High-resolution isotope-shift spectroscopy of Cd I Simon Hofs ass1 J. Eduardo Padilla-Castillo1 Sid C. Wright1 Sebastian Kray1 Russell Thomas1 Boris G. Sartakov1 Ben Ohayon2 Gerard Meijer1 Stefan Truppe1

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High-resolution isotope-shift spectroscopy of Cd I

Simon Hofs¨ass1, J. Eduardo Padilla-Castillo1, Sid C. Wright1, Sebastian Kray1, Russell

Thomas1, Boris G. Sartakov1, Ben Ohayon2, Gerard Meijer1& Stefan Truppe1∗

1Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany

2Institute for Particle Physics and Astrophysics, ETH Z¨urich, 8093 Z¨urich, Switzerland

(Dated: October 21, 2022)

We present absolute frequency measurements of the 1P1←1S0(229 nm) and 3P1←1S0(326 nm)

transitions for all naturally occurring isotopes of cadmium. The isotope shifts and hyperﬁne intervals

of the fermionic isotopes are determined with an accuracy of 3.3 MHz. We ﬁnd that quantum

interference in the laser-induced ﬂuorescence spectra of the 1P1←1S0transition causes an error of

up to 29(5) MHz in determining the hyperﬁne splitting, when not accounted for with an appropriate

model. Using a King-plot analysis, we extract the ﬁeld- and mass-shift parameters and determine

nuclear charge radius diﬀerences for the fermions. The lifetime of the 1P1state is determined to

be 1.60(5) ns by measuring the natural linewidth of the 1P1←1S0transition. These results resolve

signiﬁcant discrepancies among previous measurements.

Keywords: isotope shift, quantum interference, radiative lifetime

I. INTRODUCTION

The energy diﬀerences between isotopes of an atom or

molecule are called isotope shifts (ISs). In atoms, the

change in energy has two main contributions: the mass

shift (MS) and the ﬁeld shift (FS). The mass shift is

caused by changes in the electronic wavefunction upon

altering the nuclear mass, whereas the ﬁeld shift arises

from changes in the nuclear charge distribution [1]. The

shifts in the energy levels can be probed spectroscopically

and if the ISs are caused by the MS and FS only, there

is a linear relationship between the ISs of two transi-

tions, known as the King plot linearity. Small deviations

from this linearity can be a sensitive probe for higher-

order terms in the mass shift, the quadratic ﬁeld shift or

isotope-dependent nuclear deformation. In addition, pre-

cise values for the MS and FS factors, and deviations from

the expected linear behavior of the King plot, provide a

useful benchmark for atomic structure calculations.

Recently, it has been suggested that non-linearities in

a King plot can arise from physics beyond the Standard

Model (BSM) of particle physics [2–4]. A new intra-

atomic force between a neutron and an electron, medi-

ated by a new boson, can lead to an isotope-dependent

energy shift and the introduction of a Yukawa-type par-

ticle shift results in a non-linear King plot [5]. However,

this method of searching for new physics relies on a de-

tailed knowledge of the Standard Model contributions.

The Cd atom has recently attracted attention as a sensi-

tive probe for new physics because of its six even-even iso-

topes (even number of protons and neutrons) that have

a high natural abundance [6]. In addition, the Cd nu-

cleus (Z= 48) is only one proton pair below the Z= 50

proton shell closure. This signiﬁcantly reduces potential

non-linearities that arise from a deformed nucleus, which

∗Current address: Centre for Cold Matter, Blackett Laboratory,

Imperial College London, London SW7 2AZ.

currently limits the interpretation of isotope-shift mea-

surements with Yb[7, 8]. Cd possesses a strong cooling

transition and weak intercombination lines that can be

used for narrow-line cooling, precision spectroscopy, and

metrology [9, 10], ideal for a sensitive search for BSM

physics.

We recently showed that combining precise isotope-

shift spectroscopy with new, state-of-the-art atomic

structure calculations, allows determining the diﬀerences

in the radii of the nuclear charge distribution with high

accuracy [6]. This provides an alternative, independent

method to muonic X-ray spectroscopy or electron scatter-

ing. The charge radius is a fundamental property of the

atomic nucleus, and precise measurements of small dif-

ferences between isotopes through optical spectroscopy

provide stringent tests for nuclear theory [11, 12]. In ad-

dition, highly accurate charge radii diﬀerences are crit-

ical to understanding the nuclear contributions to non-

linearities in a King plot.

Here, we present the spectroscopic method used in [6]

to determine ISs of the bosonic 1P1←1S0and 3P1←1S0

transitions in Cd I and combine our previous results with

new measurements of the fermionic isotopes 111Cd and

113Cd. For the 1P1←1S0transition, we use enriched

Cd ablation targets and a polarization-sensitive detec-

tion scheme to assign spectral lines of diﬀerent isotopes

that otherwise overlap. We measure the hyperﬁne in-

tervals in the 1P1state of the two stable fermionic iso-

topes 111,113Cd with MHz accuracy by analyzing subtle

quantum interference eﬀects in the laser-induced ﬂuores-

cence. Knowledge of the exact lineshape allows us to

signiﬁcantly improve the ISs and resolve signiﬁcant dis-

crepancies among previous measurements. The radiative

lifetime of the 1P1state is extracted by ﬁtting the spec-

tral lineshape. The absolute transition frequencies are

determined with high accuracy. A King-plot analysis of

the two transitions allows extracting the intercept and

slope and to determine precise values for the diﬀerences

in the nuclear charge radii of the fermions. This measure-

arXiv:2210.11425v1 [physics.atom-ph] 20 Oct 2022

a) b)

τ=1.60(5)ns

τ=2.3(1)μs

1S0

F''=0 1S0

F''=0

1P1

F'=1

F'=1 F'=¹⁄�

F'=¹⁄�

F'=³⁄�

3P0,1,2

3P1

326nm 326nm

229nm 229nm

Bosons (I=0)

106,108,110,112,114,116Cd

Fermions (I=1/2)

111,113Cd

Target

buer gas

source

ablation

laser

charcoal

shield

slit

Glan-Taylor

polarizer

waveplate

mirror

LIF

emission

vacuum

window

Brewster

window

229/326nm

Δz

εL

εz

εx

θD

to PMT

lens

FIG. 1. a) A collimated atomic beam from a pulsed cryogenic

buﬀer gas source crosses the beam of a continuous wave UV

laser at ∆z= 0.73 m. The laser polarization is cleaned-up

with a Glan-Taylor polarizer and is varied using a waveplate.

b) Laser-induced ﬂuorescence (LIF) is detected with a pho-

tomultiplier tube (PMT). The linear laser polarization (L)

forms an angle θDwith the detector axis. Emitted photons

are polarized along x,z . c) Energy level diagram for naturally

abundant cadmium isotopes.

ment is also used to benchmark a recent high-level atomic

structure calculation of the MS and FS, with which we

ﬁnd excellent agreement [13]. In addition, we show that

the oﬀ-diagonal, second-order hyperﬁne interaction in the

fermions is /3 MHz, in good agreement with calcula-

tions [13].

The methods presented here are relevant to the ﬁeld

of collinear laser spectroscopy of rare isotopes produced

at accelerator facilities[14]. In these experiments, laser

spectroscopy is used to determine the fundamental prop-

erties of nuclei, including the nuclear spin, the magnetic

dipole moment, the electric quadrupole moment, and the

charge radius. Due to the low number of atoms produced

in these experiments, these properties are obtained from

strong transitions in the visible or UV part of the spec-

trum to increase the signal-to-noise ratio. We show that

quantum interference in the laser-induced ﬂuorescence of

strong transitions can cause signiﬁcant systematic errors

in determining the fundamental properties of nuclei.

II. EXPERIMENTAL SETUP

Figure 1a) shows a schematic representation of the ex-

perimental setup. We use a cryogenic buﬀer gas beam

source to produce a slow, pulsed beam of Cd atoms

with a brightness of about 1013 atoms per steradian per

pulse and a forward velocity of 100 −150 m/s[15, 16]. A

1064 nm beam from a pulsed Nd:YAG laser is focused

onto a solid Cd metal target and creates a hot cloud of

atoms by laser ablation. We use a multi-sample target

holder, enabling fast switching between targets with dif-

ferent isotopic compositions. The vaporized atoms are

cooled to 3 K by a continuous ﬂow of 1 sccm (standard

cubic centimeter per minute) cryogenic helium buﬀer gas

and are extracted into a beam through a 4 mm aperture

in the buﬀer gas cell. Charcoal-coated copper shields act

as a sorption pump for the buﬀer gas to keep the pressure

in the low 10−7mbar range. The atomic beam is probed

in a laser-induced ﬂuorescence (LIF) detector located

0.73 m from the source aperture. A slit with a width

of 2 mm along xrestricts the transverse velocities of the

atomic beam entering the LIF detector. This reduces the

Doppler broadening of the 1P1←1S0transition to be-

low 2.7 MHz for a forward velocity of 150 m/s. To excite

the 1P1←1S0transition, we use a frequency-quadrupled

continuous-wave titanium-sapphire (Ti:Sa) laser that can

generate up to 200 mW at 229 nm. For the 3P1←1S0

transition at 326 nm, we use a frequency-doubled con-

tinuous wave ring-dye laser (Sirah Matisse 2DX) with a

frequency doubling module (Spectra Physics; Wavetrain)

and a Pound-Drever-Hall locking scheme. This laser is

stabilized to a linewidth of 100 kHz using a temperature-

stabilized reference cavity. The maximum output power

is 80 mW in the UV. The laser polarization is puriﬁed

with an α-BBO-Glan-Taylor polarizer (1 : 105extinction

ratio). The angle of the linear laser polarization with re-

spect to the detector axis, θD, can be adjusted with a λ/2

waveplate. LIF of atoms that pass through the detection

zone is detected with a photomultiplier tube (PMT). The

laser beam exits the chamber through a Brewster window

to avoid back reﬂection into the interaction zone.

For the 1P1←1S0transition, we use a laser beam

with a diameter of 5 mm, nearly ﬂat-top intensity distri-

bution, and a laser power of 0.5 mW. This corresponds

to a saturation parameter of s0=Ipeak/Isat ≈1/400,

where Isat =πhcΓ/(3λ3)=1.1 W cm−2is the two-level

saturation intensity and Γ = 1/τ , with τ= 1.60(5) ns

being the excited-state lifetime (see below). The scat-

tering rate for small s0on resonance is approximately

s0Γ/2≈0.79 (µs)−1. The mean interaction time of the

atoms with the laser beam is about 30 µs so that each

atom scatters on average 24 photons. This results in a

radiation-pressure-induced Doppler shift of 1.7 MHz. In

relative measurements, such a shift is smaller than our

statistical error; for absolute measurements, it is negligi-

ble compared to the absolute uncertainty of the waveme-

ter. For the 3P1←1S0transition, 1 mW of laser power

in a Gaussian beam with a spot size of 10 mm (s0≈10) is

suﬃcient to saturate the transition. The Doppler broad-

ening due to the transverse velocity distribution in the

detector is 1.5 MHz and the radiation pressure detuning

due to the scattering of 10 photons is 0.33 MHz.

The laser wavelengths are measured with a wavemeter

(HighFinesse WS8-10) that is referenced to a calibrated,

frequency-stabilized HeNe laser at 633 nm and has a reso-

lution of 0.4 MHz. For the 229 nm transition, we measure

the frequency-doubled wavelength near 458 nm, whereas

for the 326 nm we measure the fundamental wavelength

near 652 nm.

III. ATOMIC BEAM SPECTROSCOPY

This section is split into three parts. In Section A we

show measured spectra of the 1P1←1S0and 3P1←

1S0transitions and explain the experimental methods

and data analysis used. We benchmark a sophisticated

model for the lineshape of the fermions and measure the

linewidth of the 1P1←1S0transition to infer the life-

time of the 1P1state. In Section B we discuss the re-

sults, analyze them in a King plot and calculate the nu-

clear charge radius diﬀerences for the fermions. Section

C focuses on systematic uncertainty, which is the lim-

iting factor in the accuracy of our measurements. We

compare our measurements in Cd with known properties

of the hyperﬁne intervals of the 3P1state and measure

well-known transitions in atomic copper at nearby wave-

lengths. Finally, the accuracy of relative measurements

is established by probing the linearity of our wavemeter

with an ultra-stable cavity.

A. Measurements

Figure 2 shows two ﬂuorescence spectra around 229 nm

for two diﬀerent laser polarization angles θD. The natural

linewidth of the 1P1←1S0transition and the hyperﬁne

splitting of the fermionic isotopes (∆HF) in Cd are of the

same order of magnitude as the ISs. The result is a spec-

trum with a signiﬁcant overlap of the spectral lines. This

overlap complicates the determination of the resonance

frequencies, making them dependent on the precise deter-

mination of the lineshape. The spectroscopic lineshape

of bosons and fermions is inherently diﬀerent. Bosons, in

contrast to fermions, have no nuclear spin and thus do

not exhibit a hyperﬁne structure (see Figure 1c)). In this

particular system of (F= 1/2, F0= 1/2,3/2), we see a

strong inﬂuence of quantum interference for fermions. To

separate between fermionic and bosonic peaks, we use

isotope-enriched targets and take advantage of the dif-

ferences between the ﬂuorescence emission patterns of

bosons and fermions.

A typical spectrum for 326 nm is shown in Figure 3.

The lineshape is dominated by Gaussian broadening with

a full-width at half maximum of 4.1 MHz. There is no

spectral overlap between the lines and the excited state

-1 0 1 2

-0.04

-0.02

0.02

ν-ν

114 (GHz)

Residuals

0.2

0.4

0.6

0.8

1.0

LIF signal (arb. units)

-1 0 1 2

-0.02

0.02

ν-ν

114 (GHz)

Residuals

Data

Fit

0.2

0.4

0.6

0.8

1.0

LIF signal (arb. units)

Data

Fit

106

108

111(³⁄�) 110

111(¹⁄�)

113(³⁄�)

113(¹⁄�)

112

114

116

106

108

111(³⁄�)

110

111(¹⁄�)

113(³⁄�)

113(¹⁄�)

112

114

116

θD=π/2

θD=0

FIG. 2. Isotope-shift spectrum of the 1P1←1S0transition

at 229 nm relative to 114Cd, measured under two diﬀerent

laser polarizations angles, ﬁtted with the quantum interfer-

ence model for fermions. The ﬁt residuals are shown below

the respective plot. a) θD=π/2 maximizes the laser-induced

ﬂuorescence emission of the bosons towards the detector. b)

θD= 0 suppresses the ﬂuorescence emission of the bosons

and thus improves the accuracy in determining the transition

frequencies of the fermions.

hyperﬁne levels of the fermionic isotopes are split by ap-

proximately 105Γ with negligible inﬂuence of quantum

interference. When the laser beam is not orthogonal to

the atomic beam, the spectrum of atoms with a high

forward velocity is shifted with respect to atoms with a

low forward velocity. By changing the alignment of the

laser beam to overlap the spectra, we reduce the residual

Doppler shift to ≤1 MHz. We ﬁt a Gaussian function to

the spectral lines and determine the line centers with a

statistical uncertainty of better than 1 MHz. The results

are summarized in Table II.

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High-resolutionisotope-shiftspectroscopyofCdISimonHofsass1,J.EduardoPadilla-Castillo1,SidC.Wright1,SebastianKray1,RussellThomas1,BorisG.Sartakov1,BenOhayon2,GerardMeijer1&StefanTruppe11Fritz-Haber-InstitutderMax-Planck-Gesellschaft,Faradayweg4-6,14195Berlin,Germany2InstituteforParticlePhysicsandAs...

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High-resolution isotope-shift spectroscopy of Cd I Simon Hofs ass1 J. Eduardo Padilla-Castillo1 Sid C. Wright1 Sebastian Kray1 Russell Thomas1 Boris G. Sartakov1 Ben Ohayon2 Gerard Meijer1 Stefan Truppe1

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