We theoretically investigate the Autler-Townes (AT) splitting in the photoelectron spectra of three-level ladder K2 molecule driven by a pump-probe pulse via employing the time- dependent wave packet approach. The d...We theoretically investigate the Autler-Townes (AT) splitting in the photoelectron spectra of three-level ladder K2 molecule driven by a pump-probe pulse via employing the time- dependent wave packet approach. The dependence of AT splitting on two laser intensities and wavelengths are studied in detail. We firstly quantify these effects on peak shift and AT separation. The photoelectron spectra show double splitting with symmetric profiles, but with asymmetric profiles when the wavelength is changed. The magnitude of AT splitting increases with the pump laser intensity, but does not vary with probe intensity. The shifts of the absorption peaks and the splitting between AT doublet are predicted by using an analyt- ical fitting function when the intensity/wavelength of one of the two fields is changed. These novel results are of importance for the molecular spectroscopy and may further stimulate the first principles theoretical studies analytically.展开更多
We propose a scheme to implement a two-qubit conditional quantum phase gate for the intracavity field via a single three-level ∧-type atom driven by two modes in a high-Q cavity. The quantum inforraation is encoded o...We propose a scheme to implement a two-qubit conditional quantum phase gate for the intracavity field via a single three-level ∧-type atom driven by two modes in a high-Q cavity. The quantum inforraation is encoded on the Fock states of the bimodal cavity. The gate's averaged fidelity is expected to reach 99.8%.展开更多
By using the method of eigenvectors, the atomic populations and emission spectrum are investigated in a system that consists of a cascade three-level atom resonantly interacting with a single-mode tield in a Kerr-like...By using the method of eigenvectors, the atomic populations and emission spectrum are investigated in a system that consists of a cascade three-level atom resonantly interacting with a single-mode tield in a Kerr-like medium. The atom and the field are assumed to be initially in the upper atomic state and the Fock state, respectively. Results for models with intensity-dependent coupling and with intensity-independent coupling are compared. It is found that both population dynamics and emission spectrum show no indications of atom-field decoupling in the strong field limit if the intensity-dependent coupling is taken into account.展开更多
In this paper, we study the control problem of adiabatic decoherence in a three-level atom. We will find the decoupling bang-bang group for various configurations, including the V configuration and the cascade type of...In this paper, we study the control problem of adiabatic decoherence in a three-level atom. We will find the decoupling bang-bang group for various configurations, including the V configuration and the cascade type of three-levelatom subjected to adiabatic decoherence. We also give the programs to design a sequence of periodic twinborn pulses to suppress the decoherence.展开更多
We propose a scheme to realize the nonlocal quantum entanglement of three three-level particles by using a threeparticle entangled state of three levels as a quantum channel with the aid of some local unitary transfor...We propose a scheme to realize the nonlocal quantum entanglement of three three-level particles by using a threeparticle entangled state of three levels as a quantum channel with the aid of some local unitary transformations. This scheme can be directly generalized to the nonlocal quantum entanglement of N three-level particles.展开更多
We present a scheme for probabilistically teleporting an unknown three-level bipartite entangled state by using a partial entangled three-level bipartite state as quantum channel This scheme can be directly generalize...We present a scheme for probabilistically teleporting an unknown three-level bipartite entangled state by using a partial entangled three-level bipartite state as quantum channel This scheme can be directly generalized to probabilistically teleport an unknown three-level k-particle entangled state by a partial three-level bipartite entangled state. A11 kinds of unitary transformations are given in detail We calculate the successful total probability and the total classical communication cost required for this scheme.展开更多
In this paper, two schemes for teleporting an unknown three-particle three-level entangled state are proposed. In the first scheme, two partial three-particle three-level entangled states are used as the quantum chann...In this paper, two schemes for teleporting an unknown three-particle three-level entangled state are proposed. In the first scheme, two partial three-particle three-level entangled states are used as the quantum channels, while in the second scheme, three two-particle three-level non-maximally entangled states are employed as quantum channels. It is shown that the teleportation can be successfully realized with certain probability, for both two schemes, ira receiver adopts some appropriate unitary transformations. It is shown also that the successful probabilities of these two schemes are different.展开更多
The general expressions of the average dissipative and dipole forces acting on a A-configuration three-level atom in an arbitrary light field are derived by means of the optical Bloch equations based on the atomic den...The general expressions of the average dissipative and dipole forces acting on a A-configuration three-level atom in an arbitrary light field are derived by means of the optical Bloch equations based on the atomic density matrix elements, and the general properties of the average dissipative and dipole forces on a three-level atom in the linearly-polarized high-order Bessel beams (HBBs) are analysed. We find a resonant property (with two resonant peaks) of the dissipative force and a non-resonant property (with two pairs of non-resonant peaks) of the dipole force on the three-level atom, which are completely different from those on the two-level atom. Meanwhile we find a saturation effect of the average dissipative force in the HBB, which comes from the saturation of the upper-level population. Our study shows that the general expressions of the average dissipative and dipole forces on the three-level atom will be simplified to those of the two-level atom under the approximation of large detuning. Finally, we study the axial and azimuthal Doppler cooling of atoms in ID optical molasses composed of two counter-propagating HBBs and discuss the azimuthal influence of the HBB on the Doppler cooling limit. We also find that the Doppler limit of atoms in the molasses HBB is slightly below the conventional Doppler limit of hГ/(2kB) due to the orbital angular momentum lh of the HBB.展开更多
Propagation of strong femtosecond hyper-Gaussian pulses in a cascade three-level molecular system is studied by solving numerically the Maxwell–Bloch equations by the iterative predictor-corrector finite-difference t...Propagation of strong femtosecond hyper-Gaussian pulses in a cascade three-level molecular system is studied by solving numerically the Maxwell–Bloch equations by the iterative predictor-corrector finite-difference time-domain method.Optical power limiting behavior induced by strong nonlinear two-photon absorption is observed for different orders of the femtosecond hyper-Gaussian pulses. Pulses of a higher order temporal profile are found to have a wider power range of optical limiting but a larger output saturation intensity. Both the output saturation value and the damage threshold of optical power limiting decrease with pulse duration increasing. The decrease of the pulse area along the pulse propagation is much slower than that obtained from the two-photon area theorem due to invalidity of the slowly varying amplitude approximation and the monochromatic field hypothesis.展开更多
In this paper,we present decoupling bang-bang operations for the suppression of general decoherence,bothamplitude and phase damping,in a three-level system in A-configuration.We give a program to design a sequence ofp...In this paper,we present decoupling bang-bang operations for the suppression of general decoherence,bothamplitude and phase damping,in a three-level system in A-configuration.We give a program to design a sequence ofperiodic twinborn pulses to suppress the decoherence in such the system.展开更多
The entropy squeezing of a V-type three-level atom interacting with a single-mode field and passing through the amplitude damping channel is investigated in detail. Our results show that when coupled to the single-mod...The entropy squeezing of a V-type three-level atom interacting with a single-mode field and passing through the amplitude damping channel is investigated in detail. Our results show that when coupled to the single-mode field, the atom in appropriate initial states can not only generate obvious entropy squeezing but also keep in the optimal squeezing state,while passing through the amplitude damping channel, the atom can generate entropy squeezing under the control of the weak measurement. Besides, it is proved again that as a measurement method for atomic squeezing, the entropy squeezing is precise and effective. Therefore our work is instructive for experiments in preparing three-level system information resource with ultra-low quantum noise.展开更多
The interaction of a single three-level trapped ion with two laser beams has been studied theoretically. With application of two successive unitary transformations, an analytical solution to this quantum system has be...The interaction of a single three-level trapped ion with two laser beams has been studied theoretically. With application of two successive unitary transformations, an analytical solution to this quantum system has been obtained.展开更多
In this paper, a voltage oriented control strategy for three-level PWM rectifier based on Sliding Mode Control (SMC) is introduced in order to obtain fast and accurate response of dc-bus voltage. To verify the validit...In this paper, a voltage oriented control strategy for three-level PWM rectifier based on Sliding Mode Control (SMC) is introduced in order to obtain fast and accurate response of dc-bus voltage. To verify the validity of the analysis and the feasibility of the proposed control method a set of simulation tests have been conducted using Matlab/Simulink. The simulation results show that compared to the conventional PI controller, the SMC can reduce drastically the three-level rectifier’s voltage fluctuation and improve the dynamic response of dc-bus significantly.展开更多
In the traditional three-level space vector pulse width modulation(SVPWM)algorithm,the sector judgment is computationallycomplex since the sector is divided into triangles and hexagons.In addition,the switching freque...In the traditional three-level space vector pulse width modulation(SVPWM)algorithm,the sector judgment is computationallycomplex since the sector is divided into triangles and hexagons.In addition,the switching frequency is high becausethe seven-segment switching sequence is adopted.For this reason,a new SVPWM control algorithm for three-level inverteris proposed,in which the sector judgment is simplified by dividing the sector into quasi hexagons?and the new four-segmentswitching sequence is adopted to reduce the switching frequency.Simulation results show that the total harmonic distortiongrows down with the switching frequency decreasing,moreover,the algorithm runtime is also decreased.展开更多
Aiming at the difficulty of setting the weight coefficient in the value function of model predictive torque control(MPTC)for permanent magnet synchronous motor(PMSM)driven by three-level inverter,a fine-division model...Aiming at the difficulty of setting the weight coefficient in the value function of model predictive torque control(MPTC)for permanent magnet synchronous motor(PMSM)driven by three-level inverter,a fine-division model predictive flux control(MPFC)method is proposed.First,establish a mathematical model between the motor torque and the stator flux linkage according to the mathematical equations of PMSM.Thus,the control of the motor torque and stator flux linkage in the MPTC is transformed into the control of a single stator flux linkage vector,omitting the cumbersome weight setting process in the traditional MPTC.The midpoint potential control strategy is proposed,which uses the characteristics of redundant small vectors to balance the midpoint potential.After that,a fine-division strategy is proposed,which effectively reduces the number of candidate vectors and the computational burden of the system.Finally,the proposed MPFC is compared with MPTC by simulation.The results show that the proposed fine-division MPFC effectively reduces the system calculation,and has the advantages of simple principle and better dynamic and steady-state control performance.The feasibility of the control strategy is verified.展开更多
Based on the fractional order theory and sliding mode control theory,a model prediction current control(MPCC)strategy based on fractional observer is proposed for the permanent magnet synchronous motor(PMSM)driven by ...Based on the fractional order theory and sliding mode control theory,a model prediction current control(MPCC)strategy based on fractional observer is proposed for the permanent magnet synchronous motor(PMSM)driven by three-level inverter.Compared with the traditional sliding mode speed observer,the observer is very simple and eases to implement.Moreover,the observer reduces the ripple of the motor speed in high frequency range in an efficient way.To reduce the stator current ripple and improve the control performance of the torque and speed,the MPCC strategy is put forward,which can make PMSM MPCC system have better control performance,stronger robustness and good dynamic performance.The simulation results validate the feasibility and effectiveness of the proposed scheme.展开更多
Capacitor voltage imbalance is a significant problem for three-level inverters.Due to the mid-point modulation of these inverter topologies,the neutral point potential moves up or down depending on the neutral point c...Capacitor voltage imbalance is a significant problem for three-level inverters.Due to the mid-point modulation of these inverter topologies,the neutral point potential moves up or down depending on the neutral point current direction creating imbalanced voltages among the two capacitors.This imbalanced capacitor voltage causes imbalanced voltage stress among the semiconductor devices and causes increase output voltage and current harmonics.This paper introduces a modified voltage balancing strategy using two-level space vector modulation.By decomposing the three-level space vector diagram into two-level space vector diagram and redistributing the dwell times of the two-level zero space vectors,the modified voltage balancing method ensures minimal NP voltage ripple.Compared to the commonly used NP voltage control method(using 3L SVM[9]),the proposed modified NP voltage control method offers a slightly higher neutral-point voltage ripple and output voltage harmonics but,it has much lower switching loss,code size and execution time.展开更多
The entropy squeezing for a three-level atom interacting with a single-model field is studied. A general definition of entropy squeezing for three-level atom is given according to entropic uncertainty relation of thre...The entropy squeezing for a three-level atom interacting with a single-model field is studied. A general definition of entropy squeezing for three-level atom is given according to entropic uncertainty relation of three-level system, and the calculation formalism of entropy is derived for a cascade three-level atom. By using numerical calculation, the entropy squeezing properties of a cascade three-level atom are examined. Our results show that, three-level atom can generate obvious entropy squeezing effect via choosing appropriate superposition state of three-level atom. Our results are meaningful for preparing three-level system information resources with ultra-low quantum noise.展开更多
We observe the Autler-Townes splitting effect in a △-type quantum three-level system, using the lowest three levels of a SQUID-type Al/AlOx/Al transmon qubit embedded in a three-dimensional copper microwave cavity. A...We observe the Autler-Townes splitting effect in a △-type quantum three-level system, using the lowest three levels of a SQUID-type Al/AlOx/Al transmon qubit embedded in a three-dimensional copper microwave cavity. A control tone at different strengths is applied in resonance with the transition between the first and second excited states, while the spectra between each of them and the ground state are probed by another microwave tone. The experimental result shows the difference between the two spectra, and fits well with the Lindblad master equation model.展开更多
基金The code used in our calculation is provided by Pro- fessor Ke-li Han from Dalian Institute of Chemical Physics, Chinese Academy of Science, and we appreci- ate his help and kind advice. This work was supported by the National Natural Science Foundation of China (No.11447020), the Natural Science Foundation of Hu- nan province (No.2015JJ3104), and the Scientific Re- search Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.
文摘We theoretically investigate the Autler-Townes (AT) splitting in the photoelectron spectra of three-level ladder K2 molecule driven by a pump-probe pulse via employing the time- dependent wave packet approach. The dependence of AT splitting on two laser intensities and wavelengths are studied in detail. We firstly quantify these effects on peak shift and AT separation. The photoelectron spectra show double splitting with symmetric profiles, but with asymmetric profiles when the wavelength is changed. The magnitude of AT splitting increases with the pump laser intensity, but does not vary with probe intensity. The shifts of the absorption peaks and the splitting between AT doublet are predicted by using an analyt- ical fitting function when the intensity/wavelength of one of the two fields is changed. These novel results are of importance for the molecular spectroscopy and may further stimulate the first principles theoretical studies analytically.
基金Project supported by the National Natural Science Foundation of China (Grant No 10374025).
文摘We propose a scheme to implement a two-qubit conditional quantum phase gate for the intracavity field via a single three-level ∧-type atom driven by two modes in a high-Q cavity. The quantum inforraation is encoded on the Fock states of the bimodal cavity. The gate's averaged fidelity is expected to reach 99.8%.
基金The project supported by the ‘Qing Lan' project of Jiangsu Province of China under Grant No. 2005SL002J
文摘By using the method of eigenvectors, the atomic populations and emission spectrum are investigated in a system that consists of a cascade three-level atom resonantly interacting with a single-mode tield in a Kerr-like medium. The atom and the field are assumed to be initially in the upper atomic state and the Fock state, respectively. Results for models with intensity-dependent coupling and with intensity-independent coupling are compared. It is found that both population dynamics and emission spectrum show no indications of atom-field decoupling in the strong field limit if the intensity-dependent coupling is taken into account.
文摘In this paper, we study the control problem of adiabatic decoherence in a three-level atom. We will find the decoupling bang-bang group for various configurations, including the V configuration and the cascade type of three-levelatom subjected to adiabatic decoherence. We also give the programs to design a sequence of periodic twinborn pulses to suppress the decoherence.
基金Project supported by the National Natural Science Foundation of China (Grant No 60261002) and the Science Foundation of Yanbian University (Grant No 2005-20).
文摘We propose a scheme to realize the nonlocal quantum entanglement of three three-level particles by using a threeparticle entangled state of three levels as a quantum channel with the aid of some local unitary transformations. This scheme can be directly generalized to the nonlocal quantum entanglement of N three-level particles.
基金The project supported by National Natural Science Foundation of China under Grant No.60674040China Postdoctoral Science Foundation
文摘We present a scheme for probabilistically teleporting an unknown three-level bipartite entangled state by using a partial entangled three-level bipartite state as quantum channel This scheme can be directly generalized to probabilistically teleport an unknown three-level k-particle entangled state by a partial three-level bipartite entangled state. A11 kinds of unitary transformations are given in detail We calculate the successful total probability and the total classical communication cost required for this scheme.
基金The project supported by the Natural Science Foundation of Education Bureau of Jingsu Province of China under Grant No. 04KJB140014
文摘In this paper, two schemes for teleporting an unknown three-particle three-level entangled state are proposed. In the first scheme, two partial three-particle three-level entangled states are used as the quantum channels, while in the second scheme, three two-particle three-level non-maximally entangled states are employed as quantum channels. It is shown that the teleportation can be successfully realized with certain probability, for both two schemes, ira receiver adopts some appropriate unitary transformations. It is shown also that the successful probabilities of these two schemes are different.
基金supported by the National Natural Science Foundation of China (Grant Nos 10434060 and 10674047)the Natural Science Foundation of the Jiangsu Higher Institutions of China (Grant No 06KJB510020)the Natural Science Foundation of Jiangsu University of China (Grant No 07JDG027)
文摘The general expressions of the average dissipative and dipole forces acting on a A-configuration three-level atom in an arbitrary light field are derived by means of the optical Bloch equations based on the atomic density matrix elements, and the general properties of the average dissipative and dipole forces on a three-level atom in the linearly-polarized high-order Bessel beams (HBBs) are analysed. We find a resonant property (with two resonant peaks) of the dissipative force and a non-resonant property (with two pairs of non-resonant peaks) of the dipole force on the three-level atom, which are completely different from those on the two-level atom. Meanwhile we find a saturation effect of the average dissipative force in the HBB, which comes from the saturation of the upper-level population. Our study shows that the general expressions of the average dissipative and dipole forces on the three-level atom will be simplified to those of the two-level atom under the approximation of large detuning. Finally, we study the axial and azimuthal Doppler cooling of atoms in ID optical molasses composed of two counter-propagating HBBs and discuss the azimuthal influence of the HBB on the Doppler cooling limit. We also find that the Doppler limit of atoms in the molasses HBB is slightly below the conventional Doppler limit of hГ/(2kB) due to the orbital angular momentum lh of the HBB.
基金Project supported by the National Natural Science Foundation of China(Grant No.11574082)the Fundamental Research Funds for the Central Universities,China(Grant No.2018MS050)
文摘Propagation of strong femtosecond hyper-Gaussian pulses in a cascade three-level molecular system is studied by solving numerically the Maxwell–Bloch equations by the iterative predictor-corrector finite-difference time-domain method.Optical power limiting behavior induced by strong nonlinear two-photon absorption is observed for different orders of the femtosecond hyper-Gaussian pulses. Pulses of a higher order temporal profile are found to have a wider power range of optical limiting but a larger output saturation intensity. Both the output saturation value and the damage threshold of optical power limiting decrease with pulse duration increasing. The decrease of the pulse area along the pulse propagation is much slower than that obtained from the two-photon area theorem due to invalidity of the slowly varying amplitude approximation and the monochromatic field hypothesis.
基金the National Fundamental Research Program under Grant No. 2006CB921106National Natural Science Foundation of China under Grant Nos. 10325521 and 60433050+1 种基金the SRFDP Program of Ministry of Education under Grant No. 20060003048the Key Project of Ministry of Education under Grant No. 306020
文摘In this paper,we present decoupling bang-bang operations for the suppression of general decoherence,bothamplitude and phase damping,in a three-level system in A-configuration.We give a program to design a sequence ofperiodic twinborn pulses to suppress the decoherence in such the system.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12064012 and 11374096)。
文摘The entropy squeezing of a V-type three-level atom interacting with a single-mode field and passing through the amplitude damping channel is investigated in detail. Our results show that when coupled to the single-mode field, the atom in appropriate initial states can not only generate obvious entropy squeezing but also keep in the optimal squeezing state,while passing through the amplitude damping channel, the atom can generate entropy squeezing under the control of the weak measurement. Besides, it is proved again that as a measurement method for atomic squeezing, the entropy squeezing is precise and effective. Therefore our work is instructive for experiments in preparing three-level system information resource with ultra-low quantum noise.
基金The project supported by the Natural Science Foundation of Education Committee of Anhui Province of China under Grant No. 2004kj186
文摘The interaction of a single three-level trapped ion with two laser beams has been studied theoretically. With application of two successive unitary transformations, an analytical solution to this quantum system has been obtained.
文摘In this paper, a voltage oriented control strategy for three-level PWM rectifier based on Sliding Mode Control (SMC) is introduced in order to obtain fast and accurate response of dc-bus voltage. To verify the validity of the analysis and the feasibility of the proposed control method a set of simulation tests have been conducted using Matlab/Simulink. The simulation results show that compared to the conventional PI controller, the SMC can reduce drastically the three-level rectifier’s voltage fluctuation and improve the dynamic response of dc-bus significantly.
基金National Natural Science Foundation of China(No.61261029)
文摘In the traditional three-level space vector pulse width modulation(SVPWM)algorithm,the sector judgment is computationallycomplex since the sector is divided into triangles and hexagons.In addition,the switching frequency is high becausethe seven-segment switching sequence is adopted.For this reason,a new SVPWM control algorithm for three-level inverteris proposed,in which the sector judgment is simplified by dividing the sector into quasi hexagons?and the new four-segmentswitching sequence is adopted to reduce the switching frequency.Simulation results show that the total harmonic distortiongrows down with the switching frequency decreasing,moreover,the algorithm runtime is also decreased.
基金National Natural Science Foundation of China(No.51867012)。
文摘Aiming at the difficulty of setting the weight coefficient in the value function of model predictive torque control(MPTC)for permanent magnet synchronous motor(PMSM)driven by three-level inverter,a fine-division model predictive flux control(MPFC)method is proposed.First,establish a mathematical model between the motor torque and the stator flux linkage according to the mathematical equations of PMSM.Thus,the control of the motor torque and stator flux linkage in the MPTC is transformed into the control of a single stator flux linkage vector,omitting the cumbersome weight setting process in the traditional MPTC.The midpoint potential control strategy is proposed,which uses the characteristics of redundant small vectors to balance the midpoint potential.After that,a fine-division strategy is proposed,which effectively reduces the number of candidate vectors and the computational burden of the system.Finally,the proposed MPFC is compared with MPTC by simulation.The results show that the proposed fine-division MPFC effectively reduces the system calculation,and has the advantages of simple principle and better dynamic and steady-state control performance.The feasibility of the control strategy is verified.
基金National Natural Science Foundation of China(No.61463025)Opening Foundation of Key Laboratory of Opto-Technology and Intelligent Control(Lanzhou Jiaotong University),Ministry of Education(No.KFKT2018-8)。
文摘Based on the fractional order theory and sliding mode control theory,a model prediction current control(MPCC)strategy based on fractional observer is proposed for the permanent magnet synchronous motor(PMSM)driven by three-level inverter.Compared with the traditional sliding mode speed observer,the observer is very simple and eases to implement.Moreover,the observer reduces the ripple of the motor speed in high frequency range in an efficient way.To reduce the stator current ripple and improve the control performance of the torque and speed,the MPCC strategy is put forward,which can make PMSM MPCC system have better control performance,stronger robustness and good dynamic performance.The simulation results validate the feasibility and effectiveness of the proposed scheme.
文摘Capacitor voltage imbalance is a significant problem for three-level inverters.Due to the mid-point modulation of these inverter topologies,the neutral point potential moves up or down depending on the neutral point current direction creating imbalanced voltages among the two capacitors.This imbalanced capacitor voltage causes imbalanced voltage stress among the semiconductor devices and causes increase output voltage and current harmonics.This paper introduces a modified voltage balancing strategy using two-level space vector modulation.By decomposing the three-level space vector diagram into two-level space vector diagram and redistributing the dwell times of the two-level zero space vectors,the modified voltage balancing method ensures minimal NP voltage ripple.Compared to the commonly used NP voltage control method(using 3L SVM[9]),the proposed modified NP voltage control method offers a slightly higher neutral-point voltage ripple and output voltage harmonics but,it has much lower switching loss,code size and execution time.
基金Project supported by the National Natural Science Foundation of China(Grant No.11374096)
文摘The entropy squeezing for a three-level atom interacting with a single-model field is studied. A general definition of entropy squeezing for three-level atom is given according to entropic uncertainty relation of three-level system, and the calculation formalism of entropy is derived for a cascade three-level atom. By using numerical calculation, the entropy squeezing properties of a cascade three-level atom are examined. Our results show that, three-level atom can generate obvious entropy squeezing effect via choosing appropriate superposition state of three-level atom. Our results are meaningful for preparing three-level system information resources with ultra-low quantum noise.
基金Supported by the National Basic Research Program of China under Grant Nos 2011CBA00304,2014CB848700 and 2014CB921401
文摘We observe the Autler-Townes splitting effect in a △-type quantum three-level system, using the lowest three levels of a SQUID-type Al/AlOx/Al transmon qubit embedded in a three-dimensional copper microwave cavity. A control tone at different strengths is applied in resonance with the transition between the first and second excited states, while the spectra between each of them and the ground state are probed by another microwave tone. The experimental result shows the difference between the two spectra, and fits well with the Lindblad master equation model.