We use linear entropy of an exact quantum state to study the entanglement between internal electronic states and external motional states for a two-level atom held in an amplitude-modulated and tilted optical lattice....We use linear entropy of an exact quantum state to study the entanglement between internal electronic states and external motional states for a two-level atom held in an amplitude-modulated and tilted optical lattice. Starting from an unentangled initial state associated with the regular 'island' of classical phase space, it is demonstrated that the quantum resonance leads to entanglement generation, the chaotic parameter region results in the increase of the generation speed, and the symmetries of the initial probability distribution determine the final degree of entanglement. The entangled initial states are associated with the classical 'chaotic sea', which do not affect the final entanglement degree for the same initial symmetry. The results may be useful in engineering quantum dynamics for quantum information processing.展开更多
The existence of specific biorhythms and the role of geomagnetic and/or solar magnetic activities are well-established by appropriate correlations in chronobiology. From a physical viewpoint, there are two different a...The existence of specific biorhythms and the role of geomagnetic and/or solar magnetic activities are well-established by appropriate correlations in chronobiology. From a physical viewpoint, there are two different accesses to biorhythms to set up connections to molecular processes: quantum mechanical perturbation theoretical methods and their resonance dominators to characterize specific interactions between constituents. These methods permit the treatment of molecular processes by circuits with characteristic resonances and “beat-frequencies”, which result from primarily fast physical processes. As examples, the tunneling processes between DNA base pairs (H bonds), the ATP decomposition and the irradiation of tumor cells are accounted for.展开更多
We study quantum motion around a classical heteroclinic point of a single trapped ion interacting with a strong laser standing wave. We construct a set of exact coherent states of the quantum system and from the exact...We study quantum motion around a classical heteroclinic point of a single trapped ion interacting with a strong laser standing wave. We construct a set of exact coherent states of the quantum system and from the exact solutions reveal that quantum signatures of chaos can be induced by the adiabatic interaction between the trapped ion and the laser standing wave, where the quantum expectation values of position and momentum correspond to the classically chaotic orbit. The chaotic region on the phase space is illustrated. The energy crossing and quantum resonance in time evolution and the exponentially increased Heisenberg uncertainty are found. The results suggest a theoretical scheme for controlling the unstable regular and chaotic motions.展开更多
Following the quantum theory-based physical model of the human body,a new interpretation of the traditional Chinese medicine(TCM)principle of"Cunkou reads viscera"is presented.Then,a Gaussian pulse wave mode...Following the quantum theory-based physical model of the human body,a new interpretation of the traditional Chinese medicine(TCM)principle of"Cunkou reads viscera"is presented.Then,a Gaussian pulse wave model as a solution to the Schrodinger equation is shown to accurately describe 19 different pulse shapes,and to quantitatively capture the degree of YinYang attributes of 13 pulse shapes.Furthermore,the model suggests using pulse depth and strength as leading-order quantity and pulse shape as first-order quantity,to characterize the hierarchical resonance between the human body and the environment.The future pulse informatics will focus on determining an individual’s unique quantum human equilibrium state,and diagnose its health state according to the pulse deviation from its equilibrium state,to truly achieve the high level of TCM:"knowing the normal state and reaching the change".展开更多
The single photon scattering properties in a pair of waveguides coupled by a whispering-gallery resonator in- teracting with a semiconductor quantum dot are investigated theoretically. The two waveguides support four ...The single photon scattering properties in a pair of waveguides coupled by a whispering-gallery resonator in- teracting with a semiconductor quantum dot are investigated theoretically. The two waveguides support four possible ports for an incident single photon. The quantum dot is considered a V-type system. The incident direction-dependent single photon scattering properties are studied and equal-output probability from the four ports for a single photon incident is discussed. The influences of backscattering between the two modes of the whispering-gallery resonator for incident direction-dependent single photon scattering properties are also pre- sented.展开更多
The hybrid metal-organic framework [(CH3)2NH2]Fe(HCOO)3 with a perovskite-like structure exhibits a variety of unusual magnetic behaviors at low temperatures. While the long-distance super-exchange through the Fe-...The hybrid metal-organic framework [(CH3)2NH2]Fe(HCOO)3 with a perovskite-like structure exhibits a variety of unusual magnetic behaviors at low temperatures. While the long-distance super-exchange through the Fe-(Y-CH-O- Fe exchange path leads to a canted antiferromagnetic ordering at TN - 19 K, a second transition of magnetic blocking develops at TB- 9 K. The stair-shaped magnetization hysteresis loops below TB resemble the behaviors of resonant quantum tunneling of magnetization in single-molecular quantum magnets. Moreover, the magnetic relaxation also exhibits several features of resonant quantum relaxation, such as the exponential law with a single characteristic relaxation time, and the nonmonotonic dependence of relaxation rate on the applied magnetic field with a much faster relaxation around the resonant fields. The origin of quantum tunneling behaviors in the [(CH3)2NH2]Fe(HCOO)3 metal-organic framework is discussed in terms of magnetic phase separation due to the modification of hydrogen bonding on the long-distance super-exchange interaction.展开更多
Excited states of lnAs quantum dots (QDs) can be energetically coupled with the confined level of OaAs quantum wells (QWs) in a thin-barrier resonant tunneling diode (RTD). Single charge variation in the coupled...Excited states of lnAs quantum dots (QDs) can be energetically coupled with the confined level of OaAs quantum wells (QWs) in a thin-barrier resonant tunneling diode (RTD). Single charge variation in the coupled QD can effectively switch on/off the resonant tunneling current passing through RTD, not only for emcient single-photon detection but also for photon-number-resolving detection. We present the study of the Q,D-QW coupling effect in the quantum dot coupled resonant tunneling diode (QD-cRTD) and figure out important factors for further improving the detector performance.展开更多
We propose a new scheme on modulating the lasing performance of a quantum dot-cavity system. Compared to the conventional above-band pump, in our new scheme an additional resonant driving field is applied on the quant...We propose a new scheme on modulating the lasing performance of a quantum dot-cavity system. Compared to the conventional above-band pump, in our new scheme an additional resonant driving field is applied on the quantum dot-cavity system. By employing the master equation theory and the Jaynes-Cummings model, we are able to study the interesting phenomenon of the coupling system. To compare the different behaviors between using our new scheme and the conventional method,we carry out investigatioin for both the 'good system'and 'more realistic system', characterizing several important parameters, such as the cavity population, exciton population and the second-order correlation function at zero time delay. Through numerical simulations,we demonstrate that for both the good system and more realistic system, their lasing regimes can be displaced into other regimes in the presence of a resonant driving field.展开更多
We use the photon Green-function method to study the quantum resonant dipole-dipole interaction(RDDI) induced by an Ag nanosphere(ANP).As the distance between the two dipoles increases,the RDDI becomes weaker,whic...We use the photon Green-function method to study the quantum resonant dipole-dipole interaction(RDDI) induced by an Ag nanosphere(ANP).As the distance between the two dipoles increases,the RDDI becomes weaker,which is accompanied by the influence of the higher-order mode of the ANP on RDDI declining more quickly than that of the dipole mode.Across a broad frequency range(above 0.05 eV),the transfer rate of the RDDI is nearly constant since the two dipoles are fixed at the proper position.In addition,this phenomenon still exists for slightly different radius of the ANPs.We find that the frequency corresponding to the maximum transfer rate of RDDI exhibits a monotonic decrease by moving away one dipole as the other dipole and the ANP are kept fixed.In addition,the radius of ANP has little effect on this.When the two dipoles are far from the ANP,the maximum transfer rate of the RDDI takes place at the frequency of the dipole mode.In contrast,when the two dipoles are close to the ANP,the higher-order modes come into effect and they will play a leading role in the RDDI if they match the transition frequency of the dipole.Our results may be used in a biological detector and have a certain guiding significance for further application.展开更多
We create a potential for light with a phase mirror and then experimentally realize a photonic quantum ratchet in an all-optical system, in which ratchet effects can be observed with the naked eye up to more than 22 s...We create a potential for light with a phase mirror and then experimentally realize a photonic quantum ratchet in an all-optical system, in which ratchet effects can be observed with the naked eye up to more than 22 steps, and quantum resonance can be demonstrated. Our method also provides a new means to simulate quantum particles with classical light, and it can be applied to investigate many other quantum phenomena.展开更多
Identifying Hamiltonian of a quantum system is of vital importance for quantum information processing.In this article, we realized and benchmarked a quantum Hamiltonian identification algorithm recently proposed(Zhang...Identifying Hamiltonian of a quantum system is of vital importance for quantum information processing.In this article, we realized and benchmarked a quantum Hamiltonian identification algorithm recently proposed(Zhang and Sarovar, 2014). we realized the algorithm on a liquid nuclear magnetic resonance quantum information processor using two types of working media with different forms of Hamiltonian. Our experiment realized the quantum identification algorithm based on free induction decay signals. We also showed how to process data obtained in a practical experiment. We studied the influence of decoherence by numerical simulations. Our experiments and simulations demonstrate that the algorithm is effective and robust.展开更多
We investigate quantum state tomography(QST) for pure states and quantum process tomography(QPT) for unitary channels via adaptive measurements. For a quantum system with a d-dimensional Hilbert space, we first propos...We investigate quantum state tomography(QST) for pure states and quantum process tomography(QPT) for unitary channels via adaptive measurements. For a quantum system with a d-dimensional Hilbert space, we first propose an adaptive protocol where only 2d. 1 measurement outcomes are used to accomplish the QST for all pure states. This idea is then extended to study QPT for unitary channels, where an adaptive unitary process tomography(AUPT) protocol of d2+d.1measurement outcomes is constructed for any unitary channel. We experimentally implement the AUPT protocol in a 2-qubit nuclear magnetic resonance system. We examine the performance of the AUPT protocol when applied to Hadamard gate, T gate(/8 phase gate), and controlled-NOT gate,respectively, as these gates form the universal gate set for quantum information processing purpose. As a comparison, standard QPT is also implemented for each gate. Our experimental results show that the AUPT protocol that reconstructing unitary channels via adaptive measurements significantly reduce the number of experiments required by standard QPT without considerable loss of fidelity.展开更多
Continuous wave(CW) operation of long wave infrared(LWIR) quantum cascade lasers(QCLs) is achieved up to a temperature of 303 K. For room temperature CW operation, the wafer with 35 stages was processed into bur...Continuous wave(CW) operation of long wave infrared(LWIR) quantum cascade lasers(QCLs) is achieved up to a temperature of 303 K. For room temperature CW operation, the wafer with 35 stages was processed into buried heterostructure lasers. For a 2-mm-long and 10-μm-wide laser with high-reflectivity(HR) coating on the rear facet, CW output power of 45 m W at 283 K and 9 m W at 303 K is obtained. The lasing wavelength is around 9.4 μm locating in the LWIR spectrum range.展开更多
Rapid, accurate and sensitive detection of particular DNA sequence is critical in fundamental biomedical research and clinical diagnostics. However, conventional approaches for DNA assay often suffer from cumbersome p...Rapid, accurate and sensitive detection of particular DNA sequence is critical in fundamental biomedical research and clinical diagnostics. However, conventional approaches for DNA assay often suffer from cumbersome procedures, long analysis time and insufficient sensitivity. Recently, single-particle detection technology has emerged as a powerful tool in the biosensing area due to its significant advantages of ultrahigh sensitivity, low sample-consumption and rapid analysis time. Especially, the introduction of novel nanomaterials has greatly promoted the development of single-particle detection and its applications for DNA sensing. In this review, we summarize the recent advance in single-particle detection strategies for DNA sensing, and focus mainly on metallic nanoparticle-and semiconductor quantum dot-based single-particle detection. We highlight the emerging trends in this field as well.展开更多
Non-relativistic phase shifts for a generalized Yukawa potential V(r) =-V_0( e^(-αr)/r)-V_1( e^(-2αr)/r^2) are studied by the amplitude-phase method and by a frequently used analytic method based on a Pekeris-type a...Non-relativistic phase shifts for a generalized Yukawa potential V(r) =-V_0( e^(-αr)/r)-V_1( e^(-2αr)/r^2) are studied by the amplitude-phase method and by a frequently used analytic method based on a Pekeris-type approximation of power-law potential terms.Small variations of V_1 seem to have marginal effects on the effective potential and on exact phase shifts.However,as pointed out in this study,a Pekeris-type approximation in scattering applications often implies serious distortions of both effective potentials and phase shifts.The Pekeris-type based analytic approximation in this study seems to give low-quality scattering results for this model potential at low energies.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11175064 and 11475060the Construct Program of the National Key Discipline of Chinathe Hunan Provincial Innovation Foundation for Postgraduates under Grant No CX2014B195
文摘We use linear entropy of an exact quantum state to study the entanglement between internal electronic states and external motional states for a two-level atom held in an amplitude-modulated and tilted optical lattice. Starting from an unentangled initial state associated with the regular 'island' of classical phase space, it is demonstrated that the quantum resonance leads to entanglement generation, the chaotic parameter region results in the increase of the generation speed, and the symmetries of the initial probability distribution determine the final degree of entanglement. The entangled initial states are associated with the classical 'chaotic sea', which do not affect the final entanglement degree for the same initial symmetry. The results may be useful in engineering quantum dynamics for quantum information processing.
文摘The existence of specific biorhythms and the role of geomagnetic and/or solar magnetic activities are well-established by appropriate correlations in chronobiology. From a physical viewpoint, there are two different accesses to biorhythms to set up connections to molecular processes: quantum mechanical perturbation theoretical methods and their resonance dominators to characterize specific interactions between constituents. These methods permit the treatment of molecular processes by circuits with characteristic resonances and “beat-frequencies”, which result from primarily fast physical processes. As examples, the tunneling processes between DNA base pairs (H bonds), the ATP decomposition and the irradiation of tumor cells are accounted for.
基金The project supported by National Natural Science Foundation of China under Grant No.10575034the Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics of China under Grant No.T152504
文摘We study quantum motion around a classical heteroclinic point of a single trapped ion interacting with a strong laser standing wave. We construct a set of exact coherent states of the quantum system and from the exact solutions reveal that quantum signatures of chaos can be induced by the adiabatic interaction between the trapped ion and the laser standing wave, where the quantum expectation values of position and momentum correspond to the classically chaotic orbit. The chaotic region on the phase space is illustrated. The energy crossing and quantum resonance in time evolution and the exponentially increased Heisenberg uncertainty are found. The results suggest a theoretical scheme for controlling the unstable regular and chaotic motions.
基金the ENN Institute of Life Science and Technology for their financial support。
文摘Following the quantum theory-based physical model of the human body,a new interpretation of the traditional Chinese medicine(TCM)principle of"Cunkou reads viscera"is presented.Then,a Gaussian pulse wave model as a solution to the Schrodinger equation is shown to accurately describe 19 different pulse shapes,and to quantitatively capture the degree of YinYang attributes of 13 pulse shapes.Furthermore,the model suggests using pulse depth and strength as leading-order quantity and pulse shape as first-order quantity,to characterize the hierarchical resonance between the human body and the environment.The future pulse informatics will focus on determining an individual’s unique quantum human equilibrium state,and diagnose its health state according to the pulse deviation from its equilibrium state,to truly achieve the high level of TCM:"knowing the normal state and reaching the change".
基金Supported by the National Natural Science Foundation of China under Grant No 11105001the Anhui Provincial Natural Science Foundation under Grant Nos 1408085QA22 and 1608085MA09
文摘The single photon scattering properties in a pair of waveguides coupled by a whispering-gallery resonator in- teracting with a semiconductor quantum dot are investigated theoretically. The two waveguides support four possible ports for an incident single photon. The quantum dot is considered a V-type system. The incident direction-dependent single photon scattering properties are studied and equal-output probability from the four ports for a single photon incident is discussed. The influences of backscattering between the two modes of the whispering-gallery resonator for incident direction-dependent single photon scattering properties are also pre- sented.
基金supported by the National Natural Science Foundation of China(Grant Nos.11227405,51371192,and 51371193)the Chinese Academy of Sciences(Grant No.XDB07030200)
文摘The hybrid metal-organic framework [(CH3)2NH2]Fe(HCOO)3 with a perovskite-like structure exhibits a variety of unusual magnetic behaviors at low temperatures. While the long-distance super-exchange through the Fe-(Y-CH-O- Fe exchange path leads to a canted antiferromagnetic ordering at TN - 19 K, a second transition of magnetic blocking develops at TB- 9 K. The stair-shaped magnetization hysteresis loops below TB resemble the behaviors of resonant quantum tunneling of magnetization in single-molecular quantum magnets. Moreover, the magnetic relaxation also exhibits several features of resonant quantum relaxation, such as the exponential law with a single characteristic relaxation time, and the nonmonotonic dependence of relaxation rate on the applied magnetic field with a much faster relaxation around the resonant fields. The origin of quantum tunneling behaviors in the [(CH3)2NH2]Fe(HCOO)3 metal-organic framework is discussed in terms of magnetic phase separation due to the modification of hydrogen bonding on the long-distance super-exchange interaction.
基金Supported by the National Basic Research Program of China under Grant No 2011CB925600the National Natural Science Foundation of China under Grant Nos 11427807,91321311,10990100,11174057 and 61106092the Shanghai Science and Technology Committee under Grant No 14JC1406600
文摘Excited states of lnAs quantum dots (QDs) can be energetically coupled with the confined level of OaAs quantum wells (QWs) in a thin-barrier resonant tunneling diode (RTD). Single charge variation in the coupled QD can effectively switch on/off the resonant tunneling current passing through RTD, not only for emcient single-photon detection but also for photon-number-resolving detection. We present the study of the Q,D-QW coupling effect in the quantum dot coupled resonant tunneling diode (QD-cRTD) and figure out important factors for further improving the detector performance.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11274178,61475197 and 61590932the Natural Science Foundation of the Jiangsu Higher Education Institutions under Grant No 15KJA120002+1 种基金the outstanding Youth Project of Jiangsu Province under Grant No BK20150039the Priority Academic Program Development of Jiangsu Higher Education Institutions under Grant No YX002001
文摘We propose a new scheme on modulating the lasing performance of a quantum dot-cavity system. Compared to the conventional above-band pump, in our new scheme an additional resonant driving field is applied on the quantum dot-cavity system. By employing the master equation theory and the Jaynes-Cummings model, we are able to study the interesting phenomenon of the coupling system. To compare the different behaviors between using our new scheme and the conventional method,we carry out investigatioin for both the 'good system'and 'more realistic system', characterizing several important parameters, such as the cavity population, exciton population and the second-order correlation function at zero time delay. Through numerical simulations,we demonstrate that for both the good system and more realistic system, their lasing regimes can be displaced into other regimes in the presence of a resonant driving field.
基金supported by the National Natural Science Foundation of China(Grant Nos.11347215,11464014,and 11104113)the Natural Science Foundation of Hunan Province,China(Grant Nos.13JJ6059 and 13JJB015)the Natural Science Foundation of Education Department of Hunan Province,China(Grant Nos.13C750 and 13B091)
文摘We use the photon Green-function method to study the quantum resonant dipole-dipole interaction(RDDI) induced by an Ag nanosphere(ANP).As the distance between the two dipoles increases,the RDDI becomes weaker,which is accompanied by the influence of the higher-order mode of the ANP on RDDI declining more quickly than that of the dipole mode.Across a broad frequency range(above 0.05 eV),the transfer rate of the RDDI is nearly constant since the two dipoles are fixed at the proper position.In addition,this phenomenon still exists for slightly different radius of the ANPs.We find that the frequency corresponding to the maximum transfer rate of RDDI exhibits a monotonic decrease by moving away one dipole as the other dipole and the ANP are kept fixed.In addition,the radius of ANP has little effect on this.When the two dipoles are far from the ANP,the maximum transfer rate of the RDDI takes place at the frequency of the dipole mode.In contrast,when the two dipoles are close to the ANP,the higher-order modes come into effect and they will play a leading role in the RDDI if they match the transition frequency of the dipole.Our results may be used in a biological detector and have a certain guiding significance for further application.
基金supported by the National Basic Research Program of China(2011CB921200)the National Natural Science Foundation of China(11325419,11274289,61327901)the Fundamental Research Funds for the Central Universities(WK2470000011)
文摘We create a potential for light with a phase mirror and then experimentally realize a photonic quantum ratchet in an all-optical system, in which ratchet effects can be observed with the naked eye up to more than 22 steps, and quantum resonance can be demonstrated. Our method also provides a new means to simulate quantum particles with classical light, and it can be applied to investigate many other quantum phenomena.
基金supported by the National Natural Science Foundation of China(11175094 and 91221205)the National Basic Research Program of China(2011CB9216002)
文摘Identifying Hamiltonian of a quantum system is of vital importance for quantum information processing.In this article, we realized and benchmarked a quantum Hamiltonian identification algorithm recently proposed(Zhang and Sarovar, 2014). we realized the algorithm on a liquid nuclear magnetic resonance quantum information processor using two types of working media with different forms of Hamiltonian. Our experiment realized the quantum identification algorithm based on free induction decay signals. We also showed how to process data obtained in a practical experiment. We studied the influence of decoherence by numerical simulations. Our experiments and simulations demonstrate that the algorithm is effective and robust.
基金supported by the Natural Sciences and Engineering Research Council of Canada(NSERC)the Canadian Institute for Advanced Research(CIFAR)+3 种基金the National Natural Science Foundation of China(Grant Nos11175094,91221205,11375167,11227901 and 91021005)the National Basic Research Program of China(Grant No.2015CB921002)the National Key Basic Research Program(NKBRP)(Grant Nos.2013CB921800and 2014CB848700)the National Science Fund for Distinguished Young Scholars(Grant No.11425523)
文摘We investigate quantum state tomography(QST) for pure states and quantum process tomography(QPT) for unitary channels via adaptive measurements. For a quantum system with a d-dimensional Hilbert space, we first propose an adaptive protocol where only 2d. 1 measurement outcomes are used to accomplish the QST for all pure states. This idea is then extended to study QPT for unitary channels, where an adaptive unitary process tomography(AUPT) protocol of d2+d.1measurement outcomes is constructed for any unitary channel. We experimentally implement the AUPT protocol in a 2-qubit nuclear magnetic resonance system. We examine the performance of the AUPT protocol when applied to Hadamard gate, T gate(/8 phase gate), and controlled-NOT gate,respectively, as these gates form the universal gate set for quantum information processing purpose. As a comparison, standard QPT is also implemented for each gate. Our experimental results show that the AUPT protocol that reconstructing unitary channels via adaptive measurements significantly reduce the number of experiments required by standard QPT without considerable loss of fidelity.
基金Project supported by the National Key Research And Development Program(No.2016YFB0402303)the National Natural Science Foundation of China(Nos.61435014,61627822,61574136,61774146,61674144,61404131)+1 种基金the Key Projects of Chinese Academy of Sciences(Nos.ZDRW-XH-2016-4,QYZDJ-SSW-JSC027)the Beijing Natural Science Foundation(No.4162060,4172060)
文摘Continuous wave(CW) operation of long wave infrared(LWIR) quantum cascade lasers(QCLs) is achieved up to a temperature of 303 K. For room temperature CW operation, the wafer with 35 stages was processed into buried heterostructure lasers. For a 2-mm-long and 10-μm-wide laser with high-reflectivity(HR) coating on the rear facet, CW output power of 45 m W at 283 K and 9 m W at 303 K is obtained. The lasing wavelength is around 9.4 μm locating in the LWIR spectrum range.
基金supported by the National Natural Science Foundation of China (21325523, 21527811)the Shandong Province Science Foundation for Youths (ZR2016HQ07)the Award for Team Leader Program of Taishan Scholars of Shandong Province, China
文摘Rapid, accurate and sensitive detection of particular DNA sequence is critical in fundamental biomedical research and clinical diagnostics. However, conventional approaches for DNA assay often suffer from cumbersome procedures, long analysis time and insufficient sensitivity. Recently, single-particle detection technology has emerged as a powerful tool in the biosensing area due to its significant advantages of ultrahigh sensitivity, low sample-consumption and rapid analysis time. Especially, the introduction of novel nanomaterials has greatly promoted the development of single-particle detection and its applications for DNA sensing. In this review, we summarize the recent advance in single-particle detection strategies for DNA sensing, and focus mainly on metallic nanoparticle-and semiconductor quantum dot-based single-particle detection. We highlight the emerging trends in this field as well.
文摘Non-relativistic phase shifts for a generalized Yukawa potential V(r) =-V_0( e^(-αr)/r)-V_1( e^(-2αr)/r^2) are studied by the amplitude-phase method and by a frequently used analytic method based on a Pekeris-type approximation of power-law potential terms.Small variations of V_1 seem to have marginal effects on the effective potential and on exact phase shifts.However,as pointed out in this study,a Pekeris-type approximation in scattering applications often implies serious distortions of both effective potentials and phase shifts.The Pekeris-type based analytic approximation in this study seems to give low-quality scattering results for this model potential at low energies.