Method and device for detecting zero-expansion temperature of an ultrastable cavity

Abstract

The application relates to the technical field of optical measurement, in particular to a method and system for detecting zero-expansion temperature of an ultra-stable cavity. The method comprises the following steps: obtaining a first laser beam and a second laser beam; inputting the first laser beam into a target FP cavity from one end of the target FP cavity and inputting the second laser beam into the target FP cavity from the other end of the target FP cavity; and obtaining a target zero-expansion temperature according to temperature-related information of the target FP cavity. In the step of obtaining the target zero-expansion temperature according to the temperature-related information of the target FP cavity, the frequency variation degree of the second modulator is measured, and the target zero-expansion temperature is obtained based on the frequency variation degree of the second modulator. Compared with the prior art which needs an absolute frequency reference, only the frequency variation degree of the second modulator is measured, the requirement for the absolute frequency stability of a laser is reduced, and meanwhile, only temperature and scanning laser need to be controlled, so that the zero-expansion temperature can be quickly and simply obtained.

Description

Technical Field

[0001] This invention relates to the field of optical measurement technology, and in particular to a method and system for detecting the zero expansion temperature of an ultra-stable cavity. Background Technology

[0002] The zero-expansion point, or inflection point temperature, of an ultrastable cavity refers to the specific operating temperature at which the cavity length of an ultrastable optical reference cavity is least sensitive to temperature changes. The goal of an ultrastable cavity is to maintain an absolutely stable optical length, thereby providing an absolutely stable laser frequency reference. That is, when the operating temperature of the ultrastable cavity is strictly controlled within a very small range around the zero-expansion point, temperature changes will hardly cause changes in the cavity length, thus providing an extremely stable output frequency.

[0003] In existing technologies, methods for measuring the zero expansion point compare the laser frequency locked to an ultrastable cavity with an absolute frequency reference (such as atomic / molecular absorption lines or a more stable optical clock system). By changing the temperature of the ultrastable cavity, the drift of the laser frequency is observed; the temperature at which the frequency drift rate is minimal is the zero expansion point. This method requires an absolute frequency reference system, which is typically very expensive and complex (such as optical frequency combs or saturable absorption spectroscopy devices), and the measurement process is relatively slow. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for detecting the zero expansion temperature of an ultra-stable cavity, which reduces the requirements for the absolute frequency stability of the laser, while allowing for rapid and simplified acquisition of the zero expansion temperature.

[0005] According to a first aspect of the present invention, a method for detecting the zero expansion temperature of an ultrastable cavity is provided, the method comprising the following steps:

[0006] Acquire the target laser beam emitted by the target laser;

[0007] The target laser beam is controlled to pass through the first modulator and the first PDH optical path to obtain the first laser beam;

[0008] After the target laser beam is input into the first modulator, the key laser beam is obtained;

[0009] The key laser beam is controlled to pass through the second modulator and the second PDH optical path to obtain the second laser beam;

[0010] The first laser beam is input into the target FP cavity from one end, and the second laser beam is input into the target FP cavity from the other end.

[0011] The target zero expansion temperature is obtained based on the temperature-related information of the target FP cavity.

[0012] Specifically, the step of inputting the first laser beam into the target FP cavity from one end and inputting the second laser beam into the target FP cavity from the other end further includes:

[0013] The frequency of the first laser beam is locked to the fundamental transverse mode TEM of the target FP cavity. 00 On the mold;

[0014] The frequency of the second laser beam is locked to the first transverse mode TEM of the target FP cavity. 01 On the mold

[0015] Specifically, the step of controlling the target laser beam to pass through the first modulator and the first PDH optical path to obtain the first laser beam further includes: the target laser beam first passes through the first modulator to generate a first intermediate laser beam, and the first intermediate laser beam passes through the first PDH optical path to generate the first laser beam.

[0016] Specifically, the step of controlling the key laser beam to pass through the second modulator and the second PDH optical path to obtain the second laser beam further includes: the target laser beam first passes through the second modulator to generate a second intermediate laser beam, and the second intermediate laser beam passes through the second PDH optical path to generate the second laser beam.

[0017] Specifically, the first modulator is an acousto-optic modulator.

[0018] Specifically, the second modulator is an acousto-optic modulator or an electro-optic modulator.

[0019] Specifically, the modulation frequencies of the first PDH optical path and the second PDH optical path are not equal.

[0020] Specifically, the polarization states of the first laser beam and the second laser beam are perpendicular to each other.

[0021] Specifically, obtaining the target zero-expansion temperature based on the temperature-related information of the target FP cavity further includes the following steps:

[0022] Obtain the temperature-related information A = {A1, A2, ..., A} of the target FP cavity. i , ..., A s}, A i = (A i1 A i2 A i1 A is the i-th target temperature of the target FP cavity. i2 It is A i1 The corresponding second modulator frequency; the value of i ranges from 1 to s, where s is the number of temperature-related information items and s≥10, where A 11 To As1 The sorting is done from smallest to largest;

[0023] Based on A, obtain the frequency variation V = {V1, V2, ..., V} corresponding to A. i , ..., V s}, V i It is A i The corresponding second modulator frequency variation, where V i The following conditions must be met:

[0024] Where △T is the temperature difference between any two adjacent target temperatures within the target FP cavity;

[0025] Based on V, the target zero expansion temperature T is obtained. 0 .

[0026] According to a second aspect of the present invention, a detection system for the zero expansion point of an ultra-stable cavity is provided, the system comprising: a target laser, a first acousto-optic modulator, a second acousto-optic modulator, a target FP cavity, a first PDH optical path, a second PDH optical path, and a target frequency counter;

[0027] The target laser is used to emit a target laser beam;

[0028] The first acousto-optic modulator is used to generate a first intermediate laser beam after receiving the target laser beam;

[0029] The second acousto-optic modulator is used to receive the key laser beam after the target laser beam is input into the first modulator and generate a second intermediate laser beam;

[0030] The first PDH optical path is used to generate the first laser beam after receiving the first intermediate laser beam;

[0031] The second PDH optical path is used to generate the second laser beam after receiving the second intermediate laser beam;

[0032] The target frequency counter is used for the frequency of the second acousto-optic modulator.

[0033] Compared with the prior art, the present invention has at least the following beneficial effects:

[0034] This invention acquires a target laser beam emitted by a target laser; controls the target laser beam to pass through a first modulator and a first PDH optical path to acquire a first laser beam; inputs the target laser beam into the first modulator to acquire a key laser beam; controls the key laser beam to pass through a second modulator and a second PDH optical path to acquire a second laser beam; inputs the first laser beam into the target FP cavity from one end and the second laser beam into the target FP cavity from the other end; and acquires the target zero-expansion temperature based on the temperature-related information of the target FP cavity. In the step of acquiring the target zero-expansion temperature based on the temperature-related information of the target FP cavity, the frequency variation of the second modulator is measured, and the target zero-expansion temperature is acquired based on the frequency variation of the second modulator. It can be seen that, compared to the prior art which requires an absolute frequency reference, this invention only measures the frequency variation of the second modulator, reducing the requirement for the absolute frequency stability of the laser. Furthermore, it only requires temperature control and laser scanning, allowing for a quick and simplified acquisition of the zero-expansion temperature. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 A flowchart illustrating a method for detecting the zero expansion temperature of an ultra-stable cavity according to Embodiment 1 of the present invention;

[0037] Figure 2 This is a schematic diagram of the structure of a detection system for the zero expansion temperature of an ultra-stable cavity provided in Embodiment 2 of the present invention;

[0038] Among them, 1-target laser, 2-first modulator, 3-first PDH optical path, 4-second modulator, 5-second PDH optical path, 6-target FP cavity, and 7-target frequency counter. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0040] Example 1:

[0041] This embodiment provides a method for detecting the zero expansion temperature of an ultra-stable cavity, the method including the following steps as follows: Figure 1 As shown:

[0042] Acquire the target laser beam emitted by the target laser;

[0043] The target laser beam is controlled to pass through the first modulator and the first PDH optical path to obtain the first laser beam;

[0044] After the target laser beam is input into the first modulator, the key laser beam is obtained;

[0045] The key laser beam is controlled to pass through the second modulator and the second PDH optical path to obtain the second laser beam;

[0046] The first laser beam is input into the target FP cavity from one end, and the second laser beam is input into the target FP cavity from the other end.

[0047] The target zero expansion temperature is obtained based on the temperature-related information of the target FP cavity.

[0048] Specifically, the step of inputting the first laser beam into the target FP cavity from one end and inputting the second laser beam into the target FP cavity from the other end further includes:

[0049] The frequency of the first laser beam is locked to the fundamental transverse mode TEM of the target FP cavity. 00 On the mold;

[0050] The frequency of the second laser beam is locked to the first transverse mode TEM of the target FP cavity. 01 On the mold

[0051] Specifically, the step of controlling the target laser beam to pass through the first modulator and the first PDH optical path to obtain the first laser beam further includes: the target laser beam first passes through the first modulator to generate a first intermediate laser beam, and the first intermediate laser beam passes through the first PDH optical path to generate the first laser beam.

[0052] Specifically, the step of controlling the key laser beam to pass through the second modulator and the second PDH optical path to obtain the second laser beam further includes: the target laser beam first passes through the second modulator to generate a second intermediate laser beam, and the second intermediate laser beam passes through the second PDH optical path to generate the second laser beam.

[0053] Specifically, the first modulator is an acousto-optic modulator AOM1. The frequency of the first laser beam is locked to the fundamental transverse mode frequency ν of the target FP cavity by AOM1. 00 superior.

[0054] Specifically, the second modulator is an acousto-optic modulator or an electro-optic modulator.

[0055] In some embodiments, the center frequency of the second modulator can be determined based on the target FP cavity fundamental transverse mode TEM00 and the first-order transverse mode TEM00. 01 The frequency intervals between them are determined. For example, for a plano-concave cavity with a cavity length of 5 cm (concave surface curvature radius R2 = 1000 mm), TEM 00 The spacing between the 0 and 1 modes is approximately 215MHz, and this frequency shift can be easily achieved using an acousto-optic modulator.

[0056] In other embodiments, the frequency variation range of the second modulator is determined based on the relationship between the frequency and temperature of the target FP cavity, thereby selecting the corresponding type of the second modulator. For example, for the target FP cavity, its frequency-temperature relationship is y=a (T-T0)^2+b, where y is the target FP cavity frequency, a and b are coefficients, T is the target temperature, and T0 is the zero expansion point. a = 0.18MHz / K^2@1550nm. A 10℃ temperature change around the zero expansion point T0 results in a frequency change of approximately 18MHz. The AOM (Acousto-Optical Modulator) can satisfy frequency modulation within this range; therefore, an acousto-optic modulator can be selected as the second modulator. For a wider temperature range adjustment, an electro-optic modulator can be selected as the second modulator, with sideband frequency locking to achieve the function of the second modulator.

[0057] In some embodiments, the modulation frequencies of the first PDH optical path and the second PDH optical path are not equal. This can effectively eliminate electronic crosstalk and reduce optical crosstalk.

[0058] In some embodiments, the polarization states of the first laser beam and the second laser beam are perpendicular to each other. For example, before the first and second laser beams are incident on the target FP cavity, they can be passed through polarizers respectively to adjust their polarization directions so that they are perpendicular to each other. This can further reduce optical crosstalk and avoid interference from reflected light between the two laser beams.

[0059] Specifically, obtaining the target zero-expansion temperature based on the temperature-related information of the target FP cavity further includes the following steps:

[0060] Obtain the temperature-related information A = {A1, A2, ..., A} of the target FP cavity. i , ..., A s}, A i = (A i1 A i2 ),

[0061] Ai1 A is the i-th target temperature of the target FP cavity. i2 It is A i1 The corresponding second modulator frequency; the value of i ranges from 1 to s, where s is the number of temperature-related information items and s≥10.

[0062] Furthermore, A 11 To A s1 The sorting is done from smallest to largest.

[0063] Preferably, the temperature difference between any two adjacent target temperatures within the target FP cavity remains consistent.

[0064] Based on A, obtain the frequency variation V = {V1, V2, ..., V} corresponding to A. i , ..., V s}, V i It is A i The corresponding frequency variation of the second modulator.

[0065] Furthermore, based on A, obtain the frequency variation V = {V1, V2, ..., V} corresponding to A. i , ..., V s}, V i It is A i The corresponding step of the second modulator frequency change degree also includes the following step, V i The following conditions must be met:

[0066] Wherein, △T is the temperature difference between any two adjacent target temperatures within the target FP cavity. Those skilled in the art can set the temperature difference between any two adjacent target temperatures within the target FP cavity according to actual needs, which will not be elaborated here; preferably, when i=s, V m =0.

[0067] Based on V, the target zero expansion temperature T is obtained. 0 To further understand this, it means: traversing from V1 to V s-1 And when V i When it is the minimum value, determine T. 0 =T i .

[0068] In one specific embodiment, A i2 The following conditions must be met:

[0069] Where f1() is a function of the target temperature and the refractive index of the medium between the eyepieces, and f2() is a function of the target temperature and the length of the target FP cavity.

[0070] Furthermore, Where L0 is the initial cavity length of the target FP cavity at the reference temperature A0, and α is the thermal linear expansion coefficient of the target FP cavity.

[0071] Furthermore, Where n0 is the refractive index of the inter-cavity medium of the target FP cavity at the reference temperature A0, and β is the thermo-optic coefficient of the target FP cavity.

[0072] In summary, this embodiment provides a method for detecting the zero expansion temperature of an ultrastable cavity. The method includes the following steps: acquiring a target laser beam emitted by a target laser; controlling the target laser beam to pass through a first modulator and a first PDH optical path to acquire a first laser beam; inputting the target laser beam into the first modulator to acquire a key laser beam; controlling the key laser beam to pass through a second modulator and a second PDH optical path to acquire a second laser beam; inputting the first laser beam from one end of the target FP cavity into the target FP cavity and inputting the second laser beam from the other end of the target FP cavity into the target FP cavity; and acquiring the target zero expansion temperature based on the temperature-related information of the target FP cavity. Specifically, in the step of acquiring the target zero expansion temperature based on the temperature-related information of the target FP cavity, the frequency variation of the second modulator is measured, and the target zero expansion temperature is acquired based on the frequency variation of the second modulator. It can be seen that, compared to the prior art which requires an absolute frequency reference, this method only measures the frequency variation of the second modulator, reducing the requirement for the absolute frequency stability of the laser. Furthermore, it only requires temperature control and laser scanning, allowing for a quick and simplified acquisition of the zero expansion temperature.

[0073] In a specific embodiment, obtaining the target zero-expansion temperature based on the temperature-related information of the target FP cavity further includes the following steps, followed by:

[0074] Based on the target zero-expansion temperature, the frequency range of the second modulator is obtained as B = [B1, B2], where B1 is the second modulation frequency.

[0075] B2 is the lower limit of the modulator frequency, and B2 is the upper limit of the second modulator frequency.

[0076] Specifically, B1 meets the following conditions:

[0077] Where B0 is the center frequency of the second modulator, W1 is the first frequency change weight, W2 is the second frequency change weight, and T is the preset temperature step size.

[0078] Specifically, B2 meets the following conditions: .

[0079] Furthermore, the following steps are included to obtain W1 and W2:

[0080] Obtain known cavity frequency variation information D, D = {D1, D2, ..., D...} j , ..., D z}, D j =(D j1 D j2 D j3 D j4 ), D j1 It is the j-th known cavity frequency, D j2 It is D j1 The corresponding current temperature, D j3 It is D j1 The corresponding zero-point expansion temperature, D j4 It is D j1 The corresponding center frequency; where any D j3 The zero-point expansion temperature is obtained by comparing it with an absolute frequency reference using existing technology, and will not be elaborated here;

[0081] Based on D, obtain the weights W = {W1, W2, ..., W...} corresponding to D. j , ..., W z}, W j =(W j1 W j2 ), where W j1 It is D j The corresponding first initial frequency change weight, W j2 It is W j1 The corresponding second initial frequency change weight;

[0082] Obtain the weight W of the largest first initial frequency change from W. 1 max and the minimum first initial frequency change weight W 1 min ;

[0083] Obtain the weight of the second initial frequency change from W. 2 max and the minimum second initial frequency change weight W 2 min ;

[0084] According to W 1 max W 1 min W 2 max and W 2 min We obtained W1 and W2.

[0085] Furthermore, according to W 1 max W1 min W 2 max and W 2 min Obtaining W1 and W2 also includes the following steps:

[0086] According to W 1 max W 1 min W 2 max and W 2 min Obtain the length and width of the initial frequency change weight region, where the length ΔW1 and width ΔW2 of the initial frequency change weight region are given, and ΔW1 satisfies the following condition: ΔW1 = W 1 max -W 1 min △W2 satisfies the following condition: △W2=W 2 max -W 2 min .

[0087] Based on ΔW1 and ΔW2, the region is divided into sub-frequency weighted regions C = {C1, C2, ..., C...} t , ..., C g}, C t It is the t-th sub-frequency change weight region, where t ranges from 1 to g, and g is the number of sub-frequency change weight regions, with g being greater than 1.

[0088] Furthermore, the size information of each of the sub-frequency change weight regions is consistent; wherein, the length 'a' and the width 'b' of the sub-frequency change weight region satisfy the following condition:

[0089] W q1 It is W 11 To W j1 The weight of the q-th initial frequency change between them, where q ranges from 1 to j.

[0090] Among them, b meets the following conditions: .

[0091] Based on W and C, determine the number of frequency change weights H = {H1, H2, ..., H} corresponding to C. t H g}, H t It is C t It represents the corresponding frequency change weighting.

[0092] Furthermore, based on W and C, determine the number of frequency change weights H = {H1, H2, ..., H} corresponding to C. t H g}, H t It is C t The steps for determining the corresponding frequency change weights also include the following:

[0093] W j With any C t Perform a match;

[0094] When W j Located in C t Inside, H t The weight of the frequency changes counted is increased by 1;

[0095] When W j Not in C t Inside, H t The weights of the frequency changes counted remain unchanged.

[0096] Iterate through H and if H t When the maximum frequency change weight in H is determined, H is determined. t The center point (X) t and Y t ), to make X t As W1 and Y t As W2.

[0097] In summary, given the cavity frequency change information, the first frequency change weight and the second frequency change weight can be optimized to obtain suitable first frequency change weight and second frequency change weight, thereby obtaining the desired acousto-optic modulator frequency range and selecting the type of the second modulator.

[0098] In another embodiment, the method further includes the following steps:

[0099] The known cavity frequency change information D is classified into cavity frequency change information clusters D according to the coefficient of thermal expansion. 0 D 0 ={D 0 1, D 0 2, ..., D 0 r , ..., D 0 v}, D 0 r ={D 0 r1 D 0 r2 , ..., D 0 rj, ..., D 0 rz}, D 0 rj =(D 01 rj D 02 rj D 03 rj D 04 rj ), D 01 rj It is the j-th known cavity frequency in the r-th cavity frequency change information cluster, D 02 rj It is D 01 rj The corresponding current temperature, D 03 rj It is D 01 rj The corresponding zero-point expansion temperature, D 04 rj It is D 01 rj The corresponding center frequency;

[0100] For D 0 r Processing yields D 0 r The corresponding first frequency change weight and D 0 r The corresponding second frequency change weight can be further understood as, D 0 r The corresponding first frequency change weight and D 0 r The corresponding weight of the second frequency change can be determined by referring to steps S2 to S5, and will not be repeated here;

[0101] When the thermal expansion coefficient of the target FP cavity is related to D 0 r When the difference between them is minimized, D will be... 0 r The corresponding first frequency change weight and D 0 r The corresponding second frequency change weight is used as the first frequency change weight and the second frequency change weight of the target FP cavity.

[0102] In summary, by dividing the regions corresponding to different coefficients of thermal expansion and selecting the first and second frequency change weights suitable for the target FP cavity based on the different coefficients of thermal expansion, the type of the second modulator can be optimized.

[0103] Furthermore, B0 meets the following conditions:

[0104] R1 and R2 are the radii of curvature of the two cavity mirrors constituting the target FP cavity, L is the cavity length of the target FP cavity, p is the longitudinal mode exponent, and m and n are the transverse mode ordinal numbers. In a specific implementation, if the target FP cavity is a plano-concave cavity, R1=∞, R2=1 (in meters), and the cavity length L=0.05.

[0105] Furthermore, the following steps are included after step S700:

[0106] S800, when △B < △B0, the type of the second modulator is set to an acousto-optic modulator, where △B0 is a preset frequency change threshold, which can be set by those skilled in the art according to actual needs, and will not be elaborated here.

[0107] When △B≥△B0, the type of the second modulator is set to an electro-optic modulator.

[0108] Preferably, △B satisfies the following condition: △B=|B1-B2|.

[0109] In summary, this embodiment shows that by optimizing the first frequency change weight and the second frequency change weight based on the known cavity frequency change information, suitable first frequency change weight and second frequency change weight can be obtained, thereby obtaining the desired acousto-optic modulator frequency range and selecting the type of the second modulator.

[0110] In one specific embodiment, the method further includes the step of determining ΔT:

[0111] Obtain the set of thermal expansion coefficients and thermo-optic coefficients corresponding to D [(α1, β1), ..., (α... e ,β e ), ..., (α) k ,β k )], α e β is the coefficient of thermal expansion in group e. e It is the thermo-optic coefficient in the e-th group, where the value of e ranges from 1 to k, and k is the coefficient of thermal expansion and the number of thermo-optic coefficient groups;

[0112] Get (α) e ,β e The corresponding temperature intervals ΔT e =(△T 1 e , ..., △T λ e , ..., △T η e ), △T λ e It is the λth temperature interval, where λ ranges from 1 to η, and η is the number of temperature intervals;

[0113] Obtain △T λ e The corresponding first frequency change weight and ΔT λ e The corresponding second frequency change weight, ΔT λ e The corresponding first frequency change weight and ΔT λ e The corresponding second frequency change weights refer to the methods for obtaining W1 and W2, which will not be elaborated here;

[0114] From △T e The temperature interval corresponding to the smallest first frequency change weight and the smallest second frequency change weight is selected as ΔT.

[0115] In summary, by selecting the temperature intervals corresponding to the smallest first frequency change weight and the smallest second frequency change weight from the known temperatures, and then using fine temperature intervals, the minimum value of the curve can be located very accurately, thereby determining the zero expansion point with high precision.

[0116] Example 2:

[0117] This second embodiment provides a detection system for the zero expansion point of an ultra-stable cavity. The system includes the following steps: Figure 2 As shown:

[0118] Target laser 1, first modulator 2, second modulator 4, target FP cavity 6, first PDH optical path 3, second PDH optical path 5, target frequency counter 7;

[0119] The target laser 1 is used to emit a target laser beam;

[0120] The first modulator 2 is used to generate a first intermediate laser beam after receiving the target laser beam;

[0121] The second modulator 4 is used to receive the key laser beam after the target laser beam is input into the first modulator 2 and generate a second intermediate laser beam;

[0122] The first PDH optical path 3 is used to generate the first laser beam after receiving the first intermediate laser beam;

[0123] The second PDH optical path 5 is used to generate the second laser beam after receiving the second intermediate laser beam;

[0124] The target frequency counter 7 is used for the frequency of the second acousto-optic modulator 4.

[0125] While specific embodiments of the invention have been described in detail by way of example, those skilled in the art should understand that the examples are for illustrative purposes only and not intended to limit the scope of the invention. It should also be understood that various modifications can be made to the embodiments without departing from the scope and spirit of the invention. The scope of the invention is defined by the appended claims.

Claims

1. A method of detecting the zero-expansion temperature of an ultrastable cavity, comprising: The method includes: Acquire the target laser beam emitted by the target laser; The target laser beam is controlled to pass through the first modulator and the first PDH optical path to obtain the first laser beam; After the target laser beam is input into the first modulator, the key laser beam is obtained; The key laser beam is controlled to pass through the second modulator and the second PDH optical path to obtain the second laser beam; The first laser beam is input into the target FP cavity from one end, and the second laser beam is input into the target FP cavity from the other end. Based on the temperature-related information of the target FP cavity, the target zero-expansion temperature is obtained. This step of obtaining the target zero-expansion temperature based on the temperature-related information of the target FP cavity further includes the following steps: Obtain the temperature-related information A = {A1, A2, ..., A} of the target FP cavity. i , ..., A s }, A i = (A i1 A i2 A i1 A is the i-th target temperature of the target FP cavity. i2 It is A i1 The corresponding second modulator frequency; the value of i ranges from 1 to s, where s is the number of temperature-related information items and s≥10, where A 11 To A s1 The sorting is done from smallest to largest; Based on A, obtain the frequency variation V = {V1, V2, ..., V} corresponding to A. i , ..., V s }, V i It is A i The corresponding second modulator frequency variation, where V i The following conditions must be met: V i = (A i2 -A （i+1）2 ) / △T, where △T is the temperature difference between any two adjacent target temperatures within the target FP cavity; According to V, the target zero-expansion temperature T is obtained 0 .

2. The method of claim 1, wherein the super-stable cavity zero-expansion temperature is determined by the formula: T = 2.5 + 0.5 * (Tg + Td) - 0.5 * (Tg - Td) The step of inputting the first laser beam into the target FP cavity from one end and the second laser beam into the target FP cavity from the other end further includes: ​ locking the frequency of the first laser beam to a fundamental transverse mode TEM 00 on the mode; locking the frequency of the second laser beam to a first transverse mode TEM 01 on the mode.

3. The method for detecting the zero expansion temperature of an ultra-stable cavity according to claim 1, characterized in that, The step of controlling the target laser beam to pass through the first modulator and the first PDH optical path to obtain the first laser beam further includes: the target laser beam first passes through the first modulator to generate a first intermediate laser beam, and the first intermediate laser beam passes through the first PDH optical path to generate the first laser beam.

4. The method for detecting the zero expansion temperature of an ultra-stable cavity according to claim 1, characterized in that, The step of controlling the key laser beam to pass through the second modulator and the second PDH optical path to obtain the second laser beam further includes: the target laser beam first passes through the second modulator to generate a second intermediate laser beam, and the second intermediate laser beam passes through the second PDH optical path to generate the second laser beam.

5. The method of claim 1, wherein the super-stable cavity zero expansion temperature is determined by the formula: T = 2.5 - 0.5 * (Tg + Td) + 0.1 * (Tg - Td) The first modulator is an acousto-optic modulator. ​ 6. The method of claim 1, wherein the super-stable cavity zero expansion temperature is determined by the formula: T = 2.5 + 0.5 * (Tg + Td) - 0.5 * (Tg - Td) The second modulator is of the type of acousto-optic modulator or electro-optic modulator. ​ 7. The method for detecting the zero expansion temperature of an ultra-stable cavity according to claim 1, characterized in that, The modulation frequencies of the first PDH optical path and the second PDH optical path are not equal.

8. The method of claim 1, wherein the super-stable cavity zero expansion temperature is determined by the formula: T = 2.5 + 0.5 * (Tg + Td) - 0.5 * (Tg - Td) The polarization states of the first laser beam and the second laser beam are perpendicular to each other. ​ 9. A system for detecting the zero-expansion point of an ultrastable cavity, the system implementing the method for detecting the zero-expansion temperature of an ultrastable cavity according to any one of claims 1 to 8, characterized in that, The system includes: a target laser, a first acousto-optic modulator, a second acousto-optic modulator, a target FP cavity, a first PDH optical path, a second PDH optical path, and a target frequency counter; The target laser is used to emit a target laser beam; The first acousto-optic modulator is used to generate a first intermediate laser beam after receiving the target laser beam; The second acousto-optic modulator is used to receive the key laser beam after the target laser beam is input into the first modulator and generate a second intermediate laser beam; The first PDH optical path is used to generate the first laser beam after receiving the first intermediate laser beam; The second PDH optical path is used to generate the second laser beam after receiving the second intermediate laser beam; The target frequency counter is used for the frequency of the second acousto-optic modulator.

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