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Meas. Sci. Technol. 1 (1990) 93-105. Printed in the UK
REVIEW ARTICLE
Precision measurement aspects of
ion traps
R C Thompson
Blackett Laboratory, Imperial College, Prince Consort Road, London SW7 282, UK
Received 22 May 1989
Abstract. The use of ion traps in precision measurements of various kinds has been
growing rapidly in recent years. This review attempts to survey work in this area. It
starts with a brief description of the two main types of ion traps and how they work,
and discusses the different methods available for detection of ions in a trap and for
reducing their kinetic energy. The main part of the review deals with measurements
of the magnetic moments (g-factors) of electrons, positrons and ions in traps;
precision mass determinations, especially for rare isotopes produced in small
quantities; and measurements of microwave and optical transition frequencies in
ions, especially with applications to frequency standards in mind. The review
concludes with a very brief sketch of some of the other main uses of ion traps to
date, touching on the study of quantum jumps and ion crystals, and the
measurement of the lifetimes of excited electronic states of ions
1, Introduction
It is now more than 20 years since the first reviews of ion
traps appeared (Dehmelt 1967, 1969). Since that time, the
ion trapping technique has been applied to many different kinds of problems in physics, ranging from precise RF
spectroscopy to studies of the anisotropy of space, and
from the crystallisation of an ion cloud plasma at mK
temperatures to the quantum mechanics of a single ion
interacting with the radiation field. Clearly it is not
possible in a short article to cover all these aspects of the
technique, so this review concentrates on how various
precision measurements may be effected using ion traps.
An ion trap is an electrode structure which, by the
application of AC and/or DC potentials, possibly with the
addition of a magnetic field, is able to confine the
motions of charged particles to a small region of space.
These charged particles are generally electrons or singly
charged ions; however, some of the earliest experiments
were performed with charged aluminium particles
(Wuerker et a1 1959) and currently there are proposals to
make measurements on fully stripped and hydrogen-like
uranium (Moore et a1 1988). In the rest of this review the
word ‘ion’ will be used to refer to any charged particle in
a trap.
What then are the advantages for precision measurements offered by ion traps? These are summarised briefly
here but are dealt with more fully where they arise later in
the review.
(i) Ion traps provide a stable, well controlled environment which is free from many perturbations such as
0957-0233/90/020093
+ 13 $03.50 @ 1990 IOP Publishing Ltd
pressure effects or wall effects. There are in general
perturbations caused by the trapping fields but these can
be controlled and in some cases eliminated.
(ii) In many cases measurements can be made on very
small clouds or even a single particle. Also the observation time can be very long -in one case a single electron
was trapped for ten months (Gabrielse et al 1985) -thus
making the most efficient use possible of rare or exotic
species and avoiding any broadening of spectral lines due
to limited observation times (transit-time effects).
(iii) Cooling techniques can be used to extract kinetic
energy from the motion of confined particles. This
eliminates the Doppler effect and localises the particles at
the centre of the trap where the fields are smallest and
best approach the ideal of a three-dimensional simple
harmonic oscillator potential.
(iv) The above considerations treat the ion trap as a
convenient ‘box’ in which the ions are held. However, the
intrinsic properties of the trap itself are often used,
especially the oscillation frequencies of ions in the trap
potential. These are extremely well defined at the trap
centre and depend in a simple way on the charge to mass
ratio of the ions. They can also be employed for sensitive
detection of the ions.
The remainder of the review is structured as follows.
Section 2 deals with the principles of operation of traps,
as well as detection and cooling techniques. Sections 3 , 4
and 5 treat precision measurements of g-factors, inertial
mass and transition frequencies respectively. Finally,
other uses of traps are sketched in section 6 and future
prospects for the technique are assessed in section 7 .
93
R C Thompson
2. Principles of operation
2.1. Types of ion trap
The operation of a trap which aims to confine ions by
electromagnetic forces is limited by Earnshaw’s theorem,
which states that there cannot be a minimum of the
electrostatic potential in free space. The best that one can
do is to create a saddle-point in the potential, which is a
minimum in one direction and a maximum in another.
The lowest order potential of this form with axial
symmetry is the quadrupole potential given by
V = A(2z2 - r2)
(1)
+
where r2 = x2 y 2 and A is a constant. This potential can
be generated in a vacuum by electrodes having the shape
of the equipotential surfaces of equation ( l ) , which are
hyperboloids of revolution about the z axis. They consist
of two ‘end-caps’ (similar to hemispheres) and a ‘ring’
(like a doughnut).
( a ) Penning trap. The potential given by equation (1)
with A positive will trap a positive ion in the z direction
but as there is no restoring force in the r plane this is not
sufficient for a stable three-dimensional trap. However, if
a magnetic field B is applied parallel to the z axis then the
trajectory of a particle attracted towards the ring will
become a closed orbit consisting of a fast cyclotron
motion superimposed on a slow magnetron drift around
the centre of the trap, arising from the electric field. This
arrangement is called a Penning trap (Penning 1936) and
results in the three oscillation frequencies (e.g. Brown and
Gabrielse 1986):
Axial
w, = (4eVo/mR2)1’2
Modified cyclotron
w’, = wc/2
Magnetron
W
,
+ (w,2/4- 0 3 2 ) ” ~
= 0,/2 - (0,214 - 0,212)l ”
where the unperturbed cyclotron frequency is given by
w, = eB/m.
+
Here R2 = rg 22; where 2r0 and 22, are the diameter of
the ring and the separation of the end-caps respectively.
Vo and B are the applied potential and magnetic field and
e and m are the charge and mass of the ion. It should be
noted that the magnetron motion is unstable, i.e. energy
has to be supplied to it in order to reduce the size of the
orbit. Space charge effects limit the number density of a
spherical ion cloud to a maximum of n = 2.7 x 1015
(B/tesla)2/(M/amu) m-3. More detail can be found in
Brown and Gabrielse (1986), Toschek (1984) and
Wineland et a1 (1984).
( b ) Radiofrequency ( R F ) or Paul trap. The other main
type of trap was developed from earlier linear quadrupole
radio-frequency mass filters (Fischer 1959). It does not
use a magnetic field but instead an oscillating potential is
applied to the ion trap electrodes, generally in addition to
a DC one. The effect is to cause ions to oscillate at the
driving frequency R (the micromotion). However, as the
field is inhomogeneous, the net force time-averaged over
one cycle is non-zero so the ions act as if they were also
94
moving in an effective potential set up by the RF field (the
macromotion). Unlike a true potential, this ‘pseudopotential’ can have a global minimum in space and thus
give three-dimensional trapping. The pseudopotential
only provides an approximate description of the exact
Mathieu type equations of motion; detailed theory can be
found in reviews elsewhere (Dehmelt 1967, 1969,
Wineland et a1 1984, Toschek 1984). However, it is useful
as a guide and it gives rise to oscillation frequencies:
+
wp = 2e2Vi/m2Q2R4 2eUo/mR2
w t = 8e2Vg/m2R2R4- 4eUo/mR2.
The stability parameters a and q are defined by
a = - 16eUo/mR2R2and q = 8eVo/mR2R2.
Stable trapping is only found for certain limited ranges of
a and q which can be found in the reviews listed above.
The standard operating conditions have a and q in the
region of 0.0 and 0.4 respectively. Again, space charge
effects limit the maximum density which can be achieved,
as the ions ‘fill up’ the pseudopotential well created by the
trapping fields. This maximum density is typically
1013m-3, roughly comparable to the number density of a
gas at
Pa.
Both types of trap need to be placed in an ultra-high
vacuum (UHV) system in order to avoid collisions with
residual gas atoms which can eject ions from the trap.
Generally a base pressure at least as low as l o - ? Pa
(lo-’ mbar) is required, although a light buffer gas may
be introduced in an RF trap. Typical operating parameters
for some traps are listed in tables 1 and 2.
2.2. Detection of ions
The type of detection employed clearly depends on what
particles are in the trap and the sort of experiment being
performed. In some cases it is sufficient merely to know
how many ions there are while in other cases one wishes
to know something about the state they are in (e.g. the
polarisation state, electronic state or motional state).
(a) Electronic detection. If ions are moving between
electrodes then image currents induced in an external
circuit may be picked up and used for detection. This is
employed either directly (the so-called bolometric technique, e.g. Wineland et al 1978) or with an external drive
close to resonance which can be used in conjunction with
phase sensitive detection to amplify the signal, especially
for a single ion (Dehmelt and Walls 1968). This also
makes it possible to determine the spin and motional
state of a trapped electron via small shifts of the axial
frequency (Brown and Gabrielse 1986). An alternative
detection technique (e.g. Loch et a1 1987) makes use of
the damping of an external oscillating circuit of high
quality factor (Q) when it is connected across the endcaps. At resonance the axial oscillation of the ions is
excited and consequently the amplitude of the oscillation
in the circuit decreases as energy is extracted. The
amount of damping can be related to ion number and the
frequency at which it occurs determines the charge to
mass ratio.
Precision measurement aspects of ion traps
Table 1. Parameters of typical Penning traps. A selection of trap operating parameters is given for
four different precision experiments which are referred to later in the text. These give some idea of
the range of uses of ion traps. The symbols used are self-explanatory and are discussed in the text.
A small number of entries have had to be estimated due to the absence of specific data in the
publications. The references are: 1, Brown and Gabrielse (1986); 2, Bollinger eta/(1985); 3, Kluge
(1988).
Species
e-
P+
vDC
10.2
5.9
10
164 GHz
64 MHz
12 kHz
1
4K
< 10-8
1.8 x 1011
g-factor
4 x 10-12
External
circuit
1
3
53
5.0
3.2
76 MHz
10 MHz
660 kHz
B (TI
2fo (")
0;1271
w,127l
w1
,271
n (m-3)
Total N
Temperature
p (Pa)
elm (C k g - ' )
Use
Accuracy
Detector
Reference
Section
40
4K
< 10-8
9.6 x 107
mass
4 x 10-8
External
circuit
1
4.3
9 ~ e +
122CS+
1.o
8.0
0.82
5.9
16
740 kHz
70 kHz
3.3 kHz
109
50
eV
10-7
7.9 x 105
mass
2 x 10-7
Time of
flight
3
4.2
8.3
1.4 MHz
190 kHz
13 kHz
3 x 1013
1000
<0.1 K
<lo-?
1.1 x 107
303 MHz
2 x 10-13
cw laser
fluorescence
2
5.2
-
Table 2. Parameters of typical RF traps. As for table 1 except that the classic 1959 experiment with
charged dust particles has been included for comparison. The references are: 1, Wuerker e t a /
(1959); 2, Cutler eta/(1986); 3, Bergquist eta/(1987);4, Blatt eta/(1983).
Species
AI particles
lg9Hg+
198Hg+
Q12.n
2ro (")
210 Hz
18
0
0.0
1400
0.34
25 Hz
13 Hz
-4 x 109
100
2
500 kHz
40
37
- 0.04
750
0.38
44 kHz
47 kHz
3 x 1013
106
500 K
(He)
4.8 x i o 5
40.5 GHz
10-13
Lamp
fluorescence
21 MHz
0.93
0
0.0
730
0.38
2.8 MHZ
1.4 MHz
4.8 x i o 5
282 nm
3 x 10-11
cw laser
fluorescence
2
5.2
3
5.3
vDC
a
VAC
4
%I271
(41271
n (KI-~)
Total N
Temperature
p (Pa)
elm (C kg-')
Use
Accuracy
Detector
Reference
Section
0.008
-
Eye
1
1
( b ) Optical detection. For ions whose resonance
wavelength is attainable using lasers this is probably the
most sensitive form of detection. It involves simply
irradiating the ions on resonance and looking for fluorescent emission either at the same wavelength or at a
different one also emitted in decay from the excited state.
This has been shown to be sensitive enough to give a
good signal to noise ratio even for a single ion of barium
(Neuhauser et al 1980), magnesium (Wineland and Itano
1981, Diedrich and Walther 1987) or mercury (Bergquist
et a1 1987). It has been used in many experiments in
conjunction with optical pumping (e.g. Blatt et a1 1983)
or laser cooling (e.g. Bergquist et a1 1987) so that in these
-
1
1.6 mK
<lo-?
1?1ybi
500 kHz
40
35
-0.04
900
0.51
76 kHz
58 kHz
10"
105
- 1 eV
(He)
5.6 x 105
10.5 GHz
10-11
Pulsed
laser
fluorescence
4
5.2
cases detection is closely coupled with other parts of the
experiment.
(c) Direct detection of ions. The first two techniques
discussed are non-destructive: the ions remain in the trap
after detection. Destructive detection is also possible: in
this case the trap must be reloaded after each detection
event. Typically in such measurements the ions are
released from the trap and collected on a channel plate
detector (Schnatz et a1 1986, Kern et a1 1988). This is
clearly quite a sensitive method but requires a continuous supply of ions, which may not always be possible.
If the time taken by the ions to reach the detector is
measured, then it is possible to determine the motional
95
R C Thompson
state of the trapped ions; thus the method can be used to
detect resonance of a driving field with an oscillation of
the ions in the trap (Schnatz et al 1986).
2.3. Cooling techniques
The depths of the potential wells in ion traps are usually a
few eV or higher and trapped atomic particles tend to
have fairly high energies (compared to kT at room
temperature). There are a number of reasons why i t is
often necessary to remove energy from the ions and hence
‘cool’ them. First, it reduces losses of ions due to their
‘boiling’ out of the trap. Second, it localises them near the
centre of the trap and increases the cloud density. Third,
it may be used to remove energy coupled into the ionic
motion by one of the detection methods discussed above
or by the trapping fields in an RF trap, which cause ‘RF
heating’. Fourth, for precision measurements the
Doppler broadening and shift of spectral lines may need
to be reduced. Finally, in some experiments ions enter the
trap with very high energy (e.g. positrons from a j’
source; see Schwinberg et a1 1981a) and need to be
strongly cooled in order to proceed with the
measurements.
(a) Buffer gas cooling. Perhaps the simplest way to
cool ions is to introduce a light buffer gas into the UHV
system (e.g. Blatt et a1 1983). At sufficiently low pressures
(typically of order
Pa for hydrogen and helium) the
main effect is to damp the ionic motion and hence reduce
the temperature. This only works in an RF trap - in a
Penning trap any collisions will tend to increase the size
of the magnetron orbit. Obviously the lowest
temperature which can be achieved in this way is that of
the buffer gas so this technique cannot generally be used
to cool below room temperature.
( b ) Resistive cooling. In section 2.2 it was mentioned
that the motion of ions in a trap generates image currents
which can be used for detection. If a resistor R is
connected across the end-caps then the image currents
dissipate heat in the resistor and in this way the axial
motion can be damped at a rate proportional to e2R/m
(Dehmelt and Walls 1968, Holzscheiter 1988). The lowest
temperature attained is limited by Johnson noise in the
resistor; however, if the tuned circuit is immersed in
liquid helium this cooling process can be made very
effective, especially for electrons (e.g. Van Dyck et a1
1986).
( e ) Laser cooling. For atomic ions the most effective
method of cooling is to make use of radiation pressure
from a laser tuned just below resonance with a transition
in the ion. Ions can then only absorb light when they
move towards the laser, so they are slowed down a small
amount by the momentum of each photon absorbed (in
contrast, the re-emission process is isotropic). The cooling limit is generally given by kTmin
= hy/2, where y is the
radiative width of the excited state, as shown in numerous reviews (Stenholm 1986, 1988, Itano and Wineland
1982). For magnesium ions one photon (at 280nm)
changes the ionic velocity by 60 mm s - l and it takes
roughly 6000 absorptions to cool from room temper96
ature to Tmin,
which is about 1 mK. This cooling can take
place in much less than one second and only requires a
laser power of perhaps 10 pW due to the small size of a
typical ion orbit. In a Penning trap the laser illumination
has to be inhomogeneous in order to cool both magnetron and cyclotron motions simultaneously and this
leads to a slightly more complicated situation (Itano and
Wineland 1982, Thompson 1988).
Laser cooling is a powerful technique and has been
used extensively to produce and study ultra-cold ions in a
room temperature apparatus. However, it is only suitable
for a small number of ionic species, so ‘sympathetic
cooling’ has also been developed, where one ionic species
is cooled by collisions with a second, laser-cooled species,
also stored in the same trap (Larson et a1 1986). This
should enable the technique to be more widely used in
future, especially as sympathetic cooling perturbs the ion
less than direct laser cooling.
3. Measurement of gfactors
3.1, The geonium system
For an electron, the g-factor is defined as the ratio of its
spin magnetic moment to the Bohr magneton, p B =
ehf2m. This has been measured to a fractional precision approaching
using a single electron in a
Penning trap. This system is often called ‘geonium’ (see
Dehmelt 1988) as it consists of an electron bound to the
earth via the trap potential. The geonium pseudoatom
has four independent contributions to its energy: the
cyclotron, axial and magnetron motions discussed in
section 2.1 and the spin energy which depends on the spin
orientation with respect to the magnetic field. As with
more conventional atoms, an energy level diagram can be
constructed to show the possible states (Brown and
Gabrielse 1986).
3.2. Measurement technique
The principle of the technique is to measure both the
cyclotron frequency of the electron (0, = eB/m) and its
spin precession frequency (0, = gp,B/h = igw,) in the
same magnetic field B. The ratio yields the g-factor. Two
features make the experiment potentially very accurate.
First, U, can be determined from the three oscillation
frequencies in the trap to high accuracy from the relation
w,’
= w;2
+ w; + w,”.
This relation is exact even if the magnetic field is
misaligned with respect to the trap axis and if the trap
potential is not axially symmetrical (Brown and Gabrielse 1982, 1986). Higher order trap imperfections are
tackled by working at trap centre (using cooling techniques) where they have less effect, and by adding extra
compensation electrodes to fine-tune the potential to the
correct form (these are shown in figure 1).
Second, w, is not measured directly but rather the
‘anomaly’ frequency CO: = w , - wb. As g - 2 is only of
Precision measurement aspects of ion traps
I
I
I
'
I
l
I
I
[
I
I
1
1
Field emission point
I
2
I
I
'
I
I
I
1
ft
IcmiO
Metalked strip
2
Oiinl
2
0
1
Motor
1
i-
0 5
2
1
Gloss
is removed as described above, while the increase in
magnetron energy compresses the orbit as required, due
to the unstable nature of the magnetron motion. At exact
resonance the axial motion decouples, and this feature
can be used to give a precise determination of w,.
The final aspect of this experiment is the use of a
'magnetic bottle', that is, an extra (small) magnetic field
varying quadratically with r a n d z , to measure wb and m i .
The field arises from a ring of ferromagnetic material
incorporated into the ring electrode, and one effect is to
make w, depend on the degree of excitation in each of the
three motions and the spin state. Thus, if 0, is monitored
while an RF drive is applied at a frequency close to ob,a
shift of typically a few Hz is seen at resonance. The line
shape is asymmetrical due to the one-sided distribution
of energy in the axial motion (see figure 2), and can be
fitted to determine wb, which is close to the sharp lowfrequency edge. Similarly, the anomaly frequency is
found by monitoring 0, while irradiating close to wk. If a
spin-flip transition occurs, then 0, jumps by a certain
amount. The rate at which these jumps occur shows a
resonance at wk.
Tungsten
Figure 1. Scale drawing of an experimental Penning trap
used for the study of electrons (Brown and Gabrielse 1986).
The magnetic field is vertical and the two compensation
electrodes can be seen as well as the three normal
electrodes (two endcaps and one ring).
order
the anomaly frequency is small and need
only be measured to an accuracy of say lo-* for a lo-"
precision in g.
We now consider the cooling mechanisms and the
related question of detection of resonances. For the
cyclotron motion the cooling is automatic and follows
from the usual Larmor formula for an accelerating
charge, yielding a decay constant for the energy:
y c = 4e2w:/12m,mc3
which for wJ2z = 160 GHz ( B = 5.9 T) gives lkic =
0.08 s, corresponding to strong damping. However, for
the other two motions the radiative damping is very slow,
so another mechanism is required. The axial motion is
cooled by coupling it to an external resistance (kept at
about 10 K to reduce noise) as described in section 2.2.
Using R of order lo5 R, lly, is typically 0.02 s. Although
the damping is strong, the axial motion still has a quality
factor Q of 10' or so, allowing precise measurement of its
frequency. This is achieved by monitoring the voltage
across R as an axial drive is applied and is swept across
the resonance. The drive is in fact applied between one
end-cap and the ring; the detection uses the signal
between the second end-cap and the ring.
We can now deal with the cooling of the magnetron
motion. This is accomplished using 'motional sideband
cooling' (Brown and Gabrielse 1986), where a field of
angular frequency w, w, is generated inside the trap.
Absorption of a photon at this frequency puts energy into
both the axial and magnetron motions. The axial energy
+
I
2
0
4
6
~ ~ ~ - 1 4 1 3780
3 8 kHz
8
10
Figure 2. Experimental cyclotron resonance (Brown and
Gabrielse 1986). The shift in axial frequency is shown as a
function of applied RF drive in the region of wb (see text).
3.3 Results
These experiments have been performed over a long
period (Schwinberg et a1 1981a, b, Van Dyck et a1 1984,
1987) on both electrons and positrons. The main difference for positrons is that they are loaded off-axis from
a "Na positron source into an auxiliary trap and cooled
to low energies before transfer to the principal trap for
the measurements. The following are the most recent
results (Van Dyck et a1 1987):
ge-
= 2.002 3 19 304
376 8 (86)
g: = 2.002 319 304 375 8 (86)
These represent the most accurately known fundamental constants to date (see Cohen and Taylor
(Van
1987). The anticipated future accuracy is
Dyck et al 1988). The equality of the two g-factors is a
97
R C Thompson
test of CPT invariance (Particle Data Group 1984) and
the absolute value can, for example, be combined with
QED theory to deduce a new value for the fine-structure
constant using the relation (Mohr 1988)
+ ....
a, = (g - 2)/2 = ~4271- 0.328 478 966 (u/z)’
Similar experiments are possible for protons and
antiprotons, though work with a single particle is more
difficult due to the larger mass, which leads to weaker
coupling to the external circuit. Resonances in a small
cloud of protons have been measured (Van Dyck et al
1985) and a beam of 21 MeV antiprotons from the LEAR
storage ring at CERN has been reduced in energy and
captured in a trap (Gabrielse et a1 1986). However,
precise measurements of the proton/antiproton magnetic
moments have not yet been possible.
3.4. The g-factor of the hydrogen molecular ion
The g-factor of a bound electron differs from that of a free
electron by typically a few PPM due to relativistic and QED
corrections. In the simplest possible molecule, H:, the gfactor depends on the rotational and vibrational state
and has been calculated by Hegstrom (1979). A group at
the University of Mainz is measuring the g-factor of H i
in a Penning trap, making use of the spin dependence of
the collisional cross section of a polarised beam of
sodium atoms with the ions inside the trap (Loch et al
1987). When spin flips occur, induced by an RF field, then
the loss rate of the ions due to the collisions changes.
Thus the spin-flip frequency can be found and compared
with the cyclotron frequency in the trap. The latest result
is (Loch et al 1988)
g = 2.002 283 7 (18)
compared to a theoretical prediction of
g = 2.002 282 8 (8).
Further improvements should allow the vibrational
structure to be resolved, thus giving a more critical test of
the theory, which shows that the value of g depends on
the vibrational state of the molecule.
4. Measurement of mass
4.1. Principle of the technique
The frequencies of the three motions in a Penning trap
(see section 2.1) are directly related to the charge to mass
ratio of the ions. Thus, if all the other quantities are
known, the mass of the ions may be determined from the
oscillation frequencies. In practice, they are combined in
such a way as to eliminate the effect of the electric field,
and give the unmodified cyclotron frequency. An accurate measurement of the magnetic field or a calibration
using an isotope of known mass then yield the mass of the
unknown isotope to high accuracy. Depending on the
accuracy required, the cyclotron frequency is determined
using the relation given in section 3.2 (independent of
trap imperfections) or simply by adding wb and w, (exact
only to first order in any imperfections).
98
These measurements clearly have much in common
with those discussed in section 3, although this section
deals mostly with atomic ions rather than with electrons.
Mass measurements are particularly important for unstable nuclei, where they enable binding energies to be
determined more directly than is otherwise possible. It is
here that many of the advantages of ion traps, such as the
small sample size required and the long interaction times
obtained, come into play.
Lower resolution instruments such as the pulsed ion
cyclotron resonance (ICR) mass spectrometer (e.g. McIver
1978) are based on similar principles but are of simpler
design than precision Penning ion traps, using six plane
plates arranged in a box structure as electrodes. The
requirement here is for a resolution better than 1 amu to
identify molecular ions, but much higher resolution is
often not necessary. Such instruments can be used to
follow the course of chemical reactions with a low
pressure background gas with millisecond time resolution (McIver 1978). Higher resolution instruments
have also been constructed and have been used for mass
comparisons at the lo-’ level (Lippmaa et al 1985). A
detailed discussion of these instruments is outside the
scope of this review and the reader is referred to Hartmann and Wanczek (1982). See also March and Hughes
(1989) for a discussion of the expanding area of ion trap
mass spectrometry.
4.2. Mass measurement of rare isotopes
A group at Mainz aims to measure the masses of strings
of isotopes produced by the ISOLDE mass separator at
CERN (Kluge 1988, Kern et a1 1988). The experiment
has to be performed on-line as many of the half-lives are
short (of the order of minutes or less). However, a trap
designed to collect ions directly or indirectly from a highenergy beam is incompatible with a high-precision
measurement which needs UHV pressures, homogeneous
fields and near-perfect trap geometry. This problem is
overcome with two intermediate steps before the ions
reach the measurement trap. The first is a rhenium foil
into which the ions from ISOLDE are implanted. The
second is a so-called ‘bunching’ Penning trap which is
loaded by heating the rhenium foil to re-emit the implanted atoms which are ionised as they leave the surface.
Finally, the ions are released from the bunching trap and
travel down a transfer tube to the measurement trap
which is located in a superconducting magnet at low
pressure ( < lo-’ Pa). This final transfer is very efficient,
with up to 70% of the ejected ions being successfully
captured in the second trap (Schnatz et al 1986).
The mass measurement proceeds by applying an RF
field to the ions at a frequency corresponding to w,
(equal to wb + U,). This drives a two-quantum transition
in the ions, with energy going into both the magnetron
and the cyclotron motions. The resonance is detected by
releasing the ions out of the trap into a drift tube. Those
ions which have absorbed energy from the RF field have a
larger cyclotron orbit and hence a larger orbital magnetic
moment. When the ions reach the inhomogeneous part of
Precision measurement aspects of ion traps
(i) Tritium mass. If the mass of the tritium nucleus
(3H) can be determined at this level of precision, then
important extra information will be available in experiments which measure the 3H beta-decay spectrum with a
view towards the determination of the antineutrino rest
mass (Van Dyck et al 1988, Lippmaa et a1 1985). It is still
not known whether neutrinos have a mass or not, and the
answer to this question has important astrophysical
consequences as well as being of fundamental interest.
The ion trap mass measurement has to have an accuracy
of < lo-' in order to determine the antineutrino mass,
which may be only a few eV, with reasonable precision.
At least three research groups are already attempting to
make this measurement.
(ii) Uranium Lamb shijt. In hydrogen-like uranium the
ground state Lamb shift changes the mass by two parts in
lo9 so if a mass comparison can be made for 238U92+
and 238U91+
to an accuracy of about lo-'', the Lamb
shift could be 'weighed' to better than 10% (Moore et a1
1988). This would be very interesting as it would check
the scaling of the Lamb shift with 2, whose dominant
term is predicted to follow the relation
32
280
1
1
2 7 0 t ~ , , , ! , , , , 1 , , , , ! , , , , ,, ,,
746855
860
865
870
Frequency IHz)
,
!
,
875
,
,
,,,,j
880
Figure 3. Mean time of flight of 12,Cs ions as a function of
applied RF frequency (Kluge 1988). The resonance at lower
frequency (higher mass) is attributed to the T,,, = 21 s
isomer (see text).
the field, the cyclotron energy is converted into longitudinal kinetic energy and those ions reach the channel
plate detector earlier. Thus, the time-of-flight spectrum
shows a minimum when the RF is resonant with the twoquantum transition. Typical linewidths are a few Hz,
giving a resolving power of 3 x lo5 and a fractional
accuracy of 2 x lo-'. The magnetic field has to be
calibrated by measurements on a stable isotope of known
mass.
Figure 3 demonstrates the power of the technique. It
shows a time of flight spectrum for 122Cs,which is known
to have two half-lives (4.2 min and 21 s). There are two
resonances differing in frequency by about 3 Hz (corresponding to 0.5 MeV). If the measurement is delayed, the
left-hand peak disappears, so this must correspond to the
shorter half-life. Thus, the masses of the ground and
isomeric nuclear states have been resolved here in a mass
measurement for the first time (Kluge 1988, Kern et a1
1988). This method needs typically 50 ions for each cycle
but, as the detection process is destructive, between lo4
and lo5 detected ions are needed for a resonance curve
(taking up to one hour to record). However, the trapping
so the
efficiency into the first trap is only of order
total requirement is for about 10" ions (of the order of
1 pg). This could be improved considerably if, for
example, the ISOLDE beam could be bunched in some way
(see, for example, Moore and Gulick 1988).
4.3. Other high-precision mass measurements
It is now possible to make mass measurements of specific
particles or isotopes to a precision of io-' or lo-'' (e.g.
Van Dyck et a1 1988). These measurements allow the
determination of fundamental constants such as the
proton-electron mass ratio. This is achieved by storing
electrons and protons alternately in the same trap and
measuring the ratio of the cyclotron frequencies (Van
Dyck et a1 1985). Other possibilities also arise of which
we mention just two here.
E
= (cr/n)[ ( Z ~ ) ~ / n ~ ] F ( Z a ) m c ~
where F ( Z a ) is a slowly varying function of Z a (Mohr
1988). It would be a very difficult experiment as the
ionisation of the uranium would require high electron
energies (over 100 keV to remove the last electron) and
high currents (due to the small ionisation cross sections).
Pa) is
Furthermore, extremely high vacuum ( <
required to prevent recapture of electrons via collisions.
5. Measurement of transition frequencies
5.1. Introduction
Atomic transition frequencies can in principle be measured to very high precision, but often there is a practical
limit to the precision arising from perturbations on the
atom, which either broaden or shift the resonances.
Examples include the Doppler effect due to thermal
motion, collisions with other particles, stray electric and
magnetic fields and the effects of a finite interaction time.
In ion traps many of these perturbations can be
eliminated or at least reduced, so that the inherent high
stability of suitable transitions in ions can be realised in
experiments to measure the frequencies to high precision.
In this way several ionic hyperfine splittings have
been measured to accuracies approaching or even exceeding lo-'' (Werth 1982). It is seldom necessary to
know splittings so accurately - even studies of the
hyperfine anomaly in strings of isotopes of the same
element only requires lo-' or so (Werth 1988)-but there
are at least two important uses of such an experiment.
These are either to measure tiny changes in such a
transition frequency or to use the transition as a frequency standard in terms of which other, less precise,
measurements can be made. An example of the first of
these uses is a search for anisotropy of space by studying
the variations in a transition frequency in trapped 'Be+
99
R C Thompson
ions as the orientation of the ions changes (Prestage et a1
1985). The same system (described in section 5.2 below)
has also been used as an atomic frequency standard, and
its performance was comparable to that of caesium beam
standards (Bollinger et a1 1985).
Most (but not all) of these precise atomic frequency
measurements use laser cooling of the ions in order to
eliminate the first-order Doppler effect. This is not
necessary if the transition wavelength is greater than the
amplitude of the ionic motion (Dicke 1953), which is the
case for microwave transitions. However, the secondorder effect is still present at the lo-'' level for ion
energies of the order of 1 eV and this can only be
eliminated by cooling. Here there is a significant difference in the application of Penning and RF traps. In an
RF trap the RF heating means that only a few ions at most
can be laser cooled to very low temperatures (e.g. Bliimel
et al. 1988). For larger clouds the RF fields and collisions heat the ions faster than the energy can be removed
by the laser cooling (Blumel et al. 1989). Thus, precision experiments with laser cooling in RF traps are
often limited to single ions. On the other hand, large
clouds of up to a thousand or more ions may be easily
cooled in a Penning trap (Bollinger et all985, Thompson
et a1 1988, Plumelle et a1 1986) although the second-order
effect increases with the size of the cloud (Wineland
1984). The other point to note about the Penning trap is,
of course, the presence of the magnetic field B. This
generally means that in order to measure a transition
frequency v with high precision, a value for B has to be
found such that v is independent of B to first order, or else
field instabilities will cause severe problems. This in turn
often imposes restrictions on the hyperfine structure of
an ion if it is to be successfully employed in such a
measurement.
5.2. Microwave transitions
Several measurements have been made on microwave
transitions between hyperfine levels of ions confined in
both RF and Penning traps. Ideally one looks for a heavy
ion (so that the Doppler effect is small) with a large
hyperfine splitting (to give high fractional precision Av/v
for a given AV). Mercury satisfies these requirements well,
but has only recently been laser cooled due to problems
with the laser wavelength required (see section 5.3).
However, optical pumping experiments on mercury with
a conventional resonance lamp are possible due to a
chance coincidence of isotope shifts in "'Hg'
and
"'Hg+ with the "'Hg'
hyperfine splitting (Jardino et
a1 1981, Major and Werth 1973). Here a cloud of "'Hg'
ions in a trap is optically pumped, using light from a
"'Hg resonance lamp, into one of the hyperfine levels.
However, microwaves applied at the appropriate frequency equalise the populations of the ly9Hg+hyperfine
levels, leading to a change in the level of observed
fluorescence. This has recently been used to make a
commercial frequency standard at 40.5 GHz stable to
or so over a period of a year (Cutler et a1 1986).
100
Perhaps the greatest quantity of work has been
performed on a transition in 9Be+ which is certainly not
an ideal ion in some ways but is convenient for laser
cooling work in a Penning trap. The resonance transition
in Be' is at 313 nm. This is conveniently generated by
frequency doubling in an RDP crystal the light from a cw
ring dye laser operating at 626 nm (Bollinger et a1 1983).
The light is tuned to the low-frequency side of the 2s 2S1,2
( M I = - 3 , M - -12 ) to 2p 2P3,2 (-3, -3) transition,
and the ions (roughly 1000) are optically pumped into
the lower level of this transition (state A, say). This gives
a high level of fluorescence as the ions are continuously
re-excited by the laser. The field-independent clock transition is between the levels ( - 3,i) (state B) and ( (state C) in the ground state at a field of 0.82 T (see
figure 4(a)). It has a frequency of 303 MHz, and has been
measured to a precision of 2 x 10- 13.
The measurement proceeds as follows (Bollinger et al
1985). First the ions are prepared in state A using the
laser cooling light as described. This also ensures that the
ions are cold before each cycle. Then, with the laser off,
microwaves are applied at the electron spin-flip frequency of 24 GHz, transferring half of the population to
state B. This is followed by the interrogation at the clock
frequency which transfers some of the population to
state C (if it is resonant). Finally the spin-flip frequency is
used again, re-equalising the populations of states A and
B, which results in more transfer out of state A, if the
clock frequency was resonant. This is detected by
measuring the fluorescence level when the cooling laser is
i,t)
-
microwaves
(312, -112)
Frequency
- 303016377.265 i H z )
Figure 4. ( a ) Hyperfine structure of the 'Be' 2s 2S1,2 ground
state as a function of applied magnetic field B. The clock
transition (vl) is independent of 6 to first order at
6 = 0.8194 T. ( b ) Signal obtained on the v1 field-independent
transition for a 550 s interrogation time. The dots
are experimental and the curve is a least-squares fit
(Bollinger et a/ 1989a).
Precision measurement aspects of ion traps
first switched on again, before it has pumped all the
population back into the initial state A.
The interrogation at the clock frequency uses the
Ramsey method of separated oscillatory fields (Ramsey
1956). This means that two short (0.5 s) coherent pulses
of microwaves are separated by a period of -20 s with
no irradiation, and it results in an oscillatory lineshape,
symmetrical about line centre with a 25 mHz width.
The centre frequency has been determined to less than
0.1 mHz, allowing for systematic effects such as the
second-order Doppler effect, magnetic field fluctuations
and the rotation of the earth (Bollinger et a1 1985). More
recently improvements have been made including the use
of more efficient 7-c pulses for the population transfers and
sympathetic cooling with laser cooled Mg ions to keep
the Be' ions cold during the whole cycle (Bollinger et a1
1989a). This enables the interval between irradiation to
be raised to several hundred seconds, giving a linewidth
of < 1 mHz. Preliminary estimates of the systematic
fractional uncertainty in the measured frequency are
< 10-l4. A recent curve is shown in figure 4(b).
This experiment has been run as a frequency standard
at 303 MHz (Bollinger et al 1985). A recent suggestion by
Weinberg (1989) shows that the results of the experiment
may be interpreted as evidence for lack of non-linearity of
quantum mechanics at the lo-'' level. This test was
made a factor of lo6 more sensitive by lengthening the
interrogation time on the clock transition (Bollinger et a1
1989b). The same set-up has also been used to study
spatial anisotropy (Prestage et a1 1985). One other
application is to the study of a condensed state of ions
in a trap, that is, a crystal-like structure formed if the
ions are cooled sufficiently strongly (Gilbert et a1 1988,
see section 6 below).
It is not essential for microwave experiments in traps
to use laser cooling. In Mainz a series of experiments
have measured ground-state hyperfine splittings to high
precision (see Werth 1982, 1985, 1988) using large clouds
in RF traps at an ion energy of the order of 1 eV. These
experiments use a pulsed laser for optical pumping and
for detection via fluorescence. The second-order Doppler
effect has to be allowed for and the results also extrapolated to zero magnetic field, where the M,=O to 0
transition is field independent to first order. One of these
experiments has also been used as a frequency standard
(Knab et a1 1985).
+
5.3. Optical transitions
In recent years it has become possible to narrow the
linewidths of stabilised lasers to the kHz region (e.g.
Hough et a1 1984) and this has opened up the serious
possibility of using such narrow bandwidth lasers in the
study of optical transitions to metastable states in
trapped ions. A frequency standard in the optical region
has the clear advantage that a given fractional precision
Av/v can be achieved in a shorter time than is the case for
microwave standards, as v is a factor of lo4 or so higher.
However, it is recognised that transferring this stability
via a frequency chain of some sort into the microwave
region may well be a problem.
We concentrate here on an experiment on lg8Hg'
ions confined in a miniature RF trap. Such miniature
traps were first used by Toschek and co-workers for the
study of small clouds of Ba' ions (Neuhauser et a1 1978)
and also for the first work on single ions (Neuhauser et a1
1980). However, although Ba' has some long-lived levels
its energy level structure is not ideal for use as a
frequency standard (see below).
The Hg' experiments were performed initially on a
small cloud of collisionally cooled ions (Bergquist et a1
1985). Up to 5 pW of laser radiation at the resonance line
(194 nm) was produced by frequency doubling and mixing techniques (Hemmati et a1 1983) and this was used to
detect the presence of the ions in their ground state. A
second laser source at 563 nm also irradiated the ions
and excited them by Doppler-free two-photon spectroscopy (see, for example, Thompson 1985) into a longlived 'D,,, state, thus reducing the level of 194 nm
fluorescence seen. These initial experiments showed a
linewidth in the spectra of 420kHz and their most
interesting feature was the presence of sidebands on the
two-photon resonance due to the secular motion of the
ions in the RF field (at approximately 1 MHz), revealing
this effect for the first time in optical spectra (Bergquist et
a1 1985).
More recently these experiments have been improved
by using a single laser-cooled mercury ion in a similar
trap (Bergquist et al 1987). Here the single-photon
transition at 282nm to the same metastable level was
excited using frequency-doubled radiation. Since after a
period of exposure to this radiation with the 194nm
beam off, the ion is left either in the ground state or in the
metastable state, it suffices to turn the 194 nm radiation
back on and to determine if there is or is not any
immediate fluorescence, so the result of each 'cycle' is
either a zero or a one. At the start of each cycle it is
ensured that the ion is back in the ground state by
measuring the level of fluorescence. In this way the twophoton excitation probability can be determined as a
function of laser frequency.
The results of this experiment are shown in
figures 5(a) and (b). The first scan (a) shows the central
carrier with two motional sidebands on each side while
the high-resolution scan ( b ) shows just the central carrier
and the first upper sideband at 1.45 MHz. The linewidth
here is about 30 kHz, which arises mainly from residual
laser frequency fluctuations (the natural linewidth of the
transition is just 2 Hz). It is possible to determine the
temperature of the ion from the intensity of the first
sideband, and this gives T = 1.7 mK, which corresponds
to the theoretical Doppler cooling limit for Hg'. At this
temperature the average vibrational quantum number
( a ) in the trap pseudopotential well is about 11.
Even lower temperatures were obtained by subsequently switching the cooling from the 194nm resonance transition (with large natural linewidth) to the
282 nm transition, with small natural linewidth and
hence a much lower cooling limit. In fact the transition
rate on this transition is too low for the method to work
so it has to be artificially enhanced by introducing a third
101
R C Thompson
belonging to a different electron core configuration,
which appears to be extremely long-lived. This would
lead to the effective loss of ions from the experiment if it
could not be tackled in some way, although it has been
suggested that this level itself could be used in a standard
of some sort (Blatt et al 1989, Lehmitz et a1 1989).
Similarly, barium has often been suggested as a possibility
(see for example Toschek 1984) but although the laser
cooling wavelengths are suitable and the metastable
states have lifetimes of many seconds, the candidate
transitions lie in the infrared region and there are also
some complicated Raman-type resonances which are only
now beginning to be fully understood (Sauter et a1 1988).
Dehmelt (1982) has suggested a series of possible
standards in elements such as Tl' and In+ where the 'So
to 3P, transition might make an optical standard with a
possible reproducibility of lo-'' (see also Nagourney
1988). However, such transitions are extremely difficult
to probe with current laser technology and it may be
some time before serious progress can be made in their
study experimentally.
Frequency detuning [in MHz)
6. Other uses of ion traps
0.80
Ib)
,
-60
A
0
60
1
I
120
" 1340 1400 1460
Frequency detuning (inkHz1
1520 1580
Figure 5. ( a )Quantised signal showing the E2 allowed
ZS1,2-2Ds,z transition in a single, laser-cooled l9'Hgf ion,
as a function of laser detuning at 282 nm. The recoilless
absorption resonance is in the centre and two Doppler
sidebands can be seen on each side. ( b ) High resolution
scan showing carrier and first sideband. The linewidth is
30 kHz at 282 nm and the relative intensities indicate
T= 1.6 f 0.5 mK (Bergquist e t a / 1987).
radiation field to empty the Dsj2state. This shortens the
lifetime and makes the temperature limit correspondingly higher, but still lower than the previous one. In this
way ( n ) = 0.05 is achieved, corresponding to T = 47 pK.
This is the lowest temperature yet achieved in an ion trap
(Diedrich et a1 1989).
The precision of measurements made on this system
depend to a large extent on the laser linewidth achieved.
The current linewidth of roughly 1 kHz (Bergquist et a1
1989) represents a value of Av/v of lo-'' but of course
the centre of the transition can be determined to a higher
precision than this if the systematic effects are understood. If a linewidth of 2Hz could be achieved then a
measurement accuracy of
or so could be envisaged
(Bergquist et a1 1989, Wineland et a1 1987b).
Ytterbium is another possible candidate for an optical frequency standard and at least three groups around
the world are working on this ion including the National
Physical Laboratory (Barwood et a1 1989). The laser
wavelengths required are easier to produce than those for
Hg+ but the level structure is not ideal. In particular, it
appears that one candidate metastable level decays not
only to the ground state as expected but also to a level
102
The environment inside ion traps is unique and therefore
it is not surprising that unusual experiments have been
performed in them, apart from precision measurements
of the type discussed so far. For instance, it is possible to
isolate a single atomic particle and observe it for a long
period (Neuhauser et a1 1980, Wineland and Itano 1981,
Nagourney et a1 1983, Diedrich and Walther 1987). If an
ion is in its ground state it can be continuously excited
into a resonance level and its fluorescent decay back to
the ground state monitored with a photomultiplier, with
a signal of up to lo5 counts per second. If however,
the ion is excited into a metastable state somehow then the
fluorescence must stop until it decays once more to the
ground state. Thus the state of the ion can be monitored
by the presence or absence of fluorescence and this
enables the quantum jumps to and from the metastable
state to be studied (Cook and Kimble 1985).
Three experiments were performed within a short
time of each other to verify this simple analysis (Sauter et
a1 1986b, Bergquist et a1 1986, Nagourney et a1 1986).
The results were as expected except that in one experiment anomalous results were obtained when two or three
ions were trapped simultaneously (Sauter et a1 1986a, b).
There appear to be many more double and triple jumps where the fluorescence level changes by an amount
corresponding to two or three ions jumping simultaneously - than would be expected from the known time
resolution of the detection system. This effect appears to
be absent in the other experiments (see for example Itano
et a1 1988). For a review of this area see Blatt and Zoller
(1988).
The quantum jump experiments are not only of
academic interest. If ion traps are to be used either for
spectroscopy of ultra-narrow resonances or for frequency
standards based on narrow transitions, then the tran-
Precision measurement aspects of ion traps
sition rate is bound to be very low as the states involved
must be long-lived. Also, it is likely that very few ions are
used in an experiment, in order to reduce perturbations
to an acceptable level (see Wineland 1984).Therefore it is
of paramount importance that the maximum amount of
information is extracted from any transitions which do
occur. Studying the fluorescence on a second transition
in the manner described above can supply this information with essentially 100% efficiency as the ion acts as
an amplifier with very high gain (this method was used in
the work described in section 5.3;see also Dehmelt 1988).
Thus the complete study and understanding of quantum
jumps is of importance to the future development of
frequency standards based on ion traps.
One other recent development has been the successful
cooling of clouds of ions to the point where they
crystallise into a lattice with a spacing determined by a
balance between the Coulomb repulsion of the ions and
the trap potential well (see figure 6). This makes the
crystal lattice spacing typically 20 pm which is of course
enormous compared with conventional crystals. These
experiments have been performed in RF traps (Blumel et
al 1988, Wineland et al 1987a) as well as in Penning traps
(Gilbert et a1 1988). In an RF trap the crystal may take up
a fixed orientation in space, due to the slight imperfections in the trap potential. Clouds of up to 100 ions have
been studied by Blumel et al (1988) and smaller clouds
have been imaged (Diedrich et a1 1987, Wineland et a1
1987a). The transition between the ordered and disordered states shows a number of interesting features
such as hysteresis and bistability; simulations of the ions
can reproduce most of these features (Bliimel et a1 1988).
This work also sheds light on the mechanism of RF
heating in traps and shows its relation to chaos (Blumel
et a1 1989, Hoffnagle et al 1988).
In the Penning trap much larger clouds have been
studied and in this case they always rotate due to the
magnetron drift, so the crystal structure cannot be seen
so clearly. Theoretical predictions using molecular dynamics simulations (Rahman and Schiffer 1986, Dubin
and O'Neil 1988) show that there should be a definite
shell structure with little migration between shells but a
larger diffusion on each shell. This is indeed what is seen,
although a structure of open concentric cylinders was
also sometimes seen, which is not predicted theoretically.
Clearly there is much of interest in these crystal
structures. It is interesting to note that very similar effects
are predicted to occur in storage rings except that there
the basic symmetry is cylindrical rather than spherical
(Rahman and Schiffer 1988). These structures have not
yet been observed as it is more difficult to obtain low
temperatures in storage rings.
The point at which condensation occurs in traps is
generally expressed in terms of the coupling strength r,
which is essentially the ratio of the coulomb repulsion
between neighbouring particles to the kinetic energy of
each particle. Solid-like behaviour is expected when r
exceeds 170 from molecular dynamics simulations of an
infinite plasma. The values of r achieved in the experiments range up to several times this, so the results permit
a comprehensive test of the theory and therefore a fuller
understanding of phase transitions in general.
Finally it should be mentioned that ion traps have
been used for various lifetime measurements of metastable states of ions (up to tens of seconds in Li' and
Ba'). These states cannot be studied in any other
environment because the observation time has to be so
long, but the situation is ideal for traps. The measurements are reviewed by Knight in Van Dyck et a1 (1988).
7. Conclusion
The use of ion traps for studies of the properties of ions is
an area of rapid growth in physics. They have shown
their value especially in precision measurements where
the advantages of a stable, well controlled and
perturbation-free environment are obvious. In the future
it is expected that they will be used in the next generation
of frequency standards, with projected reproducibilities
of at least lo-'', and in future measurements of fundamental constants. However, it is not only standards
laboratories and the like which make use of ion traps.
There is much interest in the application of traps to the
study of fundamental physical processes such as quantum jumps, laser-atom interactions, and phase transitions as well as to routine measurements of atomic
masses, hyperfine structure and lifetimes. This is clearly a
technique which will continue to be applied in many new
areas in the future.
Acknowledgments
Figure 6. Crystalline structure of seven 24Mg+ions in an RF
trap (Diedrich et a / 1987). The mean distance between the
ions is 23 pm.
The author has benefited from many conversations with
colleagues at the National Physical Laboratory and
103
R C Thompson
Imperial College, especially Professor P L Knight. This
w o r k was supported i n p a r t by t h e UK Science and
Engineering Research Council.
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Rlchard Thompson is a
Lecturer in Physics at
Imperial College, London.
From January 1983 to
September 1986 he worked at
the National Physical
Laboratory in Teddington.
Previously he was at the
Clarendon Laboratory in
Oxford, apart from a year and
a half spent at the
Kernforschungszentrum in
Karlsruhe. West Germany. He
obtained his first degree at
Oxford in 1976 and his
doctorate in atomic
spectroscopy in 1980.
105