Method for generating non-abelian quantum pumps by quasi-periodic disorder

Abstract

This invention discloses a method for generating non-Abelian quantum pumps through quasi-periodic disorder, belonging to the technical field of methods for generating non-Abelian quantum pumps. A Ti:sapphire laser is focused inside borosilicate glass using a microscope with a numerical aperture of 0.75. The movement of the glass is precisely controlled at a speed of 40 mm per second using an Aerotech system, and waveguide structures are fabricated in the glass according to a pre-designed trajectory. The distance between each waveguide is described in Figure 2, and the z-axis direction represents the time evolution direction.

Description

Technical Field

[0001] This invention relates to a method for generating non-Abelian quantum pumps, and more particularly to a method for generating non-Abelian quantum pumps through quasi-periodic disorder, belonging to the technical field of methods for generating non-Abelian quantum pumps. Background Technology

[0002] Existing techniques utilize quasi-periodic disorder to induce quantum pumps, which is a novel method for generating quantum pumps. However, this method is only applicable to the Abelian case. When considering the Hamiltonian, previous methods do not consider the degeneracy of the Hamiltonian, i.e., the system is Abelian. If the Hamiltonian of the system is degenerate, this method cannot be used. Therefore, a method for generating non-Abelian quantum pumps through quasi-periodic disorder is designed to solve the above problems. Summary of the Invention

[0003] The main objective of this invention is to provide a method for generating non-Abelian quantum pumps through quasi-periodic disorder.

[0004] The objective of this invention can be achieved by adopting the following technical solution:

[0005] The method of generating non-Abelian quantum pumps through quasi-periodic disorder, step one: focusing a Ti:sapphire laser into borosilicate glass using a microscope with a numerical aperture of 0.75;

[0006] Step 2: Using the Aerotech system, the movement of the glass is precisely controlled at a speed of 40 mm per second, and a waveguide structure is fabricated in the glass according to a pre-designed trajectory;

[0007] Step 3: The distance between each waveguide is determined by... Figure 2 The description is as follows, and the z-axis direction represents the direction of time evolution.

[0008] Preferably, in step one, the focus is specifically on 170 μm below the surface of the borosilicate glass.

[0009] Preferably, the quantum pump has N cells, each containing four lattice points, i.e. four waveguides. The straight waveguide is A, and the remaining B, C, and D are all curved waveguides.

[0010] Preferably, each waveguide has a uniform cross-section, approximately 7 micrometers × 5 micrometers;

[0011] The distance between each waveguide is described by J1, J2, J3, and J4.

[0012] Preferably, after the optical waveguide device is fabricated, an incident laser is used to examine the characteristics of the non-Abelian quantum pump caused by disorder.

[0013] The preferred non-Abel quantum pump characteristics are specifically tested as follows:

[0014] Adjust the disorder intensity of the system to the region C=1, i.e., W=1.2; in the scheme, quasi-periodic disorder is added to the J1 term, and the distance between waveguides A and B should be subject to disorder adjustment;

[0015] A laser source with a wavelength of 808 nm is coupled into a quantum pump through waveguides C and D. The laser will propagate along a predetermined optical waveguide path, and the laser will not diverge due to the non-Abelian topology of the system.

[0016] A charge-coupled device is installed on the output side of the quantum pump to collect the light diffraction pattern.

[0017] Beneficial technical effects of the present invention:

[0018] The present invention provides a method for generating non-Abelian quantum pumps through quasi-periodic disorder, and presents a scheme for realizing quantum pumps induced by quasi-periodic disorder in optical waveguides when the system contains a non-Abelian field.

[0019] The design of the system's Hamiltonian is now given, such as... Figure 2 The figure shows the changes of the coefficients of the system's Hamiltonian over one period. Figure 2 yes Figure 3 The coefficient diagram shown is for the initial moment when the quasi-periodic disorder is 0. By adjusting the disorder intensity, we can change the system to the system required to realize the non-Abelian quantum pump, that is, the system can realize the quantum pump we need when C=1. Attached Figure Description

[0020] Figure 1 The following is a simplified structural diagram of a Hamiltonian according to a preferred embodiment of the method for generating non-Abelian quantum pumps by quasi-periodic disorder according to the present invention.

[0021] Figure 2 The evolution diagram of the Hamiltonian coefficients over one period is shown as a preferred embodiment of the method for generating non-Abelian quantum pumps by quasi-periodic disorder according to the present invention.

[0022] Figure 3 The diagram shows the evolution of the topological properties of the system after applying quasi-periodic disorder, according to a preferred embodiment of the method for generating non-Abelian quantum pumps by quasi-periodic disorder according to the present invention.

[0023] Figure 4 A preferred embodiment of the method for generating non-Abelian quantum pumps by quasi-periodic disorder according to the present invention is shown in the optical waveguide structure design diagram.

[0024] Figure 5 The output cross-section diagram after laser incident is shown as a preferred embodiment of the method for generating non-Abelian quantum pumps by quasi-periodic disorder according to the present invention. Detailed Implementation

[0025] To enable those skilled in the art to understand the technical solution of the present invention more clearly, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0026] The experimental steps are as follows: We first need to prepare an optical waveguide device.

[0027] The first step is to use a microscope with a numerical aperture of 0.75 to focus the Ti:sapphire laser into the borosilicate glass (i.e., 170 micrometers below the surface).

[0028] The second step uses the Aerotech system to precisely control the movement of the glass at a speed of 40 mm per second, and to fabricate waveguide structures within the glass according to a pre-designed trajectory. Figure 4 The distance between each waveguide is determined by Figure 2 The description shows that the z-axis represents the direction of time evolution. This completes the fabrication of a waveguide within borosilicate glass using femtosecond laser direct writing technology.

[0029] Figure 4 The input surface of the quantum pump is shown. This quantum pump has N cells, each containing four lattice points, i.e., four waveguides. The straight waveguide is A, and the remaining B, C, and D are curved waveguides. Each waveguide has a uniform cross-section (approximately 7 μm × 5 μm). The distance between each waveguide is determined by… Figure 1 and Figure 2 The J1, J2, J3, and J4 are described in the text.

[0030] After fabricating the optical waveguide device, we incident a laser and examine the characteristics of the non-Abelian quantum pump caused by disorder.

[0031] The first step is to adjust the disorder intensity of the system, such as Figure 3 As shown, the disorder intensity W is adjusted to the region C=1, i.e., W=1.2. In our scheme, the quasi-periodic disorder is added to the J1 term, so the distance between waveguides A and B should be subject to disorder adjustment.

[0032] The second step involves coupling an 808nm laser source into the quantum pump via waveguides C and D. The laser propagates along the predetermined waveguide path and does not diverge due to the non-Abelian topology of the system.

[0033] In the third step, we use a charge-coupled device installed on the output side of the quantum pump to collect the light diffraction pattern. Figure 5 The diagram shows the laser beam emitted into the waveguide at the initial stage, and the cross-section of the waveguide after one cycle. It can be observed that we have successfully constructed a quantum pump composed of optical waveguides, where the laser beam moves by a displacement determined by the system's Chern number over one cycle.

[0034] The advantages of this invention are as follows: previous methods for realizing disorder-induced quantum pumps could only be applied to Abelian systems, meaning that the system's Hamiltonian could not be degenerate. Our invention extends the applicability to systems that include system degeneracy.

[0035] The above description is merely a further embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope disclosed in the present invention, based on the technical solution and concept of the present invention, shall fall within the scope of protection of the present invention.

Claims

1. A method for generating non-Abelian quantum pumps through quasi-periodic disorder, characterized in that: Includes the following steps: Step 1: Focus the Ti:sapphire laser into the borosilicate glass using a microscope with a numerical aperture of 0.74-0.76; Step 2: Using the Aerotech system, the movement of the glass is precisely controlled at a speed of 40 mm per second, and a waveguide structure is fabricated in the glass according to a pre-designed trajectory; Step 3: The distance between each waveguide is described by the transition coefficient. The trajectory in each plane is described by a quarter circle with a radius of 1, and the z-axis direction represents the time evolution direction. After the optical waveguide device is fabricated, an incident laser is shone on it and the characteristics of the non-Abelian quantum pump caused by disorder are examined. The specific characteristics of non-Abel quantum pumps are verified as follows: Adjust the disorder intensity of the system to the region C=1, i.e., W=1.2; in the scheme, quasi-periodic disorder is added to the J1 term, and the distance between waveguides A and B should be subject to disorder adjustment; A laser source with a wavelength of 808 nm is coupled into a quantum pump through waveguides C and D. The laser will propagate along a predetermined optical waveguide path, and the laser will not diverge due to the non-Abelian topology of the system. A charge-coupled device is installed on the output side of the quantum pump to collect the light diffraction pattern.

2. The method for generating non-Abelian quantum pumps through quasi-periodic disorder according to claim 1, characterized in that: In step one, the focus is specifically on 170 μm below the surface of the borosilicate glass.

3. The method for generating non-Abelian quantum pumps through quasi-periodic disorder according to claim 1, characterized in that: A quantum pump has N cells, each containing four lattice points, i.e., four waveguides. The straight waveguide is A, and the remaining B, C, and D are all curved waveguides.

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