Method for regulating and controlling spin-orbit entangled state through spin-orbit angular momentum conversion efficiency

Abstract

The invention discloses a method for regulating and controlling a spin-orbit entangled state through spin-orbit angular momentum conversion efficiency. The light may carry three types of angular momentums. The invention relates to an intrinsic orbital angular momentum (EOAM), which is characterized in that the intrinsic orbital angular momentum (IOAM) is used as an intrinsic orbital angular momentum (ANM), the spin angular momentum (SAM), the intrinsic orbital angular momentum (IOAM), and the intrinsic orbital angular momentum (EOAM) are used as a main orbital angular momentum (EOAM) of the main orbital angular momentum (ANM) of the main orbital angular momentum (ANM) of the main orbital angular momentum (ANM) of the main orbital angular momentum. The SAM and the IOAM of the light can be mutually converted, and a spin-orbit entangled state can also be formed between the SAM and the IOAM. The SAM-IOAM mutual conversion efficiency of light is closely related to the spin-orbit entangled state of the light. Based on the relevance, the invention provides a method for regulating and controlling the spin-orbit entangled state by regulating and controlling the spin-orbit angular momentum conversion efficiency.

Description

Technical Field

[0001] This invention belongs to the field of quantum communication technology. Specifically, this patent invention is a method for controlling spin-orbit entanglement by adjusting the spin-orbit angular momentum conversion efficiency. Background Technology

[0002] There may be a correlation between two physical phenomena that are essentially the same. Exploring this correlation can help us better understand the nature of physical phenomena and thus innovate. The interaction between the spin angular momentum (SAM) and the extrinsic orbital angular momentum (EOAM) of light produces mutual coupling. There is also an interconversion between the SAM and the intrinsic orbital angular momentum (IOAM) of light. SAM and EOAM, as well as SAM and IOAM, can also form spin-orbit entangled states. Therefore, there must be some relationship between the spin-orbit interaction of light and its corresponding spin-orbit entangled state, as shown in Figure 1. There are many examples of breakthroughs achieved through interdisciplinary research in the scientific community. Combining the study of quantum entanglement and spin-orbit interaction may bring some new insights.

[0003] In the late 19th and early 20th centuries, quantum mechanics rapidly developed and matured, resolving many phenomena that classical theories could not explain, such as blackbody radiation, the photoelectric effect, and the hydrogen atom spectrum. Numerous experimental facts proved that quantum mechanics is a successful physical theory. Despite its remarkable achievements since its inception, intense debates have arisen regarding its interpretation and scope of application, particularly concerning the physical meaning of the wave function in the Schrödinger equations. Born, through analysis of the angular distribution of particles in scattering experiments, proposed a probabilistic interpretation of the wave function. Born argued that wave-particle duality is an intrinsic property of both radiation and matter particles; wave-like and particle-like properties each have their own applicable ranges. In experimental explorations of specific physical phenomena, both radiation and matter particles can exhibit either wave-like or particle-like properties, but neither ideal description alone can provide a complete explanation of the object under study. To express this incompatibility and fully describe the necessary logical relationship between them, Born proposed the complementarity principle. Heisenberg proposed the Heisenberg uncertainty relation, which reveals the fundamental difference between the laws of quantum mechanics and classical mechanics. The viewpoint represented by Bohr and Heisenberg is known as the Copenhagen interpretation, which supports the completeness of quantum mechanics. The other side, represented by Einstein and Schrödinger, supported local realism and offered sharp criticism of the Copenhagen interpretation. This is reflected in two famous papers from 1935: the Schrödinger cat paradox and the EPR (Einstein-Podolsky-Rosn) paradox. In the Schrödinger cat paradox, the term "entangled state" was first introduced. An entangled state is a superposition state that cannot be represented as a direct product of the quantum states of its subsystems. The EPR paper addressed the probabilistic interpretation of the wave function, using superposition to demonstrate that the wave function's description of physical reality is incomplete, and upholding the view of local realism (that there is no action at a distance between objects). A long-standing debate ensued between proponents of local realism and those supporting the completeness of quantum mechanics (the Copenhagen interpretation). This debate took a significant turn in 1964 when Bell, based on the views of local realism and the theory of hidden variables, proposed the famous Bell inequality. According to this inequality, entangled particles can be used to experimentally test the correctness of the completeness of quantum mechanics and the validity of local realism.Since the Bell inequality was proposed, researchers have conducted numerous experimental verifications. This has advanced our understanding of macroscopic quantum superposition states, especially entangled states. Quantum entanglement is the most famous prediction in quantum mechanics. It describes two entangled entities, even if they are separated by vast distances, where the action of one will affect the state of the other. When one entity is manipulated (e.g., by performing a quantum measurement) and its state changes, the other entity will immediately undergo a corresponding state change. Einstein called quantum entanglement "spooky action at a distance," but this is not merely a strange prediction; this phenomenon has been detected experimentally.

[0004] In the 21st century, quantum entanglement has been placed at the center of physics, closely intertwined with relativity and quantum field theory, driving research into many hot topics in mathematics and physics. Entanglement provides a completely new perspective for understanding many physical phenomena, playing an irreplaceable role in understanding and changing the world. Entanglement should be understood as the correlation between the common measurement results of at least two commutative observables. These two commutative observables can belong to different particles or the same particle; therefore, entanglement can be divided into two types: one is entanglement between multi-particle systems; the other is entanglement between different degrees of freedom within a single particle (SPE). Entangled states in multi-particle systems are established on the same degree of freedom among multiple particles, while entangled states between different degrees of freedom within a single particle are established on different degrees of freedom within a single particle, such as... Figure 2 As shown.

[0005] Entangled states between different degrees of freedom within a single particle are more robust and easier to generate than entangled states between multiple particles. Entangled states between different degrees of freedom within a single particle can be applied to technologies such as quantum measurement, quantum repeaters, entanglement purification, quantum teleportation, and the realization and authentication of quantum random number generators.

[0006] Currently, various particles can achieve entangled states, with photons being the most widely used resource. Photons are easier to control in optical devices. Furthermore, photons, as the transmission medium for modern quantum communication, possess multiple advantages such as low cost, strong robustness, and stable performance. Photons can not only establish entanglement in one degree of freedom but also achieve hyper-interactive entanglement in multiple degrees of freedom, including polarization-space, polarization-path, and time-path. Theoretical analysis shows that spin-orbit hyper-entangled states can significantly improve the capacity of quantum channels, which is crucial for enhancing the communication capacity of quantum networks.

[0007] Spin-orbit coupling, as a relativistic effect, is crucial in the study of magnetocrystalline anisotropy, non-collinear magnetism, the spin Hall effect, and spin-orbit torque. Non-paraxial beam propagation leads to the interconversion between spin angular momentum (SAM) and intrinsic orbital angular momentum (IOAM). In 2008, Sciarrino and his team first reported this conversion process at the single-photon level, and it has been extensively studied since. In 2017, Devlin et al. proposed a method to convert arbitrary SAM states into independent OAM superposition states, using a metasurface to convert left and right circularly polarized states into states with independent OAM values. In 2011, Konstantin et al. realized arbitrary spin-orbit angular momentum conversion of light based on a programmable J-plate. In 2019, Zhou et al. realized spin-orbit angular momentum conversion of light based on a dielectric metasurface that can generate a topologically charged vortex beam with a fractional distribution, marking the first realization of collinear helical beams with arbitrary orbital angular momentum values.

[0008] The primary component in the spin-orbit angular momentum interconversion is the spin-intrinsic orbital angular momentum, and the primary component of the spin-intrinsic orbital angular momentum entanglement state is also the spin-intrinsic orbital angular momentum. There is a close relationship between the spin-intrinsic orbital angular momentum conversion efficiency and the spin-orbit entanglement state. Therefore, the spin-orbit entanglement state can be adjusted by controlling the spin-intrinsic orbital angular momentum conversion efficiency, which adds a new adjustment method to the control of spin-orbit entanglement states. Summary of the Invention

[0009] The purpose of this invention is to find the relationship between spin-intrinsic orbital angular momentum conversion efficiency and spin-intrinsic orbital angular momentum entanglement state, and to provide a new method for the control of spin-intrinsic orbital angular momentum entanglement state.

[0010] This patent is based on the conservation of the projection of the total intrinsic angular momentum of the light beam onto the z-axis as light propagates along the z-axis. And the conversion efficiency formula from SAM to IOAM

[0011] And based on It can be determined and These are two mutually observable quantities that can form entangled states.

[0012] Furthermore, according to the von Neumann entropy formula, which measures the degree of entanglement in entangled states...

[0013] Using MATLAB software, the conversion efficiency and entanglement degree from SAM to IOAM were calculated based on the conversion efficiency and entanglement degree formulas. The relationship between entanglement degree and conversion efficiency was plotted based on the calculation results. Based on this relationship, the entanglement degree of the spin-orbit entangled state was controlled by adjusting the spin-orbit angular momentum conversion efficiency.

[0014] This patent exemplifies the interdisciplinary application of technology, providing a novel method for controlling spin-orbit entangled states. Attached Figure Description

[0015] Figure 1 Correlation analysis diagram; Figure 2 Two types of entangled states; Figure 3 The relationship between the degree of entanglement of entangled states and the conversion efficiency. Detailed Implementation

[0016] This patent invention discloses a method for controlling the degree of entanglement of spin-intrinsic orbital angular momentum entangled states by adjusting the spin-intrinsic orbital angular momentum conversion efficiency.

[0017] A non-paraxial beam, when strongly focused by a lens in free space, undergoes a transformation between spin and intrinsic orbital angular momentum. A non-paraxial beam is composed of circularly polarized light with different wave vectors. Assuming the cone angle of these wave vectors is θ, the projections of the non-paraxial beams SAM and IOAM onto the Z-axis are...

[0018] Assuming light propagates along the z-axis, the projection of the total intrinsic angular momentum of the light beam onto the z-axis is conserved, i.e. and The formula can be interpreted as a portion of the light's SAM being converted into IOAM, meaning that even... The beam also exhibits a spin-dependent vortex phase distribution. This effect originates from the geometric phase between plane waves with different wave vectors k. When From time to time , That is, the efficiency of converting SAM to IOAM reaches 100%.

[0019] SAM to IOAM conversion efficiency

[0020] In the above formula, when At this point, SAM is not converted to OAM, and the conversion efficiency is at its lowest, 0. and They are two mutually observable measurements, because

[0021] They can form entangled states.

[0022] Let the initial state of the non-paraxial beam propagating along the z-axis be...

[0023] When a non-paraxial beam passes through a Q-plate (different orbital angular momentum states can be produced by adjusting parameters), its initial state will become...

[0024] After a non-paraxial beam is strongly focused by a lens, assuming the angle between the direction of light propagation and the z-axis is... , Will become

[0025]

[0026] make

[0027] Will become

[0028]

[0029] The above equation represents the entangled state of light's polarization and orbital angular momentum degrees of freedom projected onto the z-axis, where the subscripts... These represent the degrees of freedom for polarization and orbital angular momentum, respectively.

[0030] The degree of entanglement of entangled states is measured using the von Neumann entropy formula below. because

[0031] Select Calculate the degree of entanglement of entangled states

[0032] In the above two equations, and Let the density matrices of the polarization and orbital angular momentum states be respectively represented. Substitute into the following formula to calculate the entanglement degree of the entangled state. The expression for the entanglement degree is shown in the following formula.

[0033] Using MATLAB, the entanglement degree and conversion efficiency of the entangled state in the above equation are calculated, and the relationship between the entanglement degree and conversion efficiency is plotted, as follows. Figure 3 As shown in the figure, the vertical axis represents the degree of entanglement of the entangled states, and the horizontal axis represents the spin-to-orbit angular momentum conversion efficiency. Figure 3 It can be seen that as the conversion efficiency increases, the entanglement degree of the entangled states first increases, then decreases, and then increases again. When the conversion efficiency is between 10% and 35%, the entanglement degree of the entangled states exceeds 0.6. When the conversion efficiency is 22%, the entanglement degree of the entangled states reaches a maximum of 0.7. According to... Figure 3 The degree of entanglement of spin-intrinsic orbital angular momentum entangled states can be controlled by the spin-intrinsic orbital angular momentum conversion efficiency.

Claims

1. A method for controlling spin-orbit entangled states by spin-orbit angular momentum conversion efficiency, characterized in that, There is a close correlation between the SAM-IOAM interconversion efficiency of light and its spin-orbit entangled state.

2. The method for controlling spin-orbit entanglement states by means of spin-orbit angular momentum conversion efficiency as described in claim 1, characterized in that, A method to control spin-orbit entanglement by adjusting the spin-intrinsic orbital angular momentum conversion efficiency.

3. A method for controlling spin-orbit entanglement states by means of spin-orbit angular momentum conversion efficiency as described in claims 1 and 2, characterized in that, Let the initial state of the non-paraxial beam propagating along the z-axis be... 。 4. A method for controlling spin-orbit entangled states by means of spin-orbit angular momentum conversion efficiency as described in claims 1, 2, and 3, characterized in that, When a non-paraxial beam passes through a Q-plate (different orbital angular momentum states can be produced by adjusting parameters), its initial state will become... 。 5. A method for controlling spin-orbit entangled states by means of spin-orbit angular momentum conversion efficiency as described in claims 1, 2, 3, and 4, characterized in that, After a non-paraxial beam is strongly focused by a lens, assuming the angle between the direction of light propagation and the z-axis is... , Will become , 。 6. A method for controlling spin-orbit entanglement states by means of spin-orbit angular momentum conversion efficiency as described in claims 1, 2, 3, 4, and 5, characterized in that, make 。 7. A method for controlling spin-orbit entangled states by means of spin-orbit angular momentum conversion efficiency as described in claims 1, 2, 3, 4, 5, and 6, characterized in that, Will become .

8. A method for controlling spin-orbit entangled states by means of spin-orbit angular momentum conversion efficiency as described in claims 1, 2, 3, 4, 5, 6, and 7, characterized in that, The above equation represents the entangled state of light's polarization and orbital angular momentum degrees of freedom projected onto the z-axis, where the subscripts... Let represent the degrees of freedom for polarization and orbital angular momentum, respectively. The degree of entanglement of the entangled state is measured using the von Neumann entropy formula below. Depend on .

9. A method for controlling spin-orbit entangled states by means of spin-orbit angular momentum conversion efficiency as described in claims 1, 2, 3, 4, 5, 6, 7, and 8, characterized in that, Select Calculate the degree of entanglement of entangled states .

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