The strength of microwave(MW)electric field can be observed with high precision by using the standard electromagnetically induced transparency and Aulter–Towns(EIT-AT)technique,when its frequency is resonant or nearl...The strength of microwave(MW)electric field can be observed with high precision by using the standard electromagnetically induced transparency and Aulter–Towns(EIT-AT)technique,when its frequency is resonant or nearly-resonant with the Rydberg transition frequency.As the detuning of MW field increases,one of the transmission peaks(single peak)is easier to measure due to its increased amplitude.It can be found that the central symmetry point of the two transmission peaks f_(1/2)is only related to the detuning of MW field△_(MW)and central symmetry point f_(0)of resonant MW field,satisfying the relation f_(1/2)=△_(MW)/2+f_(0).Thus,we demonstrate a single transmission peak method that the MW E-field can be determined by interval between the position of single peak and f_(1/2).We use this method to measure continuous frequencies in a band from-200 MHz to 200 MHz of the MW field.The experimental results and theoretical analysis are presented to describe the effectiveness of this method.For 50 MHz<△_(MW)<200 MHz,this method solves the problem that the AT splitting cannot be measured by using the standard EIT-AT techniques or multiple atomic-level Rydberg atom schemes.展开更多
This paper indicates the problem of the famous Riemann hypothesis (RH), which has been well-verified by a definite answering method using a Bose-Einstein Condensate (BEC) phase. We adopt mathematical induction, mappin...This paper indicates the problem of the famous Riemann hypothesis (RH), which has been well-verified by a definite answering method using a Bose-Einstein Condensate (BEC) phase. We adopt mathematical induction, mappings, and laser photons governed by electromagnetically induced transparency (EIT) to examine the existence of the RH. In considering the well-developed as Riemann zeta function, we find that the existence of RH has a corrected and self-consistent solution. Specifically, there is the only one pole at s = 1 on the complex plane for Riemann’s functions, which generalizes to all non-trivial zeros while s > 1. The essential solution is based on the BEC phases and on the nature of the laser photon(s). This work also incorporates Heisenberg commutators [ x^,p^]=1/2in the field of quantum mechanics. We found that a satisfactory solution for the RH would be incomplete without the formalism of Heisenberg commutators, BEC phases, and EIT effects. Ultimately, we propose the application of qubits in connection with the RH.展开更多
We study a spatiotemporal EIT problem with a dynamical boundary condition for the fractional Dirichlet-to-Neumann operator with a critical exponent.There are three major ingredients in this paper.The first is the fini...We study a spatiotemporal EIT problem with a dynamical boundary condition for the fractional Dirichlet-to-Neumann operator with a critical exponent.There are three major ingredients in this paper.The first is the finite time blowup and the decay estimate of the global solution with a lower-energy initial value.The second ingredient is the L^(q)(2 ≤q <∞) estimate of the global solution applying the Moser iteration,which allows us to show that any global solution is a classical solution.The third,which is the main ingredient of this paper,explores the long time asymptotic behavior of global solutions close to the stationary solution and the bubbling phenomenons by means of a concentration compactness principle.展开更多
In a coherent system, enhanced nonlinearity can be reached via far-detuned coupling fields in the presence of Autler–Townes splitting. We explore the absorption spectra and the Kerr nonlinearity of the coherent syste...In a coherent system, enhanced nonlinearity can be reached via far-detuned coupling fields in the presence of Autler–Townes splitting. We explore the absorption spectra and the Kerr nonlinearity of the coherent system via the interaction between a four-level atomic system and triple fields. We obtain the absorption spectra with double, triple and even quadruple peaks which depend on both the magnitude and the difference of the coupling fields. The Kerr nonlinearity always remains reversely correlated with the absorption spectra. We find that the large coupling detunings can lead to a significant growth of the Kerr nonlinearity and the degenerate four-wave mixing. Both the Kerr nonlinearity and the four-wave mixing can be managed by adjusting the detunings of the coupling fields.展开更多
We demonstrate a simple method to measure electric field intensity by using doublet electromagnetically induced transparency(EIT) spectra of cold Rb Rydberg atoms, where the frequency of the coupling laser does not ne...We demonstrate a simple method to measure electric field intensity by using doublet electromagnetically induced transparency(EIT) spectra of cold Rb Rydberg atoms, where the frequency of the coupling laser does not need to be locked. Based on the Stark splitting of the Rb Rydberg state, 10D_(3/2), under electric fields and the corresponding calculated polarizabilities, the real electric field intensity is calculated using the difference in radio-frequency diffraction between two acousto-optic modulators, which acts as a frequency criterion that allows us to measure the electrical field without locking the coupling laser. The value measured by this simple method shows a good agreement with our previous work [Opt.Express 29 1558(2021)] where the frequency of the coupling laser needs to be locked with an additional EIT spectrum based on atom vapor and a proportional–integral–differential feedback circuit. Our presented method can also be extended to the measurement of electric field based on hot Rydberg atom vapor, which has application in industry.展开更多
基金Project supported by the National Key Research and Development Program of China(Grant No.2021YFF0603704)the National Natural Science Foundation of China(Grant No.62071443)。
文摘The strength of microwave(MW)electric field can be observed with high precision by using the standard electromagnetically induced transparency and Aulter–Towns(EIT-AT)technique,when its frequency is resonant or nearly-resonant with the Rydberg transition frequency.As the detuning of MW field increases,one of the transmission peaks(single peak)is easier to measure due to its increased amplitude.It can be found that the central symmetry point of the two transmission peaks f_(1/2)is only related to the detuning of MW field△_(MW)and central symmetry point f_(0)of resonant MW field,satisfying the relation f_(1/2)=△_(MW)/2+f_(0).Thus,we demonstrate a single transmission peak method that the MW E-field can be determined by interval between the position of single peak and f_(1/2).We use this method to measure continuous frequencies in a band from-200 MHz to 200 MHz of the MW field.The experimental results and theoretical analysis are presented to describe the effectiveness of this method.For 50 MHz<△_(MW)<200 MHz,this method solves the problem that the AT splitting cannot be measured by using the standard EIT-AT techniques or multiple atomic-level Rydberg atom schemes.
文摘This paper indicates the problem of the famous Riemann hypothesis (RH), which has been well-verified by a definite answering method using a Bose-Einstein Condensate (BEC) phase. We adopt mathematical induction, mappings, and laser photons governed by electromagnetically induced transparency (EIT) to examine the existence of the RH. In considering the well-developed as Riemann zeta function, we find that the existence of RH has a corrected and self-consistent solution. Specifically, there is the only one pole at s = 1 on the complex plane for Riemann’s functions, which generalizes to all non-trivial zeros while s > 1. The essential solution is based on the BEC phases and on the nature of the laser photon(s). This work also incorporates Heisenberg commutators [ x^,p^]=1/2in the field of quantum mechanics. We found that a satisfactory solution for the RH would be incomplete without the formalism of Heisenberg commutators, BEC phases, and EIT effects. Ultimately, we propose the application of qubits in connection with the RH.
基金the NNSF of China(12071391)the Guangdong Basic and Applied Basic Research Foundation (2022A1515010069)。
文摘We study a spatiotemporal EIT problem with a dynamical boundary condition for the fractional Dirichlet-to-Neumann operator with a critical exponent.There are three major ingredients in this paper.The first is the finite time blowup and the decay estimate of the global solution with a lower-energy initial value.The second ingredient is the L^(q)(2 ≤q <∞) estimate of the global solution applying the Moser iteration,which allows us to show that any global solution is a classical solution.The third,which is the main ingredient of this paper,explores the long time asymptotic behavior of global solutions close to the stationary solution and the bubbling phenomenons by means of a concentration compactness principle.
基金Project supported by the Open Subject of the State Key Laboratory of Quantum Optics and Quantum Optics Devices (Grant No. KF202209)。
文摘In a coherent system, enhanced nonlinearity can be reached via far-detuned coupling fields in the presence of Autler–Townes splitting. We explore the absorption spectra and the Kerr nonlinearity of the coherent system via the interaction between a four-level atomic system and triple fields. We obtain the absorption spectra with double, triple and even quadruple peaks which depend on both the magnitude and the difference of the coupling fields. The Kerr nonlinearity always remains reversely correlated with the absorption spectra. We find that the large coupling detunings can lead to a significant growth of the Kerr nonlinearity and the degenerate four-wave mixing. Both the Kerr nonlinearity and the four-wave mixing can be managed by adjusting the detunings of the coupling fields.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12034012, 12074231, 12274272, and 61827824)Science and technology innovation plan of colleges and universities in Shanxi Province (Grant No. 2021L313)+2 种基金Science and Technology Project of State Grid (Grant No. 5700-202127198A-0-0-00)Fundamental Research Program of Shanxi Province (Grant No. 202203021222204)Taiyuan University of Science and Technology Scientific Research Initial Funding (Grant Nos. 20222008 and 20222132)。
文摘We demonstrate a simple method to measure electric field intensity by using doublet electromagnetically induced transparency(EIT) spectra of cold Rb Rydberg atoms, where the frequency of the coupling laser does not need to be locked. Based on the Stark splitting of the Rb Rydberg state, 10D_(3/2), under electric fields and the corresponding calculated polarizabilities, the real electric field intensity is calculated using the difference in radio-frequency diffraction between two acousto-optic modulators, which acts as a frequency criterion that allows us to measure the electrical field without locking the coupling laser. The value measured by this simple method shows a good agreement with our previous work [Opt.Express 29 1558(2021)] where the frequency of the coupling laser needs to be locked with an additional EIT spectrum based on atom vapor and a proportional–integral–differential feedback circuit. Our presented method can also be extended to the measurement of electric field based on hot Rydberg atom vapor, which has application in industry.
