A method and device for measuring weak alternating electric field based on single ion coherent state

Abstract

The application discloses a weak alternating current field measuring device based on single-ion coherent state. A single ion is confined in a surface electrode ion trap located on the surface of a vacuum cavity. A laser system emits corresponding measuring and controlling laser to the ion according to a preset time sequence. The measuring and controlling laser is Doppler cooling laser, internal state preparation laser, sideband cooling laser, blue sideband transition excitation laser or probe laser. An alternating current signal source outside the vacuum cavity emits a to-be-measured alternating current field to the surface electrode ion trap through an electric field loading electrode, and excites the ion coherent state evolution. The application also discloses a weak alternating current field measuring method based on single-ion coherent state. The to-be-measured alternating current field drives the ion coherent state, and then the laser system drives the ion blue sideband transition. The average phonon number is inversely deduced by measuring the evolution of the internal state population with time, and then the amplitude of the to-be-measured alternating current field force and the intensity of the to-be-measured alternating current field are calculated. The application can realize the measurement of the weak alternating current field in a 100 kHz-3 MHz wide frequency band.

Description

Technical Field

[0001] This invention relates to the field of quantum precision measurement technology, specifically to a method for measuring weak alternating current electric fields based on the coherent state of a single ion, and also to a device for measuring weak alternating current electric fields based on the coherent state of a single ion. Based on a trapped and cooled single ion, the device uses the coherent state dynamics response of the ion for measuring weak alternating current electric fields, and is suitable for applications such as precision sensing, weak electric field force detection, and quantum measurement. Background Technology

[0002] In recent years, ion trap systems have become a core experimental platform in quantum information science due to their unique advantages in cutting-edge fields such as quantum computing, quantum simulation, and quantum sensing. The internal and external degrees of freedom of trapped ions can be manipulated and measured with high precision, giving them excellent performance in the detection of weak signals, and showing great potential, especially in the measurement of electromagnetic fields, inertial forces, and even gravitational perturbations.

[0003] Traditional methods for measuring weak electric fields mostly rely on electrical or optical detectors. However, these methods typically face two limitations: first, insufficient sensitivity, making it difficult to effectively detect low-amplitude signals; and second, limited frequency response range, with particularly limited detection capability for high-frequency alternating electric field signals in the 100kHz–3MHz frequency band. Furthermore, existing methods also have shortcomings in achieving frequency-selective response, noise suppression, and spatial resolution, hindering their widespread application in high-precision experimental scenarios. Summary of the Invention

[0004] To address the aforementioned problems in existing technologies, this invention proposes a method for measuring weak alternating current electric fields based on single-ion coherent states, and also proposes a device for measuring weak alternating current electric fields based on single-ion coherent states, which measures the weak alternating current electric field force based on the dynamic response of single-ion coherent states.

[0005] The above-mentioned objectives of the present invention are achieved by the following technical means:

[0006] A weak AC electric field measurement device based on single-ion coherent states includes a surface electrode ion trap, in which a single ion is trapped. The surface electrode ion trap is located inside a vacuum cavity. A laser system emits a corresponding measurement and control laser to the ion in the surface electrode ion trap according to a preset timing sequence. The measurement and control laser can be a Doppler cooling laser, an internal state preparation laser, a sideband cooling laser, a blue sideband transition excitation laser, or a probe laser. An AC excitation signal output from an AC signal source outside the vacuum cavity is applied to an electric field loading electrode inside the vacuum cavity through a wire. The electric field loading electrode emits the AC electric field to be measured to the surface electrode ion trap, and the AC electric field to be measured excites the coherent state evolution of the ion on the surface electrode ion trap.

[0007] The optical detection module acquires ion fluorescence signals, converts them into electrical signals, and sends them to the data acquisition and processing module. The data acquisition and processing module then uses these electrical signals to obtain the Rabi oscillation curve and the average phonon number when the ion vibrational quantum state is in a coherent state. From the average phonon number Calculate the amplitude of the AC electric field force to be measured and the intensity of the AC electric field to be measured.

[0008] As mentioned above, the difference between the frequency of the AC electric field to be measured and the axial vibration frequency of the ions is less than the preset difference.

[0009] The ions described above are 40 Ca + When ions are present,

[0010] The corresponding Doppler cooling lasers include 397nm laser, 866nm laser and 854nm laser;

[0011] Internal state laser preparation includes 729nm laser, 854nm laser and 866nm laser;

[0012] Sideband cooling lasers include 729nm lasers, 854nm lasers, and 866nm lasers;

[0013] Blue-sideband transition-excited lasers include 729nm and 866nm lasers;

[0014] The detection lasers include 397nm and 866nm lasers.

[0015] As described above, the optical detection module includes a fluorescence collection optical system and a photodetector. The ion fluorescence signal generated by the ions is collected by the fluorescence collection optical system and converted into an electrical signal by the photodetector.

[0016] A method for measuring weak alternating current electric fields based on single-ion coherent states, utilizing a weak alternating current electric field measuring device based on single-ion coherent states as described above, is characterized by comprising the following steps:

[0017] Step 1: Construct a weak AC electric field measurement device based on single-ion coherent state;

[0018] Step 2: Trapped single ions in the surface electrode ion trap;

[0019] Step 3: Preset different laser pulse durations For the duration of each laser pulse All according to the preset number of cycles The following operation is performed repeatedly to obtain the laser pulse duration. The internal population of the following states:

[0020] Step 3.1: Use a laser system to prepare the ion vibrational quantum state into a moving ground state. The spin quantum state is prepared as a spin-down state;

[0021] Step 3.2: Based on the preset duration of the AC electric field force to be measured. An AC signal source applies a measured AC electric field to the ions trapped in the surface electrode ion trap via an electric field loading electrode, causing the vibrational quantum state of the ions to change from the ground state to the dynamic ground state. The controlled evolution is performed to a coherent state; wherein, the frequency of the AC electric field to be measured is... With ion axial vibration frequency Matching;

[0022] Step 3.3: Use a laser system to drive the blue sideband transition between the spin quantum state and the vibrational quantum state of the ion, and collect the corresponding ion fluorescence signal. When the ion fluorescence signal is detected, record the number of times the fluorescence signal is detected. Add 1; if no ion fluorescence signal is detected, then increment the number of times fluorescence signals were detected. The duration remains constant for each laser pulse. Number of times fluorescence signals were detected The initial value is 0;

[0023] Return to step 1 until the number of times steps 3.1 to 3.3 are repeated equal to the preset number of loops. :

[0024] The data acquisition and processing module calculates the corresponding internal population. ;

[0025] Step 4: The data acquisition and processing module is based on different laser pulse durations. Corresponding internal population The Rabi oscillation signal of the blue sideband was obtained;

[0026] The Rabi oscillation curve is obtained by fitting the Rabi oscillation signal of the blue sideband, and the average phonon number when the vibrational quantum state is in a coherent state is extracted from the Rabi oscillation curve. ;

[0027] Step 5: The data acquisition and processing module is based on the average phonon number. The amplitude of the AC electric field force to be measured and the intensity of the AC electric field to be measured are obtained.

[0028] As described above, step 3.1 specifically includes the following process:

[0029] The laser system emits a series of measurement and control lasers, which are Doppler cooling laser, internal state preparation laser, sideband cooling laser and internal state preparation laser in sequence, driving the ions trapped in the surface electrode ion trap to undergo Doppler cooling, first internal state preparation, sideband cooling and second internal state preparation in sequence.

[0030] As described in step 5 above, the amplitude of the AC electric field force to be measured :

[0031] ,

[0032] Indicates the axial vibration frequency of the ion; The mass of the ion; To reduce Planck's constant; The average phonon number; The duration of the AC electric field force to be measured;

[0033] The intensity of the AC electric field to be measured :

[0034] ;

[0035] in, This represents the charge of the ion.

[0036] As described above, step 3.2 also includes the following step: after the ions are excited to the coherent state, the laser system emits an internal state preparation laser to perform the third internal state preparation process.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] This invention is based on the average phonon number corresponding to the ionic coherent state (or coherent shift) generated by the weak external AC electric field to be measured in step 3.2 (coherent state excitation). With the applied AC electric field force to be measured The calibrable relationship between them is established; then, based on step 3.3 (quantum state detection), the phonon number information is mapped onto the Rabi oscillation of the blue sideband transition of the ion's inner state using a 729 nm laser-driven blue sideband transition. The average phonon number is then deduced by measuring the evolution of the proportion of inner states over time. Then the amplitude of the AC electric field force to be measured can be calculated. and the magnitude of the AC electric field to be measured .

[0039] In terms of hardware, this invention constructs a quantum detection platform capable of accurately applying and measuring the response to weak AC electric fields by introducing independent driving electrodes, a low-noise radio frequency system, coherent control lasers, and a high-efficiency readout link into a traditional ion trap device. (Independent driving electrodes refer to the electric field loading electrodes; high-efficiency readout link refers to the optical detection module, data acquisition and processing module; coherent control lasers refer to all 854 nm, 866 nm, 397 nm, and 729 nm lasers; and the low-noise radio frequency system refers to the radio frequency driving power supply in the surface electrode ion trap.) These improvements solve the problems of "impure external field coupling, high noise, unstable frequency, and insufficient readout accuracy" in existing systems, thereby significantly improving measurement sensitivity and repeatability.

[0040] High-sensitivity wideband measurement: This invention can achieve high-sensitivity measurement of weak AC electric fields in a wide frequency band of 100kHz~3MHz, which significantly broadens the measurable frequency range and improves the detection limit compared with traditional technology;

[0041] Single-ion detection electric field: using a single ion cooled to its moving ground state Using ions as detection elements, submicron-level spatial resolution and high-fidelity quantum state controlled precision were achieved, significantly reducing environmental noise and systematic errors;

[0042] Quantum coherent state characterization: The electric field strength and frequency are directly characterized by the dynamic evolution of quantum coherent states. It has natural frequency selectivity and excellent noise suppression capability, and at the same time provides the possibility for non-destructive measurement.

[0043] Good scalability: This method and device can be widely used in cutting-edge fields such as precision measurement, quantum sensing, weak force detection, calibration of fundamental physical constants, dark matter detection and new physics search, and the signal-to-noise ratio and measurement bandwidth can be improved through multi-ion or multi-mode expansion. Attached Figure Description

[0044] Figure 1 is a schematic diagram of the overall structure of the device of the present invention, which is used to intuitively show the composition of each functional module and their interconnection relationship;

[0045] Among them, 1-vacuum cavity; 2-854nm laser; 3-866nm laser; 4-397nm laser; 5-729nm laser; 6-AC signal source; 7-electric field loading electrode; 8-optical detection module; 9-data acquisition and processing module; 10-surface electrode ion trap.

[0046] Figure 2 shows a single 40 Ca + A schematic diagram of the energy level structure of ions, in which... , , , and All are energy levels. , as well as They represent the corresponding angular quantum numbers. The atomic orbital energy levels are 0, 1, and 2. 729 nm, 397 nm, 866 nm, and 854 nm are the wavelengths of the laser driving the transitions (in nanometers). 6.9 ns, 7.1 ns, 1.17 s, and 1.2 s represent the spontaneous emission lifetimes, where ns represents nanoseconds and s represents seconds. The magnetic quantum number, the magnetic field-frequency conversion factor, is expressed in MHz / G MHz per gauss. and These represent defining the corresponding energy levels as the 1 and 0 states of quantum logic, respectively.

[0047] Figure 3 is a timing diagram of the method of the present invention. The figure shows the time sequence of operations such as Doppler cooling, internal state preparation, sideband cooling, applying the AC electric field to be measured to excite the coherent state, applying a 729 nm laser pulse for sideband excitation, and fluorescence detection. It is used to intuitively illustrate the control logic of the method of the present invention in a complete measurement cycle. ms represents milliseconds.

[0048] Figure 4 is a measurement flowchart of the method of the present invention, which shows the logical relationship and working order between the steps of ion trapping and cooling, coherent state excitation, quantum state detection, and data analysis and electric field inversion.

[0049] Figure 5 shows a single 40 Ca + A schematic diagram of the phase space trajectory of ions evolving from the ground state to the coherent state under the influence of a resonant electric field. This diagram visually illustrates the coherent evolution process of ion motion modes under the excitation of an applied electric field. This represents the average phonon number.

[0050] Figure 6 shows the single [value] after the applied AC electric field to be measured has been applied for a fixed time of 0.1 ms. 40 Ca + A typical experimental curve of Rabi oscillation driven by blue-sideband transitions of ions. The horizontal axis represents the laser pulse duration, and the vertical axis represents the probability of the ion being in the excited state (D state). This curve reflects the dynamic characteristics of ions after being excited by an applied electric field to form a coherent state. By fitting the curve, the phonon number distribution and average phonon number of the ion's motion mode can be extracted, thereby further retrieving the intensity of the AC electric field to be measured.

[0051] Figure 7 is a histogram of the coherent phonon number distribution obtained by fitting the measurement data, which is used to demonstrate the quantization results and statistical characteristics obtained by the method of the present invention in weak electric field detection.

[0052] Figure 8 shows the average phonon number after a fixed time of 0.1 ms under the applied AC electric field. With inverted electric field strength The relationship diagram is shown. The diagram labels the example experimental points (average phonon number) of this invention. =2.29; Electric field strength =1.46 mV / m (unit: millivolt / meter), used to illustrate how the method of the present invention can directly invert the intensity of the AC electric field under test by measuring the average phonon number. Detailed Implementation

[0053] The present invention will be further described in detail below with reference to the embodiments, but the embodiments described herein are only for illustration and explanation and are not intended to limit the present invention.

[0054] Example 1

[0055] A weak alternating current electric field measurement device based on single-ion coherent states, such as... Figure 1 As shown, it includes a surface electrode ion trap 10, a laser system (in this embodiment, the laser system includes an 854nm laser 2, an 866nm laser 3, a 397nm laser 4, and a 729nm laser 5, where 854 nm, 866 nm, 397 nm, and 729 nm are all wavelengths of the laser), an electric field loading electrode 7, an optical detection module 8, and a data acquisition and processing module 9.

[0056] A single ion is trapped in a surface electrode ion trap 10, which is located inside a vacuum cavity 1. The laser system emits a corresponding measurement and control laser into the ion in the surface electrode ion trap 10 according to a preset timing sequence. This measurement and control laser can be a Doppler cooling laser, an internal state preparation laser, a sideband cooling laser, a blue sideband transition excitation laser, or a probe laser (in this embodiment, the trapped ion is...). 40 Ca + The ion-specific Doppler cooling lasers include 397nm laser 4, 866nm laser 3, and 854nm laser 2, used for Doppler cooling of ions; the internal state preparation lasers include 729nm laser 5, 854nm laser 2, and 866nm laser 3, used for internal state preparation of ions; the sideband cooling lasers include 729nm laser 5, 854nm laser 2, and 866nm laser 3, used for sideband cooling of ions; and the blue sideband transition excitation lasers include 729nm laser 5 and 866nm laser 3, used for driving... 40 Ca +The blue-sideband transition between the spin quantum state and the vibrational quantum state of an ion is detected by the detection laser, which includes a 397nm laser 4 and an 866nm laser 3. An AC signal source 6 outside the vacuum cavity 1 outputs an AC excitation signal, which is applied to the electric field loading electrode 7 inside the vacuum cavity 1 through a wire. The electric field loading electrode 7 emits the AC electric field to be measured to the surface electrode ion trap 10, which excites the evolution of the coherent state of the ions on the surface electrode ion trap 10. The optical detection module 8 collects the ion fluorescence signal, converts the ion fluorescence signal into an electrical signal, and sends it to the data acquisition and processing module 9. The data acquisition and processing module 9 obtains the Rabi oscillation curve and the average phonon number when the ion vibrational quantum state is in the coherent state from the electrical signal. From the average phonon number Calculate the amplitude of the AC electric field force to be measured and the intensity of the AC electric field to be measured.

[0057] In the aforementioned weak alternating current electric field measurement device based on single-ion coherent states:

[0058] Surface electrode ion trap 10: used to trap a single ion and achieve effective cooling of the vibrational quantum state, thereby ensuring that the ion is in a stable and controllable quantum state during subsequent measurements; in this embodiment, the surface electrode ion trap 10 includes an ion trap electrode (such as a radio frequency electrode and a DC control electrode) and a radio frequency drive power supply, used to stably trap a single ion and provide the required trap potential; the surface electrode ion trap 10 is placed in a vacuum chamber 1, which is used to provide an ultra-high vacuum environment to reduce the collision and interference of background gas on the trapped ions.

[0059] Laser system: Provides lasers of multiple wavelengths for Doppler cooling, sideband cooling, quantum state preparation, blue sideband transition excitation manipulation, and quantum state detection of ions; in this embodiment, the laser output by the laser system includes:

[0060] 854nm laser 2: Used to drive ions to transition from excited state to low energy state, to achieve optical pumping or cooling (such as Doppler cooling, sideband cooling).

[0061] 397nm laser 4: used for initial Doppler cooling and quantum state detection via ion fluorescence detection;

[0062] 866nm laser 3: used to assist 397nm laser 4 in forming a closed transition circuit, thereby completing Doppler cooling, and also used for internal state preparation, sideband cooling and blue sideband transition excitation;

[0063] 729nm laser 5: used for further internal state preparation and sideband cooling of ions, and also for blue sideband transition excitation of ions after a fixed time of application of an external AC electric field to be measured, thereby performing Rabi oscillation measurement to extract phonon number distribution and invert the AC electric field force to be measured.

[0064] AC signal source 6: Used to apply a weak AC excitation signal corresponding to the AC electric field to be measured to the trapped ions, so as to achieve precise loading of the external AC electric field to be measured.

[0065] Optical detection module 8 includes a fluorescence collection optical system and a photodetector. The ion fluorescence signal generated during the quantum state evolution process of ions is collected by the fluorescence collection optical system and converted into a measurable electrical signal by the photodetector. In this embodiment, the fluorescence collection optical system in optical detection module 8 includes a lens system, and the photodetector is a photomultiplier tube.

[0066] Data acquisition and processing module 9: Responsible for acquiring, fitting, and analyzing the electrical signals output by optical detection module 8. The specific fitting and analysis process is described in Example 2. Based on the measured phonon number distribution, the amplitude, frequency, and phase information of the AC electric field to be measured are obtained. In this example, data acquisition and processing module 9 includes a computer and signal processing software, used to fit the measured average phonon number. And inverse the amplitude of the AC electric field force to be measured This allows us to obtain the intensity of the AC electric field to be measured.

[0067] Electric field loading electrode 7: Used in conjunction with AC signal source 6, it applies a weak AC electric field to the trapped ion to excite its coherent state evolution.

[0068] The aforementioned weak AC electric field measurement device based on single-ion coherent states achieves high-precision manipulation of trapped ions, quantum state measurement, and highly sensitive detection of weak electric fields through the synergistic effect of the above modules.

[0069] Example 2

[0070] A method for measuring weak alternating current electric fields based on single-ion coherent states, such as... Figures 3-4 As shown, the weak AC electric field measurement device based on single-ion coherent state described in Example 1 includes the following steps:

[0071] Step 1: Construct a weak AC electric field measurement device based on single-ion coherent state.

[0072] Step 2, Ion Trapping: Trapping a single ion in the surface electrode ion trap 10; for this embodiment, a single ion is trapped in the surface electrode ion trap 10. 40 Ca + ion( 40 Ca + The energy level structure of ions is as follows Figure 2 (As shown).

[0073] Step 3: Preset different laser pulse durations For the duration of each laser pulse All according to the preset number of cycles The following operation is performed repeatedly to obtain the laser pulse duration. The internal population of the following states:

[0074] Step 3.1: Prepare the vibrational quantum state of ions into a dynamic ground state using a laser system. The spin quantum state is prepared as a spin-down state, thereby effectively suppressing the influence of thermal noise on subsequent measurements.

[0075] For this embodiment, 40 Ca + Ions in the surface electrode ion trap 10 exhibit axial and radial vibration modes, wherein, for the axial vibration mode:

[0076] ,

[0077] ,

[0078] in, The axial vibration frequency of the ions is the axial trap frequency of the ions in the surface electrode ion trap 10. The mass of the ion.

[0079] Step 3.1 as follows Figure 3 As shown, the specific process includes the following: using different measurement and control lasers emitted by the laser system, the ions trapped in the surface electrode ion trap 10 are sequentially subjected to Doppler cooling, first internal state preparation, sideband cooling, and second internal state preparation (i.e., a series of measurement and control lasers are emitted by the laser system, the measurement and control lasers being Doppler cooling laser, internal state preparation laser, sideband cooling laser, and internal state preparation laser in sequence). In this embodiment, Doppler cooling of the ions is achieved by using 397nm laser 4, 866nm laser 3, and 854nm laser 2; then the first internal state preparation process is performed; next, sideband cooling is performed using 729nm laser 5 in conjunction with 854nm laser 2 and 866nm laser 3, cooling the vibrational quantum state to the motion ground state. Subsequently, a second internal state preparation process is performed. This internal state preparation (including the first, second, and subsequent third internal state preparations) utilizes a 729nm laser 5 in conjunction with an 854nm laser 2 and an 866nm laser 3. The purpose is to uniformly reset the ion's internal state to the same spin quantum state before each electric field measurement. In this embodiment, the internal state preparation resets the ion's spin quantum state to a spin-down state (abbreviated as...). (This is to ensure the repeatability and consistency of subsequent experimental operations and measurement processes).

[0080] It should be noted that the internal state preparation process described above, as well as the internal state preparation processes in subsequent steps, only affect the internal state (i.e., the spin quantum state of the ion in the surface electrode ion trap 10) degree of freedom of the ion, and do not change the external state (i.e., the vibrational quantum state of the ion in the surface electrode ion trap 10). Therefore, this step does not affect the evolution result of the ion's external state; its role is only to provide definite initial internal state conditions for subsequent operations.

[0081] Step 3.2, coherent state excitation ( Figures 4-5 ): Based on the preset duration of the AC electric field force to be measured The AC signal source 6 applies the AC electric field to be measured to the ions trapped in the surface electrode ion trap 10 through the electric field loading electrode 7, causing the vibrational quantum state of the ions to change from the ground state to the dynamic ground state. The controlled evolution is performed until a coherent state is reached. The frequency of the AC electric field to be measured is... With ion axial vibration frequency Matching, i.e., the frequency of the AC electric field to be measured With ion axial vibration frequency The difference between them is less than the preset difference, ideally. In this embodiment, the 866nm laser 3 remains on in step 3.2.

[0082] In this invention, a single ion within the surface electrode ion trap 10 possesses three orthogonal vibrational degrees of freedom, including one axial vibrational mode and two radial vibrational modes, which are used for manipulating and measuring the ion's axial vibrational mode. For frequency-mismatched electric field components, their coupling to the ion's axial motion is negligible, does not constitute effective excitation, and does not affect the measurement results. The results obtained by this invention can be understood as the effective electric field strength containing the ion's axial vibrational frequency component within the AC electric field to be measured.

[0083] In this embodiment, an AC signal source 6 outputs an AC excitation signal of known frequency and applies it to the electric field loading electrode 7 to simulate an external AC electric field to be measured. However, the method of the present invention does not depend on the AC signal source 6 itself, but rather on the frequency of the ion axial vibration. The components of the AC electric field to be measured are consistent. In other embodiments, if it is necessary to measure the axial vibration modes of ions at different frequencies, this can be achieved through an external frequency selector or frequency conversion module.

[0084] The force exerted by the AC electric field to be measured can be written as:

[0085]

[0086] ,

[0087] in, The frequency of the AC electric field to be measured is... The phase of the AC electric field to be measured. This represents the amplitude of the AC electric field force to be measured, that is, the maximum value of the force exerted on the ions by the AC electric field to be measured. This represents the alternating electric field force to be measured. It is the imaginary unit.

[0088] Hamiltonian of ion axial vibration modes for:

[0089] ,

[0090] in, The momentum operator represents the ion's momentum in the axial vibration direction. This represents the displacement operator of ions in the axial vibration direction.

[0091] Hamiltonian of the interaction between the measured alternating electric field and ions It can be written as:

[0092] ,

[0093] At this time, the ion axial vibration mode is under the measured AC electric field force. The Hamiltonian below is in the form of a forced harmonic oscillator, and the total Hamiltonian is... for:

[0094]

[0095] ,

[0096] Define the phonon annihilation operator :

[0097] ,

[0098] Phonon production operators :

[0099] ,

[0100] have:

[0101] ,

[0102] ,

[0103] in, The characteristic length of a simple harmonic oscillator. The characteristic momentum of this simple harmonic oscillator ; is the reduced Planck constant.

[0104] The evolution of the total Hamiltonian of the quantum state under the Schrödinger picture satisfies the Schrödinger equation:

[0105] ,

[0106] in, It represents the quantum state vector of the system under the Schrödinger picture, that is, the quantum state of the system as it evolves over time, describing the complete quantum state information of the ion at a given moment.

[0107] Introducing the free evolution operator :

[0108] ,

[0109] Define the interactive picture state :

[0110] ,

[0111] for Hermitian conjugate operators (i.e., adjoint operators), due to It belongs to the unitary operator, therefore its accompanying operator is .

[0112] Regarding the time of action of the AC electric field force to be measured, both sides of the above definition are... By taking the derivative and using the chain rule, we can obtain:

[0113]

[0114] ,

[0115] Among them, the dot number Represents the derivative with respect to time, for example , .

[0116] Substituting into the Schrödinger equation The relationship, while utilizing the free evolution operator Hermitian conjugate operator derivative relationship Thus, the evolution equation form under the interaction picture is obtained:

[0117] ,

[0118] because and They are interchangeable and can be organized as follows:

[0119] ,

[0120] Right now:

[0121] ,

[0122] This will yield the form of the interactive matte painting:

[0123] ,

[0124] in, It is the interaction Hamiltonian under the original Schrödinger picture. The Hamiltonian under the interaction picture obtained through free evolution transformation is denoted as the Hamiltonian under the interaction picture. :

[0125] ,

[0126] For any operator in the Schrödinger picture In interactive matte art, it is defined as:

[0127] ,

[0128] in, This represents operators under an interaction picture, specifically operators under a Schrödinger picture. Operators evolved freely The time-dependent operator obtained by the transformation.

[0129] Therefore, for the phonon annihilation operator phonon generation operator In the context of interactive scenes, it can be written as:

[0130]

[0131] ,

[0132]

[0133] ,

[0134] : Phonon annihilation operator in the context of interaction, representing the evolution of phonon annihilation operation over time under free evolution. Phonon generation operators in an interaction-based context represent the evolution of phonon generation operations over time under free evolution.

[0135] That is, under the interaction picture, the Hamiltonian can be written as:

[0136] ,

[0137] At this time Substituting, we have:

[0138] ,

[0139] in,

[0140] ,

[0141] and Both of these indices contain The time-dependent term, therefore corresponding to the fast rotation term. In the case discussed above, when the frequency of the AC electric field to be measured... At that time, these terms in the interaction representation have a frequency of approximately 2. The rapid oscillations have a negligible average contribution over experimentally relevant timescales. Based on this, by omitting the aforementioned rapid rotation term using the rotating-wave approximation (RWA), the Hamiltonian in the interaction plot can be written as:

[0142] ,

[0143] At this point, the Hamiltonian under the interaction picture The time evolution operator for a timeless Hamiltonian is no longer included in the time-independent terminator. It can be written as:

[0144]

[0145]

[0146] ,

[0147] Indicates time;

[0148] Displacement operators corresponding to the time evolution operators of the time-independent Hamiltonian The form is:

[0149] ,

[0150] in, For complex conjugate operators, the shift operator parameter for:

[0151] ,

[0152] That is, when the AC electric field force to be measured acts for a certain period of time The post-ion from the ground state (abbreviated as) Evolves into a coherent state :

[0153] .

[0154] Ions are excited to a coherent state Then, the laser system emits an internal state preparation laser to perform the third internal state preparation process.

[0155] Step 3.3, Quantum State Detection: The laser system emits a blue-sideband transition excitation laser to the ions, driving the blue-sideband transition between the ion's spin quantum state and vibrational quantum state (in this embodiment, the 866nm laser 3 is kept on, and the 729nm laser 5 in the laser system is used to drive the blue-sideband transition between the ion's spin quantum state and vibrational quantum state). The corresponding ion fluorescence signal is collected (in this embodiment, while the 866nm laser 3 is kept on, the 397nm laser 4 is used for quantum state detection). When the ion fluorescence signal is detected, the number of times the fluorescence signal is detected is recorded. Add 1; if no ion fluorescence signal is detected, then increment the number of times fluorescence signals were detected. The duration remains constant for each laser pulse. Number of times fluorescence signals were detected The initial value is 0;

[0156] Return to step 1 until the number of times steps 3.1 to 3.3 are repeated equal to the preset number of loops. :

[0157] Data acquisition and processing module 9 calculates the corresponding internal population. .

[0158] Step 4, Data Acquisition and Processing Module 9: Based on different laser pulse durations Corresponding internal population The Rabi oscillation signal of the blue sideband is obtained;

[0159] The Rabi oscillation curve is obtained by fitting the Rabi oscillation signal of the blue sideband, and the average phonon number when the vibrational quantum state is in a coherent state is extracted from the Rabi oscillation curve. And obtain the phonon number distribution image.

[0160] This embodiment utilizes a 729nm laser to drive ions from... A Zeeman sublevel of the state A blue-sideband transition of a Zeeman sublevel records the population of the ion's internal states. With laser pulse duration The Rabi oscillation curve is as follows:

[0161] ,

[0162] in, The population of the internal state of the ion. Blue edge zone jump The Rabi frequency can be written as:

[0163] ,

[0164] in, Lamb-Dicke parameters are the Rabi frequency of the carrier wave (corresponding to the single-photon coupling strength) without phonons. , The wavenumber of the driving laser corresponding to the blue sideband transition is, in this embodiment, equal to the wavenumber corresponding to the 729nm laser 5. The wavelength of the driving laser corresponding to the blue sideband transition; The angle between the driving laser and the ion axial vibration direction corresponding to the blue sideband transition is given in this embodiment. The beam direction of the 729nm laser is equal to... 40 Ca + The angle between the axial vibration directions of the ions; It is a generalized Laguerre polynomial.

[0165] in, For coherent states in Fock state The probability, based on the coherent state definition:

[0166]

[0167] ,

[0168] The number of particles and the distribution of phonons in the coherent state in the Fock state exhibit a Poisson distribution. , Indicates the coherent state in the Fock state The projection coefficients on the surface are the coherent states. In vibration mode number Complex amplitudes on a number of phonon states. It is a coherent state in the Fock state The probability distribution on the surface describes the probability distribution of the first vibration mode when measuring this vibration mode. The probability distributed across each phonon mode.

[0169] Corresponding average phonon number Satisfying Relationship:

[0170] ,

[0171] in, This is the modulo-square operator.

[0172] In this embodiment, ions are obtained from... Coupled to The blue-sideband Rabi oscillation signal, and the Rabi oscillation curve and phonon number distribution image obtained by fitting it, such as... Figures 6-7 As shown, where The magnetic quantum number, i.e., the projected component of angular momentum along the quantization axis, represents the duration of action of the AC electric field force being measured during the measurement. Lamb-Dicke parameters in the experiment Rabi frequency of carrier wave without phonons Experimental results for fitting the average phonon number . and All are energy levels. and They represent the corresponding angular quantum numbers. The atomic orbital energy levels are 0 and 2.

[0173] Step 5: Data Analysis and Electric Field Inversion ( Figure 8 ): Data acquisition and processing module 9 is based on the average phonon number measured in step 4. The intensity of the AC electric field to be measured is obtained through the following steps:

[0174] Due to the displacement operator parameters , can be obtained Furthermore, due to From this, we can deduce the amplitude of the AC electric field force acting on the ion corresponding to the AC electric field being measured:

[0175] ,

[0176] Due to the characteristic momentum of a simple harmonic oscillator The relationship between the average phonon number and the amplitude of the AC electric field force being measured is as follows:

[0177] ,

[0178] Furthermore, the amplitude of the AC electric force to be measured and the intensity of the AC electric field to be measured satisfy the following:

[0179] ,

[0180] in, The charge of the ion (for) 40 Ca + That is, a single elementary charge e). Therefore, the strength of the AC electric field to be measured, obtained from the amplitude of the AC electric field force to be measured, is:

[0181] ,

[0182] In this embodiment, the amplitude of the AC electric field force to be measured is: N. The charge of the ion right 40 Ca + For a single elementary charge e, the intensity of the alternating electric field to be measured is: = 1.46 mV / m.

[0183] Under typical experimental conditions, the electric field force measurement sensitivity of this invention can reach sub-Zehnder Newtons, and its corresponding sensitivity for measuring the intensity of weak AC electric fields can be better than mV / m (millivolts per meter).

[0184] This invention can be applied to high-frequency weak electric field detection, electrode surface charge noise measurement, precision inertial force and vibration detection, quantum sensing and basic physics experiments.

[0185] Those skilled in the art to which this invention pertains may make various modifications or additions to the specific embodiments described, or use similar methods to replace them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. A weak alternating current electric field measurement device based on single-ion coherent states, characterized in that, The system includes a surface electrode ion trap (10), in which a single ion is trapped. The surface electrode ion trap (10) is located inside a vacuum cavity (1). The laser system emits corresponding measurement and control lasers to the ions in the surface electrode ion trap (10) according to a preset timing sequence. The measurement and control lasers are Doppler cooling lasers, internal state preparation lasers, sideband cooling lasers, blue sideband transition excitation lasers, or probe lasers. According to the preset timing sequence, the measurement and control lasers are, in sequence, Doppler cooling lasers, internal state preparation lasers, sideband cooling lasers, internal state preparation lasers, and blue sideband transition excitation lasers. The transition excitation laser, the probe laser, or the measurement and control laser are, in sequence, the Doppler cooling laser, the internal state preparation laser, the sideband cooling laser, the internal state preparation laser, the internal state preparation laser, the blue sideband transition excitation laser, and the probe laser; the AC excitation signal output by the AC signal source (6) outside the vacuum cavity (1) is applied to the electric field loading electrode (7) inside the vacuum cavity (1) through the wire, and the electric field loading electrode (7) emits the AC electric field to be measured to the surface electrode ion trap (10), and the AC electric field to be measured excites the evolution of the coherent state of the ions on the surface electrode ion trap (10); The optical detection module (8) acquires ion fluorescence signals, converts them into electrical signals, and sends them to the data acquisition and processing module (9). The data acquisition and processing module (9) obtains the Rabi oscillation curve and the average phonon number when the ion vibration quantum state is in a coherent state from the electrical signals. From the average phonon number Calculate the amplitude of the AC electric force and the intensity of the AC electric field to be measured; Amplitude of the AC electric field force to be measured : ， Indicates the axial vibration frequency of the ion; The mass of the ion; To reduce Planck's constant; The average phonon number; The duration of the AC electric field force to be measured; The intensity of the AC electric field to be measured : ； in, This represents the charge of the ion.

2. The weak alternating current electric field measurement device based on single-ion coherent states according to claim 1, characterized in that, The difference between the frequency of the AC electric field to be measured and the axial vibration frequency of the ions is less than a preset difference.

3. The weak alternating current electric field measuring device based on single-ion coherent states according to claim 1, characterized in that, The ions are 40 Ca + When ions are present, The corresponding Doppler cooling lasers include a 397nm laser (4), an 866nm laser (3), and an 854nm laser (2); The lasers used in internal state preparation include 729nm laser (5), 854nm laser (2) and 866nm laser (3); The sideband cooling lasers include a 729nm laser (5), an 854nm laser (2), and an 866nm laser (3); The blue-sideband transition-excited lasers include 729nm lasers (5) and 866nm lasers (3); The detection lasers include a 397nm laser (4) and an 866nm laser (3).

4. The weak alternating current electric field measuring device based on single-ion coherent states according to claim 1, characterized in that, The optical detection module (8) includes a fluorescence collection optical system and a photodetector. The ion fluorescence signal generated by the ions is collected by the fluorescence collection optical system and converted into an electrical signal by the photodetector.

5. A method for measuring weak alternating current electric fields based on single-ion coherent states, utilizing the weak alternating current electric field measuring device based on single-ion coherent states as described in claim 2, characterized in that, The steps include the following: Step 1: Construct a weak AC electric field measurement device based on single-ion coherent state; Step 2: Trapped a single ion in the surface electrode ion trap (10); Step 3: Preset different laser pulse durations For the duration of each laser pulse All according to the preset number of cycles The following operation is performed repeatedly to obtain the laser pulse duration. The internal population of the following states: Step 3.1: Use a laser system to prepare the ion vibrational quantum state into a moving ground state. The spin quantum state is prepared as a spin-down state; Step 3.2: Based on the preset duration of the AC electric field force to be measured. The AC signal source (6) applies the AC electric field to the ions trapped in the surface electrode ion trap (10) through the electric field loading electrode (7), causing the vibrational quantum state of the ions to change from the ground state to the dynamic ground state. The controlled evolution is performed to a coherent state; wherein, the frequency of the AC electric field to be measured is... With ion axial vibration frequency Matching; Step 3.3: Use a laser system to drive the blue sideband transition between the spin quantum state and the vibrational quantum state of the ion, and collect the corresponding ion fluorescence signal. When the ion fluorescence signal is detected, record the number of times the fluorescence signal is detected. Add 1; if no ion fluorescence signal is detected, then increment the number of times fluorescence signals were detected. The duration remains constant for each laser pulse. Number of times fluorescence signals were detected The initial value is 0; Return to step 1 until the number of times steps 3.1 to 3.3 are repeated equal to the preset number of loops. : The data acquisition and processing module (9) calculates the corresponding internal population. ; Step 4, Data Acquisition and Processing Module (9) Based on different laser pulse durations Corresponding internal population The Rabi oscillation signal of the blue sideband was obtained; The Rabi oscillation curve is obtained by fitting the Rabi oscillation signal of the blue sideband, and the average phonon number when the vibrational quantum state is in a coherent state is extracted from the Rabi oscillation curve. ; Step 5, Data Acquisition and Processing Module (9) Based on Average Phonon Number The amplitude of the AC electric field force to be measured and the intensity of the AC electric field to be measured are obtained.

6. The method for measuring weak alternating current electric fields based on single-ion coherent states according to claim 5, characterized in that, Step 3.1 specifically includes the following process: The laser system emits a series of measurement and control lasers, which are Doppler cooling laser, internal state preparation laser, sideband cooling laser and internal state preparation laser in sequence, driving the ions trapped in the surface electrode ion trap (10) to undergo Doppler cooling, first internal state preparation, sideband cooling and second internal state preparation in sequence.

7. The method for measuring weak alternating current electric fields based on single-ion coherent states according to claim 6, characterized in that, Step 3.2 further includes the following steps: after the ions are excited to the coherent state, the laser system emits an internal state preparation laser to perform the third internal state preparation process.

Images