CN111950143B - Casimir-Polder effect analysis method and system for cavity structure of hyperbolic super-structured material - Google Patents
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Abstract
The invention belongs to the technical field of quantum optics, and particularly relates to a Casimir-Polder effect analysis method of a cavity structure of a hyperbolic super-structure material, which comprises the following steps: establishing a model of a cavity structure of the hyperbolic super-structure material; determining electromagnetic properties of the hyperbolic metamaterial; calculating the energy level frequency offset of the resonance atoms and the energy level frequency offset of the non-resonance atoms; calculating resonance Casimir-Polder potential and non-resonance Casimir-Polder potential; calculating Casimir-Polder force of atoms in the cavity structure of the hyperbolic super-structure material; the Casimir-Polder potential and the Casimir-Polder force in the cavity structure of the hyperbolic super-structured material can be accurately analyzed, the reasons of the Casimir-Polder attractive force and the repulsive force generated by the cavity structure of the magnetic hyperbolic super-structured material and the cavity structure of the electric hyperbolic super-structured material can be analyzed, and the characteristics of the Casimir-Polder effect in the cavity structure of the hyperbolic super-structured material can be accurately analyzed by adjusting corresponding parameters.
Description
Technical Field
The invention belongs to the technical field of quantum optics, and particularly relates to a Casimir-Polder effect analysis method and system for a cavity structure of a hyperbolic super-structure material.
Background
The hyperbolic super-structure material is an artificial periodic structure material with orthogonal direction component abnormal dielectric constant tensor or magnetic permeability tensor, and can generate an electromagnetic wave mode of infinite wave vector in the material so as to generate a frequency curve such as hyperbola. Common hyperbolic super-structure material structures are metal dielectric layered structures, metal nanowire arrays embedded in dielectric bodies, network structures, and the like. The hyperbolic super-structure material is a multifunctional platform, can be used for designing devices exceeding the performance of conventional equipment in the fields of waveguide, imaging, sensing, quantum and thermal engineering, provides a unique electromagnetic mode by utilizing the basic wave scattering principle of engineering, and has wide application.
The Casimir-Polder effect, which is the interaction force between neutral polarizable atoms and a conductor plate, is generally considered as a result of reconstruction of the vacuum fluctuation pattern caused by the existence of boundaries, has been generalized to a variety of situations, such as the case where atoms are located near a non-dispersive and non-dissipative dielectric slab, which can be used to estimate the energy shift of atoms approaching a layered microstructure, as well as the energy shift of non-magnetic atoms having magnetic moments coupled with a quantifying magnetic field, and can be extended to the Casimir-Polder potential of a negative reflecting surface. The study of Casimir forces and Casimir-Polder forces has important roles in both theoretical and technical applications, such as nanophysics, chemical recognition of surface atoms by atomic force microscopy, and the like. In the prior art, the research on the Casimir-Polder effect is remained in an isotropic material, and the research result cannot meet the characteristics of the existing novel material. For this reason, improvements based on this are necessary.
Disclosure of Invention
Based on the above-mentioned drawbacks and deficiencies of the prior art, it is an object of the present invention to at least solve one or more of the above-mentioned problems of the prior art, in other words, to provide a solution to one or more of the above-mentioned needs.
In order to achieve the aim of the invention, the invention adopts the following technical scheme:
a Casimir-Polder effect analysis method of a cavity structure of a hyperbolic super-structured material comprises the following steps:
s1, establishing a model of a cavity structure of a hyperbolic super-structure material;
s2, determining electromagnetic properties of the hyperbolic super-structure material;
s3, calculating the energy level frequency offset of the resonance atoms and the energy level frequency offset of the non-resonance atoms;
s4, calculating resonance Casimir-Polder potential and non-resonance Casimir-Polder potential;
s5, calculating Casimir-Polder force of atoms in the cavity structure of the hyperbolic super-structure material.
As a preferred solution, the step S1 specifically includes: two identical hyperbolic super-structure material plates are selected and placed in a vacuum environment in parallel to form a hyperbolic super-structure material cavity structure, and a coordinate system is established by taking a left plate interface as a z-axis zero point; wherein the thickness of the hyperbolic super-structure material plate is d m The distance between two hyperbolic super-structure material plates is l, and the position vector r of atoms A ＝(0，0，z A ) The z-axis component being z A And z A ∈[0，l]。
Preferably, in the step S2, when the plate of the hyperbolic metamaterial is a magnetically anisotropic hyperbolic metamaterial (μ -HMM), the dielectric constant is ε, and the permeability tensor isWhen the hyperbolic super-structure material plate is an electric anisotropic hyperbolic super-structure material (epsilon-HMM), the dielectric constant tensor is +.>The magnetic permeability is mu.
As a preferable scheme, when the hyperbolic super-structure material is electrically anisotropic, the dielectric constant tensor is:
wherein,
f A representing the filling factor, f, of a non-magnetic metal in the microcells of the electrically anisotropic hyperbolic metamaterial plate A ＝d m /(d m +d d )，d d Is the thickness of the dielectric; omega shape m And gamma m The metal plasma frequency and the damping coefficient are respectively; omega shape d 、ω d And gamma d Dielectric plasma frequency, resonant frequency and damping coefficient, respectively; ω is the angular frequency of the light.
As a preferable scheme, when the hyperbolic super-structure material is magnetic anisotropic, the magnetic permeability tensor is:
wherein,
f B filling factor f of magnetic metamaterial in microcells representing magnetic anisotropic hyperbolic metamaterial plates B ＝d eff /(d eff +d d )，d eff And d d The thickness of the magnetic metamaterial and the nonmagnetic dielectric respectively; omega shape eff 、ω eff And gamma eff The plasma frequency, the resonance frequency and the damping coefficient of the magnetic metamaterial respectively.
As a preferred solution, the step S3 specifically includes: the equation of motion of the hessian burg by adopting an atomic inversion operator is obtained as follows:
wherein,for atomic inversion operators, ++>Is of the reduced Planck constant, d nk And d kn Is an electric dipole matrix element, < >>Generating operators for fields, < >>Is a field annihilation operator;
the real and imaginary parts of definition lattice Lin Zhangliang G are respectively:
wherein r' represents a source point position vector and r represents a field point position vector;
then the first time period of the first time period,
wherein δω nk Represents the frequency offset of the atomic energy level n under the influence of the atomic energy level k, G (1) Representing the scattering part of the green's function, P being the Cauchy principal value, mu 0 Is magnetic permeability in vacuum;
the non-resonant atomic energy level frequency offset is:
the resonant atomic energy level frequency offset is:
as a preferred solution, the step S4 specifically includes: green tensor G of cavity structure of hyperbolic super-structure material (1) The expression of the scattering moiety is:
wherein k is || Is the wave vector component, k, parallel to the surface in vacuum ⊥ Is a wave vector component along the z-axis direction, satisfying k ||2 +k ⊥2 ＝ω 2 /c 2 ，And->Representing the reflection coefficients of the left and right plates, respectively, p and s representing parallel and perpendicular polarizations, e σ+ And e σ′- Unit vectors respectively representing the incident wave polarization (σ') and the reflected wave polarization (σ);
the atomic dipole moment is:
the non-resonant Casimir-Polder potential is:
the resonance Casimir-Polder potential is:
preferably, in the step S5, the Casimir-Polder force in the cavity structure of the hyperbolic super-structure material includes Casimir-Polder force F of an excited atom 1 (z A ) And Casimir-Polder force F of ground state atoms 0 (z A )；
Casimir-Polder force of the ground state atom
Casimir-Polder force of the excited atom
The invention also provides a Casimir-Polder effect analysis system of the cavity structure of the hyperbolic super-structured material, which comprises an establishing module, a determining module, a first calculating module, a second calculating module and a third calculating module, wherein:
the building module is used for building a model of the cavity structure of the hyperbolic super-structure material;
a determining module for determining electromagnetic properties of the hyperbolic metamaterial;
the first calculation module is used for calculating the resonant atomic energy level frequency offset and the non-resonant atomic energy level frequency offset;
the second calculation module is used for calculating resonance Casimir-Polder potential and non-resonance Casimir-Polder potential;
and a third calculation module for calculating Casimir-Polder force of atoms in the cavity structure of the hyperbolic super-structure material.
Preferably, the building module comprises two identical plates of hyperbolic meta-structure material.
Compared with the prior art, the invention has the beneficial effects that:
1. the method can accurately analyze the Casimir-Polder potential and the Casimir-Polder force in the cavity structure of the hyperbolic super-structured material.
2. The invention can analyze the reason that Casimir-Polder attractive force and repulsive force are generated by the cavity structures of the magnetic hyperbolic super-structure material and the electric hyperbolic super-structure material.
3. According to the invention, the characteristics of the Casimir-Polder effect in the cavity structure of the hyperbolic super-structure material can be accurately analyzed by adjusting parameters of different filling factors and plate intervals.
Drawings
FIG. 1 is a computational flow diagram of a first embodiment of the present invention;
FIG. 2 is a cavity structure of a hyperbolic metamaterial according to a first embodiment of the present invention;
FIG. 3 is a schematic diagram of system I/O according to a first embodiment of the present invention;
FIG. 4 shows an embodiment of the invention in which atoms are located in a cavity structure formed by plates of an electrically anisotropic hyperbolic metamaterial, l=4λ 0 ，f A When=0.2, the resonance frequency is in the hyperbolic band, f A When the resonance frequency is in an elliptical frequency band and is in an excited state, the change curve of Casimir-Polder force is formed;
FIG. 5 shows an embodiment of the present invention in which atoms are located in a cavity structure formed by a plate of magnetically anisotropic hyperbolic metamaterial, l=4λ 0 ，f B When=0.2, the resonance frequency is in the hyperbolic band, f B When the resonance frequency is in an elliptical frequency band and is in an excited state, the change curve of Casimir-Polder force is formed;
FIG. 6 shows an excited atom of the first embodiment of the present invention at l=2λ 0 A change curve of Casimir-Polder force;
FIG. 7 shows an excited atom of the first embodiment of the present invention at l=4λ 0 A change curve of Casimir-Polder force;
FIG. 8 shows an atomic layer in an initially excited state according to a first embodiment of the present inventionl＝4λ 0 When the magnetic anisotropic hyperbolic super-constructed material plate is used, the filling factor f is changed B A profile of the Casimir-Polder force experienced by an atom.
Detailed Description
In order to more clearly illustrate the embodiments of the present invention, specific embodiments of the present invention will be described below with reference to the accompanying drawings. It is evident that the drawings in the following description are only examples of the invention, from which other drawings and other embodiments can be obtained by a person skilled in the art without inventive effort.
Embodiment one:
the embodiment provides a Casimir-Polder effect analysis method of a cavity structure of a hyperbolic super-structure material, which is shown in figure 1 and comprises the following steps:
s1, establishing a model of a cavity structure of a hyperbolic super-structure material;
s2, determining electromagnetic properties of the hyperbolic super-structure material;
s3, calculating the energy level frequency offset of the resonance atoms and the energy level frequency offset of the non-resonance atoms;
s4, calculating resonance Casimir-Polder potential and non-resonance Casimir-Polder potential;
s5, calculating Casimir-Polder force of atoms in the cavity structure of the hyperbolic super-structure material.
The step S1 specifically comprises the following steps: two identical hyperbolic super-structure material plates are selected and placed in a vacuum environment in parallel to form a hyperbolic super-structure material cavity structure, and a coordinate system is established by taking a left plate interface as a z-axis zero point; wherein the thickness of the hyperbolic super-structure material plate is d m The distance between two hyperbolic super-structure material plates is l, and the position vector r of atoms A ＝(0,0,z A ) The z-axis component being z A And z A ∈[0,l]。
In step S2, when the plate of the hyperbolic super-structured material is a magnetic anisotropic hyperbolic super-structured material (mu-HMM), the dielectric constant is epsilon and the magnetic permeability tensor isThe double curveWhen the plate of the super-structured material is an electrically anisotropic hyperbolic super-structured material (epsilon-HMM), the dielectric constant tensor is +.>The magnetic permeability is mu.
When the hyperbolic super-structure material plate is an electric anisotropic hyperbolic super-structure material, the dielectric constant tensor is anisotropic, namely the dielectric constant tensor is:
all components of the electrically anisotropic hyperbolic metamaterial have chromatic dispersion and are described by a Drude-Lorentz model, and the diagonal parameters are as follows:
in the formulas (1) and (2), f A Representing the filling factor, f, of a non-magnetic metal in the microcells of the electrically anisotropic hyperbolic metamaterial plate A ＝d m /(d m +d d )，d d Is the thickness of the dielectric; omega shape m And gamma m The metal plasma frequency and the damping coefficient are respectively; omega shape d 、ω d And gamma d Dielectric plasma frequency, resonant frequency and damping coefficient, respectively; ω is the angular frequency of the light.
When the hyperbolic super-structure material plate is a magnetic anisotropic hyperbolic super-structure material, the dielectric constant tensor is isotropic, namely the magnetic permeability tensor is:
all components of the magnetically anisotropic hyperbolic metamaterial have dispersion, and are described by a Drude-Lorentz model, and diagonal parameters are as follows:
in the formulas (3) and (4), f B Filling factor f of magnetic metamaterial in micro unit representing that hyperbolic metamaterial plate is magnetic anisotropic hyperbolic metamaterial B ＝d eff /(d eff +d d )，d eff And d d The thickness of the magnetic metamaterial and the nonmagnetic dielectric respectively; omega shape eff 、ω eff And gamma eff The plasma frequency, the resonance frequency and the damping coefficient of the magnetic metamaterial respectively.
The step S3 specifically comprises the following steps: the internal dynamics of an atom can be described by the hessian motion equation of an atomic inversion operator, which is extended to a non-reciprocal medium and written as an expression that evolves over time:
wherein,for atomic inversion operators, ++>Is of the reduced Planck constant, d nk And d kn Is an electric dipole matrix element, < >>Generating operators for fields, < >>Is field annihilationAn operator. Assuming that the atom has no transitions, the differential equation set for the expected value of the atom flip operator may be decoupled. Furthermore, the atoms are unpolarized in each of their energy eigenstates, i.e. +.>This is because of the selection rules of atoms. Because of these assumptions, rapidly oscillating off-diagonal flip operators are decoupled from each other from the off-oscillating diagonal flip operators.
The real and imaginary parts of definition lattice Lin Zhangliang G are respectively:
wherein r' represents a source point position vector and r represents a field point position vector;
the method can be characterized by comprising the following steps:
d nk ·Im[G(r A ,r A ,ω)]·d kn ＝Im[d nk ·G(r A ,r A ,ω)·d kn ]and
d kn ·Im[G Τ (r A ,r A ,ω)]·d nk ＝Im[d nk ·G(r A ,r A ,ω)·d kn ]equal and real.
Further solving:
wherein δω nk Represents the frequency offset of the atomic energy level n under the influence of the atomic energy level k, G (1) Representing the scattering part of the green's function, P being the Cauchy principal value, mu 0 Is magnetic permeability in vacuum;
because lim |ω|→0 G (1) (r,r′,ω)ω 2 /c 2 =0, the green tensor G is subjected to a virtual frequency transformation ω→iζ, and the non-resonant atomic energy level frequency offset is derived along the virtual axis portion:
the contribution of the resonance part and the spontaneous emission and transition frequency of real photonsIn relation to, when->Obtaining the atomic energy level frequency offset at resonance:
the step S4 specifically comprises the following steps: for the calculation of the Casimir-Polder forces to which atoms are subjected in the cavity structure of the doubly curved metamaterial, it is necessary to shift the resonant and non-resonant atomic energy level frequency offset δω across all subscripts k nk Summing to obtain Casimir-Polder potential, and obtaining Casimir-Polder force by carrying out position deviation on the Casimir-Polder potential, wherein the Green tensor G of the cavity structure of the hyperbolic super-structured material is obtained (1) The expression of the scattering moiety is:
wherein k is || Is the wave vector component, k, parallel to the surface in vacuum ⊥ Is a wave vector component along the z-axis direction, satisfying k ||2 +k ⊥2 ＝ω 2 /c 2 ，And->Representing the reflection coefficients of the left and right plates, respectively, p and s representing parallel and perpendicular polarizations, e σ+ And e σ′- Unit vectors respectively representing the incident wave polarization (σ') and the reflected wave polarization (σ);
in order to effectively calculate the Casimir-Polder force of atoms in a cavity structure formed by an anisotropic material, the atomic dipole moment is selected as follows:
the non-resonant Casimir-Polder potential is:
the resonance Casimir-Polder potential is:
substituting the green tensor scattering part and dipole moment of the cavity structure of the hyperbolic super-structured material into the formulas (14) and (15) to obtain the non-resonance Casimir-Polder potential and resonance Casimir-Polder potential of the cavity structure formed by the anisotropic material, wherein the non-resonance potential can be divided into two partsThe following is simplified for the two non-resonant parts and the resonant part respectively:
in step S5, the derivative of the Casimir-Polder potential with respect to position is that the Casimir-Polder forces of the atoms in the cavity structure of the hyperbolic metamaterial are caused by the self energy level shift of the atoms. Known F 1 (z A ) And F 0 (z A ) Respectively representing Casimir-Polder forces exerted by excited state atoms and ground state atoms positioned in front of a hyperbolic super-structure material plate;
the Casimir-Polder force of the ground state atom:
Casimir-Polder force of the excited atom:
Casimir-Polder force F to which the ground state atom is subjected 0 (z A ) Including only non-resonant portions F nres (z A ) And the Casimir-Polder force F to which the excited atom is subjected 1 (z A ) Comprising a resonance part F res (z A ) And a non-resonant portion F nres (z A ) Wherein the non-resonant portion is a dispersive portion of force.
And finally, carrying out numerical calculation according to the obtained expression.
In this embodiment, as shown in fig. 3, parameters of the hyperbolic super-structure material are input at the a end. And inputting the distance parameters of the two hyperbolic super-constructed material plates at the end B. And inputting the filling factor parameters at the C end. And outputting the relation between the Casimir-Polder force and the parameters of the hyperbolic super-constructed material at the D end. And outputting the relation between the Casimir-Polder force and the distance between two hyperbolic super-constructed material plates at the E end. And outputting the relation between the Casimir-Polder force and the filling factor parameter at the F end.
In this embodiment, in FIG. 4, atoms are located in a cavity formed by an electrically anisotropic sheet of hyperbolic metamaterial having a thickness d M ＝0.5λ 0 The spacing l=4λ between two parallel plates of electrically anisotropic hyperbolic metamaterial 0 Magnetic permeability μ=1, transition frequencyThe filling factor parameters are f respectively A ＝0.2，f A In the case of =0.3, the change trend of Casimir-Polder force when the atom is initially in the excited state was obtained.
In FIG. 5, atoms are located in a cavity formed by a sheet of magnetically anisotropic hyperbolic metamaterial having a thickness d M ＝0.5λ 0 The spacing l=4λ between two parallel plates of magnetically anisotropic hyperbolic metamaterial 0 Dielectric constant epsilon=1.37, transition frequencyThe filling factor parameters are f respectively A ＝0.2，f A In the case of =0.3, the change trend of Casimir-Polder force when the atom is initially in the excited state was obtained. Comparing fig. 4 and 5, the effect of two different materials on the Casimir-Polder effect can be obtained.
In FIG. 6, the thickness d of the sheet of hyperbolic metamaterial is set M ＝0.5λ 0 Resonant frequency ofLet the distance between two parallel hyperbolic super-constructed material plates be l=2λ 0 In the figure, both the electrically anisotropic hyperbolic metamaterial plate with magnetic permeability μ=1 and the magnetically anisotropic hyperbolic metamaterial plate with dielectric constant ε=1.37 are set at the same time, and the variation trend of the Casimir-Polder force is obtained.
In FIG. 7, the thickness d of the sheet of hyperbolic metamaterial is set M ＝0.5λ 0 Resonant frequency ofThe distance between two parallel hyperbolic super-structure material plates is l=4λ 0 In the figure, both the electrically anisotropic hyperbolic metamaterial plate with magnetic permeability μ=1 and the magnetically anisotropic hyperbolic metamaterial plate with dielectric constant ε=1.37 are set at the same time, and the variation trend of the Casimir-Polder force is obtained. Comparing fig. 6 and fig. 7, the Casimir-Polder effect variation characteristics in the cavity structure can be obtained under different plate spacing parameters.
In FIG. 8, a hyperbolic metamaterial plate thickness d is set M ＝0.5λ 0 The spacing between two parallel plates of hyperbolic metamaterial l=2λ 0 Resonant frequency ofFor a cavity formed by a magnetic anisotropic hyperbolic super-structure material plate, the filling factor f is set B = 0.2,0.3,0.4,0.5, the effect of different fill factors on Casimir-Polder effect can be obtained.
Compared with the prior art, the invention has the following advantages:
1. the method can accurately analyze the Casimir-Polder potential and the Casimir-Polder force in the cavity structure of the hyperbolic super-structured material.
2. The invention can analyze the reason that Casimir-Polder attractive force and repulsive force are generated by the cavity structures of the magnetic hyperbolic super-structure material and the electric hyperbolic super-structure material.
3. According to the invention, the characteristics of the Casimir-Polder effect in the cavity structure of the hyperbolic super-structure material can be accurately analyzed by adjusting parameters of different filling factors and plate intervals.
Correspondingly, as shown in fig. 2 to 3, the embodiment further provides a Casimir-Polder effect analysis system of a cavity structure of a hyperbolic super-structure material, which comprises an establishing module, a determining module, a first calculating module, a second calculating module and a third calculating module, wherein:
the building module is used for building a model of the cavity structure of the hyperbolic super-structure material;
a determining module for determining electromagnetic properties of the hyperbolic metamaterial;
the first calculation module is used for calculating the resonant atomic energy level frequency offset and the non-resonant atomic energy level frequency offset;
the second calculation module is used for calculating resonance Casimir-Polder potential and non-resonance Casimir-Polder potential;
and a third calculation module for calculating Casimir-Polder force of atoms in the cavity structure of the hyperbolic super-structure material.
The building block comprises two identical plates of hyperbolic meta-structure material.
The foregoing is only illustrative of the preferred embodiments and principles of the present invention, and changes in specific embodiments will occur to those skilled in the art upon consideration of the teachings provided herein, and such changes are intended to be included within the scope of the invention as defined by the claims.
Claims (10)
1. The Casimir-Polder effect analysis method of the cavity structure of the hyperbolic super-structured material is characterized by comprising the following steps of:
s1, establishing a model of a cavity structure of a hyperbolic super-structure material;
s2, determining electromagnetic properties of the hyperbolic super-structure material;
s3, calculating the energy level frequency offset of the resonance atoms and the energy level frequency offset of the non-resonance atoms;
s4, calculating resonance Casimir-Polder potential and non-resonance Casimir-Polder potential;
s5, calculating Casimir-Polder force of atoms in the cavity structure of the hyperbolic super-structure material.
2. The Casimir-Polder effect analysis method of a cavity structure of a hyperbolic super-structured material according to claim 1, wherein the step S1 is specifically: two identical hyperbolic super-structure material plates are selected and placed in a vacuum environment in parallel to form a hyperbolic super-structure material cavity structure, and a coordinate system is established by taking a left plate interface as a z-axis zero point; wherein the hyperbolic supercurveThe thickness of the structural material plate is d m The distance between two hyperbolic super-structure material plates is l, and the position vector r of atoms A ＝(0,0,z A ) The z-axis component being z A And z A ∈[0,l]。
3. The method for analyzing the Casimir-Polder effect of a cavity structure of a hyperbolic metamaterial according to claim 2, wherein in the step S2, when the plate of the hyperbolic metamaterial is a magnetically anisotropic hyperbolic metamaterial, the dielectric constant is epsilon and the magnetic permeability tensor is epsilonWhen the hyperbolic super-structure material plate is an electric anisotropic hyperbolic super-structure material, the dielectric constant tensor is +.>The magnetic permeability is mu.
4. A Casimir-Polder effect analysis method according to claim 3, wherein the dielectric constant tensor of the electrically anisotropic hyperbolic metamaterial is:
wherein,
f A representing the filling factor, f, of a non-magnetic metal in the microcells of the electrically anisotropic hyperbolic metamaterial plate A ＝d m /(d m +d d )，d d Is the thickness of the dielectric; omega shape m And gamma m The metal plasma frequency and the damping coefficient are respectively; omega shape d 、ω d And gamma d Dielectric plasma frequency, resonant frequency and damping coefficient, respectively; ω is the angular frequency of the light.
5. The method for analyzing the Casimir-Polder effect of a cavity structure of a hyperbolic super-structure according to claim 4, wherein the magnetic permeability tensor of the magnetically anisotropic hyperbolic super-structure material is:
wherein,
f B filling factor f of magnetic metamaterial in microcells representing magnetic anisotropic hyperbolic metamaterial plates B ＝d eff /(d eff +d d )，d eff Is the thickness of the magnetic metamaterial; omega shape eff 、ω eff And gamma eff The plasma frequency, the resonance frequency and the damping coefficient of the magnetic metamaterial respectively.
6. The method for analyzing the Casimir-Polder effect of the cavity structure of the hyperbolic metamaterial according to claim 5, wherein the step S3 specifically comprises: the equation of motion of the hessian burg by adopting an atomic inversion operator is obtained as follows:
wherein,for atomic inversion operators, ++>Is of the reduced Planck constant, d nk And d kn Is an electric dipole matrix element, < >>Generating operators for fields, < >>Is a field annihilation operator;
the real and imaginary parts of definition lattice Lin Zhangliang G are respectively:
wherein r' represents a source point position vector and r represents a field point position vector;
then the first time period of the first time period,
wherein δω nk Represents the frequency offset of the atomic energy level n under the influence of the atomic energy level k, G (1) Representing the scattering part of the green's function, P being the Cauchy principal value, mu 0 Is magnetic permeability in vacuum;
the non-resonant atomic energy level frequency offset is:
the resonant atomic energy level frequency offset is:
7. the Casimir-Polder effect analysis method of a cavity structure of a hyperbolic super-structure material according to claim 6, wherein the step S4 specifically includes: green tensor G of cavity structure of hyperbolic super-structure material (1) The expression of the scattering moiety is:
wherein k is || Is the wave vector component, k, parallel to the surface in vacuum ⊥ Is a wave vector component along the z-axis direction, satisfying k ||2 +k ⊥2 ＝ω 2 /c 2 ，And->Representing the reflection coefficients of the left and right plates, respectively, p and s representing parallel and perpendicular polarizations, e σ+ And e σ′- Unit vectors respectively representing the incident wave polarization (σ') and the reflected wave polarization (σ);
the atomic dipole moment is:
the non-resonant Casimir-Polder potential is:
the resonance Casimir-Polder potential is:
8. the method for analyzing the Casimir-Polder effect of a cavity structure of a hyperbolic metamaterial according to claim 7, wherein in the step S5, the Casimir-Polder force in the cavity structure of the hyperbolic metamaterial comprises Casimir-Polder force F of an excited atom 1 (z A ) And Casimir-Polder force F of ground state atoms 0 (z A )；
Casimir-Polder force of the ground state atom
Casimir-Polder force of the excited atom
9. The Casimir-Polder effect analysis system of the cavity structure of the hyperbolic super-structured material is characterized by comprising an establishing module, a determining module, a first calculating module, a second calculating module and a third calculating module, wherein:
the building module is used for building a model of the cavity structure of the hyperbolic super-structure material;
a determining module for determining electromagnetic properties of the hyperbolic metamaterial;
the first calculation module is used for calculating the resonant atomic energy level frequency offset and the non-resonant atomic energy level frequency offset;
the second calculation module is used for calculating resonance Casimir-Polder potential and non-resonance Casimir-Polder potential;
and a third calculation module for calculating Casimir-Polder force of atoms in the cavity structure of the hyperbolic super-structure material.
10. The Casimir-Polder effect analysis system of a cavity structure of a hyperbolic metamaterial according to claim 9, wherein the building block comprises two identical plates of the hyperbolic metamaterial.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| WO2010077464A1 (en) * | 2008-12-08 | 2010-07-08 | The Boeing Company | System and method for reducing viscous force between a fluid and a surface |
| CN111125900A (en) * | 2019-12-19 | 2020-05-08 | 杭州电子科技大学 | Method and system for calculating Casimir action force of anisotropic ferrite three-layer structure |
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2010077464A1 (en) * | 2008-12-08 | 2010-07-08 | The Boeing Company | System and method for reducing viscous force between a fluid and a surface |
| CN111125900A (en) * | 2019-12-19 | 2020-05-08 | 杭州电子科技大学 | Method and system for calculating Casimir action force of anisotropic ferrite three-layer structure |
| CN111145837A (en) * | 2019-12-19 | 2020-05-12 | 杭州电子科技大学 | Method and system for calculating Casimir torque of anisotropic ferrite three-layer structure |
Non-Patent Citations (4)
| Title |
|---|
| Casimir-Polder力对左手材料板附近的原子的动力学作用;许静平 等;物理学报;第64卷(第23期);第122-129页 * |
| Enhancement of long-distance Casimir-Polder interaction between an excited atom and a cavity made of metamaterials;Wei Fang 等;Optics Express;第27卷(第26期);第37753-37770页 * |
| Super-Coulombic atom–atom interactions in hyperbolic media;Cristian L. Cortes 等;Nature Communications;第1-8页 * |
| 复合电磁材料的Casimir效应;孙坚;中国博士学位论文全文数据库（基础科学辑）;第A005-61页 * |
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