Ion traps are used to capture charged particles. They can be used as selective mass filters or to trap ions for observation and measurement. Ions trapped in this way can also be used as part of a quantum computer. Different types of ion trap are known, but one particularly useful form that is often used for example in mass spectrometry is the quadrupole ion trap with an oscillating electric field; or trapping in two-dimensions to create an ion guide. The quadrupole ion trap has two main forms, known as the linear quadrupole ion trap and the 3D quadrupole ion trap. When operating with an electric field at a single frequency such configurations are known as Paul traps.

A 3D quadrupole ion trap typically uses a pair of hyperbolic electrodes facing each other (also referred to as end-cap electrodes) and a ring electrode located between these two. A radio-frequency AC voltage is applied to all three electrodes such that the hyperbolic electrodes are positive when the ring is negative and vice versa. Thus an alternating electric field is created between the electrodes such that a cloud of charged particles at the centre of the trap is alternately pushed in axially (spreading out radially) and then pushed in radially (spreading out axially).

Therefore the cloud may be said to alternate between a first short and fat state and a second tall and thin state.

A linear quadrupole ion trap uses four parallel rod-like electrodes arranged in a square to create the quadrupole electric field. Thus the rods define a cylinder of square cross-section. The AC voltage is applied alternately to opposite pairs of rods (diagonally opposite corners of the square) so that one pair is positive while the other pair is negative and vice versa. This AC voltage confines ions radially within the cylinder thus guiding ions so that they closely follow a given trajectory in space. End-cap electrodes can be placed at either end of the cylinder and a DC voltage is applied to them to confine the ions axially, thus retaining them in a small region around the trap centre (trapping in all three dimensions).

For a given frequency of applied voltages, a quadrupole ion trap will trap particles with a certain range of charge to mass ratio. Particles outside of that range will not be retained by the trap, but will instead be accelerated out of the trap by the applied electric field or will fall out of the trap. For this reason quadrupole ion traps are often used as a charge-to-mass filter element in mass spectrometers. Similar considerations apply for electric fields that are higher-order multipoles.

Research and work involving guiding and trapping charged particles is carried out in many different sectors. One sector is mass spectrometry in which particles are ionised and then ion guides, and in some instruments traps, are used to select a certain charge-to-mass ratio before detectors are used to detect the presence of particles. In this way, the composition of the particles can be investigated, e.g. large molecules or biological particles such as proteins. Often, the particles are fragmented during the process to examine constituent parts of the particles.

Another sector of research relates to examination of much smaller particles, typically individual atoms. These are normally held within the trap and cooled to very low temperatures and their properties are then investigated e.g. via laser excitation, while the particles remain in the trap. In the case of optical frequency standards and quantum computers, the quantum states of individual atoms can be manipulated.

Some experiments have attempted to trap two different types of particle in the same trap, e.g. one lighter particle and one heavier particle. Almost invariably the heavier particle has a lower charge-to-mass ratio than the lighter ion and this will be assumed in the following. However, those experiments found that the two types of particle separated spatially within the trap. The AC drive voltage trapped the lighter particles (having a higher charge-to-mass ratio) tightly at the centre while the heavier particles (having a lower charge-to-mass ratio) were more weakly trapped, forming in a cloud around the lighter particles, the two species electrically repelling each other. There was therefore little interaction between the two species.

According to the invention, there is provided an ion trap comprising a plurality of electrodes and a power supply arranged to provide an alternating current to said electrodes to create a time varying electric field capable of trapping two or more species of ion between the electrodes, wherein the power supply is arranged to provide an alternating current drive signal comprising a first lower frequency component suitable for trapping a first ion species and simultaneously a second higher frequency component suitable for trapping a second ion species.

Viewed from an alternative aspect, the invention provides an ion trap comprising a plurality of electrodes and a power supply arranged to provide an alternating current to said electrodes to create a time varying electric field capable of trapping at least two species of ion between the electrodes, wherein the power supply is arranged to provide an alternating current drive signal comprising at least two frequency components comprising a first lower frequency component suitable for trapping a first ion species and simultaneously a second higher frequency component suitable for trapping a second ion species.

The simultaneous application of two different frequency components, one applying predominantly to each species of ion (i.e. each species of charged particle), permits both ion species to be trapped strongly. Both species can thus be trapped close to the centre of the trap and the two species can be overlapped (rather than one forming a halo-like cloud around the other). This increases the Coulomb interaction between the two species which has numerous practical advantages. For example, where one species can be laser cooled, but the other cannot, the strong interaction between the two species can be used to cool sympathetically the species that cannot be directly cooled. This will be described in more detail later. Additionally, where one species can be visualised, e.g. by fluorescence, the presence of the other species may be made detectable by appearing as "holes" in the structure of the fluorescing species. This permits better measurement of the indirectly detectable species. Therefore preferably the second frequency component is suitable for trapping an atomic ion species that can be visualised with an optical imaging system, e.g. using a laser of suitable wavelength to cause the atomic ions to fluoresce. The method therefore preferably directly images the trapped atomic ions and thereby indirectly images the trapped heavier ion. More preferably, the atomic ions are selected from amongst those commonly used for optical visualisation, especially those with a single valence electron as these have simple transitions and exhibit simple spectra. The confined atomic ions scatter laser light so that these fluorescing ions can be observed with a suitable optical imaging system, thus permitting indirect detection of non-fluorescing (dark) ions with a much smaller charge-to-mass ratio by means of the perturbing effect on the spatial distribution and motion of the observed ions. The interaction between the atomic ions and the non-fluorescing species is greatly enhanced by applying voltages at two radio frequencies to the electrodes of the trapping apparatus. The method of choosing suitable frequencies for species with widely different charge-to-mass ratios is as specified and discussed elsewhere in this document. In order to trap two species of ion with the application of two applied frequency components, it is necessary to ensure that the effects of the two frequencies on the ions are mutually compatible, i.e. that the amplitude and frequency used for trapping one species does not destabilise the other trapped species. This can happen for example if the frequency used to trap one species is (or is sufficiently close to) a resonance frequency for the other species. In such cases, the interfering signal causes the other species to gain energy, i.e. to warm up. In the worst case, this can cause those particles to escape the trap.

If the trapping frequencies are too close together, it could be very difficult to avoid interference between the two trapping signals and it could therefore be very difficult to achieve dual particle trapping. In particular, one has to take into account the various motions of each particle (e.g. axial motion and radial motion in a linear trap) which may have different characteristic frequencies, and also harmonics and sub- harmonics of the various frequencies which may also cause unwanted resonant interaction or interference. However, as the difference in charge to mass ratios increases, the trapping frequencies can be moved further apart, thus making it easier to avoid interference and/or resonance situations.

The frequency of motion of an ion in a trap comprises of a small amplitude oscillation (so-called micromotion) at the frequency of the applied AC voltage and slower motion of the centre of mass. In order to avoid the lower frequency component (for trapping the heavier ion) from exciting the lighter ions, the first and second frequency components of the applied electric field are preferably selected such that the frequency of oscillation of the centre of mass of the lighter trapped ion is greater than the frequency of the drive signal component for trapping the heavier ion. In the case of trapping of charged particles by radio-frequency electric fields the centre of mass motion frequency of the ion is generally an order of magnitude less than the RF frequency applied to trap that ion. Therefore, preferably the second frequency component of the drive signal is more than ten times the first frequency component of the drive signal.

Preferably the power supply is arranged to control the first lower frequency component to generate an approximately harmonic potential with a first spring constant for the first species and the second higher frequency component to generate an approximately harmonic potential with a second spring constant for the second species approximately equal to the spring constant for the first species. More preferably, the power supply is arranged to control the first frequency component, the second frequency component, the amplitude of the first frequency component and the amplitude of the second frequency component such that in at least one direction the spring constant for the first species equals the spring constant for the second species.

Resonance can also arise through harmonics of the lower frequency component exciting the lighter ions. However, higher harmonics have lower amplitudes and produce narrower resonances and so as the frequency separation becomes greater, the effect of these can be ignored to a greater extent, allowing the operator to choose the two frequencies more freely, thus providing greater control over the system of charged particles. Moreover it is well-known that very narrow parametric excitation resonances are readily suppressed by a damping of the ions, such as that caused by laser cooling of ions or viscous damping arising from collisions with the background gas. Therefore, preferably the second frequency component of the drive signal is more than 15 times the first frequency component of the drive signal, more preferably 20 or 25 times the first frequency component. Yet more preferably, the second frequency component is more than 50 times the first frequency component and in some highly preferred embodiments the second frequency component is 100 times the first frequency component or more.

Using trapping frequencies with a high degree of separation is particularly beneficial for interacting particles with very different charge to mass ratios. In practice this often means particles with very different masses, although strictly speaking it is the charge to mass ratio that determines the motion of the ions for a given trapping frequency. As stated above, in this document the terms "lighter" and "heavier" are used to refer to particles with a higher charge to mass ratio and a lower charge to mass ratio respectively. In particular, the strong trapping that can be obtained with the use of two frequencies can advantageously be used to tightly confine two ion species with very different charge to mass ratios close to the centre of the trap such that the charge clouds overlap and have a strong Coulomb interaction. The trapping forces can be described in terms of an approximately harmonic potential which can be designed to have similar spring constants for two, or more, species. In some particularly preferred embodiments, the lighter ion species is an atomic ion and the heavier ion species is a large molecule, especially a biomolecule such as a protein.

Preferably the atomic ion can be directly cooled via laser cooling and preferably there is some coupling between the motion of the lighter ion and the motion of the heavier ion. This coupling of the motions permits sympathetic cooling of the heavier ion via energy transfer to the lighter ion which can be directly cooled. Thus cooling of the heavier ions to very low temperatures can be achieved in this way that would otherwise be difficult or impossible.

In some preferred embodiments the coupling of the motion between the heavy ion species and the light ion species is achieved by selecting the first and second frequency components such that the frequency of a motion component of one species is approximately equal to the frequency of a motion component of the other species. For example, in some particularly preferred embodiments using a linear quadrupole ion trap, the first and second frequency components are selected such that the frequency of axial motion of the lighter ion is approximately equal to the frequency of radial motion of the heavier ion. It will be appreciated that an exact matching is not necessary, but the term "approximately equal" is used here to mean matching these frequencies as well as possible (within the experimental constraints and precisions) to maximise energy transfer between the two species. In such embodiments, it will be appreciated that the radial and axial motion frequencies of both ion species are different from the first and second driving frequencies applied to the trap's electrodes, while at least one of the radial and axial motion frequencies of one species is beneficially matched with a motion frequency of the other species. A large cloud of ions has many normal modes of motion with frequencies that spread out from those of a single trapped ion: for a chain of ions in a linear trap the frequencies of collective axial motion are higher than those of a single ion whilst the radial modes have lower frequencies.

Preferably the lighter ion species can be visualised, e.g. through emission of light, e.g. by fluorescence. In such cases, when the lighter and heavier ions are trapped together in overlapping relationship, even when the heavier ions cannot be directly visualised, the individual lighter ions can be visualised. Information about the heavier ions can be gained by measuring properties of the visible ions. For example, the lighter ions will be displaced due to Coulomb repulsion from the heavier ion and thus provide information on the heavier ion's charge and mass. Resonance can also be used to induce motion of the heavier ion. By varying the driving voltage (in particular varying the frequency of the first component and/or varying the amplitude of the first component) applied to the electrodes of the trap, the motion of the heavier ion can be affected in a controlled fashion, thus inducing motion. By resonantly driving the heavier ion, the amplitude of its motion increases, causing further displacement of the lighter ions surrounding it. Measurement of these displacements and the resonant frequency provides further, accurate information on mass and charge.

In some particularly preferred embodiments, the lighter ion species comprises ions of alkaline-earth metals, calcium and barium being common choices with transitions at convenient wavelengths. Such singly ionised atomic ions fluoresce when illuminated with narrow bandwidth laser radiation at the wavelength of the appropriate resonance wavelength (493 nm for a barium ion and 397 nm for a calcium ion) and thus facilitate visualisation and measurement of the heavier ions as described above. Preferably, the ion trap is configured to trap an atomic ion and a large molecule. The atomic ion may be any suitable ion, but preferably facilitates the

aforementioned coupling of the motions. The optimum choice of atomic ion depends on the mass of the heavier ions of interest since the minimum difference in the lower and higher applied RF frequencies imposes a limit on the minimum ratio of the charge-to-mass ratios of the two, or more, species. The choice of atomic ion is only restricted by the availability of suitable methods for detecting such ions. Although lighter ions may be used, in some preferred embodiments, the lighter ion (e.g. atomic ion) has a mass of at least 9 atomic mass units. In other preferred embodiments the lighter ion has a mass of at least 50, or at least 100 atomic mass units. The larger molecule preferably has a mass of at least a hundred atomic mass units, more preferably at least a thousand atomic mass units, more preferably at least ten thousand atomic mass units, more preferably still at least one hundred thousand atomic mass units and in some embodiments preferably at least a million atomic mass units.

In some preferred embodiments, the ratio of the charge-to-mass ratios between the lighter particle and the heavier particle is at least 2, preferably at least 10, more preferably at least 30, more preferably still at least 100 and yet more preferably at least 300. In some embodiments, the ratio of charge-to-mass ratios may exceed 1000.

Preferably the ion trap is a quadrupole ion trap. The invention applies to all forms of quadrupole ion trap but in preferred embodiments the ion trap is a linear quadrupole ion trap. The linear quadrupole ion trap has a more open structure, permitting easier access for visualisation and for stimulation of the trapped ions, e.g. by directing one or more lasers at the ions and for collection of reflected or emitted light on a CCD or similar optical detection device. Preferably therefore the ion trap comprises four parallel elongate electrodes arranged in a square. The electrodes thus form a square cross section cylindrical region in which the ions are to be trapped.

In other embodiments, electrode configurations that produce electric fields that are multipoles of higher order than the quadrupole may also be used, and the multipolarity of the fields does not necessarily have to be the same at the different RF frequencies.

The four electrodes of a linear quadrupole trap can be grouped into two pairs of electrodes, each pair comprising diagonally opposite electrodes. The AC drive signal, i.e. the power supply output (comprising both the first and second frequencies) is applied between the pairs of electrodes so that one pair is positive while the other pair is negative and vice versa. This AC voltage traps ions radially within the cylinder. End-cap electrodes are preferably also located at either end of the cylinder and a DC voltage is applied to them to trap the ions axially.

It will be appreciated that the above description is based on trapping two species of ion in a single trap. However, the principles of the invention apply equally to trapping three or more species of ion in a single trap. Providing the three trapping frequencies are selected so that they have a mutually compatible effect on the charged particles (e.g. if they are all sufficiently well separated along the frequency spectrum), three or more species of ion could be trapped tightly within the ion trap so that all ions interact strongly with each other. Each of the frequencies of a RF quadrupole electric field can be considered to provide a pseudo-harmonic potential which is characterized by a spring constant. Therefore the first frequency is characterized by a first spring constant and the second frequency is characterized by a second spring constant. Preferably the power supply is arranged to control the first frequency component, the second frequency component, the amplitude of the first frequency component and the amplitude of the second frequency component such that in at least one direction the first spring constant equals the second spring constant. When the spring constants are equal, the two species of ion experience similar forces and thus similar displacements from the trap centre, thus overlapping spatially, giving strong interaction as described above.

The invention also extends to a mass spectrometer comprising an ion trap as described above. The invention also extends to a method of trapping a first ion species and a second ion species in an ion trap, the first ion species having a first charge to mass ratio and the second ion species having a second charge to mass ratio different from the first charge to mass ratio, the method comprising: applying an alternating current drive signal to electrodes of the ion trap comprising a first lower frequency component suitable for trapping the first ion species and a second higher frequency component suitable for trapping the second ion species.

Viewed from an alternative aspect, the invention provides a method of trapping at least a first ion species and a second ion species in an ion trap, the first ion species having a first charge to mass ratio and the second ion species having a second charge to mass ratio different from the first charge to mass ratio, the method comprising: applying an alternating current drive signal to electrodes of the ion trap comprising at least two frequency components comprising a first lower frequency component suitable for trapping the first ion species and a second higher frequency component suitable for trapping the second ion species.

It will be appreciated that the preferred features described above in relation to the apparatus apply equally and appropriately to the method.

Preferred embodiments of the invention will now be described, by way of example only, and with reference to the accompanying drawings in which:

Fig. 1 illustrates the relationship of the frequencies of the applied fields and the motional frequencies of the two ion species in one embodiment of the invention;

Fig. 2 shows a plot of the stability of the lighter ion species according to certain embodiments of the invention; Fig. 3 illustrates a linear quadrupole trap suitable for embodiments of the invention; and

Fig. 4 illustrates indirect measurement of a heavier ion species via a lighter ion species. In the following, we describe the theory of two-frequency operation of an ion trap. Equations of motion are given for two species of ions with molecular mass, charge: M _A , +1 e and M _B , +33e respectively, where M _A = 138 amu is an isotope of barium, M _B = 1.4 x 10 ⁶ amu, e.g., a large protein or molecular complex, and e is the magnitude of the charge of an electron, in the quadrupole electric field created by RF radiation with angular frequencies and ω ₂ (with ω ₂ = l OOu^). For such very different charge-to-mass ratios, and radio-frequencies, the heavy ions (molecular mass M _B ) are confined most strongly by the field at the lower frequency Ui , and trapping of ions of atomic mass M _A arises from the field at ω ₂ . Thus we obtain a superposition of two almost independent Paul traps whose centres can be made coincident or moved apart. Importantly the effective spring constants can be adjusted to be the same for both species so that all the ions interact strongly. This allows efficient sympathetic cooling of the heavy ions by laser-cooled atomic ions. This approach can be extended to charged particles with more dissimilar masses.

The Paul trap, invented by Wolfgang Paul, confines ions with an oscillating electric quadrupole field. It has many diverse applications including frequency standards and quantum computing. The mechanism of the Paul trap depends sensitively on the charge-to-mass ratio and this intrinsic feature of Paul traps is exploited for mass spectrometry. However, it implies that when species with markedly different ratios are held in a Paul trap the more weakly confined species is pushed away from the centre due to Coulomb repulsion from the strongly trapped ion(s) resulting in phase separation of the cold plasma. We describe a method of trapping charged particles with two radio-frequency (RF) quadrupole electric fields, in which two species of ions experience harmonic pseudopotentials with similar spring constants if they have extremely different charge-to-mass ratios. Both species are confined tightly near the trapping centre(s) and strongly interact with each other. Details are given for a heavy ion of mass 1.4 x 10 ⁶ amu and charge +33e in a trap with singly-charged barium ions. Atomic ions scatter laser light so that individual fluorescing ions can be observed, thus permitting indirect detection of dark ions as "holes" in the cloud. The laser radiation can also reduce the temperature of the barium ions which in turn sympathetically cool the heavy ion. The scheme described here opens the way to working with much heavier ions than has been possible in the past such as those formed from biomolecules,

nanoparticles and microscopic particles. The current state of the art in mass spectroscopy includes techniques for putting large biomolecules, and molecular complexes, of molecular weight of a few megadaltons (millions of amu) into vacuum, without fragmentation and surprisingly little change to their structure. Paul trapping of large biomolecular ions has also been discussed for DNA (a long chain molecule), but in an aqueous solution rather than the usual vacuum environment.

We describe the two-frequency operation of an ion trap for two species of ions with {molecular mass, charge} = {M _A ; QA } and {M _B ; QB } where M _A « M _B (all masses are in atomic units). The ions experience an AC quadrupole electric field created by RF radiation with angular frequencies and ω ₂ (with « ω ₂ ), plus a static quadrupole field. The Newtonian equations of motion for ions in a quadrupole field generated by a voltage V(t) = V ₀ + V _l cos _l t + V ₂ cos<¾t on the electrodes, with ω ₂ = ηω _! where n is an integer, can be put into the form of a Hill equation: d ²

-^T + - 2q _a 008(20 - 2p _a cos(2nt ₁ )]y _a = 0 (1) dt _l for ions of species α , where a = A or B in this case. Time has been rescaled so that ω _ι ί = 2ί , a _a = C _a 4V ₀ /r ₀ ² , q _a = _a 2V r ² and p _a = C _a 2V ₂ /r ₀ ² where

C _A ⁼ Q _A f° ^r species A and ζ _Β = Q _B /(M _B CO ² ) for B. The distance r ₀ characterises the curvature of the potential for a given voltage and is approximately equal to the distance of the electrodes from the centre of the quadrupole field. We use this standard form of the Hill equation for the B-ions but for species A the connection with the standard theory of the Paul trap is more obvious if we rescale time such that ω ₂ ί = 2t ₂ ; (purely for the purpose of qualitative explanation rather than computation). where q _A = p _A In ² = Q _A 2V ₂ /(M _A a> ₂ r ² ) . The damping parameter b _A = 2Μ _Α Ι ω ₂ τ where τ is the velocity damping time constant (of underdamped oscillations) accounts for the laser cooling of species A (only). We seek conditions for which ions of molecular mass M _B are confined mainly by the field at Ui , and species A is confined by the field at ω ₂ , i.e., the term proportional to q _B ( q _a with a = B ) dominates in Eq. 1 and q _A dominates in Eq. 2. An approximate method that elucidates the behaviour of the Paul trap - for certain parameters - shows that the motion can be considered as an oscillation at a secular frequency (slow) plus small- amplitude micromotion (fast) at the driving frequency. The secular motion resembles that of a particle in a harmonic pseudopotential with spring constant κ .

This is not valid when the secular frequency -JK/M is comparable with the driving frequency and there are stable solutions of the Mathieu equation for q≤ 0.9 when a = 0. We use the value q ~ 0.3 since this is the standard operating value for a Paul trap that gives robust trapping. A simplistic way to understand the behaviour governed by the Mathieu equation is to assume that the pseudopotential acts independently of the time-independent potential given by the parameter a. Stable solutions exist for a < 0 when q≠ 0 if trapping by the AC field is strong enough to overcome the static "anti-trapping" potential, e.g., for q = 0.3 there are stable solutions for -0.045 < a < 0.085. The existence of solutions for a < 0, or more precisely that (q, a) = (0.3, 0) is not on the boundary of a stability region, results in stable operation of a Paul trap in two dimensions. Note that there are many stability regions however the one closest to (q, a) = (0, 0) is relevant here. We consider ions in a quadrupole field at each frequency ω ₂ and separately (with V ₀ = 0). i. The RF driving field at ω ₂ gives spring constants

tc _A ( ₂ , ω ₂ ) = (Ql IM _A )(V ₂ l co ₂ Y /(2r ₀ ⁴ ) and

κ _Β (ν ₂ , ω ₂ ) = (Q IM _B )(V ₂ 1 ω ₂ ) ² /(2r ₀ ⁴ ) for ions of masses M _A and M _B when ii. The field at ω _{1 :} gives a spring constant

κ _Β (ν _ι , ω ₁ ) = (Q IM _B )(y _x I c¾) ² /(2r ₀ ⁴ ) for ions of mass M _B when V ₂ = 0. We do not consider ions of mass M _A since they are predominantly trapped by the field at ω ₂ .

In case i. the ratio of the spring constants is κ _Β Ι ^' κ _Α = (Q _B ² IM _B ) I(Q _A ² I M _A ) . If the two species have the same value of Q _a ² I M _a then both are strongly trapped using a single frequency. However, even when this is possible it does not allow the independent control of the secular oscillation frequencies that is vital for resonant energy transfer. Electrospray ionisation can readily produce biomolecular ions with charge Q _B = Ze with Z = 33 for relative molecular mass M = 1.4 x 10 ⁶

corresponding to M _B /Z ² = 1285, cf. M _A = 138 for atomic barium ions. The charge-to- mass ratio of graphene flakes in a Paul trap has been measured to be

3 x 10 ^"2 C kg ^"1 from which we can estimate {M, M/Z ² } ~ {1 x 10 ⁹ , 3000}. These are just two examples of many types of charged objects which have M/Z ² greater than, or equal to, the value for ¹³⁸ Ba ⁺ and for which the method we propose has advantages.

Having similar spring constants for all ions is important for the following two reasons. Firstly, equal and opposite trapping forces on two ions i _A y _A = -i< _B y _B will result in similar displacements \y _A \ « \y _B \ . In contrast, in previous work with single- frequency Paul traps the heavier ions were pushed to the outside of the trapped cloud since κ _Β « κ _Α . Secondly, for a cloud of ions at temperature T both species will congregate within a similar distance from the trap centre since by equipartition of energy, We can balance the spring constants by making

K _a (V ₂ , co ₂ ) = K _b (V _l , co _l ) . This assumes that κ _Β (V ₂ , ω ₂ ) < κ _Β (V _l , co _l ) and indeed the field at can have the dominant influence on species B even if V _! « V ₂ . This corresponds to case i for species A, as in typical experiments with atomic ions, whilst the spring constant for species B is close to that in case ii. The secular frequency (in the pseudopotential approximation) is q 12- 2 times the radio- frequency hence for q = 0.3 we have ω _Β ~ O. l u^ and ω _Α ~ 0.1 ω ₂ resulting in a hierarchy of frequencies: ω _Β < < ω _Α < ω _2. This is illustrated in Fig 1. FIG. 1 shows the frequencies present in a trap for ions of species A and B. The secular frequencies of the ions in the radial directions, x and y (shown on the upper line of Fig. 1) and for motion along the z- axis (shown on the middle line of Fig. 1) can be chosen independently in a linear ion trap. The two radio frequencies are shown as well (the tall arrows extending from the lower line of Fig. 1). A typical value for the radial frequency of an atomic ion is ω _Α = 1 MHz. The RF field needs to be sufficiently higher (here ω ₂ = 10 MHz). The radio-frequency is chosen to give strong radial trapping of species B without significantly perturbing species A (ΟΟΪ = 0.1 ω _Α gives a good margin). The oscillation frequency of species B in the trap is ω _Β ~ 0.1 ω ₂ . In the axial motion we avoid oscillation frequencies that might be excited by the fields at ωι and ω ₂ . By choosing ω _Α,ζ = ω _Β we promote resonant transfer of energy between the species.

The field at ω ₂ has negligible effect on species B and acts to increase trapping in any case; thus for these ions two-frequency operation gives a pseudopotential very similar to a standard single-frequency Paul trap (for typical operating parameters). The quadrupole field at leads to parametric resonance at frequencies given by ηω _! = 2ω _Α where the integer n is the order of the resonance. The width of these resonances decreases rapidly with increasing order making them very sensitive to damping (of the atomic ions by laser cooling). In the numerical calculations we chose ω _Α / 2π = 1 MHz as a reasonable experimental value hence {ω _Β , ω _{1 :} ω _Α , ω ₂ }/2π = 0.01 , 0.1 , 1 , 10 MHz, as illustrated in Fig. 1. The potential of a linear trap has cylindrical symmetry and secular frequencies in the x and y-directions are referred to as the radial frequency.

Figure 2 shows the stability diagram as a function of q _A = p _A In ² and q _A In ²

(where n ² = 10 ⁴ ) for ions of species A (mass M _A ), these being the amplitudes of the two cosine terms in Eq. 2. The other two parameters are set to zero, a _A = b _A = 0. The solid line that forms the top border of the shaded band is the critical line that goes through stable and unstable regions of equal densities. (NB Numerical calculations over a wider range of parameters show that the critical curve has a maximum around q _A = 0.71 . The stability region extends up to q _A = 0.91 as expected from the Mathieu equation.) More specifically, the solid zig-zagging line is the transition curve between the region of stability (underneath) and instability (above). The sharp downward cusps correspond to tongues of instability cutting into the stable region. The loci where parametric resonance causes instability extend from these cusps down to the horizontal axis, however they are not visible because of the finite resolution of the plot (even with no damping). The critical curve passing through stable and unstable regions of equal width is shown as a solid (non-zig-zagging) line at the top of the shaded band. The tongues of instability become narrower below the critical line and asymptotically their width decreases exponentially (and similarly for the stability regions going upwards). Below the lower edge of the shaded band (dashed line), a damping coefficient of b = 10 ^"4 in Eq. 1 is sufficient to suppress the parametric resonances. Thus parameters denoted by the solid dot (at co-ordinates 0.32, 0.009) sit in a stable region for two-frequency operation of the ion trap with some damping for species A. Ions of species B are stably trapped over the whole range of parameters shown here.

All calculations have been done under the assumption of a pure sinusoidal oscillation but harmonics might be important in practice. Parametric excitation of M _A by V ₂ cos(w ₂ t) produces tongues of instability which get wider as the amplitude V ₂ increases. Figure 2 has been calculated without including any damping which would in any case only suppress the instabilities. The instabilities should in theory reach all the way to the horizontal axis but the resonances are too fine for the numeric calculations to capture them. In this sense, the granularity of the numerics acts as an effective damping parameter.

Ions in a linear ion trap are confined axially by a DC voltage U ₀ on the end-caps giving a harmonic potential with spring constants K _{A I} = Q _A 2U ₀ 1 and

^K _{B Z} ^{~ K} A z Q _B I Q _A since the force depends only on the charge, where z ₀ characterises the distance of the end-caps from the trap centre. An ion of species B sits near the centre oscillating at ω _{Β Z} = ^K _{B Z} IM _B . The 3-ion configuration A-

B-A (along the z-axis) has normal modes like those of a linear molecule such as C0 ₂ . The voltage U ₀ can be adjusted so that ω _{Α ζ} is on resonance with ω _Β , the radial frequency of species B, as illustrated in Fig. 1. As well as matching frequencies we promote transfer of energy between radial and axial modes by offsetting the axes of the quadrupole fields at and ω ₂ . This radial displacement of the potentials can be implemented by unbalancing the AC voltage (at or ω ₂ ) on a pair of diagonally opposite electrodes (of the 4 electrodes in a linear quadrupole) or applying a static electric field which exerts more force on a multiply charged ion (species B) than singly charged ions (or a combination of these that minimises micromotion). Additional ions of species A position themselves approximately along the z-axis and start forming a chain (since ω _Α » ω _Α,ζ ). The axial modes of such a chain, or linear Coulomb crystal, have higher frequency than the centre-of-mass mode whereas higher-order radial modes have lower frequency as indicated in Fig. 1 (not to scale). Thus, adding more ions tends to close the gap in the frequency spectrum of normal modes where we have placed (to avoid parametric excitation of these modes). This limits the number of ions of species A that can be accommodated in the same potential well. The usual configuration gives a harmonic trapping potential with ω _Β,ζ « ω _Α,ζ with ω _Β,ζ being the lowest frequency in the system. We have confirmed the advantages of two-frequency operation of an ion trap by numerical calculations for a single ion of species B whose radial and axial oscillation frequencies are 11.4 kHz and 0.7 kHz

respectively and ions of species A with ω _{Α ζ} = 1 1.4 kHz and ω _Α = 1 MHz so that ω _{Α ζ} = ω _Β . The B-ion is deliberately displaced in the radial direction. For example, A-B- A has a bent symmetric configuration resembling that of an H ₂ 0 molecule with A- ions at coordinates (r, z) = (17.1 , ±57.9) micrometres relative to the centre of mass of the system which coincides very closely with the massive B-ion. Similarly, configurations with more ions are not linear, by design. Using a damping time τ = 60 microseconds for species A (close to the theoretical optimum for ¹³⁸ Ba ⁺ ) gives damping times of the order of 1 second for species B in the Coulomb molecule A-B- A. Whereas in the asymmetric configuration A ₄ -B-A ₅ the damping times are 66 and 44 milliseconds for the radial and axial motion of ion-B respectively. In the highly asymmetric configuration A B-A ₅ both of these damping times for the motion of the ion-B are longer. Frequency matching is readily achieved especially when the number of ions and hence the number of normal modes of the system becomes larger. We investigated the dynamics of the system of ions after its transition to a Coulomb-crystal phase. Cooling down of the majority species to this stage can be achieved by means of a conventional single-frequency operation of a linear Paul trap. ln summary, our numerical simulations show that a typical megadalton biomolecular ion can be sympathetically cooled by atomic barium ions. The heavy ion settles to the centre of the trap and the presence of this non-fluorescing (dark) ion can be deduced from its large effect on the positions of the observable atomic ions. An intrinsic part of mass spectrometry is fragmentation and observing the breaking apart of large atomic and molecular complexes bit by bit, whilst retaining fragments in the trap to determine their charge-to-mass ratio. The fragments can have a similar charge-to-mass ratio as the parent particle. , This allows the investigation of single complexes without ensemble averaging. For large charged particles there may be coupling between their rotational degrees of freedom and the translational motion of the atomic ions in the trap giving information about the moments of inertia (and shape). Another direction in which this multiple-frequency trap could be developed is cooling of mesoscopic objects to their quantum ground state and adapting the sophisticated techniques developed for quantum information processing with trapping ions (e.g. quantum gates) to investigate quantum properties. We have presented a single worked example of how to solve the problem of confining ions of widely different charge-to-mass ratios with the same effective spring constant. Many interesting possibilities follow from this extension of laser techniques for trapping and manipulating atomic ions, to charged particles with much higher mass. We have chosen a comfortably large mass ratio to demonstrate the two-frequency operation but it also works for lower mass ratios. For example ω ₂ /ω<ι = 25 < (M _B /M _A ) ^{1 2} ~ 40 would allow trapping of electrons or positrons with protons or antiprotons since trapping in an oscillating electric field does not depend on the sign of the charge of the particle. A further application of two-frequency trap operation to antimatter is the sympathetic cooling of positrons by Be ⁺ ions which has elsewhere been demonstrated experimentally in a Penning trap - this cooling of the light particles by a heavier ion represents a role reversal as compared to the above. Figure 3 shows a linear quadrupole ion trap 300 according to an embodiment of the invention. Fig. 3(a) shows the ion trap from an end view and with power source(s) supplying the appropriate voltage signals to cause dual (or multiple) particle trapping as described above. Fig. 3(b) shows a side view of the trap electrodes with the power source(s) omitted for clarity. The quadrupole ion trap 300 has six electrodes: four parallel linear rod-like electrodes 301 , 302, 303, 304 forming a cylinder with square cross section. These electrodes are driven by radio-frequency AC signals generated by power source 310 to confine the ions radially within the trap. The power source 310 has output A connected to electrode 301 , output B connected to electrode 303 (diagonally opposite electrode 301), output C connected to electrode 302 and output D connected to electrode 304 (diagonally opposite electrode 302). The electrodes are thus grouped into two pairs of diagonally opposite electrodes - a first pair 301 , 303 and a second pair 302, 304. Outputs A and B of power source 310 are identical. Likewise outputs C and D of power source 310 are identical, but of opposite sign to outputs A and B so that outputs A and B are positive while C and D are negative and vice versa. In this way, ions within the trap are alternately pushed by electrodes 301 , 303 while being pulled by electrodes 302, 304 and then are pulled by electrodes 301 , 303 while being pushed by electrodes 302, 304.

End-cap electrodes 305, 306 are provided with a DC voltage (V _DC ) which may be provided by the power source 310 or a separate power source. As shown in Fig. 3(b), the end-cap electrodes 305, 306 are of the same polarity so that they confine ions axially within the trap, pushing them towards the trap centre. Some ions 320 are illustrated at the centre of the trap 300 in Fig. 3(b).

As described above, to confine two (or more) species of ion tightly within the trap 300, the AC signals provided on outputs A, B, C and D comprise two (or more) frequencies corresponding to the charge-to-mass ratios of the ions to be trapped as discussed above.

Figure 4 illustrates a method of examining properties of a heavier charged particle using lighter fluorescing atomic ions, both being confined tightly within the trap 400. A laser beam 410 is directed at the ions within the trap with an appropriate wavelength for causing the lighter atomic ions to fluoresce. The fluorescing ions can be visualised by imaging them through lens 420 onto camera 430.

The visible atomic ions 440 are indicated as dots within the trap 400. It can be seen that these atomic ions 440 have distributed themselves evenly throughout the length of the trap due to their mutual Coulomb repulsion. This formation of ions 440 is well known in linear ion traps and is an example of a so-called Coulomb crystal. However, as indicated by arrow 450, there is a hole in the regular pattern where no fluorescing atomic ions 440 are visible. This indicates the presence of a non-visible charged particle within the trap 400 which does not fluoresce, but which does displace the other ions 440 around it through Coulomb repulsion. Note that this only occurs because both species of ion (440 and 450) are confined tightly close to the trap centre, i.e. in the same physical space. The size of the hole and the displacements of ions 440 around it can be measured to reveal information on the mass and charge of the non-visible particle 450.

Further investigation can be performed by varying the drive frequencies applied to the trap 400 to try to resonate the non-visible particle 450. As this particle 450 gains energy (heats up) due to the resonance, it will vibrate more and cause further movement of the visible ions 440, thus facilitating indirect measurements of the non-visible particle 450. Again, this is only possible where both the visible and non- visible particles 440, 450 are both confined in the same physical space.

It will be appreciated that the terms "visible" and "non-visible" are used above to indicate whether or not the particles can be detected by the camera 430 and do not refer to visibility by the naked eye.

It will also be appreciated that in the process described above in relation to Fig. 4, the atomic ions 440 have been laser cooled so as to form a Coulomb crystal within the trap 400. The trap 400 has also been arranged as described above to cause coupling between the motion of the heavier, non-visible ion 450 and the motion of the lighter atomic ions 440 so that the heavier ion 450 is also sympathetically cooled by the laser cooling process.