System and method for probing a trapped ion

Abstract

A method for probing an ion in an RF ion trap comprises: placing the ion at a target position; exciting at least one mode of motion of the ion by applying a drive signal comprising a first component h

Description

Technical Field The present disclosure relates to a system and corresponding method for probing a trapped ion. In particular, the present disclosure relates to a method for identifying a reference position in which the ion experiences a minimal amount of unwanted driven motion, also referred to as excess micromotion. Background A commonly used ion trap design is the Paul trap, also known as a radio frequency (RF) trap. In this design, RF and DC voltages are applied to various electrodes in the structure of the ion trap, thereby creating a combination of RF and DC potentials that act to confine the ion(s) in three dimensions. These potentials vary in space within the trap, which leads to the problem outlined below. It is possible to trap, store, and manipulate ions at many locations inside an ion trap. However, some trapping locations are more desirable than others. For a wide range of quantum technology applications, ranging from quantum sensors to atomic clocks and quantum computing, it is desirable to trap the ions within a few nanometers of the locations in space that have a very low RF electric field. The points are called “RF nodes" or "RF minima”. The further away the ion is from an RF node, the more it suffers from an effect called "excess micromotion”. Even for those applications that are less sensitive to excess micromotion, the RF node provides a valuable reference position for the ion within the trap, as it is well-defined in space. Excess micromotion can cause several issues for quantum technologies based on trapped ions, including degradation of laser-cooling due to distortion of the cooling transition lineshape, heating of the ions due to technical noise on the RF signal producing the trapping potential, and variation in the Rabi frequencies for various key optical and microwave transitions. The technical noise may arise from other equipment in the lab, or it may be due to thermal noise of the different electronic components. As such, detecting and minimising excess micromotion is an essential tool for many applications. This is however not a one-off procedure, as the DC potentials are never completely stable over the timescales of seconds to days in real ion traps. Laser-induced charging, contamination of the surfaces near to the ion, or changes in the outputs of the voltage supplies connected to the trap electrodes, can all lead to drifts in the position of the ion over time. This necessitates frequent re-optimisation of the position of the ion, which has become a standard procedure when working with trapped ions. Several techniques for detecting and minimising excess micromotion exist as discussed in J. Keller et al., J. Appl. Phys. 118, 104501 (2015). The majority of these techniques work by varying the position of the ion(s) in the trap, followed by detection of the amplitude of the excess micromotion at that location. Depending on the geometry of the trap, a search in 2D or 3D space is performed to find the point at which the overall induced motion is minimised, which occurs at the minimum of the RF field. Most of the existing techniques require the ion to be addressed with laser beams at the measurement location to detect the induced motion. This imposes the following limitations. Firstly, access for laser beams must allow a projection onto all possible directions of motion of the trapped ion, which may not be possible due to geometric restrictions imposed by the trap or surrounding hardware. This is also generally not possible with surface-electrode ion traps where free-space laser access is restricted to a plane parallel to the trap surface. This restriction is imposed because shining laser beams directly onto the chip can be problematic due to the resulting reflections, scatter, and possible charging of the surface, for example. Because of this constraint, systems using this trap design cannot use this method to detect induced micromotion that is out of the plane of the chip. Secondly, it is not compatible with a scalable quantum charge-coupled-device where laser access is restricted to a limited number of zones but micromotion measurement and potentially also minimisation may be required at all possible trapping locations. In contrast to laser beams, the rf trapping field is ubiquitous throughout the trap. As such, this has the potential to allow the generation of a signal indicating excess micromotion in all regions of an ion trap, even those without laser access. The technique detailed in section III.D.2 and Figure 8 of J. Keller et al., J. Appl. Phys. 118, 104501 (2015) and references therein, applies amplitude modulation to the RF field used to confine the ion, with a measurable response from the ion if the modulation frequency closely matches a motional frequency of the ion, with the magnitude of the response depending on the strength of the RF field that the ion experienced at the measurement location. No response is observed if the ion is located at the RF node, indicating successful compensation of the ion position. However, typical implementations of this technique require laser access to the measurement location in order to detect the induced motion, and additionally require precise measurements of the motional frequencies of the ion in advance in order that the RF trapping field can be modulated at the optimal frequency. These motional frequencies are typically measured using lasers, and hence this poses a challenge in trapping regions without laser access. Furthermore, the situation is greatly complicated in strongly anharmonic ion traps such as surface-electrode ion traps where the motional frequencies are also spatially-dependent. This leads to distortion or even loss of effectiveness of the excitation signal as the position of the ion is varied, see “Micromotion minimisation by synchronous detection of parametrically excited motion” D. P. Nadlinger et al., arXiv:2107.00056 (2021). The modulation frequency can be iterated between measurements in order to always generate an observable signal, but this would lead to an increase in the number of measurements required, slowing down the measurement procedure. Measurements of the anharmonicity could allow a feedforward to be applied to the modulation frequency based on the change in the ion position, but this still requires knowledge of the motional frequency at one spatial location and adds further calibration measurements to an already complex system. It is an object of the disclosure to address one or more of the above mentioned limitations. Summary According to a first aspect of the disclosure, there is provided a method for probing an ion in an ion trap, the method comprising performing the following steps: placing the ion at a target position; exciting at least one mode of motion of the ion by applying a drive signal comprising a first component having a first frequency and a second component having a second frequency, and wherein applying the second component covers a predetermined frequency range; performing a spectroscopy measurement of the ion; repeating the steps iteratively for a plurality of different target positions to obtain a set of spectroscopic measurements. For example, the method may be used to identify a level of excess micromotion of the ion. For instance, the first frequency may be a drive frequency for the ion trap. The first component may be applied for an extended duration to trap the ion. Optionally, the spectroscopic measurement provides a signal that is function of the motional state of the ion. For instance, the motional state may be a function of a level of excitation of the said at least one mode of motion. Optionally, the second frequency has a frequency window that spans over the predetermined frequency range. Optionally, the method comprises sweeping the second frequency over the predetermined frequency range. Optionally, the second frequency is a sum of the first frequency and an offset frequency or the second frequency is a difference of the first frequency minus the offset frequency. For instance the first frequency may be a predefined frequency, for example an RF frequency. The offset frequency may be a motional frequency of one or more modes of motion of the ion, or a frequency that is relatively close to a motional frequency of one or more modes of motion of the ion. The offset frequency may be swept over a predetermined range that includes one or more motional frequencies. For instance, the offset frequency may be swept between a lower frequency and an upper frequency, for example between 1 MHz and 10 MHz or between 2 MHz and 7 MHz. Optionally, the predetermined frequency range is chosen such that an offset frequency range includes at least one motional frequency. Optionally, the method comprises applying the second frequency component for a predetermined duration for exciting the said one or more modes of motion. Optionally, the predetermined duration is chosen such that the Fourier-transform-limited spectrum of the second frequency component spans a desired offset frequency range. Optionally, exciting at least one mode of motion comprises applying a pulse of white frequency noise. For instance the pulse may be a band-limited pulse. Optionally, the spectroscopy measurement of the ion is performed at the target position, or at a readout position. Optionally, the method further comprising cooling the ion between each iteration; wherein the step of cooling the ion is performed at the target position prior to exciting the said at least one 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. Optionally, wherein the ion is trapped in a trapping potential generated by the first component of the drive signal, and wherein the ion experiences excess micromotion caused by the drive signal. Optionally, the method further comprising analysing the set of spectroscopic measurements to identify a reference position; wherein in the reference position the ion experiences a minimal amount of excess micromotion. Optionally, the method further comprises moving the ion to the reference position. Optionally, the method further comprising analysing the set of spectroscopic measurements to derive an amount of excess micromotion. For example analysing the set of spectroscopic measurement may comprise fitting the spectroscopic data using a model. Optionally, wherein the spectroscopy measurement is a fluorescence measurement. Optionally, wherein performing a spectroscopy measurement comprises driving the ion to a metastable state and measuring a fluorescence emission. Optionally, 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 the readout position and to provide laser radiation at some, but not all, target positions. 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 according to the first aspect. Optionally, the ion trap comprises a plurality of DC electrodes and at least one drive electrode, the ion trap system further comprising a voltage source coupled to the DC electrodes; a signal generator coupled to the said at least one drive electrode; a laser system; a photon detector; and wherein the controller is configured to perform the following steps: place the ion at a target position using the voltage source; excite at least one mode of motion of the ion using the signal generator by applying a drive signal comprising a first component having a first frequency and a second component having a second frequency, and wherein applying the second component covers a predetermined frequency range; perform a spectroscopic measurement of the ion using the laser system and the photon detector; the controller being further configured to repeat the steps iteratively for a plurality of different target positions to obtain a set of spectroscopic measurements. For example, the drive electrode may be an RF electrode and the signal generator an RF generator. Optionally, 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 the readout position and to provide laser radiation at some, but not all, target positions. 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. Optionally, the signal generator comprises a signal source configured to generate a signal at the first frequency, and a modulator configured to generate a modulation signal at an offset frequency. According to a third aspect of the disclosure, there is provided a quantum device comprising the ion trap system according to the second aspect. For instance, the quantum device may be a quantum computer or a quantum sensor or an atomic clock. Description of the drawings The disclosure is described in further detail below by way of example and with reference to the accompanying drawings, in which: figure lisa flow chart of a method for probing 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 2C is a diagram of another 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 the ion trap used in the system of figure 3A; figure 4 is a plot of an example drive signal shown over 100 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 different target positions of the ion; figure 7 is a fluorescence map showing the probability of the ion fluorescing for various y-z positions of the ion trap. Description Figure 1 is a flow chart of a method for probing an ion in an ion trap. Ions can be single atoms, or they can be molecules, nanoparticles, dust particles, or even single electrons. The method includes the following steps: At step 110 the ion is placed at a target position. At step 120 at least one mode of motion of the ion is excited by applying a drive signal comprising a first component having a first frequency and a second component having a second frequency, and wherein applying the second component covers a predetermined frequency range. Exciting a mode of motion of the ion, also referred to as motion mode or motional mode, may be performed by modifying a drive signal used to trap the ion. For instance the drive signal may be modified such that it comprises the first component having a first frequency and the second component having a second frequency; and by sweeping the second frequency over the predetermined frequency range. Alternatively, the second frequency may be selected to span over a relatively broad spectrum (non-monochromatic), in which case there is no need to sweep the second frequency. The predetermined frequency range may be selected such that one or more motional frequencies are excited, i.e such that the captured range in the motional frequency falls within the predetermined frequency range. The first frequency is always present and is used for trapping the ion, the second frequency may be used momentarily for exciting on or more modes of motion. For a single trapped ion there are 3 motional modes. These are referred to as normal modes because they are all at 90 degrees to one another. Their orientation is set by the geometry of the DC and RF fields used to make the trapping potential, and this can be either set to a fixed orientation for all time or changed dynamically. For a chain of N trapped (cold) ions, there are N possible modes of motion along each of the 3 directions, but the directions remain the same. Depending on the number of ions, these modes look like the chain is swinging, stretching, or bending. The proposed method can be used to excite one or more motional modes. At step 130 a spectroscopic measurement of the ion is performed. The measurement 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 and a spectroscopy measurement of the ion is performed at the readout position. The spectroscopic measurement may be chosen to provide a signal that is function of a motional state of the ion. The motional state may be a function of a level of excitation of one or more modes of motion. For instance, the motional state of the ion may lead to variation of detected fluorescence emission. The nature of the variation would depend on the particular readout technique being implemented. The steps 110 to 130 are then repeated iteratively for a plurality of different target positions to obtain a set of spectroscopic measurements. 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 onto the next measurement. 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. The proposed method can be used to identify the position in the ion trap at which excess motion is at its lowest value, thereby locating the position of the RF node and allowing the ion(s) to be positioned there, if required. Therefore the proposed method can be part of a calibration method or a calibration procedure for calibrating the ion trap. 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. 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. The signal generator 270 is configured to generate a drive signal having a first component having a first frequency fl and a second component having a second frequency fl+co, or fl-u), in which co is an offset frequency. The first frequency fl is also referred to as the main frequency or drive frequency that is used to trap the ion. The second frequency fl+co is referred to as the sideband tone which can be switched on and off. The symbols (ft) and (n±oo) represent the angular frequencies of the first and second components, respectively. The controller 290 is configured to switch the second frequency component on or off, so that the second frequency is only applied during step 120 for exciting one or more motional modes. The controller 290 may also be configured to sweep the second frequency over a predetermined frequency range by varying the offset frequency co. The offset frequency co (and therefore the second frequency (n+co or fl-co) may be swept over a relatively wide frequency region in which the modes of motion are guaranteed to lie. The second frequency could also be swept over a relatively narrow range to excite one specific mode. Stated another way, the offset frequency co is swept to include the motional frequency co; of the motional mode (i), or more motional frequency values. 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). The first (main) frequency Q is chosen to trap the chosen ion. The motional frequencies are determined by the properties of the ion, the trap geometry, and the frequency and amplitude of the RF signal. The next consideration is that the ion is only trapped in a stable manner if the ratio between the motional frequency or offset frequency co and the drive frequency fl lies in a certain range, and operating in the lower part of this range is often preferable as the motion of the ion in the trap is less complex. There is also a maximum RF voltage that can be applied to the trap, this is usually limited by electrical breakdown or thermal considerations from the dissipation of this RF signal in the trap and surrounding components. The signal generator 270 may include several sub generators having specific connections to electrodes of the ion trap. 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 (lit) and S2 = Aa sin ((fl+co)t), respectively. The signals SI and S2 are then combined in a combiner to generate the drive signal Sdrive which takes the form = A3 sin (fit) + A4 sin ((fl+ co) t). More generally, the signals SI, S2 and Sdrive may be expressed as a function of a phase parameter as: SI = Ai sin (fit + 4>_1) and S2 = A? sin ((fl+oo)t + (|)_2) so that Sdrive = A3 sin (fit + 4>_3) + A4 sin ((0+ co) t + 4>_4). The first frequency fl also referred to as main frequency or drive frequency is fixed to a predetermined value. The main frequency may be an RF frequency for instance 45 MHz. The second frequency fl+co also referred to as sideband frequency is the frequency of the sideband tone that may be swept over a predetermined range of frequencies. The predetermined range of frequencies may be chosen between two frequencies above the main frequency. For example if the main frequency is 45 MHz, the sideband frequency may be swept between about 47-52 MHz. So in this example co varies between 2 and 7 MHz. The sweep rate and modulation amplitude can be controlled in order to optimise the resulting signal. Figure 2C is a diagram of another exemplary signal generator for use in the system of Figure 2A. In this example the signal generator includes a single source providing the signal SI = Ai sin (fit) coupled to a modulator providing an amplitude modulation signal Smod= A2 cos (u)t). The drive signal Sdrive is Sdrive = A3 sin (fit) + A4 sin ((fl-co)t) + As sin ((fl+u))t). More generally, the frequency range for the second frequency (fl+oo, or fl-co) is chosen such that the motional frequency coi falls within the offset frequency range (range of co). In other words, the frequency range for the offset co referred to as offset frequency range, includes one or more motional frequencies. 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, an RF generator 370, a voltage source 380, and a controller 390. Optionally another signal generator 375 may be provided to perform quantum operations. For instance the generator 375 may provide a signal Sq for the electrode 314. 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. 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,RF electrodes coupled to the RF generator 370 for trapping the ion, and an RF or a microwave electrode, also referred to as antenna, coupled to the generator 375 for performing quantum operations. In the example provided the RF Generator may be set with a main frequency chosen between about 15 to 50 MHz, for instance 45 MHz. 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 314 may be provided between the RF electrodes 313, 315. The electrode or antenna 314 is designed to carry microwave currents in order to perform quantum gates (see figure 3B). 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. 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. 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. There is no micromotion along the x-axis as the confinement along that axis is produced by DC fields rather than the radiofrequency fields responsible for micromotion. 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. In this scenario the search is performed in 3D space rather than 2D. 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. 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. 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 within the trap at which excess micromotion is to be measured. 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. The system 300 is then used to excite one or more motional modes of the ion. The controller 390 controls the RF generator 370 and to generate a drive signal Sdrive that is applied to the two RF electrodes 313 and 315. As explained above with reference to figures 2B and 2C the drive signal Sdrive has a first component having a first frequency (1 and a second component having a second frequency fl+co. The controller 390 is configured to apply the second frequency component only during step 120 for exciting one or more motional modes. If the ion is not located at an RF node or RF minimum, it experiences an oscillating electric field along a vector that depends on the geometry of the RF trapping potential, with a magnitude that depends on its offset from the RF node. If the vector along which any of the motional modes of the trapped ion are aligned have a projection onto the vector of this oscillating field, and the second frequency fl+co is present in the drive signal with a frequency offset co from the first frequency that is equal to the motional frequency uh of the trapped ion, this leads to the quantum state of this mode being displaced in position-momentum phase space. In quantum optics a displaced state refers to a state that arises when a so-called displacement operator is applied to some input state. In our example a displacement in position-momentum phase space is implemented. The input state might be a thermal state of the ion, or some non-classical state of motion. The displacement operation can be implemented in various different ways, depending on the system. Figure 4 is a plot of an example drive signal shown over 100 periods. In this example the drive signal is a radiofrequency voltage. Between the periods 0 to 40, and 60 to 100, the second frequency n+co is off and the drive signal oscillates at the main / drive frequency fl. Between the periods 40 to 60, the second frequency fl+u) is on. 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. To ensure that the offset frequency matches one of the motional frequencies u)j of the ion during step 120, it may be ramped in a series of discrete steps between the lower and upper limits between which the mode frequencies are guaranteed to lie. The hold duration for each step is chosen such that a desired displacement of the motional modes is produced when the frequency at is on resonance with the mode frequency Wi, and the step size is set to match the Fourier-transform-limited bandwidth associated with the hold duration. Alternatively, a smooth ramp of the frequency of the second component throughout step 120 could be applied. As an alternatively to the frequency ramp described above, one or more motional modes may instead be excited by applying the second frequency Q+co at a constant offset co from the first frequency Q but broadening the spectrum of the second frequency component. The central frequency and duration for which the second frequency is applied may be chosen such that the Fourier-transform-limited spectrum of the second frequency spans the desired range of offsets from the first frequency. When using atomic ions for which the motional frequencies would lie in the range of a few MHz, a typical duration for the pulse of the second frequency would be around 200 ns. Another possible implementation would be to apply a band-limited pulse of white frequency noise that spans the same range as the frequency sweep. The white frequency noise may be generated by a waveform generator. In order to obtain the band-limited pulse, the drive signal may be passed through a digital or analogue bandpass filter such that the noise outside of the relevant frequency range is discarded. After excitation of one or more motional modes , 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. 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. 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. The cooler the ion, the higher the chance of producing the metastable state, which does not fluoresce. A hot ion does not reach the metastable state, and therefore will fluoresce. The amount of heating is proportional to excess motion of the ion. 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 low fluorescence intensity for a hot ion and a high fluorescence intensity for a cool ion. In a specific example the laser system 340 has a narrow-linewidth laser used to excite a so-called 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 that is driven. Reduction in contrast of this state transfer indicates that one or more of the motional states were displaced. If the ion was close to the motional ground state before the measurement began, sideband transitions can be driven which offer enhanced sensitivity to smaller ion position offsets from the rf null and can differentiate between offsets along the different trap axes. Measurement of the motional sidebands is a standard technique for ion thermometry, and other alternative techniques may be used. Figure 5A is a state diagram illustrating electron shelving detection using a metastable state. The diagram shows the ground state 2.5^ / 2, the excited state 2P1 / 2, and the metastable state 2D5 / 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 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. 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. 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 different target positions to obtain a set of spectroscopic measurements. Figure 6 is a plot showing the fluorescence measurements obtained for different target positions. Each point is the result of several measurements at a given position but identical sweep parameters. Advantageously, the sweep parameters are constant for every single measurement. The number of measurements may vary, for example 10 or more measurements may be used. For the plot of figure 6, 50 measurements were performed at each point, which is a compromise between the final uncertainty on the location of the RF null whilst keeping the run-time of the experiment reasonably short. The cooler the ion, the higher the chance of producing the metastable state, which does not fluoresce. A hot ion does not reach the metastable state, and therefore will fluoresce. The positions between about 80-130 (a.u) display a minimum fluorescence associated with a lower temperature of the ion 305 and therefore low levels of excess motion. The position around 105 (a.u) may be chosen as an optimal position in the trap with minimum excess motion and may be used as a reference position. Figure 7 is a fluorescence map showing the probability of the ion fluorescing for various y-z positions of the ion trap. There is a global minimum in the fluorescence response from the ion when it is located at the rf node portion associated with the YZ plane at this particular x-coordinate. A model for the resulting signal is used to fit the experimental data, and the ion position at the remote location can be automatically updated via a servo algorithm. For example the plot of figure 6 may be fitted using a model. The model allows extracting the value of excess motion at all points where the probability of fluorescing was not close to zero. Where it is close to zero, one can only place an upper bound on the value since the measurement with these parameters was not sensitive enough to resolve very low amplitudes of motion. The experiment could then be repeated with different parameters in order to enhance its sensitivity, if required. The fit model uses equations from quantum optics to convert the observed reduction in the transition probability to the metastable electronic state to the state of motion of the ion that resulted from the exposure to the sideband tone at the measurement location. Since the sideband tone implements the displacement operator, it will produce a so-called coherent state of motion if the excited mode was originally in its quantum-mechanical ground state. This is included in the fitting function and produces an accurate fit to the whole dataset. The most important free parameters of the fit are (1) the location of the RF null, where the added energy will be minimised, and (2) how the electric field of the sideband tone varies as a function of the distance of the ion from the RF null, which is related to the curvature of the radiofrequency trapping potential. It would also be possible to fit a simpler function such as a Gaussian or Lorentzian curve to the data in order to just extract the position of the RF null, at the expense of not accurately representing the data away from the RF null. The system and method of the present disclosure permit identifying the position of minimum excess motion while removing the requirement for laser access at the position of interest and knowledge of the motional frequencies of the trapped ion at that location. Therefore system calibrations and other quantum operations can be performed in a location of the trap where there is no laser access (e.g. laser-free gates). 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. A skilled person will appreciate that variations of the disclosed arrangements are possible without departing from the disclosure. 23 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

1. A method for probing an ion in an ion trap, the method comprising performing the following steps:placing the ion at a target position;exciting at least one mode of motion of the ion by applying a drive signal comprising a first component having a first frequency and a second component having a second frequency, and wherein applying the second component covers a predetermined frequency range;performing a spectroscopy measurement of the ion;repeating the steps iteratively for a plurality of different target positions to obtain a set of spectroscopic measurements.

2. The method as claimed in claim 1, wherein the spectroscopic measurement provides a signal that is function of the motional state of the ion.

3. The method as claimed in claim 1 or 2, wherein the second frequency has a frequency window that spans over the predetermined frequency range.

4. The method as claimed in claim 1 or 2, comprising sweeping the second frequency over the predetermined frequency range.

5. 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.

6. The method as claimed in claim 5, wherein the predetermined frequency range is chosen such that an offset frequency range includes at least one motional frequency.

7. The method as claimed in claim 6, comprising applying the secondfrequency component for a predetermined duration for exciting the said one or more modes of motion.

8. The method as claimed in claim 7, wherein the predetermined duration is chosen such that a Fourier-transform-limited spectrum of the second frequency component spans a desired offset frequency range.

9. The method as claimed in claim 1, wherein exciting at least one mode of motion comprises applying a pulse of white frequency noise.

10. The method as claimed in any one of the preceding claims, wherein the spectroscopy measurement of the ion is performed at the target position, or at a readout position.

11. The method as claimed in claim 10 , further comprising cooling the ion between each iteration; wherein the step of cooling the ion is performed at the target position prior to exciting the said at least one 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.

12. The method as claimed in any one of preceding claims, wherein the ion is trapped in a trapping potential generated by the first component of the drive signal, and wherein the ion experiences excess micromotion caused by the drive signal.

13. The method as claimed in claim 12, further comprising analysing the set of spectroscopic measurements to identify a reference position; wherein in the reference position the ion experiences a minimal amount of excess micromotion.

14. The method as claimed in claim 13, further comprising moving the ion to the reference position.

15. The method as claimed in any one of the claims 12 to 14, further comprising analysing the set of spectroscopic measurements to derive an amount of excess micromotion.

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

17. 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.

18. The method as claimed in claim 11, 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 the readout position and to provide laser radiation at some, but not all, target positions.

19. 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 18.

20. The ion trap system as claimed in claim 19, wherein the ion trap comprises a plurality of DC electrodes and at least one drive electrode, the ion trap system further comprising a voltage source coupled to the DC electrodes; a signal generator coupled to the said at least one drive electrode; a laser system; a photon detector; and wherein the controller is configured to perform the following steps:place the ion at a target position using the voltage source;excite at least one mode of motion of the ion using the signal generator by applying a drive signal comprising a first component having a first frequency and a second component having a second frequency, and wherein applying the second component covers a predetermined frequency range;perform a spectroscopic measurement of the ion using the laser system and the photon detector;the controller being further configured to repeat the steps iteratively for a plurality of different target positions to obtain a set of spectroscopic measurements.

21. The ion trap system as claimed in claim 20, 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.

22. The ion trap system as claimed in claim 20, wherein the signal generator comprises a signal source configured to generate a signal at the first frequency, and a modulator configured to generate a modulation signal at an offset frequency.

23. A quantum device comprising the ion trap system of any one of the claims 19 to 22.

Images