A method for measuring periodic electric field force

Abstract

The present invention discloses a method for measuring periodic electric field force. By using a first laser to initialize the populations of all ytterbium ions to be measured that have undergone Doppler cooling, and then using a second laser modulated by a quantum phase-locked sequence to cause the populations of the ytterbium ions to be measured to transition to 2 F 7 / 2 (F = 3) state. Subsequently, the detection results of the ytterbium ions to be measured are demodulated by a quantum phase-locked sequence to obtain the amplitude of the electric field force of the periodic electric field to be measured. By means of the quantum phase-locked technology, the accuracy and reliability of the measurement of the periodic electric field force are improved, and it is applicable to the measurement of weak periodic electric field force. By pumping the population of the ytterbium ions to be measured in the 2 F 7 / 2 (F = 3) state to 2 [3 / 2] 3 / 2 (F = 1) state and spontaneously emitting to 2 S 1 / 2 (F = 1) state, and then using a laser to detect the population, the fluorescence detection efficiency and accuracy are improved, and the accuracy of the measurement of the periodic electric field force is further improved.

Description

Technical Field

[0001] This application relates to the technical field of quantum information processing, and in particular to a method for measuring periodic electric field force. Background Art

[0002] Measuring the periodic weak force brought by an alternating electric field can measure the magnitude of the alternating electric field in three-dimensional space, which is beneficial to quantitatively analyze the noise of the surrounding alternating electromagnetic field and give corresponding shielding solutions, improve the accuracy of precision measurement, and thus promote the development of the precision measurement field.

[0003] Currently, most of the existing methods for measuring periodic electric field force use a single trapped ion to measure the amplitude of the periodic electric field force, including the following two: One of the existing methods for measuring periodic electric field force is to use the injection locking method to measure the amplitude of the alternating electric field force. By trapping a single magnesium ion in a quadrupole trap and applying a laser with a red-detuned laser frequency on the in-well optical path as Doppler cooling light, the ion is cooled from the ion cloud state to the ion crystal state, so as to achieve stable trapping in the trap. Then, a laser with a blue-detuned laser frequency is applied along the trap axis direction, so that the ion oscillates periodically back and forth along the trap axis direction at a frequency equal to the trap frequency, forming a stable oscillation system, and a weak alternating electric field is added to the DC electrode as a perturbation, so that the stable oscillation of the ion along the trap axis direction and the alternating perturbation on the DC electrode constitute the injection locking condition. Finally, this method combines the principle of injection locking. By scanning the frequency of the perturbation electric field and using a high-speed stroboscopic camera to record the spatial position of the ion at each perturbation electric field frequency, the spatial position information of the ion when the perturbation signal frequency is in the injection locking region is obtained, and the force information of the perturbation signal on the ion is extracted; The second of the existing methods for measuring periodic electric field force also uses the injection locking method to measure the high-frequency periodic electric field force. The difference is that the frequency of the injection signal is set to be equal to the ion trap frequency, and the change of the ion fluorescence signal is recorded by a photomultiplier tube (PMT) and fitted to obtain the amplitude of the force exerted by the injection signal on the ion.

[0004] However, when measuring weak periodic electric field force by injection locking, it is necessary to make the frequency of the perturbation electric field close to the trap frequency. The trap frequency of the ion trap along the trap axis direction is about in the order of hundreds of kHz, which poses extremely high requirements on the shooting frame rate of the camera, and most cameras do not have the ability to record the spatial position of the ion and the corresponding time information at the same time, making it difficult to measure weak periodic electric field force by trapping a single ion. Summary of the Invention

[0005] The purpose of the present invention is to solve at least to a certain extent one of the technical problems existing in the prior art.

[0006] To this end, an embodiment of the present invention provides a method for measuring a periodic electric field force, which realizes the measurement of a weak periodic electric field force by using a trapped single ion.

[0007] To achieve the above technical objectives, the technical solutions adopted in the embodiments of the present invention include:

[0008] An embodiment of the present invention provides a method for measuring a periodic electric field force, including the following steps:

[0009] Use a first laser to initialize all the populations of the ytterbium ions to be measured that have been Doppler cooled to the 2 S 1 / 2 (F = 0) state. The ytterbium ions to be measured are pre-trapped in a preset alternating electric field and are within the coverage of the measured periodic electric field that has been modulated;

[0010] Use a second laser modulated by a quantum phase-locked sequence to cause the population of the ytterbium ions to be measured to transition from the 2 S 1 / 2 (F = 0) state to the 2 F 7 / 2 (F = 3) state. The quantum phase-locked sequence includes a series of π pulses;

[0011] Use a third laser to pump the population of the ytterbium ions to be measured in the 2 F 7 / 2 (F = 3) state to the 2 [3 / 2] 3 / 2 (F = 1) state, so that the population of the ytterbium ions to be measured in the 2 [3 / 2] 3 / 2 (F = 1) state spontaneously emits radiation to the 2 S 1 / 2 (F = 1) state;

[0012] Use a fourth laser to detect the population of the ytterbium ions to be measured in the 2 S 1 / 2 (F = 1) state to obtain a detection result;

[0013] Demodulate the detection result according to the quantum phase-locked sequence to obtain the electric field force amplitude of the measured periodic electric field.

[0014] In addition, a method for measuring a periodic electric field force according to an embodiment of the present invention above may further have the following additional technical features:

[0015] Further, in a method for measuring a periodic electric field force according to an embodiment of the present invention, the Doppler cooling of the ytterbium ions to be measured specifically includes:

[0016] Use a fifth laser to perform 2 S1 / 2 state to 2 P 1 / 2 Doppler cooling of the state.

[0017] Furthermore, in an embodiment of the present invention, the alternating electric field is generated by a blade trap, the blade trap includes a first DC blade, a second DC blade, a first AC blade and a second AC blade, a plurality of DC electrodes are respectively arranged on the first DC blade and the second DC blade, a first AC electrode and a first DC bias are arranged on the first AC blade, and a second AC electrode and a second DC bias are arranged on the second AC blade.

[0018] Furthermore, in an embodiment of the present invention, the method for trapping the ytterbium ions to be measured by using the alternating electric field includes the following steps:

[0019] Generate the alternating electric field through the first AC blade and the second AC blade;

[0020] Use the alternating electric field to trap the ytterbium ions to be measured in the radial direction of the blade trap.

[0021] Furthermore, in an embodiment of the present invention, the modulation of the periodic electric field to be measured includes the following steps:

[0022] Modulate the periodic electric field to be measured with a first frequency and a first phase.

[0023] Furthermore, in an embodiment of the present invention, the modulation of the second laser includes the following steps:

[0024] Calculate a first time according to the first frequency;

[0025] Use an arbitrary waveform generator to generate a series of π pulses to obtain the quantum phase-locked sequence, and the time interval between two adjacent π pulses is the first time;

[0026] Modulate the second laser with the quantum phase-locked sequence.

[0027] Furthermore, in an embodiment of the present invention, the demodulating the detection result according to the quantum phase-locked sequence to obtain the electric field force amplitude of the periodic electric field to be measured includes:

[0028] Demodulate the displacement amplitude of the ytterbium ions to be measured from the detection result according to the quantum phase-locked sequence;

[0029] Calculate the electric field force amplitude according to the displacement amplitude.

[0030] Further, in an embodiment of the present invention, demodulating the displacement amplitude of the ytterbium ion to be measured from the detection result according to the quantum phase-locked sequence includes:

[0031] Scanning the detection result at each of the time intervals to obtain a fringe contrast, where the fringe contrast is the fringe contrast corresponding to the population of the ytterbium ion to be measured scanned at each of the time intervals;

[0032] Calculating a second frequency according to the first frequency, where the second frequency is the angular frequency of the periodic electric field to be measured;

[0033] Fitting a relational expression among the fringe contrast, the displacement amplitude, the number of π pulses in the quantum phase-locked sequence, and the second frequency to obtain a fitting curve;

[0034] Based on the fitting curve, calculating the displacement amplitude according to the fringe contrast, the number of π pulses in the quantum phase-locked sequence, and the value of the second frequency.

[0035] Further, in an embodiment of the present invention, calculating the amplitude of the electric field force according to the displacement amplitude includes:

[0036] Generating motion information of the ytterbium ion to be measured under the action of the periodic electric field to be measured according to the displacement amplitude, the second frequency, and the first phase;

[0037] Taking the derivative of the motion information to obtain velocity information of the ytterbium ion to be measured under the action of the periodic electric field to be measured;

[0038] Obtaining the amplitude of the electric field force according to the velocity information.

[0039] Further, in an embodiment of the present invention, the wavelength of the first laser is 369.5 nm, the wavelength of the second laser is 467 nm, the wavelength of the third laser is 760 nm, and the wavelength of the fourth laser is 370 nm.

[0040] Advantages and beneficial effects of the present invention:

[0041] In the embodiment of the present invention, the state of the ytterbium ion to be measured under the periodic electric field to be measured is initialized by using the first laser, so that all the populations of the ytterbium ion to be measured are in 2 S 1 / 2 (F = 0) state, and then the population of the ytterbium ion to be measured is changed from 2 S 1 / 2 (F = 0) state to 2 F 7 / 2(F = 3) state, and subsequently, the detection result of the ytterbium ion to be measured is demodulated through a quantum phase-locking sequence to obtain the electric field force amplitude of the periodic electric field to be measured. Based on the high sensitivity of the quantum system, the quantum phase-locking technology is used to improve the accuracy and reliability of the measurement of the periodic electric field force, which is applicable to the measurement of weak periodic electric field forces; by placing the ytterbium ion to be measured in 2 F 7 / 2 (F = 3) state population is pumped to 2 [3 / 2] 3 / 2 (F = 1) state, so that the ytterbium ion to be measured is in 2 [3 / 2] 3 / 2 (F = 1) state population spontaneously emits to 2 S 1 / 2 (F = 1) state, and the detection result is obtained by detecting the population of the ytterbium ion to be measured in 2 S 1 / 2 (F = 1) state. Compared with directly detecting the population of the ytterbium ion to be measured in 2 F 7 / 2 (F = 3) state, it has higher fluorescence detection efficiency and accuracy, further improving the accuracy and reliability of the measurement of the periodic electric field force. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following introduces the relevant technical solution drawings in the embodiments of the present application or the prior art. It should be understood that the drawings introduced below are only for conveniently and clearly expressing some embodiments of the technical solutions in the present application. For those skilled in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0043] Figure 1 is a schematic flow chart of a specific embodiment of a method for measuring periodic electric field force according to the present invention;

[0044] Figure 2 is a schematic structural diagram of a blade trap in a specific embodiment of a method for measuring periodic electric field force according to the present invention;

[0045] Figure 3 is a schematic electrode structure diagram of a blade trap in a specific embodiment of a method for measuring periodic electric field force according to the present invention;

[0046] Figure 4 is a schematic diagram of a quantum phase-locking sequence in a specific embodiment of a method for measuring periodic electric field force according to the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0047] Embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary and are only used to explain the present application and should not be construed as a limitation to the present application. For the step numbers in the following embodiments, they are only set for the convenience of explanation and illustration, and no limitation is imposed on the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0048] The terms "first", "second", "third", "fourth", etc. in the specification, claims and drawings of the present invention are used to distinguish different objects rather than to describe a specific order. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but optionally further includes steps or units not listed, or optionally further includes other steps or units inherent to these processes, methods, products or devices.

[0049] Referring to "embodiments" in the present invention means that specific features, structures or characteristics described in connection with the embodiments can be included in at least one embodiment of the present invention. The appearance of this phrase in various positions in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. Those skilled in the art explicitly and implicitly understand that the embodiments described herein can be combined with other embodiments.

[0050] When the prior art measures a weak periodic electric field force by injection locking, it is necessary to make the frequency of the perturbing electric field close to the trap frequency. The trap frequency of the ion trap along the trap axis direction is about in the order of hundreds of kHz, which poses extremely high requirements on the frame rate of the camera. Moreover, the vast majority of cameras do not have the ability to simultaneously record the spatial position of ions and the corresponding time information, making it difficult to measure the weak periodic electric field force by using a single trapped ion. For this reason, the present invention proposes a method for measuring a periodic electric field force. By using a first laser to initialize the state of a ytterbium ion to be measured under the periodic electric field to be measured, all the populations of the ytterbium ion to be measured are in 2 S 1 / 2 (F = 0) state, and then using a second laser modulated by a quantum phase-locking sequence to cause the population of the ytterbium ion to be measured to transition from 2 S 1 / 2 (F = 0) state to 2 F 7 / 2(F = 3) state, and subsequently, the detection result of the ytterbium ion to be measured is demodulated through a quantum phase-locking sequence to obtain the amplitude of the electric field force of the periodic electric field to be measured. Based on the high sensitivity of the quantum system, the quantum phase-locking technology is used to improve the accuracy and reliability of the measurement of the periodic electric field force, which is applicable to the measurement of weak periodic electric field forces; by placing the ytterbium ion to be measured in 2 F 7 / 2 (F = 3) state, the population is pumped to 2 [3 / 2] 3 / 2 (F = 1) state, so that the ytterbium ion to be measured is in 2 [3 / 2] 3 / 2 (F = 1) state, and the population of the ytterbium ion to be measured in 2 S 1 / 2 (F = 1) state spontaneously emits to 2 S 1 / 2 (F = 1) state, and the detection result is obtained by detecting the population of the ytterbium ion to be measured in 2 F 7 / 2 (F = 3) state. Compared with directly detecting the population of the ytterbium ion to be measured in

[0051] The following describes in detail a method for measuring periodic electric field force according to an embodiment of the present invention with reference to the accompanying drawings.

[0052] Referring to Figure 1 , a method for measuring periodic electric field force in an embodiment of the present invention mainly includes the following steps S101 - S105:

[0053] S101. Use the first laser to initialize all the populations of the ytterbium ion to be measured that has been Doppler cooled to 2 S 1 / 2 (F = 0) state;

[0054] Among them, the ytterbium ion to be measured is pre-trapped in a preset alternating electric field and is within the coverage of the modulated periodic electric field to be measured.

[0055] It can be understood that the ytterbium ion to be measured has a relatively high movement speed at room temperature, making it difficult to study the characteristics of the ytterbium ion to be measured and inconvenient for measuring the electric field force of the periodic electric field to be measured based on the ytterbium ion to be measured. Therefore, in the embodiment of the present invention, the ytterbium ion to be measured trapped by the preset alternating electric field is Doppler cooled to reduce the movement speed of the ytterbium ion to be measured and trap the ytterbium ion to be measured at a fixed position, so as to facilitate the subsequent study of the characteristics of the ytterbium ion to be measured, such as state detection, and further facilitate the measurement of the periodic electric field force based on the detection result of the ytterbium ion to be measured.

[0056] It can be understood that in the embodiments of the present invention, the ytterbium ions to be measured pre-trapped in a preset alternating electric field are trapped single ions. By initializing all the populations of the ytterbium ions to be measured to 2 S 1 / 2 (F = 0) state, and operating on the population of the ytterbium ions to be measured in the 2 S 1 / 2 (F = 0) state in the subsequent process, the population used to measure the periodic electric field force in the trapped single ions is maximized, and the measurement accuracy and reliability of the weak periodic electric field force are improved.

[0057] According to prior knowledge, in precision measurement experiments, due to the weak intensity of the signal to be measured, the signal to be measured is easily submerged in environmental noise and instrument noise, resulting in too low signal-to-noise ratio of the measurement result, and even unable to detect the signal to be measured. The prior art usually adopts the method of lock-in amplification to increase the signal-to-noise ratio of weak signal detection. In view of the high sensitivity of the quantum system, weak changes in external electric fields, magnetic fields and other signals will affect the quantum system. In the embodiments of the present invention, on the basis of the traditional lock-in amplification technology, the periodic electric field to be measured is modulated to improve the signal-to-noise ratio of the detection of the periodic electric field to be measured, and further improve the measurement accuracy and reliability of the weak periodic electric field force.

[0058] As an alternative embodiment, the periodic electric field to be measured is modulated by a first frequency and a first phase.

[0059] Specifically, in the embodiments of the present invention, the periodic electric field to be measured is modulated at a first frequency f and a first phase ε 0 to convert the periodic electric field to be measured into a time-varying electric field.

[0060] Optionally, in some embodiments, the first laser is a laser with a wavelength of 369.5 nm.

[0061] As an alternative embodiment, the Doppler cooling of the ytterbium ions to be measured specifically includes:

[0062] Using a fifth laser to perform 2 S 1 / 2 state to 2 P 1 / 2 state Doppler cooling.

[0063] Optionally, in some embodiments, the ytterbium ions to be measured can be replaced with other ions that can be Doppler cooled using lasers, such as Be ions, Mg ions, Ca ions, Sr ions, Ba ions, Hg ions, Cd ions. It can be understood that when other ions are selected to measure the periodic electric field to be measured, the wavelengths of the lasers used in each step should also be changed accordingly, and in these embodiments, the energy states of ion transitions are also different from those of the embodiments using ytterbium ions.

[0064] As an alternative embodiment, the alternating electric field is generated by the blade trap.

[0065] Referring to Figure 2 , the blade trap adopted in the embodiment of the present invention is divided into a DC electrode region and an AC electrode region, and specifically includes a first DC blade, a second DC blade, a first AC blade and a second AC blade. A plurality of DC electrodes are respectively arranged on the first DC blade and the second DC blade, a first AC electrode RF1 and a first DC bias DC11 are arranged on the first AC blade, and a second AC electrode RF2 and a second DC bias DC12 are arranged on the second AC blade.

[0066] It can be understood that in the embodiment of the present invention, by respectively arranging a plurality of DC electrodes on the first DC blade and the second DC blade, independent control of the voltage of each DC electrode is achieved.

[0067] Optionally, in some embodiments, five DC electrodes DC1-DC5 are arranged on the first DC blade, and five DC electrodes DC6-DC10 are arranged on the second DC blade, as Figure 2 shown.

[0068] In some embodiments, the electrode arrangements of the first DC blade, the second DC blade, the first AC blade and the second AC blade are as Figure 3 shown. Compared with the traditional quadrupole ion trap, the blade trap adopted in the embodiment of the present invention can accurately apply a voltage to the independently controllable DC electrodes arranged on the first DC blade and the second DC blade, improving the control effect on the alternating electric field for trapping the ytterbium ions to be measured. The electric potential in the central region of the blade trap can be:

[0069]

[0070] In the formula, represents the DC voltage component; βY 2 +γZ 2 ) represents the AC voltage component; X, Y, Z are the axial (radial) principal axis directions of the blade trap; V RF is the amplitude of the AC voltage; Ω is the frequency of the AC voltage; V DC is the DC voltage; R is the distance between the center of the blade trap and the electrodes in the radial plane; κ′, α′, β′, γ′, κ, α, β, γ are the geometric structure factors of the blade trap.

[0071] As an alternative embodiment, the method for trapping the ytterbium ions to be measured by using an alternating electric field includes the following steps:

[0072] 1) Generating an alternating electric field through the first AC blade and the second AC blade;

[0073] 2) Use an alternating electric field to trap the ytterbium ions to be measured in the radial direction of the blade trap.

[0074] Optionally, in some embodiments, when generating an alternating electric field through the blade trap, a weak electric field signal with a modulation angular frequency of ω f = 2πf can be added to the DC electrode of the blade trap to achieve precise measurement of the weak electric field forces generated by the alternating electric field and the DC electric field in three-dimensional space.

[0075] S102. Use a second laser modulated by a quantum lock-in sequence to change the population of the ytterbium ions to be measured from 2 S 1 / 2 (F = 0) state to 2 F 7 / 2 (F = 3) state;

[0076] Among them, referring to Figure 4 , the quantum lock-in sequence includes a series of π pulses.

[0077] It can be understood that the ytterbium ions to be measured will perform periodic micro-motions in the blade trap under the action of the electric field force of the periodic electric field to be measured, and the periodic micro-motions of the ytterbium ions to be measured introduce the Doppler effect during the process of changing the population of the ytterbium ions to be measured from 2 S 1 / 2 (F = 0) state to 2 F 7 / 2 (F = 3) state. Combining prior knowledge, it can be known that when the population of the ytterbium ions to be measured changes from 2 S 1 / 2 (F = 0) state to 2 F 7 / 2 (F = 3) state and the Doppler effect is generated, the wavelength of the radiation changes due to the relative motion of the wave source and the observation point: in front of the moving wave source, the wave is compressed, the wavelength becomes shorter, and the frequency becomes higher (blue shift); behind the moving wave source, the opposite effect occurs, that is, the wavelength becomes longer and the frequency becomes lower (red shift); the higher the speed of the wave source, the greater the Doppler effect generated. According to the degree of wave red (blue) shift, the speed of the wave source moving along the observation direction can be calculated. In the embodiment of the present invention, the second laser modulated by the quantum lock-in sequence is used to change the population of the ytterbium ions to be measured from 2 S 1 / 2 (F = 0) state to 2 F 7 / 2 (F = 3) state, forming a dynamical decoupling sequence. In the subsequent process of the ytterbium ions to be measured transitioning to 2 F 7 / 2After detecting the population of the (F = 3) state, a quantum phase-locked sequence can be used to demodulate the detection result to obtain the force information of the ytterbium ion to be measured during periodic micromotion, thereby realizing the measurement of the electric field force of the periodic electric field to be measured.

[0078] Optionally, in some embodiments, the second laser is a laser with a wavelength of 467 nm.

[0079] In an embodiment of the present invention, the time interval between two adjacent π pulses is related to the first frequency.

[0080] As an alternative implementation, the modulation of the second laser includes the following steps:

[0081] 1) Calculate the first time τ according to the first frequency f;

[0082] Optionally, in some embodiments, the first time

[0083] 2) Use an arbitrary waveform generator (AWG) to generate a series of π pulses to obtain a quantum phase-locked sequence;

[0084] Wherein, the time interval between two adjacent π pulses is the first time τ.

[0085] The quantum phase-locked sequence generated in the embodiment of the present invention is not only used for the modulation of the second laser and the demodulation of the subsequent detection result, but also can act as a filter. In some embodiments, taking the first time as an example, under the action of the quantum phase-locked sequence, the frequency components of the periodic electric field to be measured that are close to f (such as the absolute value of the difference between the frequency and f is less than or equal to a preset threshold) and equal to f after modulation will be retained, while the frequency components far from f (such as the absolute value of the difference between the frequency and f is greater than the preset threshold) will be filtered.

[0086] 3) Modulate the second laser using the quantum phase-locked sequence.

[0087] Optionally, in some embodiments, the quantum phase-locked sequence is applied to an acousto-optic modulator (AOM) to achieve the modulation of the second laser.

[0088] S103. Use the third laser to pump the population of the ytterbium ion to be measured in the 2 F 7 / 2 (F = 3) state to 2 [3 / 2] 3 / 2 (F = 1) state, so that the ytterbium ion to be measured in the 2 [3 / 2] 3 / 2 (F = 1) state spontaneously emits radiation to 2 S 1 / 2 (F = 1) state;

[0089] According to prior knowledge, 2 F 7 / 2 (F = 3) state has a long energy level lifetime. When the population of the ytterbium ions to be measured is in 2 F 7 / 2 (F = 3) state, the spontaneous emission fluorescence photon rate is very low (less than 1 per minute). Therefore, it is impossible to directly use 2 F 7 / 2 (F = 3) state's spontaneous emission fluorescence as detection. In the embodiment of the present invention, the third laser is used as the repumping light to pump the population of the ytterbium ions to be measured in 2 F 7 / 2 (F = 3) state to 2 [3 / 2] 3 / 2 (F = 1) state, so that the population of the ytterbium ions to be measured in 2 [3 / 2] 3 / 2 (F = 1) state spontaneously emits to 2 S 1 / 2 (F = 1) state. Subsequently, directly detect the population of the ytterbium ions to be measured in 2 S 1 / 2 (F = 1) state, which is equivalent to detecting the population of the ytterbium ions to be measured in 2 F 7 / 2 (F = 3) state, and has higher fluorescence detection efficiency and accuracy, improving the accuracy and reliability of the subsequent measurement of the periodic electric field force.

[0090] Optionally, in some embodiments, the third laser is a laser with a wavelength of 760 nm.

[0091] S104. Use the fourth laser to detect the population of the ytterbium ions to be measured in 2 S 1 / 2 (F = 1) state to obtain a detection result;

[0092] Optionally, in some embodiments, the fourth laser is a laser with a wavelength of 370 nm.

[0093] Combined with what is described in step S103, the embodiment of the present invention uses the fourth laser as the detection light to detect the population of the ytterbium ions to be measured in 2 S 1 / 2 (F = 1) state, realizing the state detection of the ytterbium ions to be measured from 2 S 1 / 2 (F = 0) state to 2 F 7 / 2 (F = 3) state.

[0094] S105. Demodulate the detection result according to the quantum lock-in sequence to obtain the electric field force amplitude of the periodic electric field to be measured.

[0095] Among them, as can be seen from step S102, the ytterbium ions to be measured will perform periodic micro-movements in the blade trap under the action of the electric field force of the periodic electric field to be measured:

[0096] x(t) = x 0 sin(ω f t + ε 0 )

[0097] where x 0 represents the displacement amplitude of the ytterbium ions to be measured. When the population of the ytterbium ions to be measured jumps from the 2 S 1 / 2 (F = 0) state to the 2 F 7 / 2 (F = 3) state, the interaction between the periodic micro-movement of the ytterbium ions to be measured and the second laser generates the Doppler effect, causing the detuning between the ytterbium ions to be measured and the second laser:

[0098] Δ(t) = kv(t) = kx 0 ω f cos(ω f t + ε 0 )

[0099] By using the quantum phase-locked sequence to demodulate the detection result, the displacement amplitude of the ytterbium ions to be measured during periodic micro-movement can be obtained, and then the amplitude of the electric field force of the periodic electric field to be measured can be calculated.

[0100] In some embodiments, step S105 can be further divided into the following steps S1051 - S1052:

[0101] Step S1051: Demodulate the displacement amplitude of the ytterbium ions to be measured from the detection result according to the quantum phase-locked sequence;

[0102] In some embodiments, the step of demodulating the displacement amplitude of the ytterbium ions to be measured from the detection result by using the quantum phase-locked sequence includes:

[0103] 1) Scan the detection result at each time interval to obtain the fringe contrast;

[0104] where the fringe contrast is the fringe contrast corresponding to the population of the ytterbium ions to be measured scanned at each time interval.

[0105] 2) Calculate the second frequency according to the first frequency;

[0106] where the second frequency is the angular frequency ω f = 2πf.

[0107] 3) Fit the relationship among the fringe contrast, the displacement amplitude, the number of π pulses in the quantum phase-locked sequence, and the second frequency to obtain the fitting curve;

[0108] According to prior knowledge, it is assumed that the amplitude of the electric force of the periodic electric field to be measured is a constant F 0 , and the electric force of the periodic electric field to be measured can be expressed as F(t) = F 0 cos(ω f t), and the vibration frequency of the simple harmonic oscillator is ω t . In the case of no resistance, the motion equation of the simple harmonic oscillator can be expressed as:

[0109]

[0110] Let the motion equation of the simple harmonic oscillator can be simplified to

[0111]

[0112] At the initial time t = 0 (the electric force of the periodic electric field to be measured has not acted on the ion), the simple harmonic oscillator is in a static equilibrium state (ignoring the micro-motion of the ion): x(0) = 0; From this, it can be obtained that:

[0113]

[0114] Since ω f << ω t , cos(ω f t) >> cos(ω t t):

[0115]

[0116] The ytterbium ion to be measured undergoes periodic micro-motion in the blade trap under the action of the electric force of the periodic electric field to be measured:

[0117] x(t) = x 0 sin(ω f t + ε 0 )

[0118] During the process of the population of the ytterbium ion to be measured transitioning from the 2 S 1 / 2 (F = 0) state to the 2 F 7 / 2 (F = 3) state, the interaction between the periodic micro-motion of the ytterbium ion to be measured and the second laser produces the Doppler effect, causing the detuning between the ytterbium ion to be measured and the second laser:

[0119] Δ(t) = kv(t) = kx 0 ω f cos(ω f t + ε 0 )

[0120] Let A = kx 0 It can be obtained that:

[0121] Δ(t) = Aω f cos(ω f t + ε 0 )

[0122] Assume the angle is the angle between the Bloch vector on the equatorial plane and the x-axis. The detuning can be understood as the angular velocity of the Bloch vector rotating around the z-axis.

[0123] Referring to Figure 4 , after the first pulse, free evolution for τ time, then the angle between the vector and the x-axis is

[0124]

[0125] After being flipped by the first π pulse, the angle between the vector and the x-axis becomes:

[0126]

[0127] After being flipped by the second π pulse, the angle between the vector and the x-axis becomes:

[0128]

[0129] After being flipped by the third π pulse, the angle between the vector and the x-axis becomes:

[0130]

[0131] According to the above derivation, it can be summarized that after being flipped by n π pulses, the angle between the vector and the x-axis becomes:

[0132] Before the last pulse, the free evolution time is τ, and at this time the angle between the vector and the x-axis is:

[0133]

[0134] After arrangement, it can be obtained that:

[0135]

[0136] Finally, apply one more pulse to make the Bloch vector on the equatorial plane rotate around an arbitrary rotation axis Φ by

[0137]

[0138] It can be obtained that:

[0139]

[0140] It can be obtained by using the transformation of trigonometric functions:

[0141]

[0142] The simplification steps are as follows:

[0143]

[0144] It can be obtained:

[0145]

[0146] The probability that the measurement system is in the upper energy level after the Ramsey experiment is:

[0147]

[0148] Substitute α into the probability formula of Ramsey

[0149]

[0150] For the phase ε of the force 0 (the first phase) take the average value within [0, 2π], and it can be obtained:

[0151]

[0152] Among them,

[0153]

[0154] So the above formula can be expressed as

[0155]

[0156] According to the definition of Bessel function:

[0157]

[0158] So:

[0159]

[0160] Therefore, the fringe contrast J 0 and the displacement amplitude x 0 、the number n of π pulses in the quantum phase-locked sequence and the second frequency ω f The relational expression among the three is:

[0161]

[0162] In the embodiment of the present invention, a relational expression among the fringe contrast, the displacement amplitude, the number of π pulses in the quantum phase-locked sequence, and the second frequency is fitted to obtain a fitting curve.

[0163] 4) Based on the fitting curve, the displacement amplitude is calculated according to the values of the fringe contrast, the number of π pulses in the quantum phase-locked sequence, and the second frequency.

[0164] Step S1052: Calculate the amplitude of the electric field force according to the displacement amplitude.

[0165] 1) According to the displacement amplitude x 0 , the second frequency ω f and the first phase ε 0 generate the motion information of the ytterbium ion to be measured under the action of the periodic electric field to be measured;

[0166] Under the action of the electric field force of the periodic electric field to be measured, the ytterbium ion to be measured makes periodic micro-motions (motion information) in the blade trap:

[0167] x(t) = x 0 sin(ω f t + ε 0 )

[0168] According to the displacement amplitude x 0 calculated in step S1051, combined with the second frequency ω f and the first phase ε 0 obtain the motion information x(t) of the ytterbium ion to be measured under the action of the periodic electric field to be measured.

[0169] 2) Differentiate the motion information to obtain the velocity information of the ytterbium ion to be measured under the action of the periodic electric field to be measured;

[0170] Differentiate the motion information x(t) = x 0 sin(ω f t + ε 0 ) to obtain the velocity information of the ytterbium ion to be measured under the action of the periodic electric field to be measured:

[0171] v(t) = ω f x 0 cos(ω f t + ε 0 )

[0172] 3) Obtain the amplitude of the electric field force according to the velocity information.

[0173] Combining the periodic electric field force measurement method described in steps S101 - S105, it can be seen that in the present invention, the ytterbium ion to be measured under the periodic electric field to be measured is state-initialized by using the first laser, so that all the populations of the ytterbium ion to be measured are in 2 S1 / 2 (F = 0) state, and then use a second laser modulated by a quantum phase-locked sequence to cause the population of the ytterbium ion to be measured to transition from 2 S 1 / 2 (F = 0) state to 2 F 7 / 2 (F = 3) state. Subsequently, the detection result of the ytterbium ion to be measured is demodulated through a quantum phase-locked sequence to obtain the amplitude of the electric field force of the periodic electric field to be measured. Based on the high sensitivity of the quantum system, the quantum phase-locked technology is used to improve the accuracy and reliability of the measurement of the periodic electric field force, which is applicable to the measurement of weak periodic electric field forces; by making the ytterbium ion to be measured in the 2 F 7 / 2 (F = 3) state is pumped to 2 [3 / 2] 3 / 2 (F = 1) state, so that the ytterbium ion to be measured is in the 2 [3 / 2] 3 / 2 (F = 1) state and spontaneously emits to the 2 S 1 / 2 (F = 1) state, and the detection result is obtained by detecting the population of the ytterbium ion to be measured in the 2 S 1 / 2 (F = 1) state. Compared with directly detecting the population of the ytterbium ion to be measured in the 2F 7 / 2 (F = 3) state, it has higher fluorescence detection efficiency and accuracy, and further improves the accuracy and reliability of the measurement of the periodic electric field force.

[0174] The periodic electric field force measurement method of the embodiments of the present invention uses trapped ions as highly precise and ultrasensitive electromagnetic force detectors, and adopts quantum phase-locked technology to measure the ultra-weak force generated by a periodic electric field on a single trapped ion. It is applicable to the detection of forces in any direction within a nanoscale spatial range under a low-frequency periodic force field, and the measured sensitivity of the weak force is on the order of yoctonewton.

[0175] In some alternative embodiments, the functions / operations mentioned in the block diagrams may not occur in the order mentioned in the operation diagrams. For example, depending on the functions / operations involved, two consecutive blocks shown may actually be executed substantially simultaneously or the blocks can sometimes be executed in the reverse order. In addition, the embodiments presented and described in the flowcharts of the present application are provided by way of example for the purpose of providing a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logical flows presented herein. Alternative embodiments are foreseeable, in which the order of various operations is changed and the sub-operations described as part of larger operations are executed independently.

[0176] Those skilled in the art can implement the present application as set forth in the claims without undue experimentation using ordinary skills. It can also be understood that the specific concepts disclosed are merely illustrative and are not intended to limit the scope of the present application, which is determined by the full scope of the appended claims and their equivalents.

[0177] It should be understood that various parts of the present application can be implemented by hardware, software, firmware, or a combination thereof. In the above-described embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable program execution system. For example, if implemented in hardware, as in another embodiment, any one or a combination of the following techniques well known in the art can be used: discrete logic circuits having logic gate circuits for implementing logical functions on data signals, application specific integrated circuits having appropriate combinational logic gate circuits, programmable gate arrays (PGAs), field programmable gate arrays (FPGAs), etc.

[0178] In the foregoing description of this specification, descriptions with reference to the terms "one embodiment / example", "another embodiment / example", or "certain embodiments / examples", etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0179] Although the embodiments of the present application have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present application, and the scope of the present application is defined by the claims and their equivalents.

[0180] The above has specifically described the preferred embodiments of the present application, but the present application is not limited to the described embodiments. Those skilled in the art can also make various equivalent deformations or substitutions without departing from the spirit of the present application, and these equivalent deformations or substitutions are all included within the scope defined by the claims of the present application.

Claims

1. A method for measuring periodic electric field force, characterized in that, it includes the following steps: Initialize all the populations of the ytterbium ions to be measured that have been Doppler cooled using a first laser to 2 S 1 / 2 (F = 0) state, where the ytterbium ions to be measured are pre-trapped in a preset alternating electric field and within the coverage of a modulated periodic electric field to be measured; Use a second laser modulated by a quantum phase-locked sequence to cause the population of the ytterbium ions to be measured to transition from 2 S 1 / 2 (F = 0) state to 2 F 7 / 2 (F = 3) state, and the quantum phase-locked sequence includes a series of pulses; Use a third laser to place the ytterbium ions to be measured in 2 F 7 / 2 (F = 3) state population is pumped to 2 [3 / 2] 3 / 2 (F = 1) state, so that the ytterbium ions to be measured are in 2 [3 / 2] 3 / 2 (F = 1) state population spontaneously emits to 2 S 1 / 2 (F = 1) state; Use a fourth laser to detect the population of the ytterbium ions to be measured in the 2 S 1 / 2 (F = 1) state to obtain a detection result; Demodulate the detection result according to the quantum lock-in sequence to obtain the electric field force amplitude of the periodic electric field to be measured; The modulation of the periodic electric field to be measured includes the following steps: Modulate the periodic electric field to be measured with a first frequency and a first phase, converting the periodic electric field to be measured into a time-varying electric field, where the first frequency is related to the time interval between two adjacent pulses; The step of demodulating the detection result according to the quantum lock-in sequence to obtain the electric field force amplitude of the periodic electric field to be measured includes: Demodulate the displacement amplitude of the ytterbium ion to be measured from the detection result according to the quantum lock-in sequence; Calculate the electric field force amplitude according to the displacement amplitude.

2. A method for measuring periodic electric field force according to claim 1, characterized in that, The Doppler cooling of the ytterbium ion to be measured specifically includes: Use a fifth laser to perform 2 S 1 / 2 state to 2 P 1 / 2 state Doppler cooling on the ytterbium ions to be measured.

3. A method for measuring periodic electric field force according to claim 1, characterized in that, The alternating electric field is generated by a blade trap, and the blade trap includes a first DC blade, a second DC blade, a first AC blade and a second AC blade. A plurality of DC electrodes are respectively arranged on the first DC blade and the second DC blade. A first AC electrode and a first DC bias are arranged on the first AC blade, and a second AC electrode and a second DC bias are arranged on the second AC blade.

4. A method for measuring periodic electric field force according to claim 3, characterized in that, The method for trapping the ytterbium ion to be measured by using the alternating electric field includes the following steps: Generate the alternating electric field through the first AC blade and the second AC blade; Use the alternating electric field to trap the ytterbium ion to be measured in the radial direction of the blade trap.

5. A method for measuring periodic electric field force according to claim 1, characterized in that, The modulation of the second laser includes the following steps: Calculate the first time according to the first frequency; A series of pulses are generated by using an arbitrary waveform generator to obtain the quantum phase-locked sequence, and the time interval between two adjacent pulses is the first time; Modulate the second laser by using the quantum lock-in sequence.

6. A method for measuring periodic electric field force according to claim 1, characterized in that, The step of demodulating the displacement amplitude of the ytterbium ion to be measured from the detection result according to the quantum lock-in sequence includes: Scan the detection result at each time interval to obtain a fringe contrast, and the fringe contrast is the fringe contrast corresponding to the population of the ytterbium ion to be measured scanned at each time interval; Calculate the second frequency according to the first frequency, and the second frequency is the angular frequency of the periodic electric field to be measured; Fitting is performed on the relational expression among the stripe contrast, the displacement amplitude, the number of pulses in the quantum phase-locked sequence, and the second frequency to obtain a fitting curve; ​ Based on the fitting curve, calculate the displacement amplitude according to the fringe contrast, the number of pulses in the quantum lock-in sequence, and the value of the second frequency. ​ 7. A method for measuring periodic electric field force according to claim 6, characterized in that, The step of calculating the electric field force amplitude according to the displacement amplitude includes: Generate the motion information of the ytterbium ion to be measured under the action of the periodic electric field to be measured according to the displacement amplitude, the second frequency and the first phase; Derive the motion information to obtain the velocity information of the ytterbium ion to be measured under the action of the periodic electric field to be measured; Obtain the electric field force amplitude according to the velocity information.

8. A method for measuring periodic electric field force according to any one of claims 1-7, characterized in that, The wavelength of the first laser is 369.5 nm, the wavelength of the second laser is 467 nm, the wavelength of the third laser is 760 nm, and the wavelength of the fourth laser is 370 nm.

Images