A method for obtaining narrow linewidth atomic clock frequency transition spectral lines

Abstract

The present invention provides a method for obtaining a narrow-linewidth atomic clock frequency transition spectral line. Under the premise of not changing the overall free evolution time, the Ramsey process is divided into multiple free evolution processes. After each free evolution stage, the atomic population is non-destructively detected using far-detuned light. The atomic phase accumulation in the current free evolution process is deduced according to the atomic population, and the phase accumulation is applied to the atoms in a manner of modulating the phase of subsequent microwave pulses to increase the total phase accumulation of the atoms in the free evolution time. Finally, the atomic population on the sub-energy level of the ground state hyperfine energy level is detected using resonant light to obtain the narrow-linewidth atomic clock frequency transition spectral line, thereby achieving a significant improvement in the performance of the atomic clock at a very low cost.

Description

Technical Field

[0001] The invention relates to the technical field of atomic frequency standards, and in particular to a method for obtaining narrow-linewidth atomic clock frequency transition spectral lines. Background Art

[0002] Atomic frequency standards are time and frequency standards with excellent performance. They are also called atomic clocks in the field of time measurement. As the most accurate time and frequency standard, atomic clocks have important applications in many fields such as navigation, communication, power grid, and national defense. Researchers have achieved the ultimate in the pursuit of atomic clock performance, and the proposal of many theories has also guided the progress of experiments.

[0003] There are two types of atomic frequency standards: active (active) and passive (passive). The former directly outputs the standard frequency from the quantum oscillator, while the latter cannot directly output the standard frequency. Instead, it obtains an error signal through the degree of stimulated transition absorption of the quantum system (resonance or not), and corrects the frequency of the voltage-controlled crystal oscillator, and the crystal oscillator outputs the standard frequency. Compared with active atomic frequency standards, passive atomic frequency standards have the advantages of small size, light weight, low power consumption, etc., which are easy to achieve mass production. Therefore, among all types of atomic frequency standards, the market share of passive atomic frequency standards has reached more than 90%.

[0004] The frequency stability of a passive atomic frequency standard affects the overall performance of the atomic frequency standard. Improving the frequency stability of a passive atomic frequency standard is the most important goal in the design of an atomic frequency standard. The frequency stability of a passive atomic frequency standard is mainly expressed by the following formula:

[0005]

[0006] Among them, Δν is the line width of the atomic clock frequency transition spectrum, ν0 is the atomic clock frequency transition frequency, SNR is the atomic clock frequency transition spectrum line signal-to-noise ratio, T c is the atomic clock period.

[0007] It can be seen from the formula that the frequency stability of the atomic clock can be improved by narrowing the spectral line width Δv, increasing the transition frequency v0, increasing the spectral line signal-to-noise ratio SNR, and shortening the clock period T c In recent years, atomic optical clocks have been vigorously developed because their transition frequency is about 4 orders of magnitude higher than that of microwave clocks, and the corresponding stability limit is also reduced by nearly 4 orders of magnitude. In atomic microwave clocks, the advantage of cesium atomic clocks over rubidium atomic clocks is that the cesium atomic transition frequency is approximately 1.35 times that of rubidium atomic transition frequency. When other parameters remain unchanged, its stability limit is also about 1.35 times lower.

[0008] Currently, the optimization direction of atomic clocks mainly focuses on selecting atomic media with higher transition frequencies and atomic spectral lines with higher signal-to-noise ratios. However, there is still little research on methods to narrow the linewidth of atomic clock frequency transition spectral lines.

[0009] The frequency transition spectrum of an atomic clock is called Ramsey fringes, and the process of obtaining the frequency transition spectrum of an atomic clock is also called the Ramsey process. Figure 3 As shown in the upper part, the current Ramsey process is as follows: first, apply a microwave pulse with an area of ​​π / 2 to the atom to prepare the atom to the superposition state of the ground state hyperfine energy level, then let the atom evolve freely for a period of time T, and then apply a microwave pulse with the same phase or a specific phase difference as the previously applied microwave pulse (here, a phase delay of 90° is used as an example), and finally, the atomic clock frequency transition spectrum line is obtained by detecting the atomic population on the sub-energy level of the ground state hyperfine energy level. The line width of the atomic clock frequency transition spectrum line obtained at this time is determined by the time interval between the two applied microwave pulses (i.e., the free evolution time T), which is generally 1 / 2T. With the continuous development of atomic frequency standard technology, higher requirements are placed on the frequency stability of atomic clocks, so it is necessary to further narrow the line width of the atomic clock frequency transition spectrum line. Summary of the invention

[0010] The purpose of the present invention is to solve the shortcomings existing in the prior art, and a method for obtaining narrow linewidth atomic clock frequency transition spectral lines is proposed. Under the premise of not changing the free evolution time T, the phase accumulation of atoms in the free evolution time is obtained by detecting the atomic population with far-detuned light, and the phase accumulation is fed back to the applied microwave pulse in real time, so that the atomic transition spectral lines are greatly narrowed, thereby achieving a significant improvement in the performance of the atomic clock at an extremely low cost.

[0011] To achieve the above object, the present invention adopts the following technical solutions:

[0012] A method for obtaining narrow linewidth atomic clock frequency transition spectral lines specifically comprises: dividing a Ramsey process into n time-series continuous free evolution processes, wherein n is a positive integer greater than 1; each free evolution process comprises a primary microwave pulse action stage, an atomic free evolution stage, and a secondary microwave pulse action stage; the secondary microwave pulse action stage of the first (n-1) free evolution process also comprises a far-detuned light detection stage, and the secondary microwave pulse action stage of the nth free evolution process also comprises a resonant light detection stage.

[0013] The far-detuned light detection stage includes: using far-detuned light to perform non-destructive detection on the atomic population, inferring the atomic phase accumulation in the current free evolution process according to the atomic population, and applying this phase accumulation to the atoms by modulating the phase of subsequent microwave pulses to increase the total phase accumulation of the atoms in the Ramsey process.

[0014] The resonance light detection stage includes: using resonance light to detect the atomic population on the sub-energy levels of the ground state hyperfine energy level, thereby obtaining the atomic clock frequency transition spectrum.

[0015] Preferably, the first stage of free evolution process includes:

[0016] Step 1-1: A microwave pulse action stage: Apply a microwave pulse to the atom with an area of ​​S, a time of t, and a phase of The first microwave pulses prepared atoms into a superposition of ground-state hyperfine levels;

[0017] Step 1-2: The first free evolution stage of atoms: allow atoms to evolve freely and perform phase accumulation within the first free evolution time T1;

[0018] Step 1-3: Second microwave pulse action stage: Apply microwave pulses with an area of ​​S and a time of t to the atoms and a phase delay relative to the first microwave pulse The secondary microwave pulse;

[0019] Step 1-4: The first far-detuned light detection phase: Use far-detuned light to detect the atomic structure within the first detection time t1, and calculate the atomic phase accumulation within the first free evolution time T1 based on the detected atomic structure.

[0020] Preferably, the i-th (i=2, 3, ..., n-1) segment free evolution process includes:

[0021] Stepi-1: A microwave pulse action phase: Apply a microwave pulse with an area of ​​S and a time of t to the atom and a phase delay relative to the first microwave pulse A microwave pulse;

[0022] Stepi-2: The i-th free evolution stage of atoms: Let the atoms evolve freely for the i-th time T i Free evolution and phase accumulation are performed within the system;

[0023] Stepi-3: Second microwave pulse action stage: Apply microwave pulses with an area of ​​S and a time of t to the atoms and a phase delay relative to the first microwave pulse The secondary microwave pulse;

[0024] Step i-4: The i-th far-out-of-harmonic light detection phase: Use the far-out-of-harmonic light to detect the i-th time t i The atomic structure is detected within the i-th segment, and the free evolution time T of the i-th segment is calculated based on the detected atomic structure. i The atomic phases within the .

[0025] Preferably, the nth stage free evolution process is:

[0026] Step 1: A microwave pulse action phase: Apply a microwave pulse with an area of ​​S and a time of t to the atom and a phase delay relative to the first microwave pulse A microwave pulse;

[0027] Step n-2: The nth free evolution stage of atoms: Let the atoms evolve freely for the nth time T n Free evolution and phase accumulation are performed within the system;

[0028] Step-3: Second microwave pulse action stage: Apply microwave pulses with an area of ​​S and a time of t to the atoms and a phase delay relative to the first microwave pulse The secondary microwave pulse of is the total atomic phase accumulation during the first (n-1) segments of free evolution;

[0029] Stepn-4: Resonance light detection stage: Use resonant light to detect the atomic population on the sub-energy levels of the ground state hyperfine energy level, so as to obtain the narrow linewidth atomic clock frequency transition spectrum.

[0030] Preferably, a Ramsey process is divided into two time-series continuous free evolution processes.

[0031] Preferably, in the first microwave pulse action stage of the free evolution process, the microwave pulse is represented by a classical electromagnetic field, the atom is simplified into a two-level system, and the state of the atom is obtained by analyzing the density matrix equation:

[0032]

[0033] Where Δ is the population difference between the two atomic energy levels, b e is the microwave Rabi frequency, is the microwave phase, δ μμ′ is the coherence between the two energy levels of the atom, Ω μ is the detuning of the microwave frequency relative to the atomic transition frequency.

[0034] Finally, the interaction between microwave pulses and atoms is expressed in matrix form:

[0035]

[0036] in, is the real part of the atomic coherence, is the imaginary part of the atomic coherence, is a 3×3 interaction matrix whose elements are:

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] Preferably, in the atomic free evolution stage, the effects of microwave field and light field are not added, and only the decoherence of atoms is considered.

[0048] Preferably, in the far-detuned light detection stage of the first free evolution process, the process of using far-detuned light to detect atomic population is non-destructive detection, and only the decoherence of atoms is considered; when relaxation is considered, the interaction matrix between far-detuned light and atoms is expressed as:

[0049]

[0050]

[0051] Among them, γ1 is the transverse relaxation rate, which characterizes the atomic coherence; γ2 is the longitudinal relaxation rate, which characterizes the atomic population difference, T=T1+T2.

[0052] Preferably, S = π / 2, t = 2 ms, T1 = 8ms, t1 = 2ms, T2 = 8ms, is the atomic phase accumulation of the first stage of free evolution.

[0053] Preferably, after a microwave pulse stage in the first stage of the free evolution process, the atoms are prepared to the lower energy level, and the atomic state is expressed as:

[0054]

[0055] After the resonant light detection phase of the second free evolution process, the final state of the atom is represented by the matrix:

[0056]

[0057] Compared with the prior art, the beneficial effects of the present invention are as follows: without changing the overall free evolution time, the present invention divides the Ramsey process into multiple free evolution processes, and after each free evolution stage, uses far-detuned light to perform non-destructive detection of the atomic population, and calculates the atomic phase accumulation in the current free evolution according to the atomic population, and applies this phase accumulation to the atoms by modulating the microwave pulse phase, thereby increasing the total phase accumulation of the atoms in the free evolution time, and finally obtaining a narrow-linewidth atomic clock frequency transition spectrum, thereby achieving a significant improvement in the performance of the atomic clock at a very low cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 FIG. 4 is a timing diagram of the Ramsey process in one embodiment of the present invention.

[0059] Figure 2 FIG. 4 is a flow chart of a Ramsey process according to an embodiment of the present invention.

[0060] Figure 3 It is a timing comparison diagram of the Ramsey process in the prior art and the Ramsey process in one embodiment of the present invention.

[0061] Figure 4 The figure is a comparison diagram between normal Ramsey fringes in the prior art and improved Ramsey fringes in one embodiment of the present invention. DETAILED DESCRIPTION

[0062] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the embodiment of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the described embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the scope of protection of the present invention. It can be understood that some technical means of the various embodiments described herein can be replaced or combined with each other without conflict.

[0063] In the description of the present invention, if there are terms such as "first", "second", etc., they are only used to distinguish the objects described, and do not have any order or technical meaning. Therefore, the objects defined as "first", "second", etc. may explicitly or implicitly include one or more of the objects. In addition, "one" or "a" and similar words do not indicate a quantity limitation, but indicate the existence of at least one, and "multiple" means not less than two.

[0064] In the description of the present specification, reference to "one embodiment" or "some embodiments" etc. means that one or more embodiments of the present invention include a specific feature, structure or characteristic described in conjunction with the embodiment. Therefore, the phrases "in one embodiment", "in some embodiments", "in some other embodiments", "in some other embodiments", etc. appearing in different places in this specification do not necessarily refer to the same embodiment, but mean "one or more but not all embodiments", unless otherwise specifically emphasized in other ways.

[0065] See also Figure 1 The present invention provides a method for obtaining narrow linewidth atomic clock frequency transition spectral lines, which specifically includes: dividing a Ramsey process into n time-series continuous free evolution processes, wherein n is a positive integer greater than 1; each free evolution process includes a primary microwave pulse action stage, an atomic free evolution stage, and a secondary microwave pulse action stage; the secondary microwave pulse action stage of the first (n-1) free evolution process also includes a far-detuned light detection stage, and the secondary microwave pulse action stage of the nth free evolution process also includes a resonant light detection stage.

[0066] Among them, the far-detuned light detection stage includes: using far-detuned light to perform non-destructive detection of atomic population, inferring the atomic phase accumulation in the current free evolution process based on the atomic population, and applying this phase accumulation to atoms by modulating the phase of subsequent microwave pulses to increase the total phase accumulation of atoms in the Ramsey process.

[0067] The resonant light detection stage includes: using resonant light to detect the atomic population on the sub-energy levels of the ground state hyperfine energy level, thereby obtaining the atomic clock frequency transition spectrum.

[0068] The present invention divides the Ramsey process into multiple free evolution processes without changing the overall free evolution time. After each free evolution stage, the atomic population is non-destructively detected using far-detuned light. The atomic phase accumulation in the current free evolution period is inferred based on the atomic population, and the phase accumulation is applied to the atoms by modulating the phase of subsequent microwave pulses, thereby increasing the total phase accumulation of the atoms in the free evolution time, and finally obtaining a narrow-linewidth atomic clock frequency transition spectrum, thereby achieving a significant improvement in the performance of the atomic clock at a very low cost.

[0069] See also Figure 2 In some preferred embodiments of the present invention, the first free evolution process includes:

[0070] Step 1-1: A microwave pulse action stage: Apply a microwave pulse to the atom with an area of ​​S, a time of t, and a phase of The first microwave pulses prepared atoms into a superposition of ground-state hyperfine levels;

[0071] Step 1-2: The first free evolution stage of atoms: allow atoms to evolve freely and perform phase accumulation within the first free evolution time T1;

[0072] Step 1-3: Second microwave pulse action stage: Apply microwave pulses with an area of ​​S and a time of t to the atoms and a phase delay relative to the first microwave pulse The secondary microwave pulse;

[0073] Step 1-4: The first far-detuned light detection phase: Use far-detuned light to detect the atomic structure within the first detection time t1, and calculate the atomic phase accumulation within the first free evolution time T1 based on the detected atomic structure.

[0074] Furthermore, the i-th (i=2, 3, ..., n-1) segment free evolution process includes:

[0075] Stepi-1: A microwave pulse action phase: Apply a microwave pulse with an area of ​​S and a time of t to the atom and a phase delay relative to the first microwave pulse A microwave pulse;

[0076] Stepi-2: The i-th free evolution stage of atoms: Let the atoms evolve freely for the i-th time T i Free evolution and phase accumulation are performed within the system;

[0077] Stepi-3: Second microwave pulse action stage: Apply microwave pulses with an area of ​​S and a time of t to the atoms and a phase delay relative to the first microwave pulse The secondary microwave pulse;

[0078] Step i-4: The i-th far-out-of-harmonic light detection phase: Use the far-out-of-harmonic light to detect the i-th time t i The atomic structure is detected within the i-th segment, and the free evolution time T of the i-th segment is calculated based on the detected atomic structure. i The atomic phases within the .

[0079] Furthermore, the nth free evolution process is:

[0080] Step 1: A microwave pulse action phase: Apply a microwave pulse with an area of ​​S and a time of t to the atom and a phase delay relative to the first microwave pulse A microwave pulse;

[0081] Step n-2: The nth free evolution stage of atoms: Let the atoms evolve freely for the nth time T n Free evolution and phase accumulation are performed within the system;

[0082] Step-3: Second microwave pulse action stage: Apply microwave pulses with an area of ​​S and a time of t to the atoms and a phase delay relative to the first microwave pulse The secondary microwave pulse of is the total atomic phase accumulation during the first (n-1) segments of free evolution; the total atomic phase accumulation can be specifically inferred by using far-detuned light to detect the atomic layout in each far-detuned light detection stage;

[0083] Stepn-4: Resonance light detection stage: Use resonant light to detect the atomic population on the sub-energy levels of the ground state hyperfine energy level, so as to obtain the narrow linewidth atomic clock frequency transition spectrum.

[0084] It should be noted that the area S of the microwave pulse, the action time t of the microwave pulse, the phase of the first microwave pulse The detection time of far-detuned light, the specific values ​​of each phase delay, etc. can be reasonably set according to actual conditions.

[0085] See also Figure 3 The upper part and Figure 4 The current Ramsey process is as follows: first, apply a microwave pulse with an area of ​​π / 2 to the atom to prepare the atom to the superposition state of the ground state hyperfine energy level, then let the atom evolve freely for a period of time T, and then apply a microwave pulse with the same phase or a specific phase difference as the previous microwave pulse (here, a phase delay of 90° is used as an example), and finally, the atomic clock frequency transition spectrum is obtained by detecting the atomic population on the sub-energy level of the ground state hyperfine energy level. The line width of the atomic clock frequency transition spectrum obtained at this time is determined by the time interval between the two applied microwave pulses (i.e., the free evolution time T), which is generally 1 / 2T.

[0086] See also Figure 3 The lower part and Figure 4 In some embodiments of the present invention, a Ramsey process is divided into two free evolution processes with continuous time sequence. The specific process is: first, an area of ​​π / 2, time t, and phase t are applied to the atom. The microwave pulse prepares the atoms to the superposition state of the ground state hyperfine energy level, and then allows the atoms to evolve freely for a period of time T1, and then acts on the phase delay of the previously applied microwave pulse The microwave pulse is then used to detect the atomic population using far-detuned light, and the atomic phase accumulation in the T1 time is calculated based on the detected atomic population, and then the phase delay is applied The microwave pulse is then used to allow the atoms to evolve freely for a period of time T2, and then a phase delay of The microwave pulse is then used to detect the atomic population on the sub-energy level of the ground state hyperfine energy level with resonant light, thereby obtaining the atomic clock frequency transition spectrum. The atomic phase accumulation obtained by the Ramsey process of the present invention is more than the atomic phase accumulation obtained by the normal Ramsey process. The final reflection in the Ramsey fringes is the narrowing of the line width, which can greatly improve the performance of the atomic clock.

[0087] In some embodiments, for a diffuse reflection cold atomic clock, the parameters in the two-stage free evolution process are set as follows: S = π / 2, t = 2ms, T1 = 8ms, t1 = 2ms, T2 = 8ms, in, is the atomic phase accumulation during the first stage of free evolution, The atomic structure can be detected and inferred using far-detuned light in the first far-detuned light detection stage.

[0088] The following is an explanation of the principles of the two-stage free evolution process:

[0089] In the first stage of microwave pulse action in the free evolution process, according to the semiclassical theory, the microwave pulse is represented by the classical electromagnetic field, the atom is simplified into a two-level system, and the state of the atom is obtained by analyzing the density matrix equation:

[0090]

[0091] Where Δ is the population difference between the two atomic energy levels, b e is the microwave Rabi frequency, is the microwave phase, δ μμ′ is the coherence between the two energy levels of the atom, Ω μ is the detuning of the microwave frequency relative to the atomic transition frequency.

[0092] Finally, the interaction between microwave pulses and atoms is expressed in matrix form:

[0093]

[0094] in, is the real part of the atomic coherence, is the imaginary part of the atomic coherence, is a 3×3 interaction matrix whose elements are:

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105] During the free evolution stage of atoms, the effects of microwave fields and light fields are not added, and only the decoherence of atoms needs to be considered.

[0106] At the same time, in the far-detuned light detection stage of the first free evolution process, the process of using far-detuned light to detect atomic population is a non-destructive detection, and only the decoherence of atoms needs to be considered. When considering relaxation, the interaction matrix between far-detuned light and atoms is expressed as:

[0107]

[0108]

[0109] Among them, γ1 is the transverse relaxation rate, which characterizes the atomic coherence; γ2 is the longitudinal relaxation rate, which characterizes the atomic population difference, T=T1+T2.

[0110] After a microwave pulse phase in the first free evolution process, the atoms are prepared to the lower energy level, and the atomic state is expressed as:

[0111]

[0112] For the normal Ramsey process, Figure 3 As shown in the upper part of , the final state of the atom can be represented by the matrix:

[0113]

[0114] As for the Ramsey process of the present invention, Figure 3 As shown in the lower part of , after the resonant light detection stage of the second free evolution process, the final state of the atom can be expressed by the matrix:

[0115]

[0116] Taking the diffuse reflection cold atomic clock as an example, the microwave pulse time t is generally 2ms, the normal Ramsey free evolution time T is 22ms, the first atomic free evolution time T1 of the present invention is set to 8ms, the far detuned light detection time t1 is set to 2ms, and the second atomic free evolution time T2 is set to 8ms. The Ramsey fringes finally calculated are as follows: Figure 4 As shown. It can be seen that by improving the Ramsey action process, the line width of the Ramsey fringe spectrum (atomic clock frequency transition spectrum) has been effectively narrowed, thereby achieving a significant improvement in the performance of the atomic clock at a very low cost.

[0117] In summary, the present invention provides a method for obtaining narrow linewidth atomic intermediate frequency transition spectral lines. Without changing the overall free evolution time, the Ramsey process is divided into multiple free evolution processes. After each free evolution stage, the atomic population is non-destructively detected using far-detuned light. The atomic phase accumulation in the current free evolution period is calculated based on the atomic population, and the phase accumulation is applied to the atoms by modulating the phase of microwave pulses to increase the total phase accumulation of the atoms in the free evolution time, and finally a narrow linewidth atomic clock frequency transition spectral line is obtained, thereby achieving a significant improvement in the performance of the atomic clock at a very low cost.

[0118] The present invention has been described by the above-mentioned relevant embodiments, however, the above-mentioned embodiments are only examples for implementing the present invention. It must be pointed out that the disclosed embodiments do not limit the scope of the present invention. On the contrary, changes and modifications made without departing from the spirit and scope of the present invention are all within the scope of patent protection of the present invention.

Claims

1. A method for obtaining narrow linewidth atomic clock frequency transition spectral lines, characterized in that: A Ramsey process is divided into n time-sequentially continuous free evolution processes, wherein n is a positive integer greater than 1; each free evolution process includes a first microwave pulse action stage, an atomic free evolution stage, and a second microwave pulse action stage; the second microwave pulse action stage of the first (n-1) free evolution process also includes a far-detuned light detection stage, and the second microwave pulse action stage of the nth free evolution process also includes a resonant light detection stage; The far-detuned light detection stage includes: using far-detuned light to non-destructively detect the atomic population, inferring the atomic phase accumulation in the current free evolution process according to the atomic population, and applying this phase accumulation to the atoms by modulating the phase of subsequent microwave pulses to increase the total phase accumulation of the atoms in the Ramsey process; The resonance light detection stage includes: using resonance light to detect the atomic population on the sub-energy levels of the ground state hyperfine energy level, thereby obtaining the atomic clock frequency transition spectrum; The first stage of free evolution process includes: Step 1-1: A microwave pulse action stage: Apply a microwave pulse to the atom with an area of ​​S, a time of t, and a phase of The first microwave pulses prepared atoms into a superposition of ground-state hyperfine levels; Step 1-2: The first free evolution stage of atoms: allow atoms to evolve freely and perform phase accumulation within the first free evolution time T1; Step 1-3: Second microwave pulse action stage: Apply microwave pulses with an area of ​​S and a time of t to the atoms and a phase delay relative to the first microwave pulse The secondary microwave pulse; Step 1-4: The first far-detuned light detection phase: Use far-detuned light to detect the atomic structure within the first detection time t1, and calculate the atomic phase accumulation within the first free evolution time T1 based on the detected atomic structure; The i-th (i=2,3,…,n-1) segment free evolution process includes: Stepi-1: A microwave pulse action phase: Apply a microwave pulse with an area of ​​S and a time of t to the atom and a phase delay relative to the first microwave pulse A microwave pulse; Stepi-2: The i-th free evolution stage of atoms: Let the atoms evolve freely for the i-th time T i Free evolution and phase accumulation are performed within the system; Stepi-3: Second microwave pulse action stage: Apply microwave pulses with an area of ​​S and a time of t to the atoms and a phase delay relative to the first microwave pulse The secondary microwave pulse; Step i-4: The i-th far-out-of-harmonic light detection phase: Use the far-out-of-harmonic light to detect the i-th time t i The atomic structure is detected within the i-th segment, and the free evolution time T of the i-th segment is calculated based on the detected atomic structure. i The atomic phases within accumulate; The nth free evolution process is: Step 1: A microwave pulse action phase: Apply a microwave pulse with an area of ​​S and a time of t to the atom and a phase delay relative to the first microwave pulse A microwave pulse; Step n-2: The nth free evolution stage of atoms: Let the atoms evolve freely for the nth time T n Free evolution and phase accumulation are performed within the system; Step-3: Second microwave pulse action stage: Apply microwave pulses with an area of ​​S and a time of t to the atoms and a phase delay relative to the first microwave pulse The secondary microwave pulse of is the total atomic phase accumulation during the first (n-1) segments of free evolution; Stepn-4: Resonance light detection stage: Use resonant light to detect the atomic population on the sub-energy levels of the ground state hyperfine energy level, so as to obtain the narrow linewidth atomic clock frequency transition spectrum.

2. The method for obtaining narrow linewidth atomic clock frequency transition spectral lines according to claim 1, characterized in that: A Ramsey process is divided into two time-series continuous free evolution processes.

3. The method for obtaining narrow linewidth atomic clock frequency transition spectral lines according to claim 2, characterized in that: In the first stage of microwave pulse action in the free evolution process, the microwave pulse is represented by the classical electromagnetic field, the atom is simplified into a two-level system, and the state of the atom is obtained by analyzing the density matrix equation: Where Δ is the population difference between the two atomic energy levels, b e is the microwave Rabi frequency, is the microwave phase, δ μμ′ is the coherence between the two energy levels of the atom, Ω μ is the detuning of the microwave frequency relative to the atomic transition frequency; Finally, the interaction between microwave pulses and atoms is expressed in matrix form: in, is the real part of the atomic coherence, is the imaginary part of the atomic coherence, is a 3×3 interaction matrix whose elements are:

4. The method for obtaining narrow linewidth atomic clock frequency transition spectral lines according to claim 3, characterized in that: In the atomic free evolution stage, the effects of microwave field and light field are not added, and only the decoherence of atoms is considered.

5. The method for obtaining narrow linewidth atomic clock frequency transition spectral lines according to claim 4, characterized in that: In the first stage of the free evolution process, the process of using far-detuned light to detect atomic population is a non-destructive detection, and only the decoherence of atoms is considered. When relaxation is considered, the interaction matrix between far-detuned light and atoms is expressed as: Among them, γ1 is the transverse relaxation rate, which characterizes the atomic coherence; γ2 is the longitudinal relaxation rate, which characterizes the atomic population difference, T=T1+T2.

6. The method for obtaining narrow linewidth atomic clock frequency transition spectral lines according to claim 5, characterized in that: S = π / 2, t = 2ms, T1 = 8ms, t1 = 2ms, T2 = 8ms, is the atomic phase accumulation of the first stage of free evolution.

7. The method for obtaining narrow linewidth atomic clock frequency transition spectral lines according to claim 6, characterized in that: After a microwave pulse phase in the first free evolution process, the atoms are prepared to the lower energy level, and the atomic state is expressed as: After the resonant light detection phase of the second free evolution process, the final state of the atom is represented by the matrix:

Images