Abstract:
An atomic ion clock with a first ion trap and a second ion trap, where the second ion trap is of higher order than the first ion trap. In one embodiment, ions may be shuttled back and forth from one ion trap to the other by application of voltage ramps to the electrodes in the ion traps, where microwave interrogation takes place when the ions are in the second ion trap, and fluorescence is induced and measured when the ions are in the first ion trap. In one embodiment, the RF voltages applied to the second ion trap to contain the ions are at a higher frequency than that applied to the first ion trap. Other embodiments are described and claimed.

Description:
PRIORITY CLAIM 
     This application claims the benefit of U.S. Provisional Application No. 60/967,090, filed 31 Aug. 2008. 
    
    
     GOVERNMENT INTEREST 
     The invention claimed herein was made in the performance of work under a NASA contract, and is subject to the provisions of Public Law 96-517 (35 USC 202) in which the Contractor has elected to retain title. 
    
    
     FIELD 
     The present invention relates to atomic clocks, and more particularly, to atomic ion clocks. 
     BACKGROUND 
     Ultra-stable atomic clocks find widespread applications in navigation, communications, and scientific measurements and experiments, to name just a few. An atomic clock comprises a gas cell or vacuum tube to confine an ensemble of reference atomic oscillators, isolated from changes in the environment where the clock operates. In many instances, an atomic clock comprises a quartz oscillator, where the frequency of the quartz oscillator is corrected and accurately maintained by exploiting the physics of the reference atomic oscillators. Sampling the output of the quartz oscillator at specific oscillation intervals provides the ticks of the atomic clock. 
     One type of atomic clock is an atomic ion clock where the two lowest energy levels of the ions determine the frequency of the “atomic oscillators”. The ions are confined within an ion trap by the use of radiofrequency (RF) and static (DC) electric fields. For the two lowest energy levels with an energy difference of ΔE, the frequency ω associated with the ion atomic oscillators is given by ΔE=           ω, where           is Planck&#39;s constant.
     Mercury (Hg) ion atomic clocks offer some advantages over other high-performance clocks being developed today.  FIG. 1  illustrates the two lowest energy levels (split from the  2 S 1/2  energy level) for  199 Hg+ ions, labeled  102  and  104 , sometimes referred to as the upper clock level and the lower clock level, respectively. A  202 Hg discharge lamp may be used to provide ultraviolet light with wavelength 194 nm, so that an ion may be excited from upper clock level  102  to  2 P 1/2  optically excited state  106 . This is pictorially represented by photon absorption line  108 , showing that the energy difference between energy levels  106  and  102  corresponds to the energy of a photon with a wavelength of 194 nm. When an ion is in optically excited state  106 , it may then transition to lower clock level  104 , as pictorially represented by photon emission line  110 , emitting a photon at a wavelength smaller than 194 nm. In this way, with ions initially populating energy level  102 , fluorescence is observed because the absorption of 194 nm light leads to the emission of light at a lower wavelength (higher frequency). 
     Once ions are driven into lower clock level  104 , they no longer absorb and scatter the 194 nm photons. Fluorescence will resume when an interrogating microwave radiation is tuned to the approximately 40.507 GHz transition between energy levels  102  and  104 , thereby leading to a repopulation of ions to upper clock level  102 . The fluorescence response peaks when the microwave radiation is at approximately 40.507 GHz, and will decrease as the microwave frequency is tuned away from 40.507 GHz.  FIG. 2  illustrates a sample data fluorescence response curve, giving photon count as a function of frequency offset from the center frequency (approximately 40.507 GHz) of the interrogating microwave radiation. 
     Rather than look directly for a peak fluorescence response, some atomic clocks will modulate the interrogating microwave radiation at two frequencies ν 0 +Δν and ν 0 −Δν, and will vary ν 0  until the fluorescence response at frequency ν 0 +Δν is substantially equal to the fluorescence response at frequency ν 0 −Δν. When this occurs, the two frequencies are essentially centered about the peak fluorescence response frequency, so that ν 0  is essentially the peak response frequency and is a measure of the frequency transition between upper and lower clock levels  102  and  104 . 
     The above description of a mercury atomic ion clock may be represented at the system level by  FIG. 3 , illustrating ion trap  302 , with optical windows  304  and  306 , and microwave window  308 . The source of optical radiation is labeled  310 , and optical detector  312  measures the fluorescence. Oscillator  314  provides a reference frequency, which is modulated by modulator  316  to ν 0 +Δν and ν 0 −Δν, and microwave radiator  318  interrogates the ions in ion trap  302  via microwave window  308 . These component systems are monitored and controlled by control system  320 , so that the frequency of oscillator  314  is controlled to provide equal fluorescence responses at the two frequencies ν 0 +Δν and ν 0 −Δν. The output of oscillator  314  provides a stable frequency reference to be used as the basis for an atomic clock. (A clock will count the cycles, and add one second after an appropriate number of cycles have been accumulated.) 
     The atomic clock system of  FIG. 3  is operated in two phases, a first phase in which lamp  310  optically stimulates the ions so that optical detector  312  may detect fluorescence, but where microwave radiator  318  is off; and a second phase, where lamp  310  is off and the microwave radiator  318  is on so that upper clock level  102  may be repopulated. 
     U.S. Pat. No. 5,420,549, hereinafter referred to as the &#39;549 patent, discloses a mercury ion atomic clock in which a linear quadruple ion trap is electrically separated into two regions. The regions are co-linear, have the same number of electrodes, and are driven by the same RF field to contain the ions; but separate DC voltages are applied to each region to shuttle the ions from one region to the other. Fluorescence is stimulated only when the ions are in the first ion trap, whereas the resonance interrogating microwave radiation is applied only when the ions are in the second ion trap region. As explained in the &#39;549 patent, by separating the ion trap into two regions, a resonance region and a fluorescence region, the resonance region may be made much smaller than the fluorescence region, making it easier to magnetically shield the resonance region, as well as simplifying thermal control. Other advantages are described in the &#39;549 patent. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates energy level transitions for mercury ions. 
         FIG. 2  illustrates a fluorescence response curve for mercury ions. 
         FIG. 3  illustrates a prior art atomic clock at the system level. 
         FIG. 4  illustrates, at the system level, an atomic clock according to an embodiment. 
         FIG. 5  illustrates voltage waveforms for shuttling ions according to an embodiment. 
         FIG. 6  illustrates the relative electrical phases of electrodes in a first ion trap and a second ion trap according to an embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Described herein is an atomic ion clock embodiment, with improvements over the embodiments described in the &#39;549 patent. In the description that follows, the scope of the term “some embodiments” is not to be so limited as to mean more than one embodiment, but rather, the scope may include one embodiment, more than one embodiment, or perhaps all embodiments. 
       FIG. 4  illustrates an atomic ion clock at the system level according to an embodiment. The embodiment comprises two ion traps: quadrupole ion trap  402  and multipole ion trap  404 . Multipole ion trap  404  may be a quadrupole ion trap, but in general it is expected to have more poles (electrodes) than a quadrupole. For example, for some embodiments, multipole ion trap  404  may be a 16-pole ion trap (e.g., 16 electrodes). These ion traps are electrically isolated from each other. This isolation is pictorially represented by gap  406 . The system components in  FIG. 4 , except for control system  408 , are labeled with the same numerals as their corresponding system components in  FIG. 3 . The ions may be  199 Hg+ ions, but embodiments are not necessarily limited to mercury ions. 
     Increasing the pole order of an ion trap used for microwave clock interrogations leads to less RF ion motion in the trapping fields than experienced in a quadrupole trap. RF trapping forces are generated by ion “micro-motion” in the spatial gradient of the trapping fields, known as the pondermotive force. This force should overcome the space-charge forces of a large cloud of ions, usually much larger than the thermal motion of ions at room temperature. 
     Ion micro-motion leads directly to a special relativistic time dilation (2 nd -order Doppler shift) shift of the clock resonance frequency of the moving  199 Hg +  ions, denoted by the fractional frequency shift Δf/f, which is given by 
                 Δ   ⁢           ⁢   f     f     =       -     1     (     k   -   1     )         ⁢       q   2       8   ⁢     πɛ     0   ⁢               ⁢     mc   2         ⁢       N   L     .             
This expression is seen to be proportional to the linear number density N/L, where N is the total ion number and L is the ion trap length. In this expression, q is the elementary charge, mc 2  is the Hg ion rest mass energy, and ε 0  is the permittivity of free space. This equation is derived from the Boltzmann equation describing the ion plasma inside the multipole trap and applies to a linear multipole trap with 2k electrodes and assumes a cold cloud with negligible thermal ion energy. A similar 1/(k−1) suppression of frequency-pulling exists for the low space charge or single particle limit where only thermal motion is present. That is, for higher pole traps the motion driven by the trapping field is reduced by the 1/(k−1) factor.
 
     A 16-pole trap reduces second-order Doppler frequency pulling seven-fold compared to a linear quadrupole trap. Because the multipole trap is typically longer than quadrupole traps used for frequency standards, another reduction in 2 nd -order Doppler shift is gained because the linear ion density N/L is reduced. 
     Long term variations in ion number that lead to frequency changes in clock output are greatly reduced by the use of a multipole trap for ion clock resonance interrogations. 
     Ion shuttling between ion traps  402  and  404  allows separation of the state selection process from the clock microwave resonance process so that each trap may be independently optimized for its task. This separation of functions has proven to be a powerful tool with ions because the beam of ions may be reversed in direction, halted, and transported from one trap to the other with an insignificant loss of atoms. 
     For the embodiment of  FIG. 4 , quadrupole linear ion trap  402  tightly confines ions for optical state selection, whereas for multipole ion trap  404  the ions are more loosely confined and the microwave atomic transitions are executed. A DC voltage ramp is applied to control the ion shuttling between quadrupole ion trap  402  and the more weakly confining multipole ion trap  404 . In quadrupole ion trap  402 , the ion cloud is squeezed to a relatively small radius for efficient optical state selection, and space-charge interaction within the ion cloud may be stronger than thermal energies. In this particular embodiment, space charge interaction energy is also larger than the well depth for ions in multipole ion trap  404 , and a restriction on the slew rate of the voltage ramping waveform then results. The voltage ramping used to move ions from one trap to the other should proceed slowly to allow for ion thermalization with a buffer gas (typically neon or helium). This typically requires a ramp voltage change of state to be more than 100 ms and as much as 500 ms. 
     In the embodiment of  FIG. 4 , the DC voltage ramp to quadrupole ion trap  402  is provided by DC line  410 , and the DC voltage ramp to multipole ion trap  404  is provided by DC line  412 , where the DC voltages are controlled by control system  408 . These DC voltage lines are connected to the electrodes of their respective ion traps. 
     Typical voltage ramps are illustrated in  FIG. 5 , where curve  502  represents the voltage ramp for a quadrupole ion trap, and curve  504  represents the voltage ramp for a multipole ion trap, such as for example a 16-POLE ion trap. These curves do not represent actual waveform values, but are meant to illustrate a method of shuttling ions from one ion trap to another. 
     Referring to  FIG. 5 , just before time t 1 , the voltage of the quadrupole ion trap is relatively positive, whereas the voltage of the multipole ion trap is relatively negative, so that the positively charged mercury ions are confined in the multipole ion trap. From time t 1  to time t 2 , the voltage of the quadrupole ion trap is brought from a relatively positive value to a relatively negative value (a negative going transition), followed by bringing the voltage of the multipole ion trap to a relatively positive value at time t 3  (a positive going transition). This process shuttles, the ions away from the multipole ion trap and to the quadrupole ion trap. 
     This process is reversed at times t 4 , t 5 , and t 6 , where at time t 4  the voltage of the multipole ion trap is brought from a relatively positive value to a relatively negative value at time t 5 , and from time t 5  to time t 6  the voltage of the quadrupole ion trap is brought from a relatively negative value to a relatively positive value. This process shuttles the ions back to the multipole ion trap. The process represented at times t 7 , t 8 , and t 9  shuttles the ions back to the quadrupole ion trap. 
     For some embodiments, typical DC voltage swings may be on the order of a few volts, where the voltage ramp time width may be on the order of a few hundred milliseconds. 
     In addition to the DC voltages, RF voltages for confining the ions in their respective traps are also applied as shown in  FIG. 4 . RF line  414  provides RF voltages ±U 1  sin Ω 1 t to quadrupole ion trap  402 , and RF line  416  provides RF voltages ±U 2  sin Ω 2 t to multipole ion trap  404 , were these RF voltages are controlled by control system  408 . A ± symbol is used in the description of these RF voltages to indicate that each RF line is actually a pair of RF lines, where the two lines making up a pair are driven in opposite phase. These RF voltage lines are connected to the electrodes of their respective ion traps. For each ion trap, the phase of the RF voltage applied to any one electrode is shifted by π radians relative to its nearest neighbor electrodes. 
     For example, RF line  414  comprises two RF lines, one driven at voltage U 1  sin Ω 1 (t+Φ) and the other at voltage −U 1  sin Ω 1 (t+Φ), where Φ is some phase. If an electrode is driven at voltage U 1  sin Ω 1 (t+Φ), then its two nearest neighbors are driving at voltage −U 1  sin Ω 1 (t+Φ). Similar remarks apply to RF line  416 . 
     In practice, the DC voltage may be superimposed (added) to the RF voltages, so that separate DC lines  410  and  412  are not needed. However, for ease of illustration, separate DC voltage lines are shown. 
     For some embodiments, the ion traps are positioned to be co-linear with each other separated by small gap  406 . The width of gap  406  should be short relative to the diameter of the electrode rods in the ion traps. For most embodiments, it is expected that each ion trap has its electrodes cylindrically spaced about a longitudinal axis. This is pictorially illustrated in  FIG. 6 , illustrating electrodes  402 A and  402 B belonging to quadrupole ion trap  402 , and electrodes  404 A,  404 B,  404 C, and  404 D belonging to multipole ion trap  404 . For simplicity, not all electrodes are shown. In the example of  FIG. 6 , both ion traps are co-linear with their centered about longitudinal axis  602 . 
     If both ion traps are operated at the same RF frequency for confining the ions (i.e., Ω 1 =Ω 2 ), then co-aligning a quadrupole ion trap to an arbitrary multipole ion trap may result in holes in the ion confining fields, whereby a “hole” is a region with a well depth of essentially zero where ions may escape and collide with that part of the ion trap structure that surrounds the electrodes. However, for some configurations where at least some of the electrodes of the quadrupole ion trap may be co-aligned with some of the electrodes of the multipole ion trap, these holes may be mitigated by driving such co-aligned electrodes with opposite phase. For example, referring to  FIG. 6 , the phase of the RF voltage driving electrode  402 A is π radians out of phase with the RF voltage driving electrode  404 A. This is noted by arbitrarily assigning +V to electrode  402 A and assigning −V to electrode  404 A. In similar fashion, the phase of the RF voltage driving electrode  402 B is π radians out of phase with the RF voltage driving electrode  404 D. Note that for the particular embodiment of  FIG. 6 , electrodes  402 A and  402 B are spaced relative to one another so that they are driven in opposite phase. 
     In general, it may not be feasible to align the electrodes as indicated in  FIG. 6  because of the number of electrodes for the multipole ion trap relative to that of the lower order ion trap, which may be a quadruple ion trap for some embodiments. Accordingly, for some embodiments, the frequency of the RF voltage driving the electrodes of the multipole ion trap is not equal to the frequency of the RF voltage driving the electrodes of the lower order ion trap. For example, for some embodiments, the RF frequency driving the multipole ion trap may be higher than that of the lower order ion trap. As one particular example, the frequency for the multipole ion trap may be approximately twice that of the lower order ion trap. That is, for some embodiments, Ω 2 &gt;Ω 1 , whereas for some other embodiments, Ω 2 ˜2Ω 1 . For properly chosen frequencies, it is found that the resulting holes will open and close faster than the time for which the ions may generally drift through, thereby mitigating the effects of the holes. 
     Various modifications may be made to the described embodiments without departing from the scope of the invention as claimed below.