Signal amplifier design method based on spin bit-nano mechanical oscillator composite system

Abstract

The invention discloses a signal amplifier design method based on a spin bit-nano mechanical oscillator composite system. The signal amplifier design method comprises the following steps: 1) constructing the spin bit-nano mechanical oscillator composite system; 2) using a strong pumping field, a weak detection field and a magnetic field to jointly act on the spin bit-nano mechanical oscillator composite system in the step 1) to realize coupling of spin bits and nano mechanical oscillators; and 3) adjusting the intensity of the strong pumping field in the step 2) according to the gain factor alpha of the expected detection wave. According to the signal amplifier design method based on the spin bit-nano mechanical oscillator composite system, the design of the signal amplifier based on the spin bit-nano mechanical oscillator composite system can be guided; according to the invention, the amplification factor of the signal amplifier can be adjusted by changing the intensity of the strong pumping field.

Description

Technical Field

[0001] The present invention relates to an optical signal amplifier, and in particular to a method for designing a signal amplifier based on a spin bit-nanomechanical oscillator composite system. Background Art

[0002] As an important optical phenomenon, four-wave mixing (FWM) provides a new approach for the development of novel nanophotonic devices (such as signal amplifiers, parametric oscillators, etc.) (Choi JW, Sohn BU, Chen GFR, et al. Disorder robust, ultra-low power continuous-wave four-wave mixing in a topological waveguide [J]. Nanophotonics, 2025, 14 (91), 1333–1344.). Currently, research on FWM has made significant progress in many systems. For example, based on the nonlinear response characteristics of a two-level system, the Boyd team established the theoretical framework of four-wave parametric amplification for the first time, laying the foundation for subsequent experimental research (Boyd R W, Raymer M G, Narum P, Barter DJ. Four-wave parametric interactions in a strongly driven two-level system [J]. Physical Review A, 1981, 24 (1), 411–422.).

[0003] Paspalakis et al. studied the four-wave mixing characteristics of semiconductor quantum dot / metal nanoparticle composite systems. The results showed that by precisely controlling the interparticle spacing, the four-wave mixing spectrum can be freely converted between double peaks and triple peaks (Paspalakis E, Evangelou S, Kosionis SG, Terzis A F. Strongly modified four-wave mixing in a coupled semiconductor quantum dot-metal nanoparticle system[J]. Journal of Applied Physics, 2014, 115(8), 083106(1-9).). Li's team used the four-wave mixing effect in a semiconductor quantum dot / metal nanoparticle composite system to obtain an ultra-high detection wave gain (about ~1.43×10 5)(Li JB,He MD,Chen L Q.Four-wave parametric amplification in semiconductor quantum dot-metallic nanoparticle hybrid molecules[J].Optics Express,2014,22(20),24734–24741.); They also observed a bistability four-wave mixing response in a system consisting of a semiconductor quantum dot and a photonic crystal nanocavity[8]. Wu et al. studied the optical bistability and four-wave mixing signals in a composite system consisting of a photonic crystal nanocavity, a single nitrogen-vacancy center embedded in the cavity, and an adjacent photonic waveguide (Li JH,YuR,Ding C,WuY.Optical bistability and four-wave mixing with a single nitrogen-vacancy center coupled to aphotonic crystal nanocavity in the weak-coupling regime[J].Optcis Express,2014,22(1),15024–15038.). Elder et al. established a universal theoretical framework for four-wave mixing parametric amplification of spin-orbit modes (Elder HF, Dacha SK, Murphy TE, Sprangle P. Theory of four wave mixing-based parametric amplification of spin-orbit modes [J]. Optics Express, 2024, 32 (4), 6494-6506.).

[0004] Obviously, studying the nonlinear optical properties of the spin bit-nanomechanical oscillator composite system is of great significance. However, related research has been rarely reported so far. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a method for designing a signal amplifier based on a spin bit-nanomechanical oscillator composite system.

[0006] To solve the above technical problems, the present invention proposes a technical solution: a method for designing a signal amplifier based on a spin bit-nanomechanical oscillator composite system, comprising the following methods:

[0007] 1) Constructing a spin bit-nanomechanical oscillator composite system;

[0008] 2) using a strong pump field, a weak probe field, and a magnetic field to act on the spin bit-nanomechanical oscillator composite system of step 1), so that the spin bit and the nanomechanical oscillator are coupled;

[0009] 3) Adjusting the intensity of the strong pump field in step 2) according to the gain factor α of the expected detection wave.

[0010] In the above-mentioned signal amplifier design method based on the spin bit-nanomechanical oscillator composite system, preferably, in step 3), the relationship between the gain factor α and the intensity of the strong pump field is:

[0011] α=FWM(I pu ) / FWM(I pu =0.01kHz 2 );I pu is the strong pump field intensity;

[0012]

[0013] Among them, σ 01 represents the transition operator of a particle from the ground state |0> to the excited state |1>,

[0014] μ represents the electric dipole moment of the spin bit,

[0015] E pr * represents the conjugate of the electric field strength of the pump field,

[0016] represents Planck's constant,

[0017] Γ2 represents the dephasing rate of the spin bit.

[0018] The above-mentioned signal amplifier design method based on the spin bit-nanomechanical oscillator composite system is preferably, 01 The expression is C1=Γ2-i(Δ pu -δ pr -g0gw0);Δ pu : refers to the detuning between the spin bit energy level splitting frequency and the pump field frequency; δ pr : represents the detection-pump detuning; g: represents the coupling strength between the spin bit and the phonon, w0 is the population inversion of the spin bit;

[0019] μ represents the electric dipole moment of the spin bit; Ω pu represents the Rabi frequency of the pump field;

[0020]

[0021] Γ1 represents the relaxation rate of the spin bit;

[0022]

[0023] i represents the imaginary unit, ω r : represents the vibration frequency of the fundamental bending mode; γ r : represents the decay rate of the nanomechanical oscillator;

[0024]

[0025] Compared with the existing technology, the advantages of the present invention are: the signal amplifier design method based on the spin bit-nanomechanical oscillator composite system of the present invention can guide the design of the signal amplifier based on the spin bit-nanomechanical oscillator composite system; in the present invention, the amplification factor of the signal amplifier can be adjusted by adjusting the intensity of the strong pump field. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 Schematic diagram of the spin bit-nanomechanical oscillator composite system in Example 1.

[0027] Figure 2 This is the energy level diagram of the spin bit-nanomechanical oscillator composite system in Example 1.

[0028] Figure 3 is the change of the four-wave mixing signal with the probe-pump detuning δ when the spin-nanomechanical oscillator coupling strength g is changed. pr The changing relationship.

[0029] Figure 4 This is an enlarged view of the left peak (L) and right peak (R) in the four-wave mixing spectrum.

[0030] Figure 5 for Figure 3 Zoomed in view of the “middle” peak.

[0031] Figure 6 is the enhancement factor α i Curve of (i=L, R, M1, M2, M3) changing with the spin-nanomechanical oscillator coupling strength g.

[0032] Figure 7 is Δ pu = 1MHz, the spin-oscillator coupling strength g is changed, and the four-wave mixing signal changes with the probe-pump detuning δ pr The changing relationship.

[0033] Figure 8 is Δ pu= -1MHz, the spin-oscillator coupling strength g is changed, and the four-wave mixing signal changes with the probe-pump detuning δ pr The changing relationship.

[0034] Figure 9 is Δ pu =1MHz when the enhancement factor α i The relationship between (i=L,R,M1,M2) and coupling strength g.

[0035] Figure 10 is Δ pu = -1MHz when the enhancement factor α i The relationship between (i=L,R,M1,M2) and coupling strength g.

[0036] Figure 11 To change the pump intensity I pu , the four-wave mixing signal changes with the probe-pump detuning δ pr The changing relationship.

[0037] Figure 12 This is the amplification of the L and R peaks in the four-wave mixing spectrum.

[0038] Figure 13 This is the amplification of the M1, M2, and M3 peaks in the four-wave mixing spectrum.

[0039] Figure 14 is the enhancement factor α i (i=L,R,M1,M2,M3) with pump intensity I pu The changing relationship of puc0 with I puc1 Corresponding to the low bistability threshold and the high bistability threshold respectively; the parameter is I pu =10GHz 2 . DETAILED DESCRIPTION

[0040] In order to facilitate understanding of the present invention, the present invention will be described more comprehensively and meticulously below in conjunction with preferred embodiments, but the protection scope of the present invention is not limited to the following specific embodiments.

[0041] It should be noted that when an element is described as being "fixed, fixed, connected or communicated with" another element, it can be directly fixed, fixed, connected or communicated with the other element, or it can be indirectly fixed, fixed, connected or communicated with the other element through other intermediate connectors.

[0042] Unless otherwise defined, all technical terms used hereinafter have the same meanings as those generally understood by those skilled in the art. The technical terms used herein are only for the purpose of describing specific embodiments and are not intended to limit the scope of protection of the present invention.

[0043] Example 1

[0044] A method for designing a signal amplifier based on a spin bit-nanomechanical oscillator composite system includes the following methods:

[0045] 1) Constructing a spin bit-nanomechanical oscillator composite system;

[0046] 2) using a strong pump field, a weak probe field, and a magnetic field to act on the spin bit-nanomechanical oscillator composite system of step 1), so that the spin bit and the nanomechanical oscillator are coupled;

[0047] 3) Adjust the intensity of the strong pump field in step 2) according to the gain factor α of the expected detection wave. The relationship between the gain factor α and the intensity of the strong pump field is: α = FWM (I pu ) / FWM(I pu =0.01kHz 2 );I pu is the intensity of the strong pump field.

[0048] In this embodiment, if Figure 1 As shown. The spin bit-nanomechanical oscillator composite system in the embodiment is simultaneously subjected to a strong pump field (E pu ,ω pu ) and weak detection field (E pr ,ω pr ) effect, the strong pump field and the weak detection field are both microwave. The energy level diagram of the spin bit-nanomechanical oscillator composite system is shown in Figure 2 As shown. The motion of the magnetic needle tip along the z-axis is quantized. When an external magnetic field acts on the spin bit of a single nitrogen vacancy center, the spin can be modeled as an S=1 / 2 spin bit system with large frequency splitting. Here, |↓>=|m s =1> and |↑>=|m s =0> is the ground state of the nitrogen vacancy center with spin -1. When an external magnetic field is applied to the center, the center is in a detuned state. s =-1> energy level can be ignored (Bin W, Zhu KD. Microwaveprobe for intrinsic parameters in a hybrid spin-nanoresonator system[J]. Journal of Applied Physics, 2013, 113(12), 124306(1-5).).

[0049] Under the spin wave approximation, the total Hamiltonian of the spin bit-nanomechanical oscillator composite system can be expressed as:

[0050]

[0051] Where H: represents the Hamiltonian of the system;

[0052] represents Planck's constant;

[0053] Δ pu : refers to the detuning between the spin bit energy level splitting frequency and the pump field frequency;

[0054] σ z :Represents half of the population inversion (σ z =(σ 11 -σ 00 ) / 2);

[0055] σ 10 : represents the transition operator of a particle from the excited state |1> to the ground state |0>;

[0056] σ 01 : represents the transition operator of a particle from the ground state |0> to the excited state |1>;

[0057] ω r : represents the vibration frequency of the fundamental bending mode;

[0058] b + (b): represents the phonon creation (annihilation) operator;

[0059] g: represents the coupling strength between the spin bit and the phonon;

[0060] Ω pu : represents the Rabi frequency of the pump field;

[0061] μ: represents the electric dipole moment of the spin bit;

[0062] E pr : represents the electric field strength of the pump field;

[0063] E pr * : represents the conjugate of the electric field strength of the pump field;

[0064] δ pr : represents the probe-pump detuning;

[0065] i: represents the imaginary unit;

[0066] t: indicates time.

[0067] where Δ pu =ω e -ω pu It refers to the detuning between the frequency of the spin bit energy level splitting and the pump field frequency, ω r is the vibration frequency of the fundamental bending mode, b+ (b) represents the phonon creation (annihilation) operator, The Rabi frequency corresponding to the pump field, w = 2σ z =σ 11 -σ 00 is the population inversion of the spin bit, δ pr =ω pr -ω pu represents the probe-pump detuning. is the coupling strength between the spin bit and the phonon, μ B refers to the Bohr magneton, a0 represents the zero-point fluctuation amplitude of the oscillator, G m is the magnetic field gradient. In fact, with G m The tip of the magnetic needle will induce a magnetic field

[0068] Using the commutation relations between Heisenberg's equations of motion and operators, the corresponding quantum Langevin equation can be written:

[0069]

[0070] Where Θ = b + +b, Γ1(Γ2) represents the relaxation (dephasing) rate of the spin bit, γ r =ω r / Q is the decay rate of the nanomechanical oscillator, and Q is the quality factor of the oscillator. Solving the equations, we can obtain the expression of the four-wave mixing signal:

[0071]

[0072] in w0 is the population inversion of the spin bit.

[0073]

[0074] The composite system of this embodiment is composed of a spin bit at the gem nitrogen vacancy center and a nanomechanical oscillator. The parameters are as follows: r =1MHz,Γ2=1kHz,Q=10 6 , and γ r =10 -3 kHz.

[0075] exist Figure 3 In the figure, it is shown that when the pump field resonates with the spin level splitting (i.e., Δ pu =0MHz), the effect of the spin-nanomechanical oscillator coupling strength g on the four-wave mixing signal. The results show that the four-wave mixing spectrum is at ω r= ±1 MHz, two sharp peaks (marked as L / R peaks) appear, which provides a new method for accurately measuring the frequency of nanomechanical oscillators. Figure 4 Shows the enlarged view of L peak and R peak. Figure 4 It can be clearly observed that the maximum value of the L(R) peak is nonlinearly related to the spin-nanomechanical oscillator coupling strength g. It is worth noting that these two peaks are related to δ pr =0MHz axisymmetric distribution, and the "middle" peaks are almost completely overlapped. Taking this into account, we Figure 5 A magnified image of the "middle" peak was drawn in

[15] , revealing that it is actually composed of three independent peaks (i.e., M1, M2, and M3). Interestingly, the peak values ​​of these three peaks remain constant despite the continuous increase in the spin-nanomechanical oscillator coupling strength g. Figure 5 The novel features of the four-wave mixing spectrum can be attributed to the specific quantum transitions between the spin bit modified states. The M1 peak originates from the three-photon resonance induced by the optical force: the electron absorbs two pump photons and emits a photon with a frequency of ω. pu -ω r The photon of the modified state |↓,n> transitions to the |↑,n+1> state. The M2 peak is caused by the Rayleigh resonance induced by the optical force, corresponding to the quantum transition from the modified state |↑,n> to |↓,n+1>. The generation of the M3 peak is mainly attributed to the Ac-Stark resonance. To more intuitively present the dependence of these peaks on g, this embodiment defines a four-wave mixing signal enhancement factor: α i =FWM(g) / FWM(g=1kHz)(i=L,R,M1,M2,M3). Regarding the L peak, α L As the coupling strength g increases, it shows a trend of first increasing and then decreasing: As the spin-nanomechanical oscillator coupling strength g increases, α L Initially, it increases monotonically and reaches a peak value of 2.42×10 3 It is worth noting that a significant bistability effect is observed in the g∈(93.29,105.15)kHz range. The experimental data show that α M1 Always equal to α M2 , which shows that the M1 peak and the M2 peak have a pr =0MHz axis presents symmetrical distribution. M1 With α M3 At the bistable threshold g c0 At the same time, it reaches the maximum value, and then at the bistable threshold g c1 As the coupling strength g increases further, the two eventually become stable. i The curve of (i=L,R,M1,M2,M3) changing with the spin-nanomechanical oscillator coupling strength g is shown in Figure 6 As shown, the parameters used are: pump intensity Ipu =10GHz 2 , where g c0 With g c1 They refer to the low bistability threshold and the high bistability threshold, respectively.

[0076] As Figure 3-Figure 6 We further explored the effect of the pump field and the spin bit in a non-resonant state (Δ pu ≠0MHz), the four-wave mixing signal changes with the detection-pump detuning amount δ pr The changing law of . pu =1 MHz, in the four-wave mixing spectrum, not only can two symmetrical peaks (L peak and R peak) be observed, but also two tiny "bumps" appear outside the L and R peaks. It is worth noting that the peak value of the L peak varies significantly with the change of the spin-nanomechanical oscillator coupling strength g. Figure 7 The inset in the figure shows that the four-wave mixing spectrum has evolved into a four-peak structure. pu =-1MHz, the situation changes significantly. Figure 8 As shown in the figure, the two "bumps" migrate from the outside of the L and R peaks to their inside. It is important to note that the M1 peak only pu ≥38.78kHz 2 The M2 peak requires I pu ≥40.21kHz 2 Therefore, M 1, The four-wave mixing signal enhancement factor of the M2 peak is defined as: M1 =FWM(I pu ) / FWM(I pu =38.78kHz 2 ) M1 ; α M2 =FWM(I pu ) / FWM(I pu =40.21kHz 2 ) M2 . Figure 9 Shows that when Δ pu =1MHz, the enhancement factor α i Curve of the change of coupling strength g. α L (α R ) continues to rise with the increase of g. D =83.98kHz, reaching a peak of 35.50 and then remaining stable. Although the coupling strength g changes, the parameter α M1 Still close to 1. Figure 10 In, α L It rises sharply to a peak of 1174.73 at point F, and then drops to around 1 after crossing point F. It is not difficult to see that Δ pu=-1MHz, the coupling strength threshold required to generate the M1 (M2) resonance peak is significantly higher than Δ pu =1MHz. Combined Figure 2 and Figure 3 The results show that the four-wave mixing signal shows a significant dependence on the spin-nanomechanical oscillator coupling strength, and its spectral line characteristics and enhancement factor both change significantly with the change of coupling strength.

[0077] Figure 11-14 It is shown that under the condition of ultra-strong spin-nanomechanical oscillator coupling (g = 200kHz>>Γ2), when the pump field resonates with the spin bit (Δ pu =0MHz), the effect of pump intensity on the four-wave mixing signal. Figure 11 The four-wave mixing spectrum shows a five-peak structure, and the peak value of each peak depends significantly on the pump intensity. Figure 12 This is an enlarged view of the two sideband peaks (L and R peaks). Figure 13 They are the magnified images of M1, M2, and M3 peaks respectively. pu From 1kHz 2 Increased to 1000kHz 2 When M j The evolution trend of the peaks (j=1,2,3) shows significant differences. pu =1kHz 2 When the signal intensity of M1 and M2 peaks is weak. pu =2kHz 2 When the pump intensity I pu Continuously increasing, the peak-to-peak value of M3 is [2kHz 2 ,38.98kHz 2 ] range only slightly increased. However, the evolution of the M1 peak and the M2 peak is quite different. pu From 0.01kHz 2 Increased to 38.98kHz 2 When I pu =1000kHz 2 When M1(M2) peak value drops to I pu =500kHz 2 To quantify the effect of the peaks of the above five peaks on the pump intensity I pu We define the corresponding four-wave mixing signal enhancement factor: i =FWM(I pu ) / FWM(I pu =0.01kHz 2 )(i=L,R,M1,M2);α M3=FWM(I pu ) / FWM(I pu =2.0kHz 2 ) M3 It is important to note that the L, R, M1, and M2 peaks are only in I pu ≥0.01kHz 2 The M3 peak requires I pu ≥2.0kHz 2 When I pu =38.98kHz 2 When α L (α R ) reaches a peak value of 25.0. In addition, when I pu =200.51kHz 2 When α M1 Reaching a peak of 75297.81 and α M3 The peak value is 1606.16. This phenomenon confirms that the M1 peak is highly sensitive to the pump intensity. In addition, the bistability effect occurs in the pump intensity range I pu ∈(38.99,200.50)kHz 2 . Enhancement factor α i The relationship between (i=L,R,M1,M2,M3) and the spin-oscillator coupling strength g is as follows Figure 14 As shown, I puc0 with I puc1 Corresponding to the low bistability threshold and the high bistability threshold respectively, the parameter is I pu =10GHz 2 .

Claims

1. A method for designing a signal amplifier based on a spin bit-nanomechanical oscillator composite system, characterized in that: Includes the following methods: 1) Constructing a spin bit-nanomechanical oscillator composite system; 2) using a strong pump field, a weak probe field, and a magnetic field to act on the spin bit-nanomechanical oscillator composite system of step 1) to achieve coupling between the spin bit and the nanomechanical oscillator; 3) Adjusting the strong pump field intensity in step 2) according to the gain factor α of the expected detection wave.

2. The method for designing a signal amplifier based on a spin bit-nanomechanical oscillator composite system according to claim 1, characterized in that: In step 3), the relationship between the gain factor α and the strong pump field intensity is: α=FWM(I pu ) / FWM(I pu =0.01kHz 2 );I pu is the intensity of the strong pump field; Among them, σ 01 represents the transition operator of a particle from the ground state |0> to the excited state |1>, μ represents the spin bit electric dipole moment, E pr * represents the conjugate of the electric field strength of the pump field, represents Planck's constant, Γ2 represents the dephasing rate of the spin bit.

3. The method for designing a signal amplifier based on a spin bit-nanomechanical oscillator composite system according to claim 2, characterized in that: The expression is C1=Γ2-i(Δ pu -δ pr -g0gw0);Δ pu : refers to the detuning between the spin bit energy level splitting frequency and the pump field frequency; δ pr : represents the detection-pump detuning; g: represents the coupling strength between the spin bit and the nanomechanical oscillator, w0 is the population inversion of the spin bit; μ represents the electric dipole moment of the spin bit; Ω pu represents the Rabi frequency of the pump field; Γ1 represents the relaxation rate of the spin bit i represents the imaginary unit, ω r : represents the vibration frequency of the fundamental bending mode; γ r : represents the decay rate of the nanomechanical oscillator;

Images