Phononic crystal structure and sensor
The phononic crystal structure addresses quantum spin interactions with phonons by creating a band gap in the phonon dispersion relation, enhancing excitation efficiency and reducing blurring, thus improving measurement sensitivity.
Patent Information
- Application Number
- JP2024003485
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2024-01-12
- Publication Date
- 2025-07-25
AI Technical Summary
The energy states of quantum spins are quantized but suffer from blurring due to disturbances, particularly from interactions with lattice vibrations (phonons), leading to decreased excitation efficiency and relaxation of excited states.
A phononic crystal structure with a periodic arrangement of unit cells, featuring non-equivalent sub-lattices and uneven mass distribution, creates a band gap in the phonon dispersion relation, isolating the quantum spin's excitation frequency, thereby reducing interactions with phonons and suppressing relaxation.
This configuration enhances excitation efficiency and reduces energy spectrum width, improving measurement sensitivity and accuracy by minimizing blurring and relaxation of quantum spins.
Smart Images
Figure 2025109537000001_ABST
Abstract
Description
Technical Field
[0001] This specification relates to a phononic crystal structure and a sensor.
Background Art
[0002] Magnetic field sensing by optically detected magnetic resonance (ODMR) using a material having a quantum spin inside is known. Non-Patent Document 1 discloses diamond having an NV-color center as a material having a quantum spin.
Prior Art Documents
Non-Patent Documents
[0003]
Non-Patent Document 1
Summary of the Invention
Problems to be Solved by the Invention
[0004] The energy states of quantum spins are quantized. However, due to disturbances, the energy spectrum peaks of quantum spins have a width, resulting in blurring in the measurement system. Also, since the excited state relaxes, the excitation efficiency by microwaves decreases. One of these main factors is the interaction between quantum spins and lattice vibrations (phonons).
Means for Solving the Problems
[0005] The phononic crystal structure disclosed in this specification is composed of a material with a quantum spin in which a quantum state is realized in a defect. The phononic crystal structure has a periodic structure formed by combining a plurality of unit cells, which are the smallest repeating structures.
[0006] According to the above structure, due to the periodicity of the lattice, a band gap can be generated in the frequency of the phonon dispersion relation. Therefore, for example, by including the excitation frequency of the quantum spin in the band gap, the interaction between the quantum spin and the phonon can be suppressed. Since the relaxation of the quantum spin can be suppressed, it becomes possible to increase the excitation efficiency. Also, since the energy spectrum width of the quantum spin can be reduced, it becomes possible to suppress the blurring generated in the measurement system.
Brief Description of the Drawings
[0007]
Figure 1
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Modes for Carrying Out the Invention
Examples
[0008] (Overview of the Phononic Crystal Structure) The phononic crystal structure is composed of a material with a quantum spin in which a quantum state is realized in a defect. Various materials can be used as the material with a quantum spin. For example, at least one of diamond, SiC, hBN, GaN, etc. may be used.
[0009] In addition, the phononic crystal structure has a periodic structure formed by combining a plurality of unit cells. The unit cell is the smallest repeating structure. Various structures can be used for the periodic structure. For example, it may be a periodic structure of a two-dimensional structure or a three-dimensional structure.
[0010] FIG. 1 shows a top view of the phononic crystal structure 20 in this embodiment. In this embodiment, the case where diamond is used as the material of the phononic crystal structure 20 will be described. As a representative example of the quantum spin realized in diamond, there is an NV-color center (NV center). The NV center is a composite defect in which one carbon atom is replaced by nitrogen and is connected to an adjacent vacancy. Details of the NV center will be described later.
[0011] Also, in this embodiment, the case where a honeycomb structure of a two-dimensional structure is used as the periodic structure will be described. The phononic crystal structure 20 includes a plurality of unit cells UC. By combining a plurality of unit cells UC, a honeycomb structure in which hexagons are arranged without gaps is formed. The hexagon may be a regular hexagon in which the lengths of all sides are equal, or a hexagon stretched in one direction.
[0012] Figure 2 shows an enlarged top view of a representative unit cell UC. Figure 3 shows a perspective view of a representative unit cell UC. The unit cell UC includes vertices A1, A2, midpoints M1a, M1b, M2a, M2b, and a center CP. The vertices A1, A2 correspond to the vertices of a hexagon. The midpoints M1a, M1b, M2a, M2b correspond to the midpoints of the sides of the hexagon. The center CP corresponds to the midpoint of the side connecting vertex A1 and vertex A2. The midpoints M1a and M1b, and the midpoints M2a and M2b are point-symmetric with respect to the center CP. Also, vertices A1 and A2 are point-symmetric with respect to the center CP. Therefore, the center CP is the center point of symmetry. That is, the hexagon of the unit cell UC has a shape that is point-symmetric with respect to the center CP.
[0013] The midpoint M1a and the midpoint M2a are connected by periodic boundary conditions. Also, the midpoint M1b and the midpoint M2b are connected by periodic boundary conditions. As a result, as shown in Figure 1, a honeycomb structure in which hexagons are repeatedly arranged is formed.
[0014] Here, consider a center line BL passing through the center CP. The unit cell UC can be divided by the center line BL into a plurality of sub-lattices SC1 and SC2. The sub-lattices SC1 and SC2 constitute a periodic structure existing within the unit cell UC.
[0015] The sub-lattice SC1 includes three beams B1a, B1b, B1c. The beam B1a connects the vertex A1 and the midpoint M1a. The beam B1b connects the vertex A1 and the midpoint M1b. The beam B1c connects the vertex A1 and the center CP.
[0016] The sub-lattice SC2 includes three beams B2a, B2b, B2c and a mass portion MA. The mass portion MA is a circular portion centered at the vertex A2 and having a radius R. The beam B2a connects the mass portion MA and the midpoint M2a. The beam B2b connects the mass portion MA and the midpoint M2b. The beam B2c connects the mass portion MA and the center CP.
[0017] The unit cell UC has at least one of the distribution of the effective spring constant and the distribution of the mass component being non-uniform with respect to the center CP. In this embodiment, the distribution of the mass component of the unit cell UC is non-uniform with respect to the center CP of the unit cell UC. Specifically, the mass portion MA is not arranged in the sub-cell SC1, but the mass portion MA is arranged in the sub-cell SC2. Thereby, an inequality is given such that the mass component of the sub-cell SC2 is larger than that of the sub-cell SC1.
[0018] (Structure of the ODMR microscope 1) Fig. 4 shows a schematic structure of an ODMR (Optically Detected Magnetic Resonance) microscope 1 provided with the phononic crystal structure 20 of this embodiment. The ODMR microscope 1 includes a stage 10, a sample 11, a probe stage 12, a microwave antenna 13, a coil 14, a phononic crystal structure 20, a laser light source 31, a mirror 32, a lens 33, and a camera 34.
[0019] The sample 11 is arranged on the stage 10. The base end of the phononic crystal structure 20 is fixed to the probe stage 12, and the tip is in a floating state in the air. The tip of the phononic crystal structure 20 is arranged close to or in contact with the upper side of the sample 11. The phononic crystal structure 20 can be scanned over the sample 11 by a control mechanism (not shown). An NV center 20n is provided at the tip of the phononic crystal structure 20. The NV center 20n is irradiated with microwaves around 3 GHz while scanning the frequency by the microwave antenna 13. An external magnetic field is applied to the NV center 20n by the coil 14. Thereby, the electron spin of the NV center 20n is controlled.
[0020] The laser light LA emitted from the laser light source 31 is irradiated onto the NV center 20n by the mirror 32 and the lens 33. The red NV fluorescence NF emitted from the NV center 20n is condensed by the lens 33 and condensed onto the camera 34 via the mirror 32. The Zeeman splitting width measured by the camera 34 is proportional to the magnetic field felt by the NV center 20n. Therefore, the magnetic field can be measured from the splitting width. That is, the applied magnetic field can be calculated from the energy difference (frequency difference) between the two peaks of the resonance spectrum.
[0021] (Problem) The quantum spin typified by the diamond NV center has spin 1 and a Hamiltonian D(S Z ) 2 described by. D is positive. The spin state |0> has an energy eigenvalue of 0. The spin states |±1> have an energy eigenvalue of D and are degenerate.
[0022] In the above-described ODMR microscope 1, when there is no external magnetic field, the spin states |±1> are degenerate. On the other hand, when an external magnetic field is applied, the spin states |±1> are non-degenerate due to Zeeman splitting. In the ODMR microscope 1, since the magnitude of the Zeeman splitting can be measured, the strength of the magnetic field can be detected.
[0023] As shown in FIG. 5, the energy states of the quantum spin are quantized. However, the energy states of the states |0> and |±1> are blurred due to disturbances. In FIG. 5, for clarity, the blurring of the energy states is shown by a gray gradation. Also, as shown in FIG. 6, the state excited to |±1> relaxes to |0> due to interaction with other degrees of freedom. The relaxation factors are various, such as temperature and impurities inside and outside the crystal, but one of the fundamental factors is the interaction with lattice vibrations (phonons). The interaction with phonons is an effect that exists even when the crystal has no impurities at all at absolute zero. The interaction with phonons is approximately represented by the following equation (1). [Number] Here, each symbol is: γ: spin relaxation rate, δ: Dirac delta function, λ q : spin-phonon interaction coefficient, ω q : phonon dispersion relation, q: wave number or polarization.
[0024] (Solution means) In the above equation (1), the spin relaxation rate γ corresponds to the reciprocal of the lifetime of the excited quantum spin. That is, the smaller the spin relaxation rate γ, the longer the lifetime. Therefore, the smaller the spin relaxation rate γ, the smaller the width of the energy spectrum peak of the quantum spin, and the blurring of the measurement system can be suppressed, so the measurement sensitivity can be increased. Also, the smaller the spin relaxation rate γ, the more the relaxation of the quantum spin can be suppressed, so the excitation efficiency can be increased. And from the above equation (1), it can be seen that when there is no state of energy D in the phonon dispersion, the blurring and relaxation of the spectrum width as described above can be suppressed. Therefore, in the technology of this specification, a configuration in which there is no state of energy D in the phonon dispersion is realized by using the characteristics (such as the inequality of the unit cell) of the phononic crystal structure 20. This will be described below.
[0025] The phononic crystal structure 20 of this embodiment includes two sub-lattices SC1 and SC2 in the unit cell UC. And it has the characteristic that the two sub-lattices are non-equivalent. Thereby, a band gap can be formed in the frequency in the dispersion relation of phonons, which are the quanta of lattice vibrations. Also, by appropriately setting at least one of the distribution of the mass component or the distribution of the effective spring constant to be uneven, a band gap can be formed so as to include the excitation frequency of the quantum spin (e.g., 2.87 GHz in diamond).
[0026] Fig. 7 shows the phonon dispersion curve. Fig. 7 represents the dispersion relation of phonons in the phononic crystal structure 20 (Fig. 1) of this embodiment. Fig. 7 is obtained by using simulation to find the eigenenergy of lattice vibrations. In the simulation, regarding diamond, the density ρ = 3515 [kg / m 31. Young's modulus = 70 [GPa] and Poisson's ratio = 0.17 were used.
[0027] In FIG. 7, the white circles (〇) are comparative examples. In the comparative examples, the two sub-lattices are equivalent. That is, in the comparative examples, in FIG. 2, the sub-lattice SC2 does not have the mass part MA. Therefore, an equality is given such that the mass components of the sub-lattice SC1 and the mass components of SC2 are equal with respect to the center CP. On the other hand, in FIG. 7, the black circles (●) are the present embodiments. In the present embodiments, as shown in FIGS. 1 and 3, the sub-lattice SC2 has the mass part MA. Therefore, the two sub-lattices SC1 and SC2 are non-equivalent in the distribution of the mass components.
[0028] Also, as shown in FIG. 3, the distance between each of the vertices A1 and A2 and the center CP is defined as the distance L. Also, the height is H, the radius of the mass part MA is R, and the width of each of the plurality of beams is W. In the simulation, the height H = 300 nm and the radius R = 0.9×L were fixed. Then, the simulation was performed by varying the distance L and the width W variously. FIG. 7 shows the results when the distance L = 581 nm and the width W = 200 nm.
[0029] As can be seen from the simulation results in FIG. 7, the white circles (〇) of the comparative examples are distributed in the entire frequency band. That is, in the comparative examples, there is no band gap in the frequency in the dispersion relation. On the other hand, in the black circles (●) of the present embodiments, a large gap of about 1 GHz can be formed near the excitation frequency of the quantum spin (near 3 GHz). That is, in the frequency in the dispersion relation, the band gap BG can be made to exist so as to include the excitation frequency of the quantum spin.
[0030] It was confirmed that the frequency band of the band gap BG does not change significantly even if the width W varies by about 10 percent. That is, it can be seen that the phononic crystal structure 20 of the present embodiment has a high degree of design freedom.
[0031] (Effect) According to the phononic crystal structure 20 of the present embodiment, due to the inhomogeneity of the unit cell UC, a band gap BG can be generated in the frequency of the phonon dispersion relation. And the excitation frequency of the quantum spin can be included in the band gap BG. Thereby, the interaction between the quantum spin and the phonon can be suppressed. That is, since there is no phonon state to which the energy D escapes, the relaxation of the quantum spin can be prevented from occurring. Since the energy spectrum width of the quantum spin can be reduced, the blur occurring in the measurement system can be suppressed. Also, since the relaxation of the quantum spin can be suppressed, the excitation efficiency can be increased.
[0032] Fig. 8 shows the simulation results of the energy spectrum width of the quantum spin. Graph G0 is a comparative example, and graph G1 is the present embodiment. The energy spectrum width of the quantum spin is width EW0 in the comparative example and width EW1 in the present embodiment. Also, the peak value of the energy spectrum is value EP0 in the comparative example and value EP1 in the present embodiment. As shown in Fig. 8, width EW1 can be made smaller than width EW0. Also, value EP1 can be made larger than value EP0. Thereby, it can be seen that in the present embodiment, the blur of the energy state can be suppressed to less than half.
[0033] As described above, specific examples of the present invention have been described in detail, but these are merely examples and do not limit the scope of the claims. The technology described in the claims includes various modifications and changes of the specific examples illustrated above. Also, the technical elements described in this specification or the drawings exhibit technical usefulness alone or in various combinations, and are not limited to the combinations described in the claims at the time of filing. Also, the technology illustrated in this specification or the drawings can achieve a plurality of purposes simultaneously, and achieving one of those purposes itself has technical usefulness.
[0034] (Modification example) The band gap can be formed in various ways, such as the distribution of the effective spring constant and the non-uniformity of the distribution of the mass components in the unit cell UC. For example, the band gap may be formed by appropriately adjusting at least one of the distribution of the thickness of the beams constituting the unit cell UC, the distribution of the mass portions connected to the beams, and the distribution of the hollow portions (holes).
[0035] The unit cell can be in various forms. For example, the distribution of the effective spring constant may be non-uniform. In this case, the width and height of the beams may be made different between a plurality of sub-cells, or the arrangement position and density of the hollow portions may be made different. Also, the mode of making the distribution of the mass components non-uniform is not limited to the mode using the mass portions. For example, the mass distribution may be made non-uniform by making the width and height of the beams different, or by the arrangement density of the hollow portions.
[0036] In this embodiment, diamond is used as the material having quantum spins, but it is not limited to this form. It is possible to use materials having color centers, such as SiC and hBN.
[0037] In this embodiment, a two-dimensional honeycomb structure is used as the periodic structure, but it is not limited to this form. Any structure can be used as long as it has periodicity. For example, a one-dimensional structure or a three-dimensional structure can also be used. Also, for example, various structures such as a square lattice structure and a triangular lattice structure can be used. Also, a structure composed of beams or a structure composed of a plurality of holes arranged periodically can also be used.
[0038] The aspects of the present technology are listed below. [Aspect 1] It is composed of a material having quantum spins in which a quantum state is realized in the defect, A phononic crystal structure having a periodic structure formed by combining a plurality of unit cells which are the smallest repeating structures. [Aspect 2] The phononic crystal structure according to Aspect 1, in which a band gap exists at a frequency in the dispersion relation of phonons which are quanta of lattice vibrations. [Aspect 3] The unit cell includes a plurality of sub-cells, The plurality of sub-cells constitute a periodic structure existing within the unit cell, the phononic crystal structure according to Embodiment 2. [Embodiment 4] The phononic crystal structure according to Embodiment 3, wherein at least one of the distribution of the effective spring constant and the distribution of the mass component possessed by each of the plurality of sub-cells is non-uniform with respect to the center of the unit cell. [Embodiment 5] The distribution of the effective spring constant and the distribution of the mass component are formed by at least one of the distribution of the thickness of the beams constituting the unit cell, the distribution of the mass portions connected to the beams, and the distribution of the hollow portions, the phononic crystal structure according to Embodiment 4. [Embodiment 6] The material having the quantum spin is at least one of diamond, SiC, hBN, and GaN, the phononic crystal structure according to any one of Embodiments 1-5. [Embodiment 7] The periodic structure includes a two-dimensional structure, The periodic structure is at least one of a honeycomb structure, a square lattice structure, and a triangular lattice structure, the phononic crystal structure according to any one of Embodiments 1-6. [Embodiment 8] A sensor including a phononic crystal structure, The phononic crystal structure, is composed of a material having a quantum spin in which a quantum state is realized in a defect, includes a periodic structure formed by combining a plurality of unit cells that are the smallest repeating structures, the phononic crystal structure has a band gap at a frequency in the dispersion relation of phonons, which are quanta of lattice vibrations, and the excitation frequency of the quantum spin is included within the band gap. Sensor. [Embodiment 9] The unit cell includes a plurality of sub-cells, The sensor according to aspect 8, wherein the plurality of sub-lattices constitute a periodic structure existing in the unit lattice. [Aspect 10] At least one of the distribution of the effective spring constant and the distribution of the mass component of the unit lattice is uneven with respect to the center of the unit lattice, The sensor according to aspect 9, wherein the distribution of the effective spring constant and the distribution of the mass component are formed by at least one of the distribution of the thickness of the beams constituting the unit lattice, the distribution of the mass portions connected to the beams, and the distribution of the hollow portions.
Description of Reference Numerals
[0039] 1: ODMR microscope 20: Phononic crystal structure BG: Band gap CP: Center SC1, SC2: Sub-lattices UC: Unit lattice
Claims
1. Composed of a material with a quantum spin in which a quantum state is realized in a defect, A phononic crystal structure having a periodic structure formed by combining a plurality of unit cells which are the smallest repeating structures.
2. The phononic crystal structure according to Claim 1, wherein a band gap exists in the frequency in the dispersion relation of phonons which are quanta of lattice vibrations.
3. The unit cell includes a plurality of sub-lattices, The phononic crystal structure according to Claim 2, wherein the plurality of sub-lattices constitute a periodic structure existing in the unit cell.
4. The phononic crystal structure according to Claim 3, wherein at least one of the distribution of the effective spring constant and the distribution of the mass component possessed by each of the plurality of sub-lattices is uneven with respect to the center of the unit cell.
5. The phononic crystal structure according to Claim 4, wherein the distribution of the effective spring constant and the distribution of the mass component are formed by at least one of the distribution of the thickness of the beams constituting the unit cell, the distribution of the mass portions connected to the beams, and the distribution of the hollow portions.
6. The phononic crystal structure according to Claim 1, wherein the material having the quantum spin is at least one of diamond, SiC, hBN, and GaN.
7. The periodic structure has a two-dimensional structure, The phononic crystal structure according to Claim 1, wherein the periodic structure is at least one of a honeycomb structure, a square lattice structure, and a triangular lattice structure.
8. A sensor provided with a phononic crystal structure, The phononic crystal structure, Composed of a material with a quantum spin in which a quantum state is realized in a defect, Having a periodic structure formed by combining a plurality of unit cells which are the smallest repeating structures, The phononic crystal structure has a band gap in the frequency in the dispersion relation of phonons which are quanta of lattice vibrations, The excitation frequency of the quantum spin is included within the band gap, A sensor.
9. The unit cell includes a plurality of sub-lattices, The sensor according to Claim 8, wherein the plurality of sub-lattices constitute a periodic structure existing in the unit cell.
10. At least one of the distribution of the effective spring constant and the distribution of the mass component possessed by the unit cell is uneven with respect to the center of the unit cell, The distribution of the effective spring constant and the distribution of the mass component are formed by at least one of the distribution of the thickness of the beam constituting the unit cell, the distribution of the mass portion connected to the beam, and the distribution of the hollow portion. The sensor according to claim 9.