A method for detecting electric field based on multiple frequency conversion of Rydberg atoms

Abstract

The present invention discloses a method for detecting electric field based on multiple frequency conversion of Rydberg atoms, which belongs to the field of electromagnetic field detection. The present invention adopts two cascaded cesium atomic pools, obtains the wavelength of the incident signal, local oscillator signal, coupled light and detection light of the second-stage cesium atomic pool according to the output signal of the first-stage cesium atomic pool, collects the output signal of the second-stage cesium atomic pool, and finally realizes high-sensitivity detection of the electric field. The present invention reduces the interference of environmental noise on the electric field to be measured by combining multiple frequency conversion technology with Rydberg atom detection technology, and provides a solution for reducing design difficulty and cost and improving detection accuracy for detecting electric field strength based on Rydberg atoms.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic field detection, including multiple frequency conversion, zero intermediate frequency and signal modulation technologies, and specifically relates to a method for detecting electric field based on multiple frequency conversion of Rydberg atoms. Background Art

[0002] Since Rydberg atoms have extremely large electric dipole moments, they are very sensitive to external electric fields, and their measurement sensitivity is much higher than existing traditional wireless measurement technologies. By utilizing the electromagnetically induced transparency (EIT) effect and AT (Autler-Townes, AT) splitting effect of Rydberg atoms, the electric field measurement based on Rydberg atoms can trace the electric field strength back to the Planck constant, and the measurement of the electric field can be converted into the measurement of the frequency. The basic parameters of the atoms can also be used to perform self-calibration measurements, which will greatly improve the measurement accuracy of the electric field. However, the electric field detection technology using single frequency conversion may cause a false signal of "mirror interference" after the frequency conversion. In this case, the required receiving frequency and the interference signal may both appear in the intermediate frequency range, thereby interfering with the signal to be received.

[0003] In the invention patent with publication number CN112730999A and titled "A device and method for measuring microwave electric field strength", a method of adding an auxiliary microwave electric field is disclosed. This method is based on the traditional wireless superheterodyne receiving structure. In order to improve the signal-to-noise ratio of the experimental results, the intensity of the coupled light is amplitude modulated to detect the electric field strength of the microwave frequency band to be measured. This invention lacks the ability to detect the electric field to be measured at a higher operating frequency. Environmental noise may cause certain interference to the electric field to be measured, thereby affecting the accuracy of electric field measurement. At the same time, its design difficulty and cost may be relatively high in later applications. Summary of the invention

[0004] The present invention aims at the problems existing in the technical background and proposes a method for detecting electric field based on multiple frequency conversion of Rydberg atoms. The present invention combines Liouville master equation, multiple frequency conversion technology, zero intermediate frequency technology and signal modulation technology to achieve high-sensitivity detection of the electric field to be measured.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A method for detecting electric field based on multiple frequency conversion of Rydberg atoms, comprising the following steps:

[0007] S1: The first-level detection light is incident on the first-level cesium atom pool to make the cesium atoms transition from the ground state energy level to the intermediate state energy level;

[0008] S2: injecting the first-stage coupled light into the first-stage cesium atom pool to excite the cesium atoms to transition from the intermediate state energy level to the first Rydberg state energy level, so that the cesium atoms form Rydberg atoms;

[0009] S3: using a known baseband electric field to modulate the amplitude or frequency of a known carrier electric field to obtain an electric field signal to be measured;

[0010] S4: The electric field signal to be measured and the frequency f L1 , amplitude is A L1 The local oscillator electric field signal of the first-stage Rydberg cesium atom is radiated into the first-stage Rydberg cesium atom pool and interacts with the Rydberg atom;

[0011] S5: by collecting the first-stage detection light output signal passing through the first-stage cesium atomic pool, the amplitude A1 and the frequency f1 thereof are obtained;

[0012] S6: According to the amplitude A1 and frequency f1 of the first-stage detection light output signal, determine the wavelength of the second-stage coupling light and the second-stage detection light, determine the amplitude A1 and frequency f1 of the second-stage incident signal, and obtain the amplitude A of the second-stage local oscillator electric field signal L2 , frequency f L2 ;

[0013] S7: injecting the second-stage detection light into the second-stage cesium atom pool to make the cesium atoms transition from the ground state energy level to the intermediate state energy level;

[0014] S8: injecting the second-stage coupled light into the second-stage cesium atom pool to excite the cesium atoms to transition from the intermediate state energy level to the first Rydberg state energy level, so that the cesium atoms form Rydberg atoms;

[0015] S9: radiating the second-stage incident signal and the second-stage local oscillator electric field signal into the second-stage Rydberg cesium atom pool to interact with the Rydberg atoms;

[0016] S10: Collect the second-stage detection light output signal after the second-stage cesium atomic pool, and obtain the second-stage detection light output signal amplitude A2, which is the amplitude value of the electric field signal to be measured; at the same time, obtain the frequency of the second-stage detection light output signal, and determine its baseband electric field frequency f base and carrier frequency f2, and then determine the frequency f of the electric field signal to be measured s =f L1 +f L2 +f2, f2 is zero when the zero intermediate frequency solution is adopted in step 6.

[0017] Specifically, in step S3, the amplitude of the known carrier electric field is modulated by using the known baseband electric field, and the calculation formula for amplitude modulation is:

[0018] v(t)=V ca (1+m acosω s t)cosω ca t (1)

[0019] In the formula, m a It is called the amplitude modulation index, V ca is the intensity of the carrier electric field, ω s is the angular frequency of the baseband electric field, ω ca is the angular frequency of the carrier electric field, t is the time, and v(t) is the electric field signal to be measured.

[0020] In step S6, the wavelengths of the second-stage coupled light and the second-stage detection light are calculated as follows:

[0021] According to the frequency f1 of the first-stage detection light output signal, the frequency of the oscillation in the envelope of the first-stage detection light output signal is used as the main frequency f1 of the detection light output signal. L2 ; Set the main frequency f L2 As the resonance frequency between the first Rydberg state energy level and the second Rydberg state energy level in the second-stage cesium atomic pool; then determine the energy level structure of the first Rydberg state and the second Rydberg state in the second-stage cesium atomic pool according to the resonance frequency; finally, select the ground state and intermediate state structure that conform to the first Rydberg state and the second Rydberg state, so as to determine the wavelength of the second-stage coupling light and the second-stage detection light.

[0022] In step S6, the amplitude and frequency of the second-order incident signal and the second-order local oscillator electric field signal are calculated in the following manner:

[0023] The frequency of the second-stage incident signal is set to f1, and the frequency of the second-stage local oscillator electric field signal is set to f L2 At the same time, the amplitude of the second-level incident signal is set to A1, and the amplitude of the second-level local oscillator electric field signal is A L2 Set to 100A1. Since the frequency f1 of the first-stage detection light output signal includes the frequencies of other interference signals such as noise signals, a zero intermediate frequency solution is adopted, that is, the frequency of the second-stage local oscillator electric field signal is required to be the same as the main frequency of the first-stage detection light output signal, and the amplitude of the second-stage local oscillator electric field signal is much larger than the amplitude of the first-stage detection light output signal.

[0024] The present invention combines multiple frequency conversion technology with Rydberg atom measurement technology by adopting two cascaded cesium atomic pools, thereby reducing the interference of environmental noise on the electric field to be measured, and providing a solution for reducing the design difficulty and cost and improving the detection accuracy for detecting the electric field strength based on Rydberg atoms; at the same time, it provides a feasible solution for future research based on Rydberg atom array antennas. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 This is the four-level structure diagram of the first-level cesium atomic gas cell.

[0026] Figure 2 This is the four-level structure diagram of the second-level cesium atomic gas cell.

[0027] Figure 3 This is the output signal of the first frequency conversion of numerical simulation.

[0028] Figure 4 This is the output signal of zero intermediate frequency after the second frequency conversion of numerical simulation.

[0029] Figure 5 Schematic diagram of the Rydberg atomic experiment apparatus. DETAILED DESCRIPTION

[0030] S1: The first-level detection light is incident on the first-level cesium atom pool to make the cesium atom transition from the ground state energy level to the intermediate state energy level. Figure 1 This is the four-level structure diagram of the first-level cesium atomic gas chamber. |1>6S 1 / 2 (F=4) is the ground state energy level, |2>6P 3 / 2 (F=5) is the intermediate state energy level, and the wavelength of the detection light of the first-level cesium atomic pool is 852nm.

[0031] S2: The first-stage coupled light is incident on the first-stage cesium atom pool to excite the cesium atoms to transition from the intermediate state energy level to the first Rydberg state energy level, so that the cesium atoms form Rydberg atoms. Figure 1 As shown, |3>(25S 1 / 2 ) and |4>(25P 3 / 2 ) are the first Rydberg state and the second Rydberg state of the first-level Rydberg atom, respectively. The wavelength of the coupling light of the first-level cesium atom pool is 515nm.

[0032] S3: Use the known baseband electric field to modulate the amplitude of the known carrier electric field to obtain the electric field signal to be measured; the known baseband electric field frequency is f base =1kHz, the carrier electric field frequency is known to be f c =345.686GHz, the local oscillator electric field signal frequency of the first-level cesium Rydberg atom is f L1 =338.75GHz, amplitude is A L1 =0.6V / m.

[0033] S4: radiate the electric field signal to be measured and the local oscillator electric field signal of the first-stage Rydberg cesium atom into the first-stage Rydberg cesium atom pool to interact with the Rydberg atoms.

[0034] S5: Collect the output signal of the detection light after passing through the first-stage cesium atomic pool, and obtain its amplitude A1=0.006V / m and frequency f1. Figure 3 This is a schematic diagram of the first frequency conversion signal changing with time drawn through numerical simulation.

[0035] S6: According to the amplitude A1 and frequency f1 of the first-stage detection light output signal, the wavelength of the second-stage coupling light and the second-stage detection light is determined, and the amplitude and frequency of the second-stage incident signal and the second-stage local oscillator electric field signal are determined. The wavelength of the second-stage cesium Rydberg atomic cell detection light is 780nm, and the wavelength of the coupling light is 480nm; the frequency of oscillation in its envelope surface is obtained by the frequency f1 as f L2 =6.936GHz, the frequency of the second-stage incident signal is set to f1, the amplitude is set to A1=0.006V / m, and the frequency of the second-stage local oscillator electric field signal is set to f L2 =6.936GHz, the amplitude of the second-level local oscillator electric field signal is set to A L2 =0.6024V / m, the amplitude of the second-level local oscillator electric field signal is much larger than the amplitude of the second-level incident signal.

[0036] S7: The second-level detection light is incident on the second-level cesium atom pool to make the cesium atoms transition from the ground state energy level to the intermediate state energy level. Figure 2 The figure shows the four-level structure of the second-level cesium atomic gas chamber, |1′>6S 1 / 2 (F=4) is the ground state energy level, |2′>6P 3 / 2 (F=5) is the intermediate state energy level.

[0037] S8: The second-stage coupled light is incident on the second-stage cesium atom pool to excite the cesium atoms to transition from the intermediate state energy level to the first Rydberg state energy level, so that the cesium atoms form Rydberg atoms. Figure 2 As shown, |3′>47D 5 / 2 and |4′>48P 3 / 2 They are the first Rydberg state and the second Rydberg state of the second-level Rydberg atom respectively.

[0038] S9: radiate the second-level incident signal and the second-level local oscillator electric field signal into the second-level Rydberg cesium atom pool to interact with the Rydberg atoms.

[0039] S10: Collect the second-stage detection light output signal after the second-stage cesium atomic pool, and obtain the second-stage detection light output signal amplitude A2=0.000335V / m, which is the amplitude value of the electric field signal to be measured; obtain the frequency of the second-stage detection light output signal, and determine its baseband electric field frequency f base =1kHz and carrier frequency f2, and then determine the frequency f of the electric field signal to be measured s =f L1 +f L2 +f2=345.686GHz, in step 6 of this embodiment, a zero intermediate frequency solution is adopted, so f2 is zero; at the same time, the change of the baseband electric field frequency is used to determine whether there are other interference signals. Among them, Figure 4 Schematic diagram of the change of zero intermediate frequency signal over time after the second frequency conversion in numerical simulation.

[0040] The basic principles of steps S4 and S9 are as follows:

[0041] The Liouville equation is:

[0042]

[0043] In the formula represents the rate of change of particle population with time, It is expressed as the reduced Planck constant, i is the imaginary unit, L(ρ) is the relaxation term of atomic interaction, and H is the total Hamiltonian of the interaction under the spin wave representation.

[0044]

[0045] in,

[0046] Δ p =ω1+ω p -ω2

[0047] Δ c =ω2+ω c -ω3

[0048] Δ L =ω4+ω L -ω3

[0049]

[0050]

[0051] Ω p ,Ω c ,Ω ca ,Ω L are the Rabi frequencies of the detection light, coupled light, carrier electric field, and local oscillator electric field signals, ω p represents the angular frequency of the probe light, ω c represents the angular frequency of the coupled light, ω L Represents the angular frequency of the local oscillator electric field signal, ω s Represents the angular frequency of the baseband electric field; Δ p represents the detuning amount of the probe light, Δ c represents the detuning amount of the coupled light, Δ L represents the detuning amount of the local oscillator electric field signal; ω1 represents the angular frequency of the ground state energy level |1>, ω2 represents the angular frequency of the intermediate state energy level |2>, ω3 represents the angular frequency of the first Rydberg state energy level |3>, ω4 represents the angular frequency of the second Rydberg state energy level |4>, H 34 and H 43 Indicates the parameters of the intermediate process of calculation.

[0052] When the detection light, coupled light, local oscillator electric field signal and Rydberg atom interaction are all in a resonant state, the calculation expression of the particle population number changing with the modulated electric field signal under steady-state conditions is as follows:

[0053]

[0054] Among them, γ2 is the spontaneous radiation rate of the intermediate state energy level, A0, A, B, C, D, E, F represent the variables of the calculation intermediate process, ρ 21 is the particle population between the first and second energy levels.

[0055] Therefore, the calculation formula of the detection light transmittance power after the detection light passes through the first-stage cesium Rydberg cesium atomic cell is as follows:

[0056]

[0057] Among them, Im{} represents the imaginary part, k p =2π / λ p is represented by the detection light wave vector, P0 is the initial incident detection light power, L is the distance the detection light propagates in the Rydberg cesium atomic cell, and λ p is the wavelength of the detection light, C is the parameter given by the atomic system parameters, μ p is the transition matrix element between the ground state and the intermediate state, ε0 is the vacuum dielectric constant, and N0 is the particle number density.

[0058] By using the Liouville master equation, under the action of the signal electric field amplitude modulation, the result of the particle population between the ground state and the intermediate state changing with the modulated signal under steady-state conditions is obtained, and the photodetector acquisition signal after the first frequency conversion is obtained, that is, the relationship between the detection light transmittance power and the amplitude modulation signal field. Similarly, using a similar method to the above, after the first frequency conversion, by calculating and processing the Liouville master equation, the detection light transmittance power of the electromagnetically induced transparency and AT splitting phenomenon of the second frequency conversion is detected, and finally an intermediate frequency signal or a zero intermediate frequency signal is obtained.

[0059] The experimental system of this embodiment is as follows Figure 5 shown.

[0060] Among them, 1 is the first-stage detection light, 2 is the first-stage coupling light, 3 is the first-stage cesium Rydberg atomic cell, 4 is the modulated signal, 5 is the first-stage local oscillator electric field signal, 6 and 7 are half-wave plates, 8 is the first-stage detection light output signal, 9 is the second-stage detection light, 10 is the second-stage coupling light, 11 is the second-stage incident signal, 12 is the second-stage cesium Rydberg atomic cell, 14 and 15 are half-wave plates, 16 is the second-stage detector, and 17 is an oscilloscope.

[0061] In summary, the present invention relates to a method based on Rydberg atom superheterodyne, zero intermediate frequency, secondary frequency conversion, digital and analog signals (frequency modulation, phase modulation, mixing, etc.). The present invention reduces the interference of environmental noise on the electric field to be measured by combining multiple frequency conversion technology with Rydberg atom measurement technology, and provides a solution that can reduce the design difficulty and cost for future applications based on Rydberg atom electric field measurement; at the same time, it provides a feasible solution for future research based on Rydberg atom array antennas.

Claims

1. A method for detecting electric field based on multiple frequency conversion of Rydberg atoms, characterized in that: The following steps are involved: S1: The first-level detection light is incident on the first-level cesium atom pool to make the cesium atoms transition from the ground state energy level to the intermediate state energy level; S2: injecting the first-stage coupled light into the first-stage cesium atom pool to excite the cesium atoms to transition from the intermediate state energy level to the first Rydberg state energy level, so that the cesium atoms form Rydberg atoms; S3: using a known baseband electric field to modulate the amplitude or frequency of a known carrier electric field to obtain an electric field signal to be measured; S4: The electric field signal to be measured and the frequency f L1 , amplitude is A L1 The local oscillator electric field signal of the first-stage Rydberg cesium atom is radiated into the first-stage Rydberg cesium atom pool and interacts with the Rydberg atom; S5: by collecting the first-stage detection light output signal passing through the first-stage cesium atomic pool, the amplitude A1 and the frequency f1 thereof are obtained; S6: According to the amplitude A1 and frequency f1 of the first-stage detection light output signal, determine the wavelength of the second-stage coupling light and the second-stage detection light, determine the amplitude A1 and frequency f1 of the second-stage incident signal, and obtain the amplitude A of the second-stage local oscillator electric field signal L2 , frequency f L2 ; S7: injecting the second-stage detection light into the second-stage cesium atom pool to make the cesium atoms transition from the ground state energy level to the intermediate state energy level; S8: injecting the second-stage coupled light into the second-stage cesium atom pool to excite the cesium atoms to transition from the intermediate state energy level to the first Rydberg state energy level, so that the cesium atoms form Rydberg atoms; S9: radiating the second-stage incident signal and the second-stage local oscillator electric field signal into the second-stage Rydberg cesium atom pool to interact with the Rydberg atoms; S10: Collect the second-stage detection light output signal after the second-stage cesium atomic pool, and obtain the second-stage detection light output signal amplitude A2, which is the amplitude value of the electric field signal to be measured; at the same time, obtain the frequency of the second-stage detection light output signal, and determine its baseband electric field frequency f base and carrier frequency f2, and then determine the frequency f of the electric field signal to be measured s =f L1 +f L2 +f2.

2. A method for detecting electric field based on multiple frequency conversion of Rydberg atoms as claimed in claim 1, characterized in that: In step S3, the amplitude of the known carrier electric field is modulated by using the known baseband electric field, and the calculation formula for amplitude modulation is: v(t)=V ca (1+m a cosω s t)cosω ca t (1) In the formula, m a It is called the amplitude modulation index, V ca is the intensity of the carrier electric field, ω s is the angular frequency of the baseband electric field, ω ca is the angular frequency of the carrier electric field, t is the time, and v(t) is the electric field signal to be measured.

3. A method for detecting electric field based on multiple frequency conversion of Rydberg atoms as claimed in claim 2, characterized in that: The method for calculating the wavelength of the second-stage coupled light and the second-stage detection light is: According to the frequency f1 of the first-stage detection light output signal, the frequency of the oscillation in the envelope of the first-stage detection light output signal is used as the main frequency f1 of the detection light output signal. L2 ; Set the main frequency f L2 As the resonance frequency between the first Rydberg state energy level and the second Rydberg state energy level in the second-stage cesium atomic pool; then determine the energy level structure of the first Rydberg state and the second Rydberg state in the second-stage cesium atomic pool according to the resonance frequency; finally, select the ground state and intermediate state structure that conform to the first Rydberg state and the second Rydberg state, so as to determine the wavelength of the second-stage coupling light and the second-stage detection light.

4. A method for detecting electric field based on multiple frequency conversion of Rydberg atoms as claimed in claim 3, characterized in that: In step S6, the amplitude and frequency of the second-order incident signal and the second-order local oscillator electric field signal are calculated in the following manner: The frequency of the second-level incident signal is set to f1, and the frequency of the second-level local oscillator electric field signal is set to f L2 At the same time, the amplitude of the second-level incident signal is set to A1, and the amplitude of the second-level local oscillator electric field signal is A L2 Set to 100A1; f2 is zero when using the zero intermediate frequency solution.

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