System and method for determining a motional frequency of a trapped ion

Abstract

A method for determining a motional frequency of an ion in an ion trap is presented. The method includes the following steps: placing the ion at a target position; exciting a mode of motion of the ion placed at the target position by applying an excitation signal to at least one antenna, performing a spectroscopic measurement of the ion. The excitation signal has a first component at a first frequency and a second component at a second frequency. The steps are repeated iteratively to obtain a set of spectroscopic measurements. The set of spectroscopic measurements is analysed to identify the motional frequency at the target position.

Description

[0001] SYSTEM AND METHOD FOR DETERMINING A MOTIONAL FREQUENCY OF A TRAPPED ION

[0002] Technical Field

[0003] The present disclosure relates to a system and corresponding method for determining a motional frequency of a trapped ion.

[0004] Background

[0005] Knowledge of the motional frequencies of a trapped ion is a crucial prerequisite for many applications, including quantum information processing. There are several existing techniques for precise measurements of these frequencies, but the majority require laser access to the location where the motional frequencies need to be measured. However there are many situations for which there is no laser access to the location of interest, and so alternative methods are required.

[0006] Some laser-free methods for detection of the motional frequencies exist. In publication by D. J. Wineland and H. G. Dehmelt, J. Appl. Phys. 46, 919 (1975), the image currents induced in trap electrodes by the motion of the ion can be resonantly enhanced and amplified, but this ultimately leads to thermalisation of the ion’s motion with the electrode in which the image current is being induced, resulting in ion temperatures that are far too high for quantum information processing applications.

[0007] Motion of the ion can also be excited by applying oscillating electric fields to a trap electrode at a frequency close to the motional frequency, but often this is precluded by aggressive electronic filtering between the source of the de voltage and the trap electrode, which is designed to suppress noise and prevent heating of the trapped ion. In miniaturised ion traps with integrated near-field microwave antennas, it is possible to couple to the motion of the ion via motional sideband transitions on radio / microwave-frequency magnetic-dipole transitions, removing the need for laser access to the measurement location (See C. Ospelkaus et al., Phys. Rev. Lett. 101, 090502 (2008) ). This approach however requires the antenna to be designed such that the produced magnetic field gradient has a projection onto the motional mode of interest. Even in the case where the projection is optimal and a strong gradient is produced via an ion-electrode distance in the range of tens of microns, microwave powers on the order of watts may be required in order to generate sufficiently high Rabi frequencies for the sideband transitions. This precludes the measurement of the frequencies of modes that are almost normal to the direction of the magnetic field gradient, as the microwave power requirements become prohibitively high and can lead to damage of the ion trap.

[0008] It is an object of the disclosure to address one or more of the above mentioned limitations.

[0009] Summary

[0010] According to a first aspect of the disclosure, there is provided a method for determining a motional frequency of an ion in an ion trap, the method comprising performing the following steps: placing the ion at a target position; exciting a mode of motion of the ion placed at the target position by applying an excitation signal to at least one antenna, the excitation signal having a first component at a first frequency and a second component at a second frequency; performing a spectroscopic measurement of the ion; repeating the steps iteratively to obtain a set of spectroscopic measurements; and analysing the set of spectroscopic measurements to identify the motional frequency at the target position.

[0011] For instance the excitation signal may be applied for a predetermined duration for exciting the mode of motion.

[0012] Optionally, the method further comprises cooling the ion between each iteration.

[0013] Optionally, the spectroscopic measurement is performed at the target position or at a readout position.

[0014] Optionally, cooling the ion is performed at the target position prior to exciting the mode of motion, or at the readout position, or at a first position different from the target position and the readout position before placing the ion at the target position.

[0015] Optionally, the said at least one antenna comprises a first antenna configured to receive the first component and a second antenna configured to receive the second component.

[0016] Optionally, the said at least one antenna is a single antenna configured to receive both the first component and the second component.

[0017] The antenna or antennas may be provided within the ion trap, or external to the ion trap. For instance, the antenna or antennas may be implemented as electrodes.

[0018] Optionally, the excitation signal excites the mode of motion at a difference frequency between the first frequency and the second frequency; and wherein the steps are repeated iteratively for a plurality of difference frequencies to obtain the set of spectroscopic measurements. For instance, the difference frequency may be selected to be close to the motional frequency of the motional mode.

[0019] For instance, the difference frequency may be varied across a range in which the motional mode frequency is present.

[0020] Optionally, the first frequency and the second frequency are RF frequencies. For instance, the difference frequency is an angular frequency which may range between about 2TT * 0.1 MHz to about 2TT * 10 MHz. The first and second frequencies may be selected to be close to a resonant frequency of the antenna.

[0021] Optionally, the method comprises applying a drive signal having a drive frequency for the ion trap.

[0022] Optionally, the first frequency of the excitation signal is chosen to be sufficiently separated from the drive frequency to prevent coupling effects.

[0023] Optionally, the method comprises applying DC voltage offsets to DC electrodes associated with the target location to rotate a principal axes of motion such that an oscillating electric field generated by the at least one antenna couples to the motional mode.

[0024] Optionally, the spectroscopy measurement is a fluorescence measurement.

[0025] Optionally, wherein performing a spectroscopy measurement comprises driving the ion to a metastable state and measuring a fluorescence emission.

[0026] Optionally, wherein analysing the set of spectroscopic measurements comprises comparing fluorescence measurements obtained for various difference frequencies and identifying the difference frequency corresponding to a maximum fluorescence signal.

[0027] Optionally, wherein the ion trap is coupled to a laser system configured to provide laser radiation at the first position and / or at the readout position, and no laser radiation at any other positions within the ion trap; or wherein the laser system is configured to provide laser radiation at the first position and / or at the readout position and to provide laser radiation at some, but not all, target positions.

[0028] Optionally, wherein the second frequency is a sum of the first frequency and an offset frequency or wherein the second frequency is a difference of the first frequency minus the offset frequency.

[0029] According to a second aspect of the disclosure, there is provided an ion trap system comprising an ion trap coupled to a controller configured to perform the method of the first aspect.

[0030] Optionally, the ion trap comprises a plurality of DC electrodes, at least one drive electrode for receiving a drive signal, and at least one antenna for receiving an excitation signal; the ion trap system further comprising a voltage source coupled to the DC electrodes; a signal generator configured to generate the drive signal and the excitation signal; a laser system; a photon detector; and wherein the controller is configured to perform the following steps: placing the ion at a target position using the voltage source; exciting a mode of motion of the ion placed at the target position by applying the excitation signal to the at least one antenna, the excitation signal having a first component at a first frequency and a second component at a second frequency; performing a spectroscopic measurement of the ion using the laser system and the photon detector; the controller being further configured to repeat the steps iteratively to obtain a set of spectroscopic measurements; and analyse the set of spectroscopic measurements to identify the motional frequency at the target position.

[0031] For instance, the signal generator may include a first generator configured to generate the drive signal and a second generator to generate the excitation signal. The second generator may include a first source (sub-generator) to generate the first component, and a second source (sub-generator) to generate the second component.

[0032] Optionally, the signal generator comprises a combiner configured to combine a first signal at the first frequency and a second signal at the second frequency to generate the excitation signal.

[0033] Optionally, wherein the second frequency is a sum of the first frequency and an offset frequency or wherein the second frequency is a difference of the first frequency minus the offset frequency.

[0034] For instance the laser system may be configured to provide laser radiation at a first position and / or at the readout position, and no laser radiation at any other positions within the ion trap. Alternatively, the laser system may be configured to provide laser radiation at the first position and / or at the readout position and to provide laser radiation at some, but not all, target positions.

[0035] According to a third aspect of the disclosure, there is provided a quantum device comprising the ion trap system according to the second aspect.

[0036] For instance, the quantum device may be a quantum computer or a quantum sensor or an atomic clock. Description of the drawings

[0037] The disclosure is described in further detail below by way of example and with reference to the accompanying drawings, in which: figure 1 is a flow chart of a method for determining a motional frequency of an ion in an ion trap; figure 2A is a schematic diagram of an ion trap system for implementing the method of figure 1; figure 2B is a diagram of an exemplary signal generator for use in the system of Figure 2A; figure 3A is an exemplary implementation of the ion trap system of figure 2; figure 3B is a diagram of an ion trap for use in the system of figure 3A; figure 3C is a diagram of another ion trap for use in the system of figure 3A;figure 4A is a plot of an example excitation signal shown over 80 periods; figure 4B is a plot of the excitation signal of figure 4A shown over 500 periods; figure 5A is a state diagram illustrating electron shelving detection using a metastable state; figure 5B is a state diagram illustrating direct fluorescence detection; figure 6 is a plot showing fluorescence measurements obtained for a plurality of difference frequencies.

[0038] Description

[0039] Figure 1 is a flow chart of a method for determining a motional frequency of an ion in an ion trap. The mode of motion of the ion may also be referred to as motion mode or motional mode. The method includes the following steps:

[0040] At step 110 the ion is placed at a target position. At step 120 a mode of motion of the ion placed at the target position is excited. This is achieved by applying an excitation signal to at least one antenna. The excitation signal has a first component at a first frequency (flex) and a second component at a second frequency (flex -c ). This may be used to excite the mode of motion at a difference frequency (co) between the first frequency (flex) and the second frequency (flex-co). The excitation signal may be applied for a predetermined duration for exciting the mode of motion. The symbols (flex) and (flex-co) represent the angular frequencies of the first and second components, respectively. Both components of the excitation signal may be applied to a single antenna. Alternatively, the first component may be applied to a first antenna, and the second component may be applied to a second antenna. The first and second components of the excitation signal may be two individual signals, or they may be combined.

[0041] At step 130 a spectroscopic measurement of the ion is performed. This step may be performed at the target position or at a readout position. In the latter case the ion is moved from the target position to a readout position prior to performing the spectroscopic measurement. The spectroscopic measurement may be used to determine the motional state of the ion.

[0042] The steps 110 to 130 are then repeated iteratively to obtain a set of spectroscopic measurements. For instance, the steps may be repeated iteratively for a plurality of second components. When the excitation signal excites the mode of motion at a difference frequency between the first frequency and the second frequency, the steps are repeated iteratively for a plurality of difference frequencies to obtain the set of spectroscopic measurements.

[0043] At step 140 the set of spectroscopic measurements is analysed to identify the motional frequency at the target position. The motional frequency may also be referred to as the resonance frequency of the mode of interest.

[0044] Between each iteration the ion would typically be cooled down. This may be performed at step 110 or just before, so as to prevent effects of the previous iteration affecting the subsequent measurements. The step of cooling the ion may be performed at the target position, or at the readout position, or at a first position different from the target position and the readout position. The first position may be a central position in the trap where the ion may be cooled using a laser cooling technique.

[0045] Figure 2A is a schematic diagram of an ion trap system for implementing the method of figure 1. The ion trap system 200 includes an ion trap 210, a laser system 240, a signal generator 270, a voltage source 280 and a photon detector 260. A controller 290 is provided to control the laser system 240, the signal generator 270, the voltage source 280 and the detector 260.

[0046] The laser system 240 may include several lasers. The number of lasers depends on the ion species in use, and the application. For instance a first laser may be required to drive the ion into a metastable state, and a second laser for exciting fluorescence.

[0047] The signal generator 270 may include several sub generators having specific connections to electrodes of the ion trap.

[0048] The signal generator 270 may include a first generator configured to generate a first signal S_Ex (excitation signal) for exciting a mode of motion of the ion, and a second generator configured to generate a second signal S_Trap (trap signal or drive signal) for trapping the ion.

[0049] The first signal also referred to as the excitation signal, has a first component at a first frequency flex and a second component at a second frequency flex +to, or flex -to, in which to is an offset or difference frequency in angular frequency units. The first signal is used to excite the mode of motion of the ion by selecting the difference frequency (to) to be close to the resonant frequency to; of the motional mode (i) of interest. The second signal, also referred to as the drive signal or trap signal, has a third frequency fltrap, referred to as the drive frequency. The first frequency flex is preferably chosen to be relatively far from the drive frequency fltrap or any other resonances of the system or ion in order to prevent unwanted additional couplings.

[0050] The controller 290 is configured to switch the signal S_Ex on or off, so that S_Ex is only applied during step 120. Alternatively, the controller 290 may be configured to maintain the signal S_Ex on, and to change the offset frequency co in step 120 to provide the excitation.

[0051] The range of frequencies provided by the signal generator 270 is selected depending on the application and the nature of the ion to be trapped. As mentioned above ions can be single atoms, or they can be molecules, nanoparticles, dust particles, or even single electrons. Therefore frequencies from a few Hz up to GHz are used in different applications. For instance, the signal generator may be an RF generator configured to generate electrical signals having a frequency in a frequency range between 3 kilohertz (kHz) - 300 Megahertz (MHz) or a microwave (MW) generator configured to generate electrical signals having a frequency in the frequency range between 300 MHz - 300 gigahertz (GHz).

[0052] Figure 2B is a diagram of an exemplary signal generator for use in the system of Figure 2A. In this example the signal generator includes two sources providing the signals SI = Ai sin (flex t) and S2 = A2 sin ((flex +co)t), respectively. The signals SI and S2 are then combined in a combiner to generate the signal S_Ex, which takes the form A3 sin (flext) + A4 sin ((flex + co) t). The generator also includes a third source for providing the trap signal S_trap = As sin (fltrap t). More generally, the signals SI, S2 and S_Ex may be expressed as a function of a phase parameter as: SI = Ai sin (flext + 4>_1) and S2 = A2 sin ((flex +co)t + 4>_2) so that S_Ex = A3 sin (flext + 4>_3) + A4 sin ((flex + co) t + 4>_4) . The first frequency flex may be fixed to a predetermined value well separated from the drive frequency fltrap. The second frequency flex+co also referred to as sideband frequency is the frequency of the sideband tone.

[0053] The excitation signal S_Ex may be applied to a single antenna. Alternatively the signal S_Ex may be applied to two antennas: a first antenna that receives the first frequency component and a second antenna that receives the second frequency component. This may be achieved using a frequency splitter at the output of the combiner. Alternatively this may be achieved by applying the signal SI = Ai sin (flex t) and S2 = A2 sin ((flex +u))t) directly from the source, hence not using a combiner.

[0054] Figure 3A is an exemplary implementation of the ion trap system of figure 2. The trapped ion system 300 includes an ion trap 310 provided in a vacuum chamber 320. The ion trap 310 is coupled to an ion source 330, such as a barium ion source configured to provide the barium ion 305 to the ion trap. The trapped ion system 300 also includes a laser system 340; a magnetic field source 350a, 350b; a fluorescence detector 360, two signal generators 370 and 375, a voltage source 380, and a controller 390.

[0055] The RF generator 370 generates the trap signal S_Trap (trap signal) for trapping the ion. The generator 375 generates the excitation signal S_Ex for exciting a mode of motion of the ion. The signal generator 375 may also be used to perform quantum operations. The magnetic field source 350 is optional and may be used to apply a magnetic field to the ion trap. The laser system 340 may be used to perform various functions including: laser cooling, spectroscopy readout, and optionally qubit manipulation.

[0056] Figure 3B is a diagram of the ion trap 310 used in the system of figure 3A. The ion trap 310 includes three types of electrodes: DC electrodes coupled to the voltage source 380, drive electrodes (in this case RF electrodes) coupled to the RF generator 370 for trapping the ion, and an excitation electrode (for instance RF or microwave electrode), also referred to as antenna, coupled to the generator 375 for performing mode excitation and quantum operations. The antenna (excitation electrode) may be part of a resonant circuit in order to provide enhancement of voltage or current at a particular frequency. The shape of this antenna may vary depending on the nature of the ion and the application. In the example provided the RF Generator 370 may be set with a main frequency chosen between about 5 to 100 MHz, for instance 45 MHz.

[0057] In this example the ion trap 310 has two sets of outer DC electrodes labelled 311 and 312, and two RF electrodes labelled 313 and 315. An additional electrode or antenna 314 is provided between the RF electrodes 313, 315 (see figure 3B).

[0058] Each set of DC electrodes includes 5 DC electrodes labelled ABCDE and A’B’C’D’E’, respectively. The electrodes C and C’ are the central electrodes and define a central region in the ion trap. The RF electrodes 313, 314 and 315 have a longitudinal shape and are arranged side by side. The RF electrodes are sandwiched between the two sets of outer DC electrodes 311 and 312. The number of electrodes and the electrode configurations may vary. For instance, the number of DC electrodes per set could be 1, 3 or 5. The number of RF electrodes may also be increased.

[0059] The region on the X axis limited by electrodes C and C’ is referred to as the central region of the trap. This region is provided with laser access from the laser system 340. The other regions of the trap have no access to the laser system.

[0060] The RF electrodes are used to confine the ion 305 in the yz plane as shown in figure 3B. In the trap shown in figure 3B the ion 305 is confined in the y- and z-dimensions by the RF field and the RF node forms a line along the x- axis. However, the proposed method of figure 1 may be used with different ion trap designs that use the radiofrequency fields for confinement along all three axes, meaning that the RF node is just a single point.

[0061] The barium ion source 330 includes a neutral atom source to provide the neutral barium atom and an ionisation device configured to ionize the barium atom and hence provide the barium ion 305. The neutral atom source and ionisation device are not shown in the figure 3A. The neutral atom source could be, for example, a resistively heated atomic oven or an ablation target. The ionisation device could be, for example, a network of lasers of various operational wavelengths.

[0062] Depending on the level of sensitivity required for the measurement, the ion is cooled down to the Doppler temperature or in the ground state of all of its motional modes. This can be achieved using the laser system 340 by performing various laser cooling techniques. As such the controller 390 may be configured to control the laser system 340 for implementing various laser cooling techniques.

[0063] Therefore the ion 305 is prepared or cooled at the centre of the ion trap 310 also referred to as first position or central position. The ion 305 is then transported from the first position to a target position. The transportation of the ion can be accomplished by varying the voltage applied to the set of DC electrodes 311 and 312. For instance different voltages may be applied at the electrodes A,B,C,D,E of 311 to generate a positive or a negative voltage gradient. Similarly different voltages may be applied at the electrodes A’,B’,C’,D’,E’ of 312 to generate a positive or a negative voltage gradient. Depending on the charge state of the ion (positive or negative), the gradient may be used to move the ion in a desired direction. The voltages applied to the DC and RF electrodes may vary during the transport operation, with the final voltages designed to locate the ion at the target position. The controller 390 may be configured to control the voltage source 380 to implement various ion transportation techniques.

[0064] The system 300 is then used to excite one motional mode of the ion, that is a single mode for which the frequency needs to be determined. The controller 390 controls the RF generator 370 and the generator 375 to generate a signals S_Trap and S_Ex, respectively. The controller 390 is configured to apply the excitation signal S_Ex to the antenna 314 only during step 120.

[0065] This proposed approach overcomes the microwave power requirement for the detection of motional mode frequencies for trapped ion(s), whilst still making use of the antenna that is already integrated into the ion trap. Rather than using the near-field magnetic field gradient to couple to the motion of the ion, the electric field produced by the antenna 314 is utilised. In this design, the resulting electric field at the location of the ion is primarily directed perpendicular to the xy plane as shown in figure 3B. As mentioned above the shape of the antenna, which governs the EM field produced, depends on the ion and the application. In general and as in the present example, the antenna will have a single frequency where it operates most effectively, however in some designs the antenna may support multiple frequencies.

[0066] Directly supplying a tone at the motional frequency of the ion to the antenna would lead to excitation of motion, but in general the antenna will have a resonant frequency in the hundreds of megahertz to tens of gigahertz range in order to amplify the current used to produce the magnetic field gradient, which leads to significant suppression of any signal at the motional frequency which is typically in the range of hundreds of kilohertz to ten megahertz. Instead, a combination of two radiofrequency signals is delivered into the antenna. Both frequencies (flex) and (flex+w) are close to the resonant frequency of the antenna 314, and the antenna quality factor is sufficiently low as to support both of these tones. The frequencies (flex) and [flex+co] of the individual tones are sufficiently detuned from any atomic transitions in the ion(s) to avoid unwanted coupling to these transitions.

[0067] If the frequency difference between the two signals matches one of the motional frequencies of the trapped ion(s), this leads to the motion of the ion being excited. This requires a non-zero projection of the oscillating electric field generated by the antenna 314 onto the direction of motion of the motional mode. Small de voltage offsets can be applied to the electrodes near the target location of the ion in order to slightly rotate the principal axes of motion such that the oscillating field couples to the motional mode of interest without significantly altering the mode frequency.

[0068] The use of electric fields to produce a motional excitation rather than driving sideband transitions with a microwave field gradient from the same electrode means that the microwave power requirements are significantly reduced, thereby allowing the excitation of modes with much smaller projections onto the direction of the produced field.

[0069] Figure 3C is a diagram of another ion trap for use in the system of figure 3A. The ion trap 310’ is similar to the ion trap 310, and the same reference numerals are used to show corresponding features. In this case, the antenna 314 has been replaced by two antennas labelled 314a and 314b placed side by side. The first antenna 314a receives the first component S_Ex(Fl] at the first frequency flex and the second antenna 314b receives the second component S_Ex(F2] at a second frequency flex +co, or flex -co.

[0070] Figure 4A is a plot of an example excitation signal shown over 80 periods. Figure 4B is a plot of the excitation signal of figure 4A shown over 500 periods. In this example the excitation signal S_Ex is a microwave voltage. The excitation signal 400 is obtained with a generator as described with reference to figure 2B and has a first component at a first frequency flexand a second component at a second frequency flex+co, or flex-co, in which co is an offset frequency. In this example, the first frequency flex is about 2TT * 250

[0071] MHz and co is about 2TT * 2.5 MHz.

[0072] The excitation signal is used to excite the mode of motion of the ion whose frequency lies close to the difference frequency (co) between the first frequency and the second frequency.

[0073] The excitation signal may be applied to the antenna 314 for a variable period of time with variable amplitude. The amplitude of the signals and the duration of the excitation pulse can be tuned to give the required magnitude of response for the mode of interest.

[0074] Advantageously, exciting motional modes as described above does not involve the use of any laser. Therefore this step can be performed at arbitrary locations within the trap, even those without laser access. After excitation of the motional mode, the ion is returned from the target position to the first (central) region of the trap which is provided with laser access, and where spectroscopic measurements can be performed.

[0075] The controller 390 is configured to control the laser system 340 and the detector 360 to perform various spectroscopic measurements. In this example the laser system 340 is operated to excite the ion 305 in a metastable state and the detector 360 to subsequently detect fluorescence emission. This is referred to as the electron shelving detection technique.

[0076] The laser system 340 can be subdivided into several subsets of lasers. One subset is operated to excite the ion 305 into a short-lived excited state, and the detector 360 can be used to detect fluorescence emission caused by spontaneous decay from the excited state. Another subset of lasers can excite the ion into a metastable state, which subsequently prevents the ion being excited to the short-lived state by the first subset of lasers and hence no fluorescence can be observed by the detector. The probability of detecting the fluorescence signal varies as a function of the motional state of the ion 305. In general, lower levels of motional excitation of the ion result in a higher chance of producing the metastable state, from which fluoresce is not observed. A more energetic ion has a lower probability of reaching the metastable state, and therefore will have a higher probability of fluorescing. When the difference frequency co is equal to the resonant frequency C R of the motional mode, then a maximal fluorescence signal is observed.

[0077] It will be appreciated that other methods can be implemented that do not rely on producing a metastable state and would produce signals that are potentially inverted, that is observing a lower probability of detecting fluorescence for a higher levels of motional excitation and a higher probability of detecting fluorescence for lower levels of motional excitation.

[0078] In a specific example the laser system 340 has a narrow-linewidth laser used to excite a narrow optical transition, for example an optical clock transition, in the ion 305. The laser pulse duration may be chosen to give optimal state transfer for the ion in the motional ground state. If the ion was at the Doppler temperature before the measurement began, it is a carrier transition to the metastable state that is driven. Reduction in contrast of this state transfer indicates that one or more of the motional states were excited by the exciting fields. If the ion was in the motional ground state before the measurement began, sideband transitions to the metastable state can be driven which offer enhanced sensitivity to smaller exciting fields and hence allow smaller projections of the mode of interest onto the electric field produced by the antenna. Measurement of the motional sidebands is a standard technique for ion thermometry, and other alternative techniques may be used.

[0079] Figure 5A is a state diagram illustrating electron shelving detection using a metastable state. The diagram shows the ground state 25^2, the excited state 2P1 / 2, and the metastable state 2£)5 / 2. The excited state is short lived and can lead to fluorescence, while the metastable state is long lived and does not lead to fluorescence. This readout technique is applicable to most of the frequently used singly-charged atomic ions including calcium, ytterbium and barium; and variations on this technique are available for ions which have no accessible metastable states such as beryllium and magnesium which uses their hyperfine levels or Zeeman sublevels instead of their gross electronic structure. This technique is very sensitive to ion temperature, but relatively complex to implement. It will be appreciated that some ions may have different electronic structures and variations on this technique would be necessary.

[0080] Figure 5B is a state diagram illustrating direct fluorescence detection. This readout technique is applicable to almost all of the most frequently used atomic ions. It is less sensitive to ion temperature, but more convenient to implement.

[0081] Regardless of the readout technique being implemented, the steps 110 to 130 of the method of figure 1, are then repeated iteratively for a plurality of difference frequencies to obtain a set of spectroscopic measurements.

[0082] Figure 6 is a plot showing the fluorescence measurements obtained for a plurality of difference frequencies. Each point is the result of several measurements at the same difference frequency co. The number of measurements may vary, for example 10 or more measurements may be used.

[0083] The lower the level of motional excitation of the ion, the higher the chance of producing the metastable state, which does not fluoresce under application of the relevant subset of lasers. An ion with higher levels of motional excitation does not reach the metastable state, and therefore will fluoresce under the application of the same lasers. In this example a maximum probability of detecting fluorescence is observed for a difference frequency of about 1.468 MHz . This corresponds to the resonant frequency COR of the excited mode of 2 TT * 1.468 MHz.

[0084] As mentioned above, the optical system and ion trap may be designed in different ways and laser access may be provided only at the first (central position) and / or the readout position, or to the first position and to some but not all target positions.

[0085] If the target position is provided with suitable laser access, then all steps of the method including cooling and spectroscopic measurements may be provided at the target position.

[0086] The ion trap system and method of the disclosure may be used as part of a quantum device such as a quantum computer or a quantum sensor or an atomic clock.

[0087] A skilled person will appreciate that variations of the disclosed arrangements are possible without departing from the disclosure. Accordingly, the above description of the specific embodiments is made by way of example only and not for the purposes of limitation. It will be clear to the skilled person that minor modifications may be made without significant changes to the operation described.

Claims

CLAIMS1. A method for determining a motional frequency of an ion in an ion trap, the method comprising performing the following steps: placing the ion at a target position; exciting a mode of motion of the ion placed at the target position by applying an excitation signal to at least one antenna, the excitation signal having a first component at a first frequency and a second component at a second frequency; performing a spectroscopic measurement of the ion; repeating the steps iteratively to obtain a set of spectroscopic measurements; and analysing the set of spectroscopic measurements to identify the motional frequency at the target position.

2. The method as claimed in claim 1, further comprising cooling the ion between each iteration.

3. The method as claimed in claim 1 or 2, wherein the spectroscopic measurement is performed at the target position or at a readout position.

4. The method as claimed in claim 3 when depending on claim 2, wherein cooling the ion is performed at the target position prior to exciting the mode of motion, or at the readout position, or at a first position different from the target position and the readout position prior to placing the ion at the target position.

5. The method as claimed in any of the preceding claims , wherein the said at least one antenna comprises a first antenna configured to receive the first component and a second antenna configured to receive the second component.

6. The method as claimed in any one of the claims 1 to 4, wherein the said at least one antenna is a single antenna configured to receive both the first component and the second component.

7. The method as claimed in any of the preceding claims , wherein the excitation signal excites the mode of motion at a difference frequency between the first frequency and the second frequency; and wherein the steps are repeated iteratively for a plurality of difference frequencies to obtain the set of spectroscopic measurements .

8. The method as claimed in any of the preceding claims, wherein the first frequency and the second frequency are RF frequencies.

9. The method as claimed in any of the preceding claims, comprising applying a drive signal having a drive frequency for the ion trap.

10. The method as claimed in claim 9, wherein the first frequency of the excitation signal is chosen to be sufficiently separated from the drive frequency to prevent coupling effects.

11. The method as claimed in any of the preceding claims, comprising applying DC voltage offsets to DC electrodes associated with the target location to rotate a principal axes of motion such that an oscillating electric field generated by the at least one antenna couples to the motional mode.

12. The method as claimed in any one of the preceding claims, wherein the spectroscopy measurement is a fluorescence measurement.

13. The method as claimed in any one of the preceding claims, wherein performing a spectroscopy measurement comprises driving the ion to a metastable state and measuring a fluorescence emission.

14. The method as claimed in claim 12 or 13, wherein analysing the set of spectroscopic measurements comprises comparing fluorescence measurements obtained for various difference frequencies and identifying the difference frequency corresponding to a maximum fluorescence signal.

15. The method as claimed in any one of the claims 4 to 14, wherein the ion trap is coupled to a laser system configured to provide laser radiation at the first position and / or at the readout position, and no laser radiation at any other positions within the ion trap; or wherein the laser system is configured to provide laser radiation at the first position and / or at the readout position and to provide laser radiation at some, but not all, target positions.

16. The method as claimed in any one of the preceding claims, wherein the second frequency is a sum of the first frequency and an offset frequency or wherein the second frequency is a difference of the first frequency minus the offset frequency.

17. An ion trap system comprising an ion trap coupled to a controller configured to perform the method of any one of the claims 1 to 16.

18. The ion trap system as claimed in claim 17, wherein the ion trap comprises a plurality of DC electrodes, at least one drive electrode for receiving a drive signal, and at least one antenna for receiving an excitation signal; the ion trap system further comprising a voltage source coupled to the DC electrodes; a signal generator configured to generate the drive signal and the excitation signal; alaser system; a photon detector; and wherein the controller is configured to perform the following steps: placing the ion at a target position using the voltage source; exciting a mode of motion of the ion placed at the target position by applying the excitation signal to the at least one antenna, the excitation signal having a first component at a first frequency and a second component at a second frequency; performing a spectroscopic measurement of the ion using the laser system and the photon detector; the controller being further configured to repeat the steps iteratively to obtain a set of spectroscopic measurements; and analyse the set of spectroscopic measurements to identify the motional frequency at the target position.

19. The ion trap system as claimed in claim 18 , wherein the signal generator comprises a combiner configured to combine a first signal at the first frequency and a second signal at the second frequency to generate the excitation signal.

20. The ion trap system as claimed in claim 18 or 19, wherein the second frequency is a sum of the first frequency and an offset frequency or wherein the second frequency is a difference of the first frequency minus the offset frequency.

21. A quantum device comprising the ion trap system of any one of the claims 17 to 20.

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