration
thechanneldescribedabove. Alldischargeconfigurations
experiments have a magnetic moment corresponding to
produced beams of metastable helium atoms, but He∗
2 twoBohrmagnetons. Becausethespin-rotationcoupling
was only observed in the configuration described above. constantoflowvibrationallevelsofthea3Σ+stateofHe
u 2
In the experiment, we observed a strong influence of is very small [42], the Zeeman effect in higher rotational
the discharge electrode temperature on the final velocity levels follows the same pattern as in the N(cid:48)(cid:48) = 1 level
of the beam of metastable helium atoms and molecules. (see also discussion in Section IV). To generate beams of
Thisobservationmaybeexplainedbythedischargeelec- He∗ with velocities in the range 100–150m/s, the decel-
2
trodes being part of the channel through which the gas erator was operated at a repetition rate of 8.3Hz by ap-
expands, thus constituting a virtual gas reservoir for the plying250Acurrentpulsestothedecelerationsolenoids,
expansionandbeam-formationprocess. Tocoolthiscrit- resulting in maximal magnetic fields on the decelerator
icalpartofthesetuptothelowestpossibletemperatures, axis of about 1.8T and Zeeman shifts of about 1.6cm−1
the discharge assembly was mechanically connected and for the low-field-seeking magnetic sublevels. The pulse
thermally linked to the copper front plate of the valve sequences were precalculated to reach the desired final
body. Moreover, the valve and discharge assembly were velocities for molecules in these sublevels. Optimal con-
surrounded by a thermal shield cooled with liquid nitro- ditions were obtained for phase angles between 35◦ and
gen, which served the purpose of minimizing the heat 45◦, as in our previous deceleration experiments with
loadofthermalradiationfromthehotfilamentandfrom deuterium atoms [20], metastable Ne [23], and O [21].
2
components of the vacuum chamber at room tempera-
ture.
Forfastdataacquisitioninspectroscopicexperiments, C. State-selective detection of the metastable He2
the source can be operated at the full repetition rate of molecules
25Hz of the Nd:YAG-pumped dye-laser system used to
detect the metastable molecules. In this case, a 650l/s The electric discharge described in Section IIA leads
(nominal pumping speed for He) turbo molecular pump totheproductionofmetastableHeatomsinthe(1s)(2s)
sufficed to maintain the pressure in the source vacuum 1S and3S statesandofmetastableHe moleculesinthe
0 1 2
chamber in the 10−5mbar range. After the formation of a3Σ+ state. Because both atoms and molecules are en-
u
He∗ molecules, the supersonic beam passed through the trainedatthesamevelocityinthesupersonicexpansion,
2
4
FIG.2. Ion-TOFspectrumobtainedfollowingUV-laserpho- FIG. 3. He∗ neutral-TOF spectra obtained for temperatures
2
toionization at a wave number of 34467cm−1 and extracting of the nozzle assembly of 300K, 77K, and 10K. The red
the He+ and He+ ions with a pulsed extraction field applied curves correspond to fits to the experimental data that led
2
1µs after the laser pulse. The electronic noise between 1.0– totheparameterssummarizedinTableI.Seetextfordetails.
1.25µsisanartifactoriginatingfromtheelectric-fieldswitch-
on process.
the delay time between the ignition of the discharge and
thephotoionizationlaserpulse. FromthemeasuredTOF
they cannot be distinguished on the basis of their times
distributions, the velocity distribution of the metastable
of flight to a detector placed along the propagation axis
molecule in the beam can be determined.
of the supersonic beam. To observe the atoms and the
molecules separately, they were photoionized with UV
laser radiation produced by second-harmonic generation
III. RESULTS
ofaNd:YAG-pumpedpulseddyelaserandthephotoions
wereextractedthroughafield-freetime-of-flighttubeto-
A. Characterization of the supersonic beam
wardamicrochannel-platedetectorusinganelectric-field
pulse in the range 1000–2000V/cm. The UV wave num-
ber (34467cm−1) was chosen to be above the ionization The He∗ neutral-TOF spectra obtained for nozzle-
2
threshold of the metastable a3Σ+ state of He , in a re- assembly temperatures of 300K, 77K and 10K by vary-
u 2
gion free of autoionization resonances, and also above ing the delay between the discharge ignition pulse and
that of the metastable (1s)(2s) 1S state of He. Con- the firing of the ionization laser are compared in FIG. 3.
0
sequently, both He+ and He+ were observed in the ion Analyzing these neutral-TOF distributions following the
2
time-of-flight(TOF)spectrum,asisillustratedinFIG.2. procedure described in Ref. [2, 23] enables one to ex-
Theenhancedelectronicnoisevisibleinthetime-of-flight tract, in each case, the average velocity of the molecular
spectrumbetween1.0–1.25µscorrespondstothetimeat beam and the corresponding standard deviation, from
which the extraction field was applied, i.e., 1µs after the which the translational temperature of the He∗ sample
2
laser pulse. can be estimated. From fits to the experimental time-of-
To measure the photoionization spectra of He∗, the flight profiles, the mean velocity and velocity spread of
2
signalwasintegratedoveratimewindowcenteredatthe the beam are determined to be v¯=(1875, 975, 530)m/s
arrival time of He+ and recorded as a function of the andσ =(95,65,60)m/sforsourcetemperaturesof(300,
2 v
excitationwavenumber,whichwascalibratedbyrecord- 77, 10)K. When the valve body is stabilized to 10K,
ing the optogalvanic spectrum of Ne and the transmis- the beam properties are sensitive to the discharge condi-
sion through an etalon simultaneously with each spec- tions, which results in day-to-day variations of the mean
trum. High-resolutionphotoelectronspectraofHe∗ were velocityby±10m/s. Theresultsofthisanalysisaresum-
2
recorded using the technique of PFI-ZEKE photoelec- marized in Table I and indicate that the main effect of
tron spectroscopy [43] following the same procedure as cooling the nozzle is a strong reduction of the average
in our earlier study of the He+ X+2Σ+ ← He∗ a3Σ+ velocityoftheHe∗ molecules,thestandarddeviationbe-
2 u 2 u 2
photoionizing transition [38]. The internal state distri- ing almost independent of the temperature of the nozzle
butionofthemetastablemoleculeswasdeducedfromthe assembly, particularly below 100K.
rotationalstructureofthephotoelectronspectraandthe The internal-state distribution of the molecular sam-
analysis of the Rydberg series observed in the photoion- ple in the supersonic beam was determined from the ro-
ization spectra, as explained in Section IIIA. tational structure of the photoelectron spectrum of the
The flight times of the metastable molecules from the origin band of the He+ X2Σ+ ←He∗ a3Σ+ photoioniz-
2 u 2 u
point where they were generated in the discharge to the ing transition. The photoelectron spectra obtained for
point where they were photoionized by the UV laser nozzle-assembly temperatures of 10K and 300K are dis-
(called “neutral-TOF spectra” hereafter) were obtained played in FIG. 4 (a) and (b), respectively. They were
by monitoring the resulting He+ signal as a function of recordedusingthetechniqueofPFI-ZEKEphotoelectron
2
5
FIG.4. PFI-ZEKEphotoelectronspectraoftheoriginbandoftheHe+ X2Σ+ ←He∗ a3Σ+ photoionizingtransitionobtained
2 u 2 u
for nozzle-assembly temperatures of (a) 10K (blue trace), and (b) 300K (red trace). The numbers along the upper and
lower assignment bars represent the values of the rotational quantum number N(cid:48)(cid:48) of He∗ of the dominant Q-type-branch (i.e.,
2
∆N = N+−N(cid:48)(cid:48) = 0) lines of the v+ = 0 ← v(cid:48)(cid:48) = 0 and v+ = 1 ← v(cid:48)(cid:48) = 1 bands, respectively. The weak lines designated
as S(1) and S(3) are ∆N = N+−N(cid:48)(cid:48) = 2 transitions originating from the rotational levels N(cid:48)(cid:48) = 1 and 3, respectively. The
two strong, sharp lines marked by asterisks correspond to autoionization resonances which strongly enhance the intensities of
the O(3) and O(5) lines. The intensities in both spectra were normalized to the intensity of the Q(1) transition. See text for
details.
tion resonances which strongly enhance the intensity of
TABLE I. Parameters describing the velocity distribution of
the O(3)- and O(5)-branch lines as a result of rotational
thebeamofHe∗obtainedfromananalysisoftheneutral-TOF
2 channel interactions, as discussed in detail in Ref. [38].
spectra shown in FIG. 3.
The very weak lines corresponding to the lower assign-
T (K) v¯(m/s) σ (m/s) T (K) mentbarformtheQ-typebranchofthev+ =1←v(cid:48)(cid:48) =1
Source v
300 1875 95 4.4 band. The observation of these lines indicates that the
v(cid:48)(cid:48) =1levelofthea3Σ+stateofHe isweaklypopulated
77 975 65 1.9 u 2
in the supersonic beam.
10 530 60 1.8
The higher signal-to-noise ratio obtained at a nozzle-
assembly temperature of 10K indicates that the density
spectroscopy [43] by monitoring the delayed pulsed-field of He∗ is almost an order of magnitude larger than when
2
ionization of high Rydberg states (principal quantum the nozzle assembly is operated at room temperature.
number n ≥ 100) located below the successive ioniza- Whereas the rotational-line-intensity distribution of the
tionthresholdsofHe∗ asafunctionoftheUVlaserwave spectrum recorded following expansion from the 300K
2
number. As explained in Ref. [38], removal of the 3sσ nozzle is well described by a rotational temperature of
electron leads to a dominant Q-type rotational branch about 150K, the spectrum of the He∗ sample obtained
2
in the PFI-ZEKE photoelectron spectrum of He∗, corre- with the 10K nozzle assembly is characterized by a bi-
2
sponding to transitions between rotational levels of the modal rotational intensity distribution, with a cold com-
neutral molecule and the ion having the same rotational ponent corresponding to a temperature of about 150K
quantumnumber,i.e.,∆N =N+−N(cid:48)(cid:48) =0(N(cid:48)(cid:48) andN+ for levels with N(cid:48)(cid:48) ≤ 7 and a much hotter (nonthermal)
aretherotationalquantumnumbersofHe∗ andHe+,re- componentcorrespondingtorotationallevelsintherange
2 2
spectively). The positions of the Q-type transitions of N(cid:48)(cid:48) =9−21withamaximumatN(cid:48)(cid:48) =17. The10Knoz-
the v+ =0←v(cid:48)(cid:48) =0 band for N(cid:48)(cid:48) values between 1 and zle assembly thus leads to a rotationally warmer sample
21 are indicated along the upper assignment bar at the thanthe300Knozzleassembly. Thissomewhatcounter-
top of FIG. 4 (a). Weak S-type lines (i.e., lines corre- intuitive observation may be explained by the large ro-
sponding to ∆N = N+ −N(cid:48)(cid:48) = 2) are also observable tational constant (B =7.10163(54)cm−1, see Ref. [38])
0
in FIG. 4, and so are two strong and sharp autoioniza- of He∗ and the fact that only odd-N(cid:48)(cid:48) rotational levels
2
6
vent the artificial enhancement of the photoionization
signal of molecules in specific rotational levels of the
a3Σ+ state,theUV-laserwavenumberwaskeptfixedat
u
34467cm−1, in a structureless region of the photoioniza-
tion spectrum. In FIG. 5, the black trace, with a broad
peak of He∗ molecules centered at a delay of 2.05ms,
2
represents the neutral TOF distribution recorded with-
out switching any of the deceleration solenoids and cor-
responds to He∗ molecules propagating at the original
2
beam velocity of ≈500m/s through the entire decelera-
tor. When running the decelerator with current pulses
of 250A and a phase angle of 35◦, the TOF profiles ob-
served in the region between 2.9ms and 3.3ms were ob-
tained. The profiles with maxima at 2.95ms (red trace),
3.1ms (black trace) and 3.25ms (blue trace) were ob-
tained under identical conditions except that the pulse
sequences used for the deceleration were precalculated
FIG. 5. Time-of-flight profiles of He∗ detected 60mm be-
2 to decelerate metastable molecules with initial velocities
yond the last stage of the decelerator. The photoionization
of 505m/s, 500m/s, and 495m/s, respectively. Analysis
laserwassetto34467cm−1,i.e.,aboveallrelevantionization
of the time-of-flight profiles with the methods described
thresholds, to avoid the artificial enhancement of the pho-
toionizationsignalofmoleculesinspecificrotationallevelsof inRef.[23]indicatesthatthefinalvelocitiesare150m/s,
the a3Σ+ state. The black trace with a broad TOF distri- 135m/s,and120m/s,respectively,inagreementwiththe
u
bution centered at 500m/s corresponds to the undecelerated valuespredictedbynumericalparticle-trajectorysimula-
beam. The three distributions presented at times of flight tions. The structure of the peaks corresponding to the
between 2.9ms and 3.3ms were obtained using deceleration decelerated molecules is a consequence of the evolution
pulse sequences designed to decelerate molecules with initial of the phase-space distribution in the decelerator [20].
velocitiesof505m/s,500m/s,and495m/s,respectively,ata
The neutral-TOF distributions presented in FIG. 5
phase angle of 35◦.
demonstrate the possibility to tune the final velocity
of the decelerated beam in the range between 100 and
150m/s. Although the present setup allows for the de-
of the a3Σ+ state are allowed by the generalized Pauli
u celeration to lower final velocities in a straightforward
principle: Thespacingbetweensuccessiverotationallev-
way,eitherbyoperatingthedeceleratoratalargerphase
els rapidly becomes larger than the thermal collision en-
angle or by applying larger deceleration magnetic fields,
ergy when the nozzle assembly is held at low tempera-
the detection of these slow molecules becomes increas-
ture and, consequently, cooling of the rotational degrees
ingly difficult. In particular, the rather large distance of
of freedom becomes very inefficient. The broad range
60mm between the last solenoid of the decelerator and
of rotational states that are populated in the slow beam
thedetectionvolumeinevitablyreducestheparticleden-
producedwiththecoldnozzleopensupthepossibilityto
sity by transverse defocussing and longitudinal disper-
study levels with rotational energy exceeding 3000cm−1
sion effects, which play a larger role at lower final veloc-
by high-resolution spectroscopy under the collision-free
ities [20]. For the efficient generation of beams with ve-
conditions of a supersonic beam.
locitiesbelow100m/s, decelerationpulsesequenceswith
optimized phase angles, such as those already used for
B. Multistage Zeeman deceleration of He∗ trap-loading schemes [26], might be useful to focus and
2
bunch the molecules into the detection region.
Whenthenozzleassemblyandthedischargeelectrodes
are cooled down to about 10K, the He∗ molecules are
2
entrained in a supersonic beam with a mean velocity of C. Spectroscopy and rotational-state distribution
≈500m/s,whichiswellbelowthemaximalinitialveloc- of the decelerated He∗2 beam
ity tolerated by our Zeeman decelerator. As mentioned
in Section IIB, 55 deceleration stages grouped in three The maximum intensity of the peak in FIG. 5 corre-
modules suffice to decelerate He∗ to final velocities of spondingtothedeceleratedHe∗moleculesisonlyafactor
2 2
100m/s. of three weaker than the maximum intensity of the un-
Time-of-flight profiles of He∗ detected at the exit of decelerated beam. Consequently, the internal-state dis-
2
the Zeeman decelerator, i.e., at a distance of about 1m tribution of the decelerated sample can be characterized
from the nozzle orifice, are displayed in FIG. 5. These by spectroscopic methods with almost the same sensi-
profiles were obtained by the procedure (UV-laser pho- tivity as achieved for the undecelerated beam (see Sec-
toionizationmassspectrometry)usedtocharacterizethe tion IIIA). Unfortunately, it was not possible to record
beam source and discussed in Section IIIA. To pre- PFI-ZEKE photoelectron spectra in the region beyond
7
FIG. 6. Photoionization spectra of He in the vicinity of the ionization threshold from the a3Σ+ state recorded for (a) an
2 u
undecelerated beam and (b) a beam decelerated to a final velocity of 135m/s. The assignment bars indicate the positions of
theN(cid:48)(cid:48) →np(N+ =N(cid:48)(cid:48)) RydbergstatesforN+ =1−9. ThelinesmarkedbyasterisksbelongtoN =N+±1Rydberg
(N=N+)
serieswhichareperturbedbyrotationalchannelinteractions. Theintensityoftrace(b)wasmultipliedbyafactorofthreeand
vertically offset for clarity.
the last coil of the decelerator. Indeed, the detection of Theunambiguousassignmentoftransitionsoriginating
the photoelectrons following extraction in the direction from rotational levels of metastable He∗ with N(cid:48)(cid:48) values
2
parallel to the beam propagation axis was hindered by between 1 and 9 demonstrates that many rotational lev-
thebackgroundsignaloriginatingfrommetastableatoms els are populated in the decelerated sample. Moreover,
and molecules and electrons generated by the discharge. the almost identical appearance of the spectra of the de-
The stray magnetic fields along the decelerator axis fur- celerated and undecelerated samples presented in FIG. 6
therpreventedthedetectionofelectronsextractedinthe implies that the multistage Zeeman deceleration process
direction perpendicular to the beam propagation axis. is not rotationally state selective in He∗. This obser-
2
The internal-state distribution of the decelerated sample vation stands in stark contrast to what is observed in
had therefore to be determined from the photoionization the multistage Zeeman deceleration of O , for which the
2
spectrum of He∗, which is dominated by contributions decelerated sample was found to consist exclusively of
2
fromautoionizationresonancesinthevicinityoftheion- molecules in the M =2 magnetic sublevel of the J =2
J
ization thresholds (see Fig. 9 of reference [38]). fine-structurecomponentoftheN =1rotationalground
state [21]. The reasons for this very different behavior
The photoionization spectra recorded in the region lie in the very different relative magnitudes of the rota-
34125–34185cm−1fordeceleratedandundeceleratedHe∗2 tional constants and spin-rotation splittings of these two
beams are compared in FIG. 6. These spectra are molecules, and in the fact that the Paschen-Back limit
dominated by N(cid:48)(cid:48) → np(N+ = N(cid:48)(cid:48))(N=N+,N+±1) Ry- of the Zeeman effect is reached at much lower magnetic
dberg series [35, 38]. Whereas the npN+ series, fields in the metastable a3Σ+ state of He than in the
(N=N+) u 2
for which the character of the Rydberg electron is πu−, X3Σ−g ground state of O2, as is discussed in more detail
areregularandwelldescribedbyRydberg’sformula,the in the next section.
npN+ andnpN+ seriesareofmixedσ+
(N=N+−1) (N=N++1) u
and π+ character and are strongly perturbed by rota-
u
tionalchannelinteractionswiththenp(N+−2) IV. DISCUSSION AND CONCLUSIONS
(N=N+−1)
and np(N++2) series, respectively. For clar-
(N=N++1)
ity, the assignments are only given for the regular series In this article, the design and operational character-
inFIG.6andthelinesbelongingtotheperturbedseries, istics of a source of slow, velocity-tunable beams of
which have also been assigned using the multi-channel- metastable He molecules (He∗) have been presented.
2 2
quantum-defect-theorymodelsdescribedinRefs.[38,44], The molecules are formed in a discharge, entrained in
are marked by asterisks. a supersonic expansion of He, and decelerated to low ve-
8
He∗ is then entrained by the He carrier gas in a super-
2
sonic beam having a mean velocity of about 500m/s.
Phase-stable deceleration to velocities as low as 100m/s
could be achieved using a Zeeman decelerator consist-
ing of 55 stages. The velocity distribution of the de-
celerated molecules was measured by time-of-flight spec-
trometric methods and their internal-state distribution
was determined from the analysis of well-resolved Ryd-
berg series converging on the rovibrational levels of the
X2Σ+ ground electronic state of He+. The low transla-
u 2
tional temperature of the decelerated sample (less than
100mK)andthebroadrangeofpopulatedrotationallev-
els (N(cid:48)(cid:48) ranging from 1 to 21) makes this source ideally
suitedtomeasurementsoftheRydbergspectrumofHe ,
2
of the ionization energy of He∗ and of the rovibrational
2
structure of He+ by high-resolution photoionization and
2
photoelectron spectroscopic methods.
Unexpectedly, the population of metastable molecules
inthesupersonicexpansionwerefoundtobedistributed
over many more rotational levels when the valve was
cooled down to low temperature than when it was op-
erated at room temperature. We interpret this obser-
vation as arising from the fact that the rotational spac-
ings in He∗ are much larger than the thermal collision
2
energy when the nozzle assembly is held at low temper-
ature, which effectively hinders rotational cooling. The
broad range of rotational levels in the supersonic expan-
sion enabled us to study how the Zeeman deceleration
process affects the rotational-state distribution. In con-
trasttoO ,forwhichmultistageZeemandecelerationled
2
to the formation of slow beams of molecules in a single
FIG.7. ComparisonoftheZeemaneffectintheX3Σ−ground
state of O (left column) and in the a3Σ+ stateg of He magnetic sublevel of a single spin-rotational level of the
2 u 2
(right column). Top row: Zeeman energy of the rotational groundelectronicstate[21],wedidnotobserveanyrota-
states N(cid:48)(cid:48) =1−5 in the magnetic-field range between 0 and tional state selectivity in the multistage Zeeman deceler-
20T.Bottomrow: Zeemanenergyinthemagnetic-fieldrange ation of He∗. The reason for the very different behaviors
2
where the Zeeman shifts are comparable to the spin-rotation observed in O and He∗ lies in the different nature of
2 2
splittings. Note the different scales used in these panels. the Zeeman effect in these two molecules, which itself
results from the fact that He∗ has a much larger rota-
2
tional constant than O (B =7.10163(54)cm−1 [38] vs.
2 0
locity in a multistage Zeeman decelerator. At the end 1.43767638(55)cm−1 [45, 46]) and spin-rotational split-
of the decelerator, the density of He∗ is sufficiently high tings more than two orders of magnitude smaller than
2
for measurements of the Rydberg spectrum of He2 by O2 [42].
photoionization spectroscopy. TheZeemaneffectinthegroundvibrationallevelofO
2
He in its metastable a3Σ+ state has almost 20eV of X3Σ− andHe a3Σ+ arecomparedinFIG.7. InO ,the
2 u g 2 u 2
internal energy, which is enough to ionize any atom or Paschen-Backregimeisnotreachedatthemagneticfields
molecule except He. Consequently, it is not possible to up to 2T used in our experiments because of the large
form a supersonic beam of He∗ seeded in any carrier gas fine-structuresplittingoftherotationallevels. Moreover,
2
other than atomic helium. A supersonic beam of pure interactions between magnetic sublevels of the same M
J
Heexpandingfromaroom-temperaturereservoirheldat values but belonging to different rotational levels cause
high stagnation pressure, however, has a mean velocity strongnonlinearitiesandavoidedcrossingsalreadybelow
of ≈2000m/s, which is beyond the range of velocities for 5T. In He∗, the Paschen-Back regime is already reached
2
which deceleration is possible with our multistage Zee- at fields of less than 0.1T, and the large rotational spac-
man decelerator [23]. Indeed, such a beam propagates ingspreventanyavoidedcrossingsevenatfieldsinexcess
by more than the 7.2mm length of the solenoids used of15T.Consequentlythelow-field-seekingmagneticsub-
for deceleration during the switch-off time of about 8µs levels of the different rotational levels of He∗ are subject
2
of the current pulses. To overcome this limitation, we toalmostidenticalZeemanshiftsatthefieldsusedinour
have developed a source which can be cooled to 10K deceleration experiments, which makes the deceleration
and at the exit of which He∗ is generated in a discharge. processcompletelyinsensitivetothedegreeofrotational
2
9
excitation. ACKNOWLEDGMENTS
Consideration of the Zeeman effect in the rotational
levels of the a3Σ+ of He , however, reveals that none of
u 2
the magnetic sublevels of the spin-rotational levels with We thank Richard Maceiczyk and Patrick Seewald for
J(cid:48)(cid:48) = N(cid:48)(cid:48) are low-field seeking (see FIG. 7 (d)). Mul- their support in the early phase of this work. This work
tistage Zeeman deceleration of He∗ therefore acts as a is supported by the Swiss National Science Foundation
2
filter which selects the two spin-rotational components (ProjectNo.200020-149216)andtheEuropeanResearch
with J(cid:48)(cid:48) = N(cid:48)(cid:48) ±1 and rejects the third. This property Council advanced grant program (Project No. 228286).
will represent an advantage in studies of the very con- M. M. thanks ETH Zu¨rich for the support through an
gested Rydberg spectrum of He . ETH fellowship.
2
[1] M.T.BellandT.P.Softley, Mol.Phys.107,99(2009). J. Narevicius, U. Even, and M. G. Raizen, Phys. Rev.
[2] S. D. Hogan, M. Motsch, and F. Merkt, Phys. Chem. Lett. 100, 093003 (2008).
Chem. Phys. 13, 18705 (2011). [23] A.W.Wiederkehr,M.Motsch,S.D.Hogan,M.Andrist,
[3] S.Y.T.vandeMeerakker,H.L.Bethlem,N.Vanhaecke, H. Schmutz, B. Lambillotte, J. A. Agner, and F. Merkt,
and G. Meijer, Chem. Rev. 112, 4828 (2012). J. Chem. Phys. 135, 214202 (2011).
[4] E. Narevicius and M. G. Raizen, Chem. Rev. 112, 4879 [24] T.Momose,Y.Liu,S.Zhou,P.Djuricanin,andD.Carty,
(2012). Phys. Chem. Chem. Phys. 15, 1772 (2013).
[5] J. van Veldhoven, R. T. Jongma, B. Sartakov, W. A. [25] S. D. Hogan, A. W. Wiederkehr, H. Schmutz, and
Bongers,andG.Meijer, Phys.Rev.A66,032501(2002). F. Merkt, Phys. Rev. Lett. 101, 143001 (2008).
[6] J. J. Hudson, D. M. Kara, I. J. Smallman, B. E. Sauer, [26] A.W.Wiederkehr,S.D.Hogan,B.Lambillotte,M.An-
M.R.Tarbutt,andE.A.Hinds, Nature473,493(2011). drist, H. Schmutz, J. Agner, Y. Salath´e, and F. Merkt.
[7] J. J. Gilijamse, S. Hoekstra, S. Y. T. van de Meerakker, Phys. Rev. A 81, 021402(R) (2010).
G. C. Groenenboom, and G. Meijer, Science 313, 1617 [27] J. Liu, E. J. Salumbides, U. Hollenstein, J. C. J. Koele-
(2006). meij, K. S. E. Eikema, W. Ubachs, and F. Merkt, J.
[8] M. Kirste, X. Wang, H. C. Schewe, G. Meijer, K. Liu, Chem. Phys. 130, 174306 (2009).
A. van der Avoird, L. M. C. Janssen, K. B. Gubbels, [28] J. Liu, D. Sprecher, Ch. Jungen, W. Ubachs, and
G. C. Groenenboom, and S. Y. T. van de Meerakker, F. Merkt, J. Chem. Phys. 132, 154301 (2010).
Science 338, 1060 (2012). [29] D. Sprecher, J. Liu, Ch. Jungen, W. Ubachs, and
[9] E.S.Shuman,J.F.Barry,D.R.Glenn,andD.DeMille, F. Merkt, J. Chem. Phys. 133, 111102 (2010).
Phys. Rev. Lett. 103, 223001 (2009). [30] K.PachuckiandJ.Komasa, J.Chem.Phys.130,164113
[10] E.S.Shuman,J.F.Barry,andD.DeMille, Nature467, (2009).
820 (2010). [31] K. Piszczatowski, G. L(cid:32)ach, M. Przybytek, J. Komasa,
[11] M.Zeppenfeld,B.G.U.Englert,R.Glo¨ckner,A.Prehn, K.Pachucki,andB.Jeziorski, J.Chem.TheoryComput.
M. Mielenz, C. Sommer, L. D. van Buuren, M. Motsch, 5, 3039 (2009).
and G. Rempe, Nature 491, 570 (2012). [32] G.D.Dickenson,E.J.Salumbides,M.Niu,Ch.Jungen,
[12] J. F. Barry, E. S. Shuman, E. B. Norrgard, and D. De- S. C. Ross, and W. Ubachs, Phys. Rev. A 86, 032502
Mille, Phys. Rev. Lett. 108, 103002 (2012). (2012).
[13] V.Zhelyazkova,A.Cournol,T.E.Wall,A.Matsushima, [33] D. Sprecher, Ch. Jungen, W. Ubachs, and F. Merkt,
J. J. Hudson, E. A. Hinds, M. R. Tarbutt, and B. E. Faraday Discuss. 150, 51 (2011).
Sauer, arXiv.org:1308.0421 (2013). [34] G.D.Dickenson,M.L.Niu,E.J.Salumbides,J.Komasa,
[14] S.Y.T.vandeMeerakker,H.L.Bethlem,andG.Meijer, K. S. E. Eikema, K. Pachucki, and W. Ubachs, Phys.
Nature Phys. 4, 595 (2008). Rev. Lett. 110, 193601 (2013).
[15] M. Lemeshko, R. V. Krems, J. M. Doyle, and S. Kais, [35] D. Sprecher, J. Liu, T. Kra¨henmann, M. Scha¨fer, and
Mol. Phys. 111, 1648 (2013). F. Merkt, J. Chem. Phys. (2014), accepted for publica-
[16] N. Vanhaecke, U. Meier, M. Andrist, B. H. Meier, and tion.
F. Merkt, Phys. Rev. A 75, 031402(R) (2007). [36] W.-C.Tung,M.Pavanello,andL.Adamowicz, J.Chem.
[17] A. Trimeche, M. Bera, J. Cromi`eres, J. Robert, and Phys. 136, 104309 (2012).
N. Vanhaecke, Eur. Phys. J. D 65, 263 (2011). [37] C. F. Chabalowski, J. O. Jensen, D. R. Yarkony, and
[18] E. Lavert-Ofir, L. David, A. B. Henson, S. Gersten, B. H. Lengsfield III, J. Chem. Phys. 90, 2504 (1989).
J. Narevicius, and E. Narevicius, Phys. Chem. Chem. [38] M.Raunhardt,M.Scha¨fer,N.Vanhaecke,andF.Merkt,
Phys. 13, 18948 (2011). J. Chem. Phys. 128, 164310 (2008).
[19] H. L. Bethlem, F. M. H. Crompvoets, R. T. Jongma, [39] P. E. Siska, Rev. Mod. Phys. 65, 337 (1993).
S.Y.T.vandeMeerakker,andG.Meijer, Phys.Rev.A [40] U. Even, J. Jortner, D. Noy, N. Lavie, and C. Cossart-
65, 053416 (2002). Magos, J. Chem. Phys. 112, 8068 (2000).
[20] A. W. Wiederkehr, S. D. Hogan, and F. Merkt, Phys. [41] T.Halfmann,J.Koensgen,andK.Bergmann, Meas.Sci.
Rev. A 82, 043428 (2010). Technol. 11, 1510 (2000).
[21] A. W. Wiederkehr, H. Schmutz, M. Motsch, and [42] C. Focsa, P. Bernath, and R. Colin, J. Mol. Spec. 191,
F. Merkt, Mol. Phys. 110, 1807 (2012). 209 (1998).
[22] E. Narevicius, A. Libson, C. G. Parthey, I. Chavez, [43] G.Reiser,W.Habenicht,K.Mu¨ller-Dethlefs,andE.W.
10
Schlag, Chem. Phys. Lett. 152, 119 (1988). Molecular Structure, Volume IV, Constants of Diatomic
[44] D. Sprecher, Ch. Jungen, and F. Merkt, J. Phys. Chem. Molecules (VanNostrandReinholdCompany,NewYork,
A 117, 9462 (2013). 1979).
[45] K. P. Huber and G. Herzberg, Molecular Spectra and [46] L. Tomuta, M. Mizushima, C. J. Howard, and K. M.
Evenson, Phys. Rev. A 12, 974 (1975).