CN112994691A - Preparation method of non-Hermite system spin compression state - Google Patents

Preparation method of non-Hermite system spin compression state Download PDF

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CN112994691A
CN112994691A CN202110201380.5A CN202110201380A CN112994691A CN 112994691 A CN112994691 A CN 112994691A CN 202110201380 A CN202110201380 A CN 202110201380A CN 112994691 A CN112994691 A CN 112994691A
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compression
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陈星�
张升康
薛潇博
赵环
王暖让
张璐
葛军
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Beijing Institute of Radio Metrology and Measurement
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Abstract

The invention discloses a preparation method of a non-Hermite system spin compression state, which comprises the following steps: providing a non-Hermite system having an energy level structure whose atomic spin state depends on atomic interaction; applying a trapping field to the non-hermite system to cause atoms to be bound in periodic trapping potential wells to obtain a double-occupied-state of the atoms; recording a spin fluctuation signal from the trapping potential well by changing atoms from a double-occupied state to a molecular state through photoassociation, and determining a change condition of spin compression from the spin fluctuation signal; and according to the change condition of the spin compression, measuring the spin compression property when the spin compression parameter is minimum to generate a spin compression state. The invention has the advantages that: the method is simple to realize, not only does not damage the spin compression state, but also maintains the stability of the spin compression effect, has an anti-intuitive physical effect, can be applied to the optical atomic frequency standard, and breaks through the measurement limit of a quantum system.

Description

Preparation method of non-Hermite system spin compression state
Technical Field
The invention belongs to the technical field of quantum precision measurement, and particularly relates to a preparation method of a non-Hermite system spin compression state.
Background
With the development of laser technology, the precise control of atoms, ions, molecules and other micro-particles is experimentally realized. The internal structure of the micro particles is stable, the micro particles are not easily interfered by the outside, the stable physical characteristics of the micro particles are used as the basis of precision measurement, and the measurement precision of the physical quantity is greatly improved. Based on the precise control technology, quantum precise measurement promotes the innovation of the metering technology, and plays a vital role in national social development, national economy and national defense industry.
The spin compression state is a multi-body entanglement state, and can be applied to entanglement state preparation of quantum information as a means of quantum entanglement.
Traditional atomic systems are represented by Hamiltonian of Hermite, open systems need to be represented by non-Hermite Hamiltonian due to interaction with the external environment, and systems represented by non-Hermite Hamiltonian are non-Hermite systems. The non-Hermite system is realized in an optical system and the like, and a plurality of new quantum phase changes, novel topological states and the like are discovered.
Generally speaking, a non-hermitian system represents decoherence, external environment interference and the like, can cause system dissipation, and leads to unstable state or even destroyed state, and the research of the non-hermitian system is closer to a practical system and is very important for stable state and maintenance in practical experiments. In seven basic physical quantities of a new international system, six international units except Moore are based on 'seconds', and an atomic frequency standard measures time by taking the frequency of transition of an atomic internal energy level as a frequency discrimination signal, so that an ultra-high-precision time standard is obtained. Optical frequency scale measurement uncertainties based on optical frequency bands have hitherto reached 10-19Magnitude, approaching the standard quantum limit. The compression effect can further break through the limit, and precision measurement with higher precision is realized, and the compression effect comprises optical compression, spin compression, phase compression and the like. In which spin compressionThe method is particularly suitable for quantum precision measurement by utilizing an atomic system, and the multi-component spin system represents the multi-energy-level atomic system. Therefore, it is highly desirable to have a non-hermitian system that generates spin compression state and maintains the spin compression effect and entanglement effect in stable existence.
Disclosure of Invention
The invention aims to provide a preparation method of a non-Hermite system spin compression state, which solves the problems of maintaining the stability of spin compression effect and entanglement effect.
In view of the above, the present invention provides a method for preparing a non-hermitian spin compression state, which is characterized by comprising:
providing a non-Hermite system having an energy level structure whose atomic spin state depends on atomic interaction;
applying a trapping field to the non-hermite system to cause atoms to be bound in periodic trapping potential wells to obtain a double-occupied-state of the atoms;
recording a spin fluctuation signal from the trapping potential well by changing atoms from a double-occupied state to a molecular state through photoassociation, and determining a change condition of spin compression from the spin fluctuation signal;
and according to the change condition of the spin compression, measuring the spin compression property when the spin compression parameter is minimum to generate a spin compression state.
Further, the spin compression parameter is a ratio of a minimum spin fluctuation perpendicular to an average spin direction to a spin average value.
Further, the non-hermite system is a three-dimensional cold atom system.
Further, applying a trapping field to the non-Hermite system, comprising: the trapping field is applied to the cold atoms in three directions, x, y and z.
Further, the energy level structure adopts a hyperfine energy level.
Further, the atomic spin states include a spin-up state, which is located at an upper level of the hyperfine level.
Further, the atomic spin states include a spin-down state, which is located at a lower energy level than the hyperfine energy level.
Further, measuring spin compression properties when the spin compression parameters are minimal includes: and determining experimental parameters for preparing the spin compression state.
Further, the experimental parameters for determining the preparation of the spin compression state are calculated by Matlab program.
Further, still include: the best experimental parameters for preparing the spin compression state are obtained by calculating the eigenstates.
The invention achieves the following significant beneficial effects:
the realization is simple, include: providing a non-Hermite system having an energy level structure whose atomic spin state depends on atomic interaction; applying a trapping field to the non-hermite system to cause atoms to be bound in periodic trapping potential wells to obtain a double-occupied-state of the atoms; recording a spin fluctuation signal from the trapping potential well by changing atoms from a double-occupied state to a molecular state through photoassociation, and determining a change condition of spin compression from the spin fluctuation signal; and according to the change condition of the spin compression, measuring the spin compression property when the spin compression parameter is minimum to generate a spin compression state. The method has the advantages that the self-spinning compression state is not damaged, the stability of the self-spinning compression effect is maintained, the counter-intuitive physical effect is realized, the method can be applied to the optical atomic frequency standard, and the measurement limit of a quantum system is broken through.
Drawings
FIG. 1 is a flow chart of a method for preparing a non-Hermite system spin-compression state according to the present invention;
FIG. 2 is a schematic diagram of an embodiment of the present invention in which the atoms are in a double-occupied state.
Detailed Description
The advantages and features of the present invention will become more fully apparent from the following description and appended claims, taken in conjunction with the accompanying drawings and detailed description of specific embodiments of the invention. It is to be noted that the drawings are in a very simplified form and are not to scale, which is intended merely for convenience and clarity in describing embodiments of the invention.
It should be noted that, for clarity of description of the present invention, various embodiments are specifically described to further illustrate different implementations of the present invention, wherein the embodiments are illustrative and not exhaustive. In addition, for simplicity of description, the contents mentioned in the previous embodiments are often omitted in the following embodiments, and therefore, the contents not mentioned in the following embodiments may be referred to the previous embodiments accordingly.
While the invention is amenable to various modifications and alternative forms, specifics thereof have been shown by way of example in the drawings and will be described in detail. It should be understood that the inventors do not intend to limit the invention to the particular embodiments described, but intend to protect all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the claims. The same meta-module part number may be used throughout the drawings to represent the same or similar parts.
Referring to fig. 1 and 2, a method for preparing a non-hermitian spin compression state according to the present invention comprises:
step S101, providing a non-Hermite system, wherein the non-Hermite system has an energy level structure of which the atomic spin state depends on atomic interaction;
step S102, applying a trapping potential field to the non-Hermite system to enable atoms to be bound in periodic trapping potential wells so as to obtain double-occupied states of the atoms;
step S103, changing atoms from a double-occupied state to a molecular state through optical association, recording a spin fluctuation signal from the trapping potential well, and determining the change condition of spin compression from the spin fluctuation signal;
and step S104, measuring the spin compression property when the spin compression parameter is minimum according to the change condition of the spin compression so as to generate a spin compression state.
In one embodiment of the present application, in particular, the spin compression parameter is a ratio of a minimum spin fluctuation perpendicular to an average spin direction to a spin average value.
In one embodiment of the present application, in particular, the non-hermite system is a three-dimensional cold atom system.
In one embodiment of the present application, specifically, applying a trapping field to the non-hermitian system comprises: the trapping field is applied to the cold atoms in three directions, x, y and z.
In one embodiment of the present application, in particular, the energy level structure employs hyperfine energy levels.
In one embodiment of the present application, the atomic spin states include, in particular, spin-up states, which are located at an upper level of the hyperfine energy level.
In one embodiment of the present application, the atomic spin states include, in particular, spin-down states, which are located at a lower energy level of the hyperfine energy level.
In one embodiment of the present application, specifically, measuring spin compression properties when the spin compression parameter is minimal includes: and determining experimental parameters for preparing the spin compression state.
In an embodiment of the present application, specifically, the experimental parameters for determining the preparation of the spin compression state are calculated by Matlab program.
In an embodiment of the present application, specifically, further comprising: the best experimental parameters for preparing the spin-compression state are obtained by calculating the eigenstates.
According to an aspect of the embodiments of the present invention, the non-Hermite system is a three-dimensional cold atom system, and strong trapping fields are applied to cold atoms in three directions to trap the atoms in a three-dimensional photo-lattice system. The present invention is exemplified by the x-direction in which atoms are bound to periodic trapping wells, with identical periodic trapping in both the y-and z-directions.
According to an aspect of an embodiment of the invention, the non-hermite system is a non-hermite interaction system, two atoms are converted from a double-occupied state to a molecular state through light association, and the two atoms are separated and converted to a ground state in a short time, and inelastic dissipation of two bodies is introduced, so that inelastic collision interaction between the non-hermite atoms is generated.
According to an aspect of an embodiment of the invention, the two-body contact interaction, i.e. the two-body elastic collision interaction, can be expressed as
Figure BDA0002947944100000051
Wherein g isabAb represents two hyperfine structural energy levels of atoms for elastic collision coefficient, and two aggregates are considered
Figure BDA0002947944100000052
According to an aspect of an embodiment of the invention, the elastic collision effect can be converted into a spin interaction as
Figure BDA0002947944100000053
Wherein χ is a real number, said SzRepresenting the difference in population occupancy between the two hyperfine energy levels. The non-Hermite interaction, i.e. the inelastic collision interaction, can be converted analogously to a spin interaction
Figure BDA0002947944100000054
And χ is an imaginary number.
According to an aspect of an embodiment of the invention, the steps of preparing the spin-compressed state of the invention comprise:
firstly, preparing atoms in a quantum coherent state (| ↓ >), wherein a spin-down state | ↓ > represents a lower energy level a of the particles in a hyperfine energy level, and a spin-up state | ↓ > represents an upper energy level b in the hyperfine energy level structure. Coherent state (| | ↓ >) represents that the probability that a single atom is at the hyperfine lower energy level a and the probability of the single atom at the hyperfine upper energy level b are the same, and a plurality of atoms are prepared in the coherent state and are represented as
Figure BDA0002947944100000055
Spin-down state | ↓>Is shown as
Figure BDA0002947944100000056
Spin-up state | × |>Is shown as
Figure BDA0002947944100000057
And the coherent state is represented as
Figure BDA0002947944100000058
After normalization
Figure BDA0002947944100000059
Thus the direct product of a plurality of atoms is
Figure BDA00029479441000000510
In the case of two atoms, the direct product state is
Figure BDA0002947944100000061
In particular, the method comprises the following steps of,
Figure BDA0002947944100000062
to represent
Figure BDA0002947944100000063
To represent
Figure BDA0002947944100000064
To represent
Figure BDA0002947944100000065
And
Figure BDA0002947944100000066
to represent
Figure BDA0002947944100000067
Then, the two atoms are converted from a double occupational state to a molecular state through photoassociation, and in a short time, the two atoms are separated and converted to a ground state, and the dissipation effect of the two bodies inelasticity is introduced, so that the two atoms are reduced to the spinning interaction of non-Hermite
Figure BDA0002947944100000068
And χ is an imaginary number. In order to compare with the spin compression effect under the traditional elastic collision, the real number is taken as chi, the spin compression effect when the imaginary number and the real number are taken as chi is calculated and compared respectively, and the advantage of the spin compression effect generated by a non-Hermite system is reflected through the comparison.
The time evolution operator is denoted e-iH'tCharacterized in that the system evolves from one state to another under the action of the non-Hermite spin interaction system, and the final state of evolution is expressed as
Figure BDA0002947944100000069
And a is a normalization coefficient. When χ is an imaginary number, it is written as χ ═ i χ', and the evolution final state is expressed as
Figure BDA00029479441000000610
When χ is a real number, it is expressed as χ ═ χ ″, and the evolution final state is expressed as χ ═ χ ″, here
Figure BDA00029479441000000611
The invention relates to a method for preparing a compoundzAnd SxIs substituted into the Hamiltonian, SxAnd SzDenotes the total spin, which is the total spin of a plurality of particles
Figure BDA00029479441000000612
And
Figure BDA00029479441000000613
definition of
Figure BDA00029479441000000614
And
Figure BDA00029479441000000615
is a pauli matrix and 1 is an identity matrix.
Taking two kinds of particles as an example,
Figure BDA00029479441000000616
and is
Figure BDA00029479441000000617
Thus, the total spin is represented as
Figure BDA0002947944100000071
Like
Figure BDA0002947944100000072
The Hamiltonian of spin interaction can be written as
Figure BDA0002947944100000073
A four-dimensional matrix. By calculation of
Figure BDA0002947944100000074
And
Figure BDA0002947944100000075
can obtain final state psitIn relation to time, the above psitThe invention adopts Matlab programming calculation.
The spin interaction system
Figure RE-GDA0003007115540000076
Taking x ═ i and x ═ 1 as examples of the non-hermite system and the hermite system respectively, adopting the steps to prepare the system in a coherent state, then carrying out kinetic evolution on the system, and calculating the spin compression property.
Spin compression is defined as
Figure BDA0002947944100000077
Wherein
Figure BDA0002947944100000078
Is the average value of the spin,
Figure BDA0002947944100000079
representing the minimum spin fluctuation perpendicular to the mean spin direction,
Figure BDA00029479441000000710
is the spin direction in which the average value lies,
Figure BDA00029479441000000711
perpendicular to the average spin direction.
When ξ ═ 1, the system is in coherent state. When xi<1, the system generates a spin compression state, and the spin compression state preparation is realized. Wherein
Figure BDA00029479441000000712
Is the average value of the spin,
Figure BDA00029479441000000713
representing the minimum spin fluctuation perpendicular to the mean spin direction,
Figure BDA00029479441000000714
is the spin direction in which the average value lies in,
then the average spin direction is
Figure BDA00029479441000000715
Then
Figure BDA00029479441000000716
The other two directions of the coordinate system are expressed as
Figure BDA0002947944100000081
And
Figure BDA0002947944100000082
and is
Figure BDA0002947944100000083
And
Figure BDA0002947944100000084
calculation method and
Figure BDA0002947944100000085
in a similar manner to that described above,
wherein theta and phi denote angles and
Figure BDA0002947944100000086
when in use<Sy>>0，
Figure BDA0002947944100000087
For a given wave function ψ, the spin average can be given by the equation<Sx,y,z>＝<ψ|Sx,y,z|ψ>The calculation results in that,
Figure BDA0002947944100000088
when in use<Sy＞≤0，
Figure BDA0002947944100000089
Is perpendicular to the mean spin direction, and
Figure BDA00029479441000000810
and
Figure BDA00029479441000000811
and (4) correlating.
Figure BDA00029479441000000812
Represents the minimum spin fluctuation perpendicular to the mean spin direction and
Figure BDA00029479441000000813
spin compression is thus expressed as
Figure BDA00029479441000000814
By the above psitThe average of the respective rotational components may be calculated,
<Sx,y,z>＝<ψt|Sx,y,z|ψt>since for the two-particle case, Sx,y,zIs a four-dimensional matrix, | ψt>Is a column vector and
Figure BDA00029479441000000815
is phit>The transposed vector is conjugated. The spin average is calculated as the operation of the matrix product.
Figure BDA00029479441000000816
The above calculation process is substituted into the definition of the spin compression parameter. And determining experimental parameters for preparing the spin compression state by theoretically researching the spin compression parameters, wherein the calculation is obtained by Matlab program calculation. Finally, the eigenstate psitAnd determining the optimal experimental parameters for generating the spin compression effect through theoretical calculation to obtain the optimal spin compression state. When t is 0, the system is in coherent state, where ξ is 1. Over time, for Hermite systems
Figure BDA0002947944100000091
Periodic spin compression propertiesAt some time point, the spin compression parameter xi is minimum, the spin compression effect is strongest at the moment, and the generated spin compression state has the highest corresponding measurement precision. non-Hermite systems with periodic changes in spin-compression properties compared to Hermite systems
Figure BDA0002947944100000092
Spin compression evolves over time toward an optimal spin compression state. The non-hermitian system finally reaches a stable spin compression state along with the time evolution, an anti-intuitive physical effect is generated, the spin compression effect is not damaged, and the non-hermitian system is easier to obtain and more stable compared with the hermitian system.
From the above description, it can be seen that the above-described embodiments of the present application achieve the following technical effects:
the realization is simple, include: providing a non-Hermite system having an energy level structure whose atomic spin state depends on atomic interaction; applying a trapping field to the non-hermite system to cause atoms to be bound in periodic trapping potential wells to obtain a double-occupied-state of the atoms; recording a spin fluctuation signal from the trapping potential well by changing atoms from a double-occupied state to a molecular state through photoassociation, and determining a change condition of spin compression from the spin fluctuation signal; and according to the change condition of the spin compression, measuring the spin compression property when the spin compression parameter is minimum to generate a spin compression state. The method has the advantages that the self-spinning compression state is not damaged, the stability of the self-spinning compression effect is maintained, the counter-intuitive physical effect is realized, the method can be applied to the optical atomic frequency standard, and the measurement limit of a quantum system is broken through.
Any other suitable modifications can be made according to the technical scheme and the conception of the invention. All such alternatives, modifications and improvements as would be obvious to one skilled in the art are intended to be included within the scope of the invention as defined by the appended claims.

Claims (10)

1. A method for preparing a non-Hermite system spin compression state is characterized by comprising the following steps:
providing a non-Hermite system having an energy level structure whose atomic spin state depends on atomic interaction;
applying a trapping field to the non-hermite system to cause atoms to be bound in periodic trapping potential wells to obtain a double-occupied-state of the atoms;
recording a spin fluctuation signal from the trapping potential well by changing atoms from a double-occupied state to a molecular state through photoassociation, and determining a change condition of spin compression from the spin fluctuation signal;
and according to the change condition of the spin compression, measuring the spin compression property when the spin compression parameter is minimum to generate a spin compression state.
2. The method for preparing a spin-compressed state of the non-hermite system according to claim 1, wherein the spin compression parameter is a ratio of a minimum spin fluctuation perpendicular to a mean spin direction to a spin mean value.
3. Method for the preparation of the spin-compacted state of the non-hermite system according to claim 1, characterized in that the non-hermite system is a three-dimensional cold atom system.
4. The method for preparing a spin-compressed state of a non-hermitian system according to claim 3, wherein applying a trapping field to said non-hermitian system comprises: the trapping field is applied to the cold atoms in three directions, x, y and z.
5. The method for preparing a non-hermite system spin-compression state according to claim 1, wherein the energy level structure adopts a hyperfine energy level.
6. The method for preparing a non-hermite system spin-compression state according to claim 5, wherein the atomic spin state includes a spin-up state, which is located at an upper level of a hyperfine level.
7. The method for preparing a non-hermite system spin-compression state according to claim 6, wherein the atomic spin state includes a spin-down state, which is located at a lower energy level of the hyperfine energy level.
8. The method for preparing a spin-compressed state of the non-hermite system according to claim 1, wherein measuring the spin compression property when the spin compression parameter is minimum comprises: and determining experimental parameters for preparing the spin compression state.
9. The method for preparing a spin-compressed state of a non-hermite system according to claim 8, wherein the experimental parameters for determining the spin-compressed state are calculated by Matlab program.
10. The method for preparing a non-hermitian spin compressed state according to claim 9, further comprising: the best experimental parameters for preparing the spin compression state are obtained by calculating the eigenstates.
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US20140354275A1 (en) * 2013-06-03 2014-12-04 The Trustees Of Princeton University Atomic magnetometry using pump-probe operation and multipass cells
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