A Rydberg atom electric field reading system and method based on weak measurement technology

Abstract

This application discloses a Rydberg atom electric field readout system and method based on weak measurement technology. A readout architecture combining Rydberg atom electric field sensing and optical weak measurement is constructed. Specifically, a weak measurement readout link is established by a pre-selection module and a post-selection module, enabling coordinated setting of the pre-selection and post-selection states. The probe light and coupling light act together on the Rydberg atomic vapor cell, allowing the atomic energy level response within the Rydberg atomic vapor cell induced by the measured electric field to be mapped as a change in optical field polarization. This effectively suppresses technical noise introduced during measurement and amplifies the signal using weak measurement technology. Therefore, the system's detection sensitivity to the electric field is improved, and the readout accuracy of the electric field signal is significantly enhanced.

Description

Technical Field

[0001] This application relates to the field of Rydberg atomic electric field sensing technology, and in particular to a Rydberg atomic electric field readout system and method based on weak measurement technology. Background Technology

[0002] Electric field measurement technology has significant applications in wireless communication, electromagnetic environment monitoring, radar detection, and fundamental physics research. Depending on the frequency range, electric field measurements can include low-frequency electric fields, radio-frequency electric fields, and microwave electric fields. With the increasing complexity of electromagnetic systems, higher demands are placed on the sensitivity, stability, and anti-interference capabilities of electric field sensors. Existing electric field measurement technologies are mostly based on traditional electronic devices or antenna structures, and their measurement performance is easily affected by device size, material noise, and external electromagnetic interference. For example, in weak electric field measurements, problems such as insufficient sensitivity and high noise levels often exist.

[0003] In recent years, electric field sensing technology based on Rydberg atoms has attracted attention due to its high sensitivity to external electric fields. High-precision measurements of electric fields can be achieved by detecting changes in the energy level structure or optical response of Rydberg atoms. However, existing readout methods typically rely on strong light-atomic interactions or high probe light intensity, which can easily introduce additional noise and interfere with the sensitivity of electric field readout. Furthermore, the applied electric field (especially low-frequency / quasi-static electric fields) is partially attenuated by the atomic medium, plasma, surrounding atoms, or free charges before reaching the Rydberg electrons, resulting in an effective electric field actually felt by the atoms being smaller than the applied electric field. This creates a shielding effect, affecting the measurement performance of the electric field.

[0004] Therefore, existing technologies still suffer from limited readout sensitivity and insufficient noise suppression capabilities in high-sensitivity electric field readout based on Rydberg atoms. A new system and method are urgently needed to achieve high-sensitivity readout of electric field signals and improve the measurement accuracy of electric fields. Summary of the Invention

[0005] To address the aforementioned issues, this application provides a Rydberg atom electric field readout system and method based on weak measurement technology, aiming to improve the accuracy of electric field measurement by achieving high-sensitivity readout based on the Rydberg atom electric field.

[0006] The embodiments of this application disclose the following technical solutions:

[0007] The first aspect of this application provides a Rydberg atom electric field readout system based on weak measurement technology, the system comprising:

[0008] Weak measurement components, laser source components, dichroic mirror components, Rydberg atomic vapor cell, Helmholtz coil, first quarter-wave plate, photodetector and processor;

[0009] The weak measurement component includes a pre-selection module and a post-selection module, which together construct a weak measurement readout link; the laser source component includes a first laser source as a detection source and a second laser source as a coupling source; and the dichroic mirror component includes a first dichroic mirror and a second dichroic mirror.

[0010] The Helmholtz coil surrounds the Reedburg atomic vapor cell to counteract the ambient geomagnetic field;

[0011] The pre-selection module is used to modulate the probe light emitted by the first laser source into a pre-selection state;

[0012] The first dichroic mirror is used to transmit the probe light of the pre-selected state to the Rydberg atom vapor cell to pump the Rydberg atoms from the ground state to the excited state;

[0013] The second dichroic mirror is used to transmit the coupled light emitted by the second laser source to the Rydberg atomic vapor cell to pump the excited Rydberg atoms to the Rydberg state; it is also used to reflect the received signal light to the first quarter-wave plate and then to the post-selection module; wherein, the signal light is the probe light emitted from the Rydberg atomic vapor cell when the Rydberg atomic vapor cell is placed in the electric field to be measured, and the signal light has a polarization change of the light field induced by the electric field to be measured;

[0014] The first quarter-wave plate is used to convert the Stokes parameters;

[0015] The post-selection module is used to project the received signal light into the post-selection state; the change in light field polarization causes a change in light intensity after passing through the post-selection module.

[0016] The photodetector is used to detect the light intensity of the beam output by the post-selection module;

[0017] The processor is used to calculate the polarization change of the light field caused by the electric field under test based on the light intensity detected by the photodetector, and then calculate the electric field strength of the electric field under test.

[0018] In one alternative implementation of the first aspect, the processor is specifically used for:

[0019] Obtain the angle between the subsequent selection state and the preceding selection state; the subsequent selection state and the preceding selection state are within a preset orthogonal range;

[0020] Obtain the absolute value of the difference between the included angle and 90°, and use it as the subsequent selection angle;

[0021] Based on the light intensity and the post-selection angle, the polarization change of the light field induced by the electric field under test is calculated.

[0022] In one alternative implementation of the first aspect, the relationship between the light intensity detected by the photodetector and the polarization change of the light field is expressed as follows:

[0023] ( )≈ 0 [1+ ( )cot ε ];

[0024] In the formula, ( () indicates the light intensity detected by the photodetector. I 0 represents the initial light intensity of the first laser source. η After indicating the probability of success, β Let E(t) represent the effective field phase transition coefficient, and E(t) represent the electric field strength of the electric field to be measured. ε Indicates the subsequent selection angle, β E(t) represents the change in optical field polarization induced by the electric field to be measured, and t represents time.

[0025] In one alternative implementation of the first aspect, the system further includes: a first half-wave plate disposed between the first quarter-wave plate and the post-selection module; the signal light transmitted by the first quarter-wave plate first reaches the first half-wave plate and then reaches the post-selection module;

[0026] The first half-wave plate is used to counteract the half-wave loss caused by the second dichroic mirror.

[0027] In one alternative implementation of the first aspect, the pre-selection module includes a first polarizer; the post-selection module includes a second quarter-wave plate and a second polarizer.

[0028] In one alternative implementation of the first aspect, the coupling light and the probe light are combined within the Rydberg atomic vapor cell.

[0029] In one alternative implementation of the first aspect, the system further includes: a signal generator and an electric field transmitter interconnected;

[0030] The signal generator is used to provide a voltage signal to the electric field transmitter;

[0031] The electric field transmitter is used to generate the electric field to be measured under the drive of the voltage signal;

[0032] The voltage signal is a low-frequency voltage signal, a radio frequency voltage signal, or a voltage signal in the microwave frequency band;

[0033] Wherein, the low-frequency voltage signal is used to drive the electric field transmitter to generate the low-frequency electric field to be measured; the radio frequency voltage signal is used to drive the electric field transmitter to generate the radio frequency electric field to be measured; and the microwave frequency voltage signal is used to drive the electric field transmitter to generate the microwave electric field to be measured.

[0034] In one alternative implementation of the first aspect, the system further includes: a third quarter-wave plate and a second half-wave plate; the third quarter-wave plate and the second half-wave plate are disposed between the second laser source and the Rydberg atomic vapor cell, for modulating the coupled light emitted by the second laser source into elliptically polarized light.

[0035] In an alternative implementation of the first aspect, the system further includes a lens; the lens is disposed between the post-selection module and the receiving unit of the photodetector, for focusing the light beam emitted from the post-selection module onto the receiving unit.

[0036] The second aspect of this application provides a method for reading out the electric field of a Rydberg atom based on weak measurement techniques. This method is applied to the system described in any implementation of the first aspect. The method for reading out the electric field of a Rydberg atom based on weak measurement techniques includes:

[0037] When the Rydberg atomic vapor cell is placed in the electric field to be tested, and both the first laser source and the second laser source are turned on, the pre-selection module modulates the probe light emitted by the first laser source into a pre-selection state.

[0038] The probe light in the preselected state is transmitted through the first dichroic mirror to the Rydberg atom vapor cell to pump Rydberg atoms from the ground state to the excited state; and the coupled light emitted by the second laser source is transmitted through the second dichroic mirror to the Rydberg atom vapor cell to pump the excited Rydberg atoms to the Rydberg state; the ambient geomagnetic field is counteracted by the Helmholtz coil;

[0039] The received signal light is reflected by the second dichroic mirror to the first quarter-wave plate, and then reaches the post-selection module; wherein, the signal light is the probe light emitted from the Rydberg atomic vapor cell when the Rydberg atomic vapor cell is placed in the electric field to be measured, and the signal light has the light field polarization change induced by the electric field to be measured;

[0040] The Stokes parameters are converted from the first quarter-wave plate;

[0041] The received signal light is projected into the post-selection state by the post-selection module; the change in light field polarization causes a change in light intensity after passing through the post-selection module.

[0042] The intensity of the light beam output by the post-selection module is detected by the photodetector.

[0043] The processor calculates the polarization change of the light field caused by the electric field under test based on the light intensity detected by the photodetector, and then calculates the electric field strength of the electric field under test.

[0044] Compared with the prior art, this application has the following beneficial effects:

[0045] This application provides a Rydberg atom electric field readout system and method based on weak measurement technology, constructing a readout architecture that combines Rydberg atom electric field sensing with optical weak measurement. A weak measurement readout link is established by a pre-selection module and a post-selection module, enabling coordinated setting of the pre-selection and post-selection states. The probe light and coupling light act together on the Rydberg atomic vapor cell, allowing the atomic level response within the Rydberg atomic vapor cell induced by the measured electric field to be mapped as a change in optical field polarization. This effectively suppresses technical noise introduced during measurement and amplifies the signal using weak measurement technology. Therefore, the system's detection sensitivity to the electric field is improved, and the readout accuracy of the electric field signal is significantly enhanced. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 A schematic diagram of a Rydberg atom electric field readout system based on weak measurement technology is provided for an embodiment of this application;

[0048] Figure 2 A schematic diagram of another Rydberg atom electric field readout system based on weak measurement technology provided in this application embodiment;

[0049] Figure 3 A schematic diagram of another Rydberg atom electric field readout system based on weak measurement technology provided in this application embodiment;

[0050] Figure 4 Energy level structure diagram of rubidium atoms considering two-photon detuning;

[0051] Figure 5A flowchart of a Rydberg atom electric field readout method based on weak measurement technology provided in this application embodiment. Detailed Implementation

[0052] In Rydberg atomic electric field sensing technology, the Rydberg atomic vapor cell is used as the electric field sensing medium. The electric field signal is measured by detecting the effect of an applied electric field on the energy level structure or optical response of Rydberg atoms. In existing Rydberg atomic electric field sensing schemes, electric field information is mostly read out through direct changes in the atomic response. Weak electric fields are those with low signal amplitudes, such as low-frequency electric fields, radio-frequency electric fields, and microwave electric fields. Under weak electric field measurement conditions, the atomic response amplitude induced by the electric field is small, and the readout process is easily affected by system instability and environmental disturbances, causing the measurement signal to be easily submerged by noise, thus limiting the readout sensitivity and measurement accuracy of the electric field signal. While enhancing the atomic response or increasing the readout intensity can improve measurement performance to some extent, it also increases system disturbances and affects measurement stability.

[0053] Through research, the inventors proposed a Rydberg atom electric field readout system and method based on weak measurement technology. In this system, the electric field causes a change in the polarization of the light field; specifically, the amplitude and relative phase of the horizontal and vertical polarization states of the probe light passing through the Rydberg atomic vapor cell change. By applying pre-selection and post-selection modules in the system, the polarization changes caused by the electric field acting on the Rydberg atomic vapor cell can be captured simply and conveniently, while suppressing the technical noise present in the system. This system ensures the most critical detection performance, improves detection accuracy, and suppresses system technical noise.

[0054] The Rydberg atom electric field readout system based on weak measurement technology provided in this application mainly includes: a weak measurement component, a laser source component, a dichroic mirror component, a Rydberg atomic vapor cell, a Helmholtz coil, a first quarter-wave plate, a photodetector, and a processor. The weak measurement component includes a pre-selection module and a post-selection module, which together construct the weak measurement readout link. The laser source component includes a first laser source as a detection source and a second laser source as a coupling source. The dichroic mirror component includes a first dichroic mirror and a second dichroic mirror.

[0055] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0056] Figure 1 This is a schematic diagram of a Rydberg atom electric field readout system based on weak measurement technology, provided as an embodiment of this application. Figure 1 As shown, the Rydberg atom electric field readout system based on weak measurement technology provided in this application includes:

[0057] First laser source 01, front selection module W1, first dichroic mirror 03, Rydberg atomic vapor cell 04, second laser source 05, second dichroic mirror 06, Helmholtz coil 10, first quarter-wave plate 11, back selection module W2, photodetector 16, and processor 17.

[0058] In this system, the first laser source 01 serves as a detection source, emitting detection light; the second laser source 05 serves as a coupling source, emitting coupling light. For example, if the Rydberg atomic vapor cell 04 is specifically a rubidium atomic vapor cell, then the wavelength of the detection light emitted by the first laser source 01 is 780 nm, and the wavelength of the coupling light emitted by the second laser source 05 is 480 nm. It should be noted that Rydberg atoms are not limited to rubidium atoms; for example, they can also be cesium atoms. Therefore, the operating wavelengths of the first laser source 01 and the second laser source 05 depend on the specific Rydberg atom. The rubidium atomic vapor cell is merely one example implementation of the Rydberg atomic vapor cell 04 in the system described in this application; correspondingly, 780 nm and 480 nm are also merely example operating wavelengths of the first laser source 01 and the second laser source 05.

[0059] like Figure 1 As shown, the Helmholtz coil 10 in the system is encircled around the Rydberg atomic vapor cell 04 to counteract the ambient geomagnetic field during system measurements, thereby facilitating more accurate electric field measurements. Figure 1 In the diagram, it can be seen that the Rydberg atomic vapor cell is under the electric field to be measured (e.g., Figure 1 (As shown by the three arcs in the middle), this is a prerequisite for measuring the electric field to be measured. To facilitate understanding of how the system works, the working methods of each component in the system are described below.

[0060] In this embodiment, the pre-selection module W1 and the post-selection module W2 work together to construct a weak measurement readout link. That is, in this application, the modulation capability of the pre-selection module W1 and the post-selection module W2 to the polarization state of the light beam is a key component for realizing weak measurement of electric field disturbances to the optical field, achieving noise suppression, and effectively amplifying the signal-to-noise ratio.

[0061] In the system, the pre-selection module W1 is used to modulate the probe light emitted by the first laser source 01 into a pre-selection state;

[0062] The first dichroic mirror 03 is used to transmit the probe light of the pre-selected state to the Rydberg atom vapor cell 04, so as to pump the Rydberg atoms from the ground state |g> to the excited state |e>. 1,2 >;

[0063] The second dichroic mirror 06 is used to transmit the coupled light emitted by the second laser source 05 to the Rydberg atomic vapor cell 04, so as to excite the excited state |e 1,2 >The Rydberg atom is pumped to the Rydberg state|r>.

[0064] For ease of description, when the Rydberg atomic vapor cell 04 is placed in the electric field to be measured, the probe light emitted from the Rydberg atomic vapor cell 04 is called the signal light. In this embodiment, the influence of the electric field to be measured on the polarization change of the light field is determined mainly by transmitting and measuring the signal light, thereby measuring the electric field signal. In this embodiment, the second dichroic mirror 06 is also used to reflect the received signal light to the first quarter-wave plate 11, and then to the post-selection module W2.

[0065] The first quarter-wave plate 11 is used to convert the Stokes parameters. Since the Stokes parameters can be used to solve polarization changes, it is also necessary to use the first quarter-wave plate to convert the Stokes parameters in this embodiment of the application.

[0066] The post-selection module W2 projects the received signal light into the post-selected state. This completes the post-selection process in weak measurement technology, and also completes the final stage of adjustment for the polarization state of the signal light in the system's optical path. Subsequently, the system only needs to collect the signal light beam and perform mathematical calculations to ultimately achieve the measurement objective.

[0067] The photodetector 16 is used to detect the light intensity of the beam (signal beam) output by the post-selection module W2;

[0068] The processor 17 is used to calculate the polarization change of the light field caused by the electric field to be measured based on the light intensity detected by the photodetector 16, and then calculate the electric field strength of the electric field to be measured.

[0069] This application provides a Rydberg atom electric field readout system and method based on weak measurement technology, constructing a readout architecture that combines Rydberg atom electric field sensing with optical weak measurement. Specifically, a weak measurement readout link is established by a pre-selection module W1 and a post-selection module W2, enabling coordinated setting of the pre-selection and post-selection states. The probe light and coupling light act together on the Rydberg atomic vapor cell O4, allowing the atomic energy level response within the Rydberg atomic vapor cell O4 caused by the measured electric field to be mapped as a change in light field polarization. This effectively suppresses technical noise introduced during measurement and amplifies the signal using weak measurement technology. Therefore, the system's detection sensitivity to the electric field is improved, and the readout accuracy of the electric field signal is significantly enhanced.

[0070] In this embodiment, to better achieve the measurement of the electric field under test, it is necessary to precisely control the energy levels of the Rydberg atoms. To this end, the spatial positions of the components in the optical path can be controlled to ensure that the lasers generated by the first laser source 01 and the second laser source 05 are combined within the Rydberg atomic vapor cell 04. That is, within the Rydberg atomic vapor cell 04, the coupling light and the probe light are combined.

[0071] Figure 2 A schematic diagram of another Rydberg atomic electric field readout system based on weak measurement technology provided in this application embodiment. Figure 2 This demonstrates example implementations of the previous and next selection modules. Figure 2 The front selection module includes a first polarizer 02, and the rear selection module includes a second quarter-wave plate 13 and a second polarizer 14. As an example, both the first polarizer 02 and the second polarizer 14 are linear polarizers.

[0072] exist Figure 2 In the system architecture example, the Rydberg atom electric field readout system based on weak measurement technology further includes a first half-wave plate 12. The first half-wave plate 12 is used to compensate for the half-wave loss caused by the second dichroic mirror 06, thereby making the measurement results based on the Rydberg atom electric field more accurate and reliable. This first half-wave plate 12 is disposed between the first quarter-wave plate 11 and the post-selection module (i.e., the combined structure of the second quarter-wave plate 13 and the second polarizer 14). Figure 2 In the system shown, the signal light transmitted by the first quarter-wave plate 11 first reaches the first half-wave plate 12, and then reaches the second quarter-wave plate 13 and the second polarizer 14 in the post-selection module.

[0073] In this embodiment of the application, the system can be used with a commercially available electric field emitter, or a dedicated electric field emitter can be installed within the system. For example... Figure 2In the system structure example shown, the Rydberg atom electric field readout system based on weak measurement technology further includes: a signal generator 08 and an electric field transmitter 09 connected to each other. The signal generator 08 provides a voltage signal to the electric field transmitter 09. The electric field transmitter 09 generates the electric field to be measured under the drive of the voltage signal provided by the signal generator 08. When the electric field to be measured acts on the Rydberg atomic vapor cell, it causes a change in the polarization of the signal light within it. Based on the coordinated arrangement of the first polarizer 02, the second quarter-wave plate 13, and the second polarizer 14, the change in the polarization of the light field can be captured using weak measurement technology, and the signal of the electric field to be measured can be calculated.

[0074] In this embodiment, the voltage signal provided by the signal generator 08 is a low-frequency voltage signal, a radio frequency voltage signal, or a microwave frequency voltage signal, depending on the electric field measurement requirements. Furthermore, the waveform of the voltage signal is not limited; it can be any waveform, as long as it can drive the electric field transmitter 09 to generate the electric field to be measured in the corresponding frequency band. If the signal generator 08 provides a low-frequency voltage signal, the low-frequency voltage signal is used to drive the electric field transmitter to generate the low-frequency electric field to be measured; if the signal generator 08 provides a radio frequency voltage signal, the radio frequency voltage signal is used to drive the electric field transmitter to generate the radio frequency electric field to be measured; if the signal generator 08 provides a voltage signal in the microwave frequency band, the microwave frequency voltage signal is used to drive the electric field transmitter to generate the microwave electric field to be measured.

[0075] In an optional implementation, the Rydberg atomic electric field readout system based on weak measurement technology further includes a lens 15. The lens 15 is disposed between the second polarizer 14 in the post-selection module and the receiving unit of the photodetector 16, and is used to focus the light beam emitted from the second polarizer 14 in the post-selection module onto the receiving unit of the photodetector 16. In this embodiment, the lens 15 can adjust and control the beam direction, achieving precise matching between the signal light and the receiving unit of the photodetector 16, thereby achieving effective collection of the signal light. As an example, the lens 15 can be a convex lens.

[0076] This application embodiment can further configure a laser collecting tube 07 in the system. The first dichroic mirror 03 is also used to reflect the coupled light emitted from the Rydberg atomic vapor cell 04 into the laser collecting tube 07, thereby collecting the laser beam, avoiding interference with the surrounding environment of the system (such as light pollution), and reducing safety hazards in the operation of the system.

[0077] like Figure 2As shown, the radiation probe light from the first laser source 01 passes through the pre-selection module of the weak measurement component, namely the first polarizer 02, and is transmitted through the first dichroic mirror 03. It then enters the Rydberg atomic vapor cell 04, exciting the Rydberg atoms from the ground state |g> to the excited state |e>. 1,2 The second laser source 05 radiates coupled light, which is transmitted through the second dichroic mirror 06 and then enters the Rydberg atomic vapor cell 04, causing the Rydberg atoms to move from the excited state |e... 1,2 The energy is pumped to a Rydberg state |r>, then reflected by the first dichroic mirror 03, and enters the laser collecting tube 07. A signal generator 08 is connected to an electric field emitter 09. Here, the signal generator 08 can be an arbitrary waveform signal generator. The electric field emitter 09 is driven by the signal generator 08. The signal generator 08 provides a signal of a specific frequency and voltage to the electric field emitter 09 to generate the electric field to be measured. The electric field acts on the Rydberg atomic vapor cell 04, causing the Rydberg state |r> energy level to shift or transition. For example, a low-frequency electric field can cause the Rydberg state |r> energy level to shift; a radio frequency electric field or a microwave electric field can cause the Rydberg state |r> energy level to transition, driving the Rydberg state to a second Rydberg state. A low-frequency electric field is an electric field with a frequency in kHz. Radio frequency electric fields and microwave electric fields are electric fields with a frequency in GHz. The electric field measurements of the various sensing mechanisms described above can all utilize the structure and corresponding methods of the Rydberg atom electric field readout system based on weak measurement technology provided in the embodiments of this application.

[0078] When an electric field acts on an atom in a Rydberg state, it affects the polarization of the probe light, resulting in changes in optical field polarization. These changes manifest specifically as alterations in the amplitudes of the horizontal polarization state |H> and the vertical polarization state |V> of the probe light, as well as changes in their relative phases. Since the magnitudes of these changes are significantly different—the change in relative phase being much larger than the change in the amplitude of the polarization states—this application focuses on capturing the changes in the relative phase between the two polarization states during optical field polarization variations.

[0079] The signal light emitted from the Rydberg atomic vapor cell 04 is reflected by the second dichroic mirror 06, and then passes through the first quarter-wave plate 11 and the first half-wave plate 12. The first quarter-wave plate 11 converts the Stokes parameters, and the first half-wave plate 12 cancels the half-wave loss after reflection from the second dichroic mirror 06. The signal light then undergoes post-selection via the second quarter-wave plate 13 and the second polarizer 14. After post-selection, the lens 15 focuses and selects the outgoing beam, ensuring it more accurately illuminates the receiving unit of the photodetector 16. Finally, the processor 17 receives the light intensity and calculates the electric field strength of the applied electric field to be measured.

[0080] In this embodiment of the application, as an optional implementation, the coupled light in the Rydberg atomic vapor cell 04 of the system can be a polarization-modulated beam. The following is in conjunction with... Figure 3 This application also provides another Rydberg atom electric field readout system based on weak measurement technology, such as... Figure 3 As shown. In Figure 3 In the example system architecture, the Rydberg atom electric field readout system based on weak measurement technology further includes: a third quarter-wave plate 18 and a second half-wave plate 19. The third quarter-wave plate 18 and the second half-wave plate 19 are disposed between the second laser source 05 and the Rydberg atomic vapor cell 04, and are used to modulate the coupled light emitted by the second laser source 05 into elliptically polarized light.

[0081] To facilitate understanding of the solution logic in electric field measurement, the following section combines... Figure 4 The paper presents various formulas demonstrating how weak measurement techniques, based on weak measurement technology, are used to extract signals and improve sensitivity in the Rydberg atom electric field readout system proposed in this application. Specifically, it uses rubidium atoms as an example of Rydberg atoms. Figure 4 The energy level structure diagram of rubidium atoms considering two-photon detuning.

[0082] The traditional three-level structure of ground-excited-Rydberg states does not take into account the polarization change of the probe light. Figure 4 The energy level structure diagram shown incorporates a four-level atomic model, including two Zeeman sublevels of the intermediate state, thus integrating polarization degrees of freedom into the traditional three-level structure of ground-excited-Rydberg states. Figure 4 In this context, |g> represents the ground state, |e1> and |e2> represent the two Zeeman sublevels that are intermediate states, and |r> represents the Rydberg state.

[0083] Taking low-frequency electric fields as an example, Figure 4 The equations of motion for the energy level structure diagram shown are:

[0084] ——Formula (1-1)

[0085] ——Formula (1-2)

[0086] ——Formula (1-3)

[0087] ——Formula (1-4)

[0088] ——Formula (1-5)

[0089] In the five formulas above, z is the distance the probe light travels in the Rydberg atomic vapor cell O4, and z can range from 0 to... l Take the value from the middle. l ρ is the length of the gas chamber in the Rydberg atomic vapor cell O4. t is time, i is the imaginary unit, and ρ... 21 ρ is the density matrix element of optical coherence between |e1> and |g>. 31 ρ is the density matrix element of optical coherence between |e2> and |g>. 41 Ω represents the density matrix elements of the optical coherence between the Rydberg state |r> and the ground state |g>, with the superscript * indicating the complex conjugation of the corresponding parameters. c is the speed of light, κ = nσΓ / 2 is the coupling strength between the probe light and the atom, n is the atomic density, σ is the effective cross-sectional area of ​​the atom-light pair, Γ is the decay rate of the intermediate states |e1> and |e2>, and γ is the decay rate of the Rydberg state |r>. δ represents the energy level shift caused by the low-frequency electric field. p+ To detect the Rabi frequency of the right-hand circularly polarized component of light, Ω p- To detect the Rabi frequency of the left-hand circularly polarized component of light; Ω c+ Ω is the Rabi frequency of the right-hand circularly polarized component of the coupled light. c- is the Rabi frequency of the left-hand circularly polarized component of the coupled light.

[0090] To capture the polarization change of the probe light, the Stokes parameters can be solved. For left- and right-handed polarized light as the basis, the Stokes parameters Sx, Sy, and Sz of the probe light are expressed as:

[0091] ——Formula (2)

[0092] In the above formula, Represents Ω p- The complex conjugate of , where Re represents the real part and Im represents the imaginary part. To simplify the equations of motion of light, the time derivative term (1 / c) in equations (1-1) and (1-2) can be ignored. / t. This approximation is valid because the timescale of interest is much longer than the time it takes for light to travel through a Rydberg atomic vapor cell. Under this simplification, the equations of motion for equations (1-1) and (1-2) become:

[0093] ——Formula (3)

[0094] To obtain the steady-state solution Ω of the equation p+ and Ω p- It is necessary to express ρ 21 and ρ 31 According to formulas (1-3) and (1-4), ρ 21 and ρ 31Both with ρ 41 There is a mathematical connection. In steady state, dρ i1 Given dt = 0, i = 2,3,4, and combining formulas (1-3), (1-4), and (1-5), we obtain ρ. 21 ρ 31 ρ 41 The representation is as follows:

[0095] ——Formula (4-1)

[0096] ——Formula (4-2)

[0097] ——Formula (4-3)

[0098] The probe light emitted by the first laser source 01 is initialized to 45° linearly polarized light after passing through the weak measurement pre-selection module, then Ω p+ = -iΩ p- And S y =1. The coupled light can optionally be set to slightly elliptic (Ω). c+ ≠ Ω c- ).

[0099] z=0 indicates that the probe light has just entered the Rydberg atomic vapor cell. l This indicates that the probe light has traveled through the entire Rydberg atomic vapor cell and reached the position where it exits the Rydberg atomic vapor cell, i.e., the signal light is emitted. Ω c+ and the Rabi frequency Ω at z = 0 p+ Ω is a real number. c- and the Rabi frequency Ω at z=0 p- Since Ω is a purely imaginary number, and without loss of generality, for simplicity, we will use Ω as... c- Replace with iΩ c- Then z can be solved. l The two Rabi frequencies Ω p+ and Ω p- , can be represented as Ω f+ and Ω f- :

[0100] ——Formula (5-1)

[0101] ——Formula (5-2)

[0102] In formulas (5-1) and (5-2), Ω² eff+ and Ω² eff- As an intermediate quantity in the calculation. Ω² eff+ =Ω c- Ωi- + Ω c+ Ω i+ Ω² eff- = Ω c- Ω i+ - Ω c+ Ω i- . l It is the length of the gas chamber in the Rydberg atomic vapor cell, Ω. i+ Ω when z = 0 p+ Ω i- -iΩ when z=0 p- Ω i+ and Ω i- This is the initial probe Rabi frequency. Ω c ² = Ω c ² - + Ω c ² + Γ is the total coupling Rabi frequency, and A = κl / Γ is the total absorption rate. In equations (5-1) and (5-2)... = δ / (δ -iΓ p ) is a typical EIT coherence function, Γ p = Ω c ² / 2Γ represents the power-enhanced linewidth.

[0103] Therefore, the output intensity I of the probe light and the product of I with the Stokes parameters Sx and Sz can be expressed as follows:

[0104] ——Formula (6-1)

[0105] ——Formula (6-2)

[0106] ——Formula (6-3)

[0107] In the formula, L = δ 2 / (δ 2 + Γ 2 p ) is the Lorentz function, D = Γ p δ / (δ 2 + Γ 2 p ) is the relevant dispersion function. δ represents the energy level shift caused by the low-frequency electric field.

[0108] Ω i It is a detector light in The total Rabi frequency at =0. For linearly polarized probe light (i.e., Ω...). i+ = Ω i- =Ωi / √2) When near resonance (i.e., δ ≈ 0), the equation is further simplified. L →δ2 / Γ 2 p D → δ / Γ p Applying optical thin-condition Aδ / Γ p 1. Obtained:

[0109] ——Formula (7-1)

[0110] ——Formula (7-2)

[0111] In the formula, A is the total absorption rate, and Γ p This refers to power broadening of the linewidth. For the first-order Stark effect δ = kE, where k represents the first-order Stark polarizability, the Stokes parameter can be simplified to:

[0112] ——Formula (8-1)

[0113] ——Formula (8-2)

[0114] For a polarization state |ψ(χ, ) =cos χ|H + sin χe i |V The Stokes parameters in this representation are S′x = cos 2χ and S′y = sin 2χ cos S′z = sin 2χ sin Then χ = 0.5 arccosS′x, = arctan(S′z / S′y). Where χ represents the horizontal polarization in the polarization state |H With vertical polarization |V The amplitude distribution angle between them. The first quarter-wave plate 11 placed before the post-selection transforms the Stokes parameters according to (S′x, S′y, S′z) → (-Sz, Sy, Sx). For a weakly polarized signal satisfying S′y ≈ 1, S′x ≈ 0, S′z ≈ 0, the horizontal polarization state |H With vertical polarization state |V The phase difference between them is simplified to ≈ S′z = Sx, and the electric field simultaneously induces a horizontal polarization state |H With vertical polarization state |V The amplitude change is 0.5 arccos Sz. As mentioned earlier, the order of magnitude of the amplitude change is much smaller than the order of magnitude of the change in relative phase (i.e., phase difference). Therefore, the phase difference can be... This can be understood as a change in the polarization of the light field, where χ is a value very close to 45°. At this point, the horizontal polarization state |H| caused by the electric field has been solved. With vertical polarization state |V The changes in phase difference and amplitude between them.

[0115] The above description and analysis have explained that the electric field will cause a change in the polarization of the probe light. Returning to the weak measurement, the probe light radiated by the first laser source 01, after passing through the weak measurement pre-selection module, i.e., the first polarizer 02, is modulated into 45° linearly polarized light, that is:

[0116] |ψi = 1 / √2(|H + |V )——Formula (9)

[0117] Atoms are pumped into Rydberg states by backpropagating probe and coupling light. When an external electric field is applied, the Rydberg state undergoes energy level oscillations, i.e., δ is generated, ultimately leading to the horizontal polarization state |H| of the probe light. With vertical polarization state |V The phase difference and amplitude change between them mean that after the probe light passes through the Rydberg atomic vapor cell 04, the preceding preselected state has been determined, and this state evolves after passing through the Rydberg atomic vapor cell 04 as follows:

[0118] |Ψj = cos χ(t)e -i (t) / 2 |H + sin χ(t)e i (t) / 2 |V ——Formula (10)

[0119] In the above formula, χ(t) and The expression for (t) is:

[0120] ——Formula (11)

[0121] ——Formula (12)

[0122] In the post-selection process, the evolved probe light is projected onto a preset polarization state:

[0123] |ψ f = 1 / √2 (ie -iε |H - ie iε |V )——Formula (13)

[0124] The polarization state is almost orthogonal to the initial polarization state, and the subsequent selection angle ε is minimal at |ε|. 1. To achieve real-time detection of low-frequency electric fields, the intensity of the detected signal light is acquired to extract the signal. The intensity signal of the signal light can be expressed as:

[0125] I(t) = I0| ψ f |Ψ j | 2 = I0 2 [1 - sin(2χ(t)) cos(2ε - βE(t))]

[0126] ——Formula (14)

[0127] In the formula, I0 is the initial light intensity of the first laser source. β is the effective field phase conversion coefficient, E(t) is the electric field intensity, and β is equivalent to the series of coefficients before E(t) in formula (8-1). In |βE(t)A w / 2| Under condition 1, the signal can be further expressed as formula (15). Where A w = [sinε(cos χ(t) - sin χ(t)) - i cos ε(cos χ(t) + sinχ(t))] / [sin ε(cos χ(t) + sin χ(t)) - i cos ε(cos χ(t) - sin χ(t)) ] is the corrected weak value in the weak measurement technique.

[0128] I(t) ≈ I0η[1 + βE(t)ImA w ]——Formula (15)

[0129] In the formula, the first term is the DC quantity, and the second term reflects the influence of the electric field to be measured, and is regarded as the change ΔI. η The probability of success after selection is expressed as η = [1 - sin(2χ(t)) cos(2ε)] / 2. This can be expressed by the change ΔI = I0ηβE(t)ImA. w The final electric field strength E(t) is obtained as E(t) = ΔI / (I0ηβImA). w ). χ(t) can be taken as 45°.

[0130] In reality, the measurement process is inevitably affected by various noises. The total noise amplitude is denoted as ΔI. noise This originates from the superposition of statistically independent noise sources. Here, we consider the noise amplitude within a bandwidth Δf = 1 Hz and focus on three types of noise in the system. The first type is technical noise ΔI. te The first type is relative intensity noise, such as device defects and thermal noise, whose amplitude increases linearly with optical intensity. The second type is optical shot noise ΔI. sh The amplitude is proportional to the square root of the light intensity. The third type is electronic noise ΔI. el This refers to the constant noise floor generated by the photodetector and detection circuit, which is independent of light intensity. The three noise levels mentioned above are all noise levels under conditions without weak measurements. Therefore, the total noise level is:

[0131] ——Formula (16)

[0132] The signal amplitude at the first harmonic frequency induced by the electric field is Isig ≈ I0ηβE(t)ImA w This is equivalent to ΔI mentioned above. For the case where χ(t) takes 45°, sin(2χ(t)) = 1, therefore the formula η = [1 - sin(2χ(t)) cos(2ε)] / 2 = [1 - cos(2ε)] / 2 ≈ sin²ε. sig ≈I0 sin²εβE(t)ImA w Signal-to-noise ratio (SNR) can be written as:

[0133] ——Formula (17)

[0134] In formula (17), the parameters are selected after the angle ε and the imaginary part ImA of the weak value. w This parameter is introduced due to weak measurement. In this application, the subsequent selection state and the preceding selection state are within a preset orthogonal range, i.e., almost orthogonal. For example, the preset orthogonal range can be the interval [80°, 100°]. The angle between the subsequent selection state and the preceding selection state is obtained; the absolute value of the difference between the angle and 90° is taken as the subsequent selection angle ε. This will make ε much less than 1.

[0135] In most optical experiments, technical noise is dominant. According to formula (17), when technical noise is dominant, the last two terms within the square root of the denominator can be ignored. After canceling out the identical terms in the numerator and denominator, SNR(t, ε) can be expressed as I0ηβE(t)ImA w / ΔI te This indicates that due to ImA in the SNR(t, ε) molecule... wThe presence of weak measurements becomes important when noise is dominated by technical noise, corresponding to an ImA value in SNR. w The amplification. For the case where χ(t) takes 45°, sin(2χ(t))=1, therefore the formula η= [1-sin(2χ(t))cos(2ε)] / 2=[1-cos(2ε)] / 2≈sin²ε. ImA w ≈cotε.

[0136] For nearly orthogonal pre-selection and post-selection states, i.e. ε 1. The light intensity will decrease by a scaling factor of η≈sin²ε (η is a value greater than 0 and less than 1; since η≈sin²ε, η is also approximately equal to ε). 2 Technical noise is related to light intensity. When light intensity is reduced, technical noise can be significantly suppressed, while the electric field-induced response is amplified by an additional ImA. w ≈cotε times, thus amplifying the signal. Therefore, formula (15) can be further simplified to:

[0137] ( )≈ 0 [1+ ( )cot ε ]——Formula (18)

[0138] In the formula, ( () indicates the light intensity of the beam output by the subsequent selection module. I 0 represents the initial light intensity of the first laser source. η After indicating the probability of success, β Let E(t) represent the effective field phase transition coefficient, and E(t) represent the electric field strength of the electric field to be measured. ε Indicates the subsequent selection angle, β E(t) represents the change in optical field polarization caused by the electric field to be measured, and t represents time. Under the premise that other parameters in formula (18) can be measured, calculated or known, the electric field strength E(t) can be obtained.

[0139] Based on the Rydberg atom electric field readout system based on weak measurement technology described in the foregoing embodiments, this application also proposes a Rydberg atom electric field readout method based on weak measurement technology. This method is specifically applied to the aforementioned Rydberg atom electric field readout system based on weak measurement technology. See also... Figure 5 The process of this method includes:

[0140] S51. When the Rydberg atomic vapor cell is placed in the electric field to be tested, and both the first laser source and the second laser source are turned on, the pre-selection module modulates the probe light emitted by the first laser source into a pre-selection state.

[0141] S52, The probe light of the pre-selected state is transmitted through the first dichroic mirror to the Rydberg atom vapor cell to pump the Rydberg atoms from the ground state to the excited state; and the coupling light emitted by the second laser source is transmitted through the second dichroic mirror to the Rydberg atom vapor cell to pump the excited Rydberg atoms to the Rydberg state; the Helmholtz coil cancels the ambient geomagnetic field.

[0142] S53. The received signal light is reflected by the second dichroic mirror to the first quarter-wave plate, and then reaches the post-selection module.

[0143] The signal light is a probe light emitted from the Rydberg atomic vapor cell when the Rydberg atomic vapor cell is placed in the electric field to be measured; the signal light has a polarization change in the light field induced by the electric field to be measured.

[0144] S54. Convert the Stokes parameters from the first quarter-wave plate.

[0145] S55, The received signal light is projected to the post-selection state by the post-selection module.

[0146] The change in light field polarization causes a change in light intensity after passing through the post-selection module.

[0147] S56. The photodetector detects the light intensity of the beam output by the post-selection module.

[0148] S57. The processor calculates the polarization change of the light field caused by the electric field to be measured based on the light intensity detected by the photodetector, and then calculates the electric field strength of the electric field to be measured.

[0149] In this application, the specific calculation method for the change in polarization of the probe light caused by the electric field mentioned in this step can be understood by referring to the formulas introduced above. Since the system was already described in the preceding text... Figures 1 to 4 The technical solution has been described in considerable detail, so the method described in this embodiment will not be repeated here. For specific implementation details of some method steps, please refer to the preceding description and introduction of the system embodiment.

[0150] This application provides a Rydberg atom electric field readout method based on weak measurement technology, applied to a Rydberg atom electric field sensing system. By constructing a measurement architecture combining the Rydberg atom electric field response and weak measurement readout, high-sensitivity readout of low-frequency electric field signals is achieved. Furthermore, widely applicable weak measurement technology effectively suppresses noise during the readout process, thereby improving the accuracy and repeatability of electric field measurements while maintaining readout sensitivity. In this method, the Rydberg atom energy level response induced by an applied electric field is mapped to a change in the polarization state of a light field. Pre-selection and post-selection states are set to form a weak measurement readout link, ensuring that weak electric field perturbations can be effectively amplified and stably read out. The combined effect of pre-selection and post-selection effectively weakens technical noise unrelated to the electric field during the final readout and calculation process. Combined with analytical calculation of the light intensity signal, the effective polarization change caused by the electric field is obtained, thereby improving detection accuracy and measurement reliability under electric field conditions. It is worth noting that the system and method described in this application can be used not only for low-frequency electric fields but also for radio frequency and microwave electric fields.

[0151] It should be noted that the various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for the method embodiments, since they are basically similar to the system embodiments, the description is relatively simple, and the relevant parts can be referred to the description of the system embodiments. The above description is only one specific implementation of this application, but the protection scope of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the protection scope of this application. Therefore, the protection scope of this application should be determined by the protection scope of the claims.

Claims

1. A Rydberg atom electric field readout system based on weak measurement technology, characterized in that, include: Weak measurement components, laser source components, dichroic mirror components, Rydberg atomic vapor cell, Helmholtz coil, first quarter-wave plate, photodetector and processor; The weak measurement component includes a pre-selection module and a post-selection module, which together construct a weak measurement readout link; the laser source component includes a first laser source as a detection source and a second laser source as a coupling source; and the dichroic mirror component includes a first dichroic mirror and a second dichroic mirror. The Helmholtz coil surrounds the Reedburg atomic vapor cell to counteract the ambient geomagnetic field; The pre-selection module is used to modulate the probe light emitted by the first laser source into a pre-selection state; the pre-selection state is the optical field polarization state formed after the probe light is polarized by the pre-selection module. The first dichroic mirror is used to transmit the probe light of the preselected state to the Rydberg atom vapor cell to pump the Rydberg atoms from the ground state to the excited state; The second dichroic mirror is used to transmit the coupled light emitted by the second laser source to the Rydberg atomic vapor cell to pump the excited Rydberg atoms to the Rydberg state; it is also used to reflect the received signal light to the first quarter-wave plate and then to the post-selection module; wherein, the signal light is the probe light emitted from the Rydberg atomic vapor cell when the Rydberg atomic vapor cell is placed in the electric field to be measured, and the signal light has a polarization change of the light field induced by the electric field to be measured; The first quarter-wave plate is used to convert the Stokes parameters; The post-selection module is used to project the received signal light into the post-selection state; the change in light field polarization causes a change in light intensity after passing through the post-selection module; the post-selection state is the light field polarization state of the received signal light after being projected and filtered by the post-selection module. The photodetector is used to detect the light intensity of the beam output by the post-selection module; The processor is used to calculate the polarization change of the light field caused by the electric field under test based on the light intensity detected by the photodetector, and then calculate the electric field strength of the electric field under test.

2. The system according to claim 1, characterized in that, The processor is specifically used for: Obtain the angle between the subsequent selection state and the preceding selection state; the subsequent selection state and the preceding selection state are within a preset orthogonal range; Obtain the absolute value of the difference between the included angle and 90°, and use it as the subsequent selection angle; Based on the light intensity and the post-selection angle, the polarization change of the light field induced by the electric field under test is calculated.

3. The system according to claim 2, characterized in that, The relationship between the light intensity detected by the photodetector and the change in the polarization of the light field is as follows: ( )≈ 0 [1+ ( )cot ε ]; In the formula, ( () indicates the light intensity detected by the photodetector. I 0 represents the initial light intensity of the first laser source. η After indicating the probability of success, β Let E(t) represent the effective field phase transition coefficient, and E(t) represent the electric field strength of the electric field to be measured. ε Indicates the subsequent selection angle, β E(t) represents the change in optical field polarization induced by the electric field to be measured, and t represents time.

4. The system according to claim 1, characterized in that, The system further includes: a first half-wave plate, which is disposed between the first quarter-wave plate and the post-selection module; the signal light transmitted by the first quarter-wave plate first reaches the first half-wave plate and then reaches the post-selection module; The first half-wave plate is used to counteract the half-wave loss caused by the second dichroic mirror.

5. The system according to claim 1, characterized in that, The pre-selection module includes a first polarizer; the post-selection module includes a second quarter-wave plate and a second polarizer.

6. The system according to claim 1, characterized in that, Inside the Rydberg atomic vapor cell, the coupling light and the probe light are combined.

7. The system according to claim 1, characterized in that, The system also includes: interconnected signal generators and electric field transmitters; The signal generator is used to provide a voltage signal to the electric field transmitter; The electric field transmitter is used to generate the electric field to be measured under the drive of the voltage signal; The voltage signal is a low-frequency voltage signal, a radio frequency voltage signal, or a voltage signal in the microwave frequency band; Wherein, the low-frequency voltage signal is used to drive the electric field transmitter to generate the low-frequency electric field to be measured; the radio frequency voltage signal is used to drive the electric field transmitter to generate the radio frequency electric field to be measured; and the microwave frequency voltage signal is used to drive the electric field transmitter to generate the microwave electric field to be measured.

8. The system according to claim 1, characterized in that, The system further includes: a third quarter-wave plate and a second half-wave plate; the third quarter-wave plate and the second half-wave plate are disposed between the second laser source and the Rydberg atomic vapor cell, and are used to modulate the coupled light emitted by the second laser source into elliptically polarized light.

9. The system according to claim 1, characterized in that, The system further includes a lens; the lens is disposed between the post-selection module and the receiving unit of the photodetector, and is used to focus the light beam emitted from the post-selection module onto the receiving unit.

10. A method for reading out the electric field of a Rydberg atom based on weak measurement technology, characterized in that, The method applied to the Rydberg atom electric field readout system based on weak measurement technology according to any one of claims 1-9, the method comprising: When the Rydberg atomic vapor cell is placed in the electric field to be measured, and both the first and second laser sources are turned on, the pre-selection module modulates the probe light emitted by the first laser source into a pre-selection state; the pre-selection state is the polarization state of the light field formed after the probe light is polarized by the pre-selection module. The probe light of the pre-selected state is transmitted through the first dichroic mirror to the Rydberg atom vapor cell to pump the Rydberg atoms from the ground state to the excited state; and the coupled light emitted by the second laser source is transmitted through the second dichroic mirror to the Rydberg atom vapor cell to pump the excited Rydberg atoms to the Rydberg state; the ambient geomagnetic field is counteracted by a Helmholtz coil. The received signal light is reflected by the second dichroic mirror to the first quarter-wave plate and then to the post-selection module; wherein, the signal light is the probe light emitted from the Rydberg atomic vapor cell when the Rydberg atomic vapor cell is placed in the electric field to be measured, and the signal light has the polarization change of the light field induced by the electric field to be measured; Stokes parameters are converted from the first quarter-wave plate; The received signal light is projected onto the post-selection state by the post-selection module; the change in light field polarization causes a change in light intensity after passing through the post-selection module; the post-selection state is the light field polarization state of the received signal light after being projected and filtered by the post-selection module. The light intensity of the beam output by the selection module after detection by the photodetector; The processor calculates the polarization change of the light field caused by the electric field under test based on the light intensity detected by the photodetector, and then calculates the electric field strength of the electric field under test.

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