Method for detecting quantum state of single rare earth ion

Abstract

The invention discloses a method for detecting a quantum state of a single rare earth ion. The method is based on photonic crystal microcavity enhancement and microwave-light pulse collaborative excitation. A one-dimensional photonic crystal microcavity is arranged in a rare earth ion-doped yttrium silicate crystal, a defect is introduced to enable a resonant wavelength to be matched with a target transition wavelength, and a Purcell effect is utilized to shorten the lifetime of an excited state, improve a target transition branching ratio and enhance fluorescence radiation. Rare earth ions are excited by comprehensively using microwave pulse and light pulse, the quantum state is preprocessed by the microwave pulse, then fluorescence photons are excited and collected by the light pulse, the quantum state is judged according to the change of fluorescence intensity along with integral time, and if the quantum state is obviously increased, the quantum state is the state. According to the detection method provided by the invention, the problems of weak signal and low efficiency of the traditional detection are solved, and an efficient scheme is provided for quantum state reading.

Description

Technical Field

[0001] The present invention belongs to the technical field of quantum optical systems and micro-nano optical devices, and particularly relates to a method for detecting the quantum state of a single rare earth ion. Background Art

[0002] In the field of solid-state quantum computing and quantum storage, rare earth ions, with their well-shielded 4f electron structure, exhibit unique advantages such as extremely long spin coherence time and narrow spectral linewidth. Crystal materials doped with rare earth ions, such as praseodymium-doped yttrium silicate, have become important platforms for quantum information processing. However, the quantum state readout technology for individual rare earth ions still faces significant bottlenecks, restricting its application in high-fidelity quantum manipulation.

[0003] Existing technologies face two core challenges: First, the spatial positioning of individual rare earth ions in crystals is difficult, resulting in conventional photoluminescence excitation spectrum measurements relying on frequency domain characteristics to indirectly identify ions, which is inefficient. At the same time, the long excited state energy level lifetime of rare earth ions exacerbates the detection problem - weak light-matter interactions result in extremely small amounts of fluorescent photon radiation per unit time. Even if the detection time is extended to accumulate signals, it is still susceptible to interference from environmental background noise, making it difficult to obtain high signal-to-noise ratio data. Second, the non-recyclability of fluorescence radiation severely limits detection efficiency. When excited electrons de-excite to the ground state, there are multiple transition paths. If the electrons de-excite to non-initial energy levels, they will not be able to be re-excited by subsequent pulses, resulting in the termination of fluorescence radiation, which greatly reduces the control fidelity of quantum computing.

[0004] Existing quantum state detection methods have poor universality and are mostly designed for special isotopes with nuclear spin 1 / 2 (such as yttrium ions). They also rely on photon counting thresholds and detector efficiency, and require the difference in photon counts from two optical readouts to determine the quantum state. This leads to problems such as insufficient real-time performance and poor detection stability. Therefore, a universal method based on a microwave-light pulse synergistic excitation mechanism, combined with analysis of the dynamic trend of fluorescence intensity changes, and signal accumulation through cyclic excitation, is urgently needed to quickly and accurately determine the quantum state of single rare earth ions. This is of great significance for promoting the widespread application of rare earth ions in the field of quantum information. Summary of the Invention

[0005] In view of the defects in the above-mentioned background technology, the present invention provides a method for rapidly detecting, accurately judging and reading out the quantum state of a single rare earth ion with high precision.

[0006] The technical solution for achieving the purpose of the present invention is to provide a method for detecting the quantum state of a single rare earth ion, wherein a photonic crystal microcavity is set in a yttrium silicate crystal doped with rare earth ions, the optical properties of the microcavity are used to locate and couple the single rare earth ion to be detected, microwave pulses and light pulses matching the energy level transition frequency are applied for cooperative excitation, so that the rare earth ion releases fluorescent photons through spontaneous radiation; the fluorescent photons are collected by a fluorescence detection method, and the quantum state information of the rare earth ion is judged based on the changing trend and characteristics of the fluorescence intensity.

[0007] The photonic crystal microcavity described in the present invention is a one-dimensional photonic crystal nanobeam cavity. Defects are introduced into the one-dimensional photonic crystal to construct a microcavity structure. The resonant wavelength of the microcavity matches the target transition wavelength of the rare earth ion, generating a resonance effect. The Purcell effect shortens the excited state lifetime of the rare earth ion, while increasing the target transition branching ratio and enhancing the recyclability of the fluorescence radiation.

[0008] The method described in the present invention for detecting the quantum state of a single rare earth ion comprises the following specific steps: first, applying a microwave pulse matching the transition frequency between the rare earth ion's hyperfine ground state and auxiliary state to pump electrons in the ground state to the auxiliary state; then, applying a light pulse matching the target quantum transition frequency to excite electrons in the auxiliary state to the target excited state; when the detected fluorescence intensity reaches saturation, applying a light pulse matching the transition frequency between the auxiliary state and other excited states to return the electrons to the auxiliary ground state; repeating the excitation-detection-return-to-ground state process to accumulate fluorescence intensity data. After collecting fluorescence photons, the fluorescence detection method sets a waiting time equal to n times the lifetime of the rare earth ion's excited state to ensure that the electron transition process proceeds fully, and records the change curve of fluorescence intensity versus integration time; if the fluorescence intensity increases significantly with increasing integration time, it is determined that the initial quantum state is located at |1> g state; otherwise in |0> g state.

[0009] The one-dimensional photonic crystal nanobeam cavity described in the technical solution of the present invention includes a praseodymium-doped yttrium silicate crystal waveguide, an etched circular air hole, a tapered gradient region, and a mirror reflection region; the circular air holes are symmetrically arranged around the nanobeam cavity, and a linear defect microcavity structure is formed by adjusting the radius of the circular air holes; the radius of the air holes in the tapered gradient region varies according to a parabolic function as shown in the following formula: r i =r center +(i-1) 2 (r end -r center ) / (i max -1) 2 , Among them, r center and r endare the radii of the innermost and outermost air holes in the gradient zone, i max is the number of air holes in the gradient zone, i∈[1,i max ]; The mirror reflection area includes a circular air hole with a constant radius, forming a distributed Bragg reflector.

[0010] The method for detecting the quantum state of a single rare earth ion described in the present invention selects the microwave pulse and the light pulse based on the transition probability between the hyperfine energy levels of the rare earth ion.

[0011] The principle of the present invention is: using nanobeam cavities to enhance the interaction between rare earth ions and light fields, thereby improving the fluorescence radiation intensity and recyclability of rare earth ions; on this basis, microwave pulses and light pulses are used in combination to excite the quantum state of a single rare earth ion, and the precise readout of the quantum state is achieved by observing the changes in fluorescence intensity.

[0012] The one-dimensional photonic crystal nanobeam cavity design proposed in this paper is constructed from an yttrium silicate crystal. By introducing defects to form a resonant structure, the cavity's resonant wavelength matches the target transition wavelength of the praseodymium ion, generating a resonance effect. The high quality factor and small mode volume enhance the interaction between the praseodymium ion and the light field. The Purcell effect shortens the excited state lifetime, increases the target transition branching ratio, and enhances the fluorescence radiation cycle and photon emission.

[0013] The microwave-light pulse synergistic excitation detection method proposed by the present invention targets praseodymium ions in yttrium silicate crystals. A microwave pulse of a specific frequency is first applied to pump ground-state electrons to an auxiliary state. A matching light pulse is then used to excite the auxiliary-state electrons to the target excited state. The spontaneous emission of fluorescence photons is observed and the change in fluorescence intensity is recorded. When the fluorescence intensity saturates, another set of light pulses is applied to return the electrons to the auxiliary ground state, completing the cycle. Repeated data accumulation is performed, and the initial quantum state is determined based on the growth trend of fluorescence intensity over integration time. If the intensity increases significantly, the initial quantum state is a specific state; otherwise, it is a different state.

[0014] Compared with the prior art, the present invention has the following beneficial effects: 1. The method for detecting the quantum state of a single rare earth ion provided by the present invention utilizes a combination of microwave pulses and light pulses to excite the quantum state of a single rare earth ion, taking advantage of the regulatory effect of different pulses on the quantum state of the ion. Without relying on complex pulse sequences, it greatly improves the efficiency of quantum state detection and effectively solves the problem of low efficiency caused by the inaccurate and non-repeatable excitation process in traditional detection methods, providing strong support for fast and efficient quantum state readout in quantum computing.

[0015] 2. The present invention adopts the method of microwave-light pulse synergistic excitation and fluorescence intensity change trend analysis. The fluorescence signal is accumulated through cyclic excitation, and the quantum state is determined by directly comparing the fluorescence intensity growth rate. No photon counting threshold or complex sequence is required. The signal-to-noise ratio is improved through cyclic accumulation, achieving high-fidelity readout.

[0016] 3. The present invention utilizes a one-dimensional photonic crystal nanobeam cavity designed based on yttrium silicate crystal. With its high quality factor and small mode volume characteristics, it significantly enhances the interaction between ions and light fields within the framework of cavity quantum electrodynamics. This can solve the problem of difficulty in detection due to the weak photon radiation rate of single rare earth ions, improve the fidelity of the quantum computing readout stage, and make the detection of single rare earth ions and high-fidelity quantum manipulation of single rare earth ion quantum bit systems possible. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Schematic diagram of the fluorescence radiation of a single praseodymium ion in a yttrium silicate crystal under different conditions. Figures (a) and (b) show the fluorescence radiation transitions of the praseodymium ion with and without a cavity, respectively. Figure 2 Schematic diagram of the principle of the information state readout scheme for a single praseodymium ion according to the present invention; wherein (a) to (d) represent the information state readout scheme for |1> g Readout of quantum state; (e) to (g) represent |0> g Readout of quantum state, (h) shows the pulse timing diagram for reading quantum state information; Figure 3 A graph showing changes in the fluorescence intensity of praseodymium ions over time during the detection process using the detection method provided by an embodiment of the present invention; Figure 4 A top view of a praseodymium ion-doped yttrium silicate-based nanobeam cavity structure provided by an embodiment of the present invention; Figure 5 This is a comparison of the optical lifetime of praseodymium ions in yttrium silicate with and without the nanobeam cavity. DETAILED DESCRIPTION

[0018] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0019] Example 1 In the field of single praseodymium ion quantum state detection, due to the inability to precisely locate individual praseodymium ions in space, current methods rely primarily on photoluminescence excitation spectroscopy to measure resonant fluorescence and identify individual praseodymium ions from their frequency domain characteristics. However, the long excited state energy level lifetime of praseodymium ions presents two major technical challenges: First, the long energy level lifetime results in weak interactions between ions and photons, resulting in low fluorescence photon emission per unit time and a weak detection signal; second, the non-recyclability of fluorescence radiation significantly limits detection efficiency. Specifically, when excited electrons de-excite to the ground state, there are multiple transition paths. If the electron de-excites to the initial energy level (|1> g ) other ground state energy levels, such as |0> g and|aux. g On, even 3 Energy levels other than H4(0) will not be able to be excited again by subsequent light pulses, thus terminating the fluorescence radiation and reducing the fidelity of quantum computing manipulation, such as Figure 1 As shown in Figure (a).

[0020] In response to the above technical bottlenecks, the present invention proposes an innovative solution based on nanobeam cavity, whose working mechanism is as follows: using the resonant wavelength of the nanobeam cavity and |e>2-|1> g The transition wavelength matches the characteristics to achieve fluorescence radiation enhancement, such as Figure 1 As shown in Figure (b) in the figure. On the one hand, according to the Purcell effect theory, the nanobeam cavity produces a significant Purcell effect on the target quantum transition, significantly shortening the excited state lifetime of the praseodymium ion, accelerating the fluorescence radiation process, and significantly increasing the amount of fluorescence photon radiation per unit time (as shown by the circle comparison in the figure); on the other hand, the strong coupling between the nanobeam cavity and the light field optimizes the electron transition dynamics, significantly improving |e>2 to |1> g The target transition branching ratio promotes the electron to return to the target ground state preferentially|1> g , thereby increasing the recyclability of fluorescence radiation.

[0021] Based on the above fluorescence enhancement principle, this embodiment designs the following quantum state reading implementation steps: After completing the quantum computing task, the first step is to use quantum state tomography to collapse the unknown quantum state into one of the two ground state energy levels of the quantum bit, namely |0> g or |1> g Then, we can further use the nanobeam cavity and fluorescence detection to identify the ground state energy level to which the collapse occurs. The specific steps are as follows: (1) Applied frequency and |1> g -|aux> g Transition-matched microwave pulses, if the quantum state collapses to |1> g The microwave pulse moves electrons from |1> g Transfer to auxiliary state|aux>g Above, such as Figure 2 As shown by the arrow in Figure (a), this step realizes the pre-processing of the quantum state and lays the foundation for subsequent excitation operations.

[0022] (2) Applied frequency and |aux> g The light pulse f1 that matches the |e>3 transition is Figure 2 As shown in Figure (b), the auxiliary state |aux> g The electrons on the excited state are pumped to the excited state |e>3, and the electrons are de-excited to the three ground state energy levels through spontaneous radiation (accompanied by fluorescence radiation), such as Figure 2 As shown in Figure (c), the return value is |aux> g The probability of the electron de-exciting to the other two energy levels is 93%, and the total probability of de-excitation to the other two energy levels is 7%. After setting the waiting time to n times the excited state lifetime (T1) of the praseodymium ion to ensure that the electron transition process is fully carried out, the light pulse f1 is applied again to repeat the spontaneous emission process and accumulate the number of fluorescence photons. When the accumulated number of fluorescence photons no longer increases, it indicates that the electron has a high probability of de-excitation to |1> g or|0> g This step lays the foundation for subsequent determination of quantum state by fluorescence intensity.

[0023] (3) After observing that the fluorescence intensity in step (2) increases from small to large and tends to be stable, in order to further enhance the fluorescence signal, the fluorescence intensity of the fluorescent signal is further enhanced by applying the fluorescent signal of ... g -|e>3,|1> g -|e>3 transition resonant light pulses f2 and f3, such as Figure 2 As shown by the arrow in Figure (d), the electron is moved from |1> g or|0> g Pump back on |aux> g Return to step (1) and repeat step (2) to continuously accumulate fluorescence intensity. The pulse sequence of the whole process is as follows: Figure 2 During the whole detection process, the variation trend of total fluorescence intensity with detection time is shown in (h). Figure 3 As shown by the solid line, the fluorescence intensity increases significantly with the increase of integration time, which means that the initial quantum state is in the |1> state.

[0024] Based on the above |1> g In the readout process of the state, if the quantum state collapses to |0> g On the other hand, if we still use the above steps (1) and (2) to detect, we will find that the fluorescence intensity has changed significantly. First, the microwave pulse in step (1) will not excite the g of electrons, because the transition frequency does not match the resonance, such as Figure 2As shown in Figure (e) in the figure. Secondly, the light pulse f1 in step (2) will not excite electrons because it also does not match the resonance, as shown in Figure (e). Figure 2 As shown in Figures (f) and (g), no matter how many times step (2) is repeated, the detected signal is always the background fluorescence signal from the detection system. Although this fluorescence signal will accumulate over time, the signal is obviously much weaker, as shown in Figures (f) and (g). Figure 3 Indicated by the dotted line.

[0025] The present invention uses a fluorescence detection method to collect fluorescent photons and judge the quantum state information of rare earth ions based on the changing trend and characteristics of the fluorescence intensity. If the fluorescence intensity increases significantly with the increase of integration time, it is judged that the initial quantum state is at |1> g state; otherwise in |0> g state.

[0026] This embodiment takes the praseodymium-doped yttrium silicate-based nanobeam cavity as an example, and its structure is as follows: Figure 4 As shown, it mainly includes a praseodymium-doped yttrium silicate crystal waveguide, an etched circular air hole, a tapered gradient region, and a mirror reflection region. The circular air holes are symmetrically arranged around the nanobeam cavity, and a linear defect microcavity structure is formed by adjusting the radius of the circular air holes. The radius of the air hole in the tapered gradient region varies according to a parabolic function: r i =r center +(i-1) 2 (r end -r center ) / (i max -1) 2 Where i is the i-th circular air hole arranged from the center line of the waveguide to both sides, i∈[i,i max ],i max is the total number of circular air holes on one side, r center is the radius of the circular air hole closest to the center line, r end is the radius of the outermost circular air hole on the center line, r i is the radius of the i-th circular air hole. This structure effectively reduces radiation loss and significantly improves the quality factor of the one-dimensional photonic crystal. The mirror reflection area contains M circular air holes with constant radius. These circular air holes distributed at both ends of the waveguide constitute a distributed Bragg reflector, forming a high-reflection film, which not only helps to reduce the energy consumption in the waveguide coupling process, but also forms a reflection, so that more light energy is stored in the waveguide, further improving the quality factor. The thickness h and width W of the entire praseodymium-doped yttrium silicate core layer are bThe diameters of the holes are 200nm and 415nm, the lattice constant a is 221.5nm, the radius of the circular holes in the gradient region decreases parabolically from 80nm to 65nm, the number of air holes in the gradient region is 8 pairs, and the number of holes in the reflection region is 16 pairs. This nanobeam cavity can shorten the optical lifetime of praseodymium ions by 198 times, from 164μs to 0.828μs. Figure 5 The branching ratio of the target transition is increased from 2.8% to 99.51%, significantly improving the quantum state detection performance compared to existing technologies.

[0027] The present invention provides a single rare earth ion quantum state detection method that integrates nanobeam cavity enhancement technology and microwave-light pulse synergistic excitation. By observing the change of fluorescence intensity with integration time, high-precision quantum state readout is achieved, providing important technical support for the application of rare earth ions in the field of quantum information.

Claims

1. A method for detecting the quantum state of a single rare earth ion, characterized in that: A photonic crystal microcavity is set in a rare-earth ion-doped yttrium silicate crystal. The optical properties of the microcavity are used to locate and couple the single rare-earth ion to be detected. Microwave pulses and light pulses matching the energy level transition frequency are applied for cooperative excitation, causing the rare-earth ion to release fluorescent photons through spontaneous emission. Fluorescence detection method is used to collect fluorescent photons, and the quantum state information of rare earth ions is judged based on the changing trend and characteristics of fluorescence intensity.

2. The method for detecting the quantum state of a single rare earth ion according to claim 1, wherein: The photonic crystal microcavity is a one-dimensional photonic crystal nanobeam cavity. Defects are introduced into the one-dimensional photonic crystal to construct a microcavity structure. The resonant wavelength of the microcavity matches the target transition wavelength of the rare earth ion, generating a resonance effect. The Purcell effect shortens the excited state lifetime of the rare earth ion, while increasing the target transition branching ratio and enhancing the cyclability of the fluorescence radiation.

3. The method for detecting the quantum state of a single rare earth ion according to claim 1, wherein: First, a microwave pulse that matches the transition frequency between the rare earth ion's hyperfine ground state and the auxiliary state is applied to pump the electrons in the ground state to the auxiliary state. Then, a light pulse that matches the target quantum transition frequency is applied to excite the electrons in the auxiliary state to the target excited state. When the fluorescence intensity is detected to have reached saturation, a light pulse that matches the transition frequency between the auxiliary state and other excited states is applied to return the electrons to the auxiliary ground state. The excitation-detection-back to ground state process is repeated to accumulate fluorescence intensity data.

4. The method for detecting the quantum state of a single rare earth ion according to claim 1, wherein: After collecting the fluorescence photons, the fluorescence detection method sets the waiting time to n times the lifetime of the rare earth ion excited state to ensure that the electron transition process is fully carried out, and records the curve of the fluorescence intensity changing with the integration time; if the fluorescence intensity increases significantly with the increase of the integration time, it is judged that the initial quantum state is at Otherwise, it is in state.

5. The method for detecting the quantum state of a single rare earth ion according to claim 2, wherein: The one-dimensional photonic crystal nanobeam cavity comprises a praseodymium-doped yttrium silicate crystal waveguide, an etched circular air hole, a tapered gradient region, and a mirror reflection region. The circular air holes are symmetrically arranged around the nanobeam cavity, and a linear defect microcavity structure is formed by adjusting the radius of the circular air holes. The radius of the air holes in the tapered gradient region varies according to a parabolic function as shown in the following formula: ， in, and are the radii of the innermost and outermost air holes in the gradient zone, is the number of air holes in the gradient zone, ; The mirror reflection area includes a circular air hole with a constant radius, forming a distributed Bragg reflector.

6. A method for detecting the quantum state of a single rare earth ion according to claim 1 or 3, characterized in that: The microwave pulse and the optical pulse are selected based on the transition probability between the hyperfine energy levels of the rare earth ions.

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