Robustness-enhanced high-fidelity Rydberg atom excitation method

Abstract

The invention discloses a robustness-enhanced high-fidelity Rydberg atom excitation method, which enhances the robustness and excitation fidelity of a system by modulating the waveform of a laser pulse sequence. The method is based on a two-photon modulation method of a Rydberg atom three-level system, and non-adiabatic evolution between atom initial Hamiltonian adiabatic instantaneous eigenstates can be effectively inhibited by modulating waveform parameters of a laser pulse sequence, so that high-fidelity excitation of Rydberg atoms is realized; according to the method, the adaptability of atoms to environmental changes and experimental errors in the Rydberg state excitation process is also improved, and the robustness of the modulation process is enhanced. According to the invention, the limitation that the atom excitation efficiency is relatively low and is easily influenced by the environment in the process of carrying out Rydberg state modulation on atoms by an existing laser system is solved, the fidelity and robustness of Rydberg atom excitation are improved, and a new method is provided for preparation of the Rydberg state and regulation and control of a quantum gate.

Description

Technical Field

[0001] The present invention relates to the field of quantum control, and in particular to the field of excited state control of Rydberg atoms. Technical Background

[0002] Rydberg atoms are highly excited atoms with large principal quantum numbers. Their large electric dipole moment, long lifetime, and strong interactions make them extremely sensitive to electromagnetic fields and ideal for implementing quantum logic gates. In the field of electromagnetic measurement, researchers have achieved precise measurement of wide-bandwidth, extremely low-frequency, and very high-frequency electromagnetic fields using Rydberg atoms, with sensitivity far exceeding that of conventional antennas. In the field of quantum computing, researchers have used Rydberg atoms to implement a series of operations, including two-bit quantum logic gates, laying the foundation for quantum computing based on Rydberg atoms.

[0003] The realization of quantum electromagnetic measurement technology and quantum logic gates based on Rydberg atoms first requires high-fidelity excitation of Rydberg atoms. Fidelity is a universal indicator for evaluating atomic excitation. A fidelity of 99% can be understood as 99 out of 100 atoms being perfectly excited. The higher the fidelity, the higher the preparation rate of Rydberg atoms, the higher the sensitivity to electromagnetic fields, and the better the fidelity of the logic gate. In current research, this important indicator is often overlooked in the excited state preparation process of Rydberg atoms. Currently, adiabatic channels are often used to achieve Rydberg atom excitation, but the action time of adiabatic channels is long and the system requirements are high. When exciting a Rydberg atom system using adiabatic channel technology, the long lifespan of Rydberg atoms will lead to low excitation efficiency. Summary of the Invention

[0004] The technical problem solved by the present invention is to prepare high-fidelity excited states with enhanced robustness of Rydberg atoms. The technical solution of the present invention is to precisely control the dynamic behavior of the pulse sequence field by adopting a pulse shape parameter modification technique to achieve high-fidelity and robust excitation of Rydberg atoms.

[0005] The principle of the present invention is:

[0006] (1) Interaction between light field and atoms

[0007] Taking a two-level atomic system as an example, applying laser to the atomic system will cause energy level changes. Assuming that the corresponding eigenstates of the atom are denoted as |g> and |e>, where |g> corresponds to the ground state and |e> corresponds to the excited state, the corresponding energy is and The atomic Hamiltonian can be expressed as:

[0008]

[0009] The Pauli matrix is defined as:

[0010]

[0011] When laser irradiation causes electric dipole coupling of atoms, the total Hamiltonian of the system in the interaction representation can be obtained by taking the rotating wave approximation method:

[0012]

[0013] Where Δ=ω eg -ω,|Ω eg |=|Ω ge |=Ω R is the Rabi frequency, and φ corresponds to the phase of the coupled system.

[0014] The wave function of the interaction representation is:

[0015]

[0016] According to the Schrödinger equation, the evolution equation of the coefficients and is:

[0017]

[0018] The formal solution is:

[0019]

[0020] (2) Quantum Adiabatic Theorem

[0021] In the physical adiabatic process, the initial state of the system is the eigenstate |n(t=0)> of H(t=0). From t=0, the system evolves with time to t=T, where it is in the final state H(T) with the eigenvalue at the instant T being the eigenstate |n(T)>. The final state wave function is:

[0022]

[0023] In the adiabatic limit Down,

[0024]

[0025] When the adiabatic change is slow but the rate of change is still finite, omitting the term is the adiabatic approximation. It is generally believed that the sufficient condition for the adiabatic approximation to hold is:

[0026]

[0027] This is the quantum adiabatic condition. Under this condition, the quantum adiabatic approximate solution is:

[0028]

[0029] (3) Adiabatic shortcut and transitionless algorithm

[0030] The quantum adiabatic shortcut is a method for solving the problem of slow evolution in adiabatic processes. Its basic idea is to offset the non-adiabatic effects of the evolution process through an auxiliary Hamiltonian. Adiabatic shortcuts can be divided into three types based on the auxiliary Hamiltonian: reverse engineering algorithm, anti-non-adiabatic field algorithm, and transition-free algorithm. The principle of the transition-free algorithm is as follows:

[0031] Adiabatic evolution requires that adiabatic conditions be met, where the local adiabatic condition requires that the rate of change of system parameters is much smaller than the energy difference of the system, that is:

[0032]

[0033] In the formula, m and n represent different energy levels, t is time, E is energy, H is Hamiltonian, and |n(t)> and |m(t)> are the instantaneous eigenstates of H. The global adiabatic condition requires that the product of the energy difference and the evolution period T is much larger than π, that is, |E n -E m |T>>π.

[0034] Consider a time-dependent initial Hamiltonian:

[0035]

[0036] Where |n(t) is the instantaneous eigenstate of H0(t), E n (t) is the corresponding instantaneous eigenvalue. Under the adiabatic approximation, the adiabatic evolution can be solved as Ψ(t) = exp[iξ n (t)]|n(t)>, where:

[0037]

[0038] Where is the reduced Planck constant.

[0039] The evolution operator corresponding to adiabatic evolution is:

[0040]

[0041] Among them U ad |n(0)=exp[iξ n (t)]|n(t)>. Evolution operator with U + The Hamiltonian relationship is Substitute U ad The adiabatic evolution Hamiltonian H is obtained adWhen the adiabatic condition is not met, the system will undergo a non-adiabatic transition and cannot be driven to evolve along the eigenstate. By adding an auxiliary Hamiltonian, the non-adiabatic effect is offset and the system can evolve along the eigenstate again. The specific form of the auxiliary Hamiltonian is represented by H cd (t) = H ad (t)-H0(t), that is:

[0042]

[0043] in:

[0044]

[0045] where is the eigenstate of the adiabatic invariant.

[0046] Compared with the existing solutions, the main advantages of the present invention are:

[0047] (1) The present invention proposes a novel Rydberg atom excitation method. Compared with the traditional method, the path for achieving Rydberg atom excitation is less sensitive to environmental noise and can achieve Rydberg atom excitation more effectively.

[0048] (2) The solution of the present invention adopts a transitionless transition path, which has better excitation fidelity than the traditional adiabatic method. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Flowchart Specific implementation plan

[0050] First, we will start with the initialization of the pulse waveform parameters, including setting key parameters such as the initial amplitude, duration and phase. Then, these parameters will be carefully adjusted to optimize the characteristics of the pulse waveform. By simulating the evolution of the computing system, we can evaluate the impact of different parameter settings on the system behavior and determine the optimal pulse waveform parameters accordingly. These parameters will enable the system to reach the expected evolutionary state. Secondly, after determining the optimal parameters, these reference values are used to accurately modify the pulse sequence field to ensure that the pulse sequence can be accurately applied to the Rydberg atomic system. In this way, the state of the atoms can be effectively controlled, and the population of the Rydberg state can be measured. Throughout the process, the pulse waveform is continuously monitored and adjusted to ensure the accuracy and reliability of the experimental results.

[0051] The contents not described in detail in this specification belong to the prior art known to those skilled in the art.

Claims

1. A high-fidelity Rydberg atom excitation method with enhanced robustness, characterized in that: The main steps include: Step 1, initializing the shape parameters of the pulse sequence; Step 2, applying the initial pulse sequence to the sensitive area of the atomic gas cell; Step 3, detecting the population of Rydberg atoms in the atomic gas cell; Step 4, optimizing the shape parameters of the laser pulse to achieve the optimal population.

2. The high-fidelity Rydberg atom excitation method with enhanced robustness according to claim 1, characterized in that: Step 1 is to initially modulate the laser pulse sequence along the classical pulse Vitanov type of adiabatic evolution, which contains two laser pulses, one for probe light and the other for coupling light; define the shape parameters where Ω min It represents the reference value inversely proportional to the pulse duration L, Ω shape It represents the Rabi frequency of the laser pulse, which is modulated by waveform. shape The initial value is set to 0.

3.

3. The high-fidelity Rydberg atom excitation method with enhanced robustness according to claim 1, characterized in that: Step 2 mainly involves applying the initialized modulated pulse sequence to the atomic gas chamber through the designed experimental optical path to perform atomic excitation operations.

4. The high-fidelity Rydberg atom excitation method with enhanced robustness according to claim 1, characterized in that: Step 3 mainly evaluates the preparation of Rydberg atoms by measuring the population of Rydberg states. Theoretically, the relevant population can be calculated by the wave function of the electronic state. In experiments, the population can be determined by measuring the number of ions produced after the Rydberg atoms are ionized.

5. The high-fidelity Rydberg atom excitation method with enhanced robustness according to claim 1, characterized in that: In step 4, the shape parameter A is adjusted according to the measured population. shape , in order to achieve the optimal value of excitation.

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