CN106871888B - Phase detection method of cold atom vitreous color-einstein condensed vortex superposed state gyroscope - Google Patents

Phase detection method of cold atom vitreous color-einstein condensed vortex superposed state gyroscope Download PDF

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CN106871888B
CN106871888B CN201710031810.7A CN201710031810A CN106871888B CN 106871888 B CN106871888 B CN 106871888B CN 201710031810 A CN201710031810 A CN 201710031810A CN 106871888 B CN106871888 B CN 106871888B
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任元
汤国志
王如泉
谢璐
成蕊
汪洲
王卫杰
刘通
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Abstract

The invention relates to a phase detection method of a cold atom vitreous color-Einstein condensation vortex superposed gyroscope. And (3) injecting the vortex light in the superposed state into the bose-Einstein condensed state gas atomic group, so that the bose-Einstein condensed (BEC) atomic group obtains a certain orbital angular momentum to generate a stable vortex superposed state substance wave, and the BEC atomic group in the potential well is equivalent to a substance wave interference gyroscope. The atom density distribution of BEC can form stable interference pattern, when the system is rotated at a certain angular speed, a certain phase can be produced due to Sagnac effect, the scattering of each atom to photon is fixed, after detection light is added, the whole resonance absorption image is detected by a Charge Coupled Device (CCD), the scattering light intensity is obtained by space operation and time operation, the density distribution of BEC atomic groups is calculated, further phase information is obtained, and relative light intensity change can be obtained by space subtraction and used as gyro signal for calculating the angular speed of the system, so that the sensitivity to the angular speed of the system is realized.

Description

Phase detection method of cold atom vitreous color-einstein condensed vortex superposed state gyroscope
Technical Field
The invention relates to a phase detection method of a cold atom vitreous color-Einstein condensed vortex superposed gyroscope, which can be applied to the field of over-precision inertial navigation.
Technical Field
In 1850, a french physicist J Foucault, to study the earth's spin, first found that the rotor in high speed rotation, due to inertia, had its axis of rotation permanently pointed in a fixed direction and named gyroscope. The gyroscope is used as a main inertial navigation detection device, has wide application in the fields of navigation, aviation, aerospace, missile and the like, and has very important strategic significance on the development of the industries, national defense and other high-tech fields of a country. The traditional electromechanical gyroscope has the bottleneck of accuracy and sensitivity due to the limitation of the action mechanism, and the laser gyroscope and the optical fiber gyroscope based on the Sagnac effect have contradiction between the improvement of the accuracy and sensitivity and the volume, weight and power consumption of the gyroscope and also enter the bottleneck of development of the accuracy and sensitivity.
In recent years, the rapid development of the fields of quantum physics and low-temperature physics brings revolutionary influence to the development of novel quantum gyroscopes, and a series of quantum gyroscopes with ultrahigh precision and ultrahigh sensitivity appear, so that the advanced countries such as Europe and America attract attention. The national defense department advanced planning research institute establishes a Precise Inertial Navigation System (PINS), and takes a quantum inertial sensing technology taking a quantum effect as a core as a next generation leading inertial technology. Quantum gyroscopes can be classified into quantum spinning gyroscopes, quantum interference gyroscopes, and quantum vortex gyroscopes, according to mechanism and motion. The quantum spin gyro has excellent characteristics of high precision and miniaturization, but inevitable friction and collision exist between atoms or molecules, and precision and sensitivity of the quantum spin gyro are influenced and restricted. The quantum interference gyroscope has high theoretical precision and wide application prospect, but has contradiction between volume and sensitivity precision. In 1995, experimental realization of controlled Rb atom rarefied gas vitreous color-einstein condensation (BEC) marks realization of gas phase atomic vitreous color-einstein condensation state, namely trapping of gaseous alkali metal atoms can be realized through magneto-optical-based Time Orbital Potential (TOP), a potential well can control internal gas radicals to generate vortex, and the gyroscope has axial stability and precession. The cold atom gas is pure and thin, detection is facilitated, interaction is easy to describe, and the vortex stack state gyroscope based on the gaseous BEC can realize high-density vortex of the quantum and is convenient to miniaturize.
Different from the existing interference gyro (such as an optical gyro and an atomic interference gyro) which needs to artificially construct an interference loop, the cold atomic BEC vortex superposed gyroscope replaces the constructed interference loop through a self-formed vortex optical control loop, which not only helps to greatly reduce the noise introduced by the interference loop, but also provides possibility for high-precision detection of the interference gyro.
As for the detection method of the interference gyro, the existing optical gyro and atomic interference gyro detect phase information at a certain interference point. For the cold atom BEC vortex superimposed state gyroscope, if the method is adopted, the whole interference pattern information is inevitably lost, thereby influencing the detection precision of the system.
The method realizes the sensitivity of angular velocity by utilizing the Sagnac effect of vortex superposed state material waves, detects the phase information of an interference pattern so as to obtain the angular velocity of a system, and the accumulated phase difference in time t is proportional to the detection time, the platform angular velocity and the topological charge number of the vortex. Detecting the entire interference pattern such that the number of scattered photons NscGreatly increased and time-summed to improve angular rate sensitive sensitivity.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the defect that the existing interference gyro detection method is directly applied to a cold atom BEC vortex superposed state gyro, the method for detecting the phase information of the whole interference pattern of the gyro by utilizing space operation and time operation is provided, and the sensitivity and the precision of the system are greatly improved.
The technical solution of the invention is as follows:
(1) and (3) emitting the vortex light in the superposed state into the BEC gas atomic group, so that the BEC atomic group obtains a certain orbital angular momentum to generate a stable vortex superposed state substance wave, wherein the BEC atomic group in the potential well is equivalent to a substance wave interference gyroscope. The atom density distribution of BEC can form stable interference pattern, when the system rotates at a certain angular rate, a certain phase can be generated due to Sagnac effect, the scattering of each atom to photon is fixed, after detection light is added, the whole resonance absorption image is detected through CCD, the scattering light intensity is obtained through space operation and time operation, the density distribution of BEC atomic groups is calculated, further phase information is obtained, and relative light intensity change can be obtained through space subtraction and used as gyro signal for calculating the angular rate of the system, so that the sensitivity to the angular rate of the system is realized.
(2) And calculating the angular rate of the system by obtaining the scattered light intensity distribution through space operation and time operation and calculating the BEC atom density distribution. Realizing sensitivity to angular rate by utilizing the Sagnac effect of vortex superposed state substance waves, and detecting phase information of an interference pattern so as to obtain the angular rate of a system; the interference pattern petals are divided into 4l regions gamma along theta 2m pi/4 l ( m 0, 1.. 4l-1)k(k ═ 1, 2.., 4l), definition I0As a total light intensity, I1Is 2l regions Fk(k ═ 1,3,.., 4l-1) total light intensity, I2Is 2l regions FkTotal light intensity of ( k 2, 4.., 4l), I during the experiment1And I2The following results are obtained by temporal accumulation (1) and spatial accumulation (2):
Figure GDA0002156928860000031
Figure GDA0002156928860000032
when the potential well rotates, the light intensity I can be obtained1And I2
Figure GDA0002156928860000033
BEC cross-sectional density distribution (z ═ z) in potential well0) Proportional to the light intensity distribution:
I(r,θ,z)∝ΣΩ(r,θ,t)={1+cos[2lθ+Δφ]}|Ψ(r,θ,z)|2(10)
Δ φ can be derived from the BEC cross-sectional density distribution, and is defined as the relative intensity variation obtained by spatial subtraction:
Figure GDA0002156928860000034
obtaining δ can be used to derive the system angular rate:
Figure GDA0002156928860000041
because each atom is fixed for scattering photons, after detection light is added, a resonance absorption image is detected through a CCD (charge coupled device), phase information is obtained through time accumulation and space accumulation, delta can be obtained through space subtraction and used for calculating the angular rate of a system, and the whole interference pattern is detected to enable the number of scattered photons to be NscGreatly increasing the sensitivity.
The principle of the invention is as follows:
(1) BEC vortex superposition interference method based on Mexico cap potential well
For cold atom BECs, vortices are generated in the BEC after a certain orbital angular momentum is obtained by vortex light or other means. When the orbital angular momentum exceeds a certain limit, the vortex will automatically break into multiple vortices. To enable greater orbital angular momentum to be achieved by the BEC vortices, BEC gas radicals are distributed in a ring-like fashion using "mexican hat" potential well pickup radicals to avoid auto-fission of the vortices. Thereby forming a vortex of greater orbital angular momentum and remaining stable for a longer period of time.
The "mexican hat" potential well is formed using two lasers. Firstly, a red detuned laser beam is utilized to form a cake-shaped potential well through a cylindrical mirror, and then a superfine blue detuned laser beam is utilized to form a potential barrier at the center of the cake-shaped potential well, so that a mexican hat-shaped potential well is formed. As shown in fig. 2, the product is named because it looks like a mexican hat. The ring-shaped density distribution of the BEC gas radicals can be obtained by means of a "mexico cap" potential well.
(2) STIRAAP (Stmodular Raman Adiabag) stimulated Raman Adiabatic Process
The superimposed vortex light is injected into the gas atomic group in the wave-einstein condensed state, so that the substance wave superimposed vortex state can be generated in the BEC. The effect of the vortex rotation of the superimposed state and the gas radicals in the BEC is mainly a stimulated raman adiabatic process, namely STIRAP. The action process is shown in figure 3.
The initial irrotational state of the BEC atom is |0>,|l>And l-l>After the superimposed vortex light is emitted into the BEC atomic group, the atomsTwo Raman processes are formed by the cluster through an external source field, namely (omega) in FIG. 3+c) And (omega)-c),Ω±Is the frequency of the Labe oscillation, finally can form | +>And | ->The two vortex states are superimposed. Almost all particles stay at | +by adjusting parameters of vortex light and source light in a superposition state>And | ->Thus forming a stable material wave vortex superposition state.
(3) Angular rate sensing and detection of vortex stack states
The vortex superposed state gyroscope based on the cold atom BEC utilizes the Sagnac effect of vortex superposed state substance waves to realize sensitivity to angular velocity. Therefore, after generating a stable interference pattern, the phase information of the interference pattern needs to be detected to obtain the angular velocity of the system.
Through the orbital angular momentum transfer of the vortex optical rotation of the superposed state, a stable vortex superposed state substance wave can be formed in the BEC, and a stable standing wave is generated. The standing wave is reflected on the density distribution of the cold atoms, namely the density distribution of the cold atoms is distributed in a petal shape.
The interference pattern petals are divided into 4l regions gamma along theta 2m pi/4 l ( m 0, 1.. 4l-1)k( k 1, 2.., 4l), taking l 3 as an example, the division method is as shown in fig. 4. Definition I0As a total light intensity, I1Is 2l regions Fk(k ═ 1,3,.., 4l-1) total light intensity, I2Is 2l regions FkTotal light intensity of ( k 2, 4.., 4 l).
In the course of the experiment I1And I2Accumulated by time
Figure GDA0002156928860000051
Sum spatial accumulation
Figure GDA0002156928860000052
Thus obtaining the product.
Stacking vortex wave function:
Figure GDA0002156928860000053
wherein l is the vortex topological charge number, theta is the initial phase, and r and z are wave function position parameters.
The light intensity can thus be expressed as: i (r, θ, z) ═ 1+ cos (2l θ)]F (r, z), wherein
Figure GDA0002156928860000054
When z is equal to z0Total light intensity of0Satisfies the following conditions:
Figure GDA0002156928860000055
at the initial moment, in the case of a potential well not rotating, there are:
Figure GDA0002156928860000061
the same light intensity I can be obtained2
Figure GDA0002156928860000062
When the potential well rotates, the superposition state vortex wave function:
Figure GDA0002156928860000063
where Δ φ is the Sagnac phase.
In generalized relativity, the Sagnac phase Δ Φ of the vortex rotation is 2l Ω t, where l is the vortex topological charge number, i.e. the orbital angular momentum quantum number of the vortex rotation, t is the coherence time, and Ω is the rotation angular rate of the potential well.
The light intensity distribution is: i (r, θ, z) ═ 1+ cos (2l θ + Δ Φ) ] F (r, z)
Light intensity I1
Figure GDA0002156928860000071
Also, since the total light intensity is constant, the light intensity I2
Figure GDA0002156928860000072
BEC cross-sectional density distribution (z ═ z) in potential well0) Proportional to the light intensity distribution:
I(r,θ,z)∝ΣΩ(r,θ,t)={1+cos[2lθ+Δφ]}|Ψ(r,θ,z)|2(18)
Δ φ can be derived from the BEC cross-sectional density distribution, and is defined as the relative intensity variation obtained by spatial subtraction:
Figure GDA0002156928860000073
can obtain the product
Figure GDA0002156928860000074
So that δ can be used to derive the system angular rate.
Because the scattering of each atom for photons is fixed, after the detection light is added, the resonance absorption image is detected by the CCD, the phase is obtained by time accumulation and space accumulation, and the delta can be obtained by space subtraction as the angular rate of the system. Detecting the entire interference pattern such that the number of scattered photons NscGreatly increasing the sensitivity.
Compared with the prior art, the scheme of the invention has the main advantages that:
(1) the structure is simple, and no complex light path and a plurality of sensing and mechanical devices are provided; the mass is small, the used equipment is less, and the mass is small; the volume is small, the chip level can be achieved along with the development of the technology, and the applicable environment and conditions are wide;
(2) the time delay existing in the direct fitting image is effectively solved, the potential of realizing real-time detection is realized, and great convenience is provided for the phase information detection of the cold atom BEC vortex superposed state gyroscope;
(3) the method has high precision and larger promotion space, and the principle shows that the high precision of the scheme mainly comes from the space operation and time operation of the whole interference pattern in the detection process, so that the number of scattered photons is greatly increased, the sensitivity of angular rate sensitivity is improved, and the precision of the scheme is greatly promoted along with the development of the technology; on the other hand, due to the simple structure, the error source is greatly reduced, and the method has great advantages compared with the previous scheme.
Drawings
FIG. 1 is a schematic diagram of a phase detection method;
FIG. 2 is a schematic view of a "Mexico hat" potential well;
FIG. 3 is a schematic diagram of the effect of STIRAP (stimulated Raman adiabatic process);
FIG. 4 is a method of dividing an interference pattern simulation diagram;
FIG. 5 is a diagram of a BEC vortex stack state gyroscope;
fig. 6 is a block diagram of an absorption imaging system.
Wherein: 1 is a light beam with orbital angular momentum; 2 is a beam expander; 3 is a 1064nm 45-degree total reflection mirror; 4 is a computer with an image acquisition card; 5 is a BEC generating device; 6 is 100 times of oil immersion objective lens with large numerical aperture; 7 is a 1064nm 45-degree high-reflection mirror; 8 is a light filter; 9 is a CCD camera; 10 is cooling laser; the reference numeral 11 represents probe light; 12 is a polarization beam splitter prism; 13 is a lambda/4 wave plate; 14 is an ultra-high vacuum glass chamber (BEC vortex stack state gyroscope); 15 is a lambda/4 wave plate; 16 is a cooling laser; 17 is a polarization beam splitter prism; and 18 is a CCD camera.
Detailed description of the preferred embodiments
The implementation object of the invention is a vortex stack state gyroscope based on cold atom BEC, the specific implementation scheme is as shown in figure 1, and the specific implementation steps are as follows:
vortex stacked state gyroscopes based on cold atom BEC (as in figure 5) are sensitive to angular velocity using the Sagnac effect of vortex stacked state matter waves. Therefore, after generating a stable interference pattern, the phase information of the interference pattern needs to be detected to obtain the angular velocity of the system.
Through the orbital angular momentum transfer of the vortex optical rotation of the superposed state, a stable vortex superposed state substance wave can be formed in the BEC, and a stable standing wave is generated. The standing wave is reflected on the density distribution of the cold atoms, namely the density distribution of the cold atoms is distributed in a petal shape. Since each atom is fixed for photon scattering, after the addition of the detection light, the resonance absorption image is detected by a CCD camera (detection device as shown in fig. 6), the phases are obtained by temporal accumulation and spatial accumulation,and delta can be obtained by spatial subtraction as the angular rate of the system. Detecting the entire interference pattern such that the number of scattered photons NscGreatly increasing the sensitivity.
The interference pattern petals are divided into 4l regions gamma along theta 2m pi/4 l ( m 0, 1.. 4l-1)k( k 1, 2.., 4l), taking l 3 as an example, the division method is as shown in fig. 4. Definition I0As a total light intensity, I1Is 2l regions Fk(k ═ 1,3,.., 4l-1) total light intensity, I2Is 2l regions FkTotal light intensity of ( k 2, 4.., 4 l).
In the course of the experiment I1And I2Accumulated by time
Figure GDA0002156928860000091
Sum spatial accumulation
Figure GDA0002156928860000092
Thus obtaining the product.
Stacking vortex wave function:
Figure GDA0002156928860000093
wherein l is the vortex topological charge number, theta is the initial phase, and r and z are wave function position parameters.
The light intensity can thus be expressed as:
I(r,θ,z)=[1+cos(2lθ)]F(r,z) (20)
wherein
Figure GDA0002156928860000094
When z is equal to z0Total light intensity of0Satisfies the following conditions:
Figure GDA0002156928860000095
at the initial moment, in the case of a potential well not rotating, there are:
Figure GDA0002156928860000096
the same light intensity I can be obtained2
Figure GDA0002156928860000101
When the potential well rotates, the superposition state vortex wave function:
Figure GDA0002156928860000102
where Δ φ is the Sagnac phase.
In generalized relativity, the Sagnac phase delta phi of the vortex rotation is 2l omega t, wherein l is the orbital angular momentum quantum number of the vortex rotation, t is the coherence time, and omega is the rotation angular rate of a potential well.
The light intensity distribution is:
I(r,θ,z)=[1+cos(2lθ+Δφ)]F(r,z) (25)
light intensity I1
Figure GDA0002156928860000103
Also, since the total light intensity is constant, the light intensity I2
Figure GDA0002156928860000104
BEC cross-sectional density distribution (z ═ z) in potential well0) Proportional to the light intensity distribution:
I(r,θ,z)∝ΣΩ(r,θ,t)={1+cos[2lθ+Δφ]}|Ψ(r,θ,z)|2(28)
Δ φ can be derived from the BEC cross-sectional density distribution, and is defined as the relative intensity variation obtained by spatial subtraction:
Figure GDA0002156928860000105
the following can be obtained:
Figure GDA0002156928860000106
so that δ can be used to derive the system angular rate.
The foregoing is only a preferred embodiment of this invention and it should be noted that modifications can be made by those skilled in the art without departing from the principle of the invention and these modifications should also be considered as the protection scope of the invention. Those skilled in the art will appreciate that the details of the present invention not described in detail herein are well within the skill of those in the art.

Claims (2)

1. A phase detection method of a cold atom bose-einstein condensed vortex superposed gyroscope is characterized in that superposed vortex light is emitted into a bose-einstein condensed gas atomic group, so that the bose-einstein condensed atomic group obtains a certain orbital angular momentum to generate a stable vortex superposed state substance wave, and the bose-einstein condensed atomic group in a potential well is equivalent to a substance wave interference gyroscope; the method comprises the steps that stable interference patterns can be formed by the density distribution of atoms condensed by the bose-einstein, when a system rotates at a certain angular rate, a certain phase can be generated due to the Sagnac effect, the scattering of each atom to photons is fixed, after detection light is added, the whole resonance absorption image is detected through a charge coupling element, the scattering light intensity is obtained through spatial operation and time operation, the density distribution of the bose-einstein condensed atomic groups is calculated, phase information is further obtained, and relative light intensity change can be obtained through spatial subtraction to serve as gyro signals for calculating the angular rate of the system, so that the sensitivity to the angular rate of the system is realized.
2. The phase detection method of the cold atomic bose-einstein condensed vortex superposed gyroscope according to claim 1, which provides a method for obtaining scattered light intensity distribution by using spatial operation and time operation, calculating the density distribution of the bose-einstein condensed atoms and further calculating the angular rate of a system, and is characterized in that: sensitivity of angular velocity is realized by utilizing Sagnac effect of vortex superposed state substance wave, and interference pattern is detectedTo obtain the angular rate of the system; the interference pattern petal is divided into 4l regions gamma along theta 2m pi/4 l, m 0,1k1,2, 4l, defined as I0As a total light intensity, I1Is 2l regions FkTotal light intensity of 1,3, 4l-1, I2Is 2l regions FkTotal light intensity of 2, 4l, I during the experiment1And I2The following results are obtained by temporal accumulation (1) and spatial accumulation (2):
Figure FDA0002156928850000011
Figure FDA0002156928850000012
when the potential well rotates, the light intensity I can be obtained1And I2
Figure FDA0002156928850000013
When z is equal to z0Here, the bose-einstein condensation cross-section density distribution in the potential well is proportional to the light intensity distribution:
I(r,θ,z)∝ΣΩ(r,θ,t)={1+cos[2lθ+Δφ]}|Ψ(r,θ,z)|2(4)
wherein l is vortex topological charge number, theta is initial phase, r and z are wave function position parameters, delta phi is Sagnac phase, and psi (r, theta, z) is superposition state vortex wave function;
Δ φ can be derived from the Bose-Einstein condensation cross-section density distribution, and is defined as the relative intensity variation obtained by spatial subtraction:
Figure FDA0002156928850000021
obtaining δ can be used to derive the system angular rate:
Figure FDA0002156928850000022
because each atom is fixed for scattering photons, after detection light is added, a resonance absorption image is detected through a charge coupling element, phase information is obtained through time accumulation and space accumulation, delta can be obtained through space subtraction and used for calculating the angular rate of a system, and the whole interference pattern is detected to enable the number of scattered photons to be NscGreatly increasing the sensitivity.
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