Recently, Zhou et al. [Phys. Rev. A 79 (2009) 044304] proposed a scheme for transferring three-dimensional quantum states between remote atomic qubits confined in cavities connected by fibers through adiabatic passa...Recently, Zhou et al. [Phys. Rev. A 79 (2009) 044304] proposed a scheme for transferring three-dimensional quantum states between remote atomic qubits confined in cavities connected by fibers through adiabatic passage. In order to avoid the decoherence due to spontaneous emission, Zhou et al. utilized the large detuning atom-field interaction. In the present paper, we discuss the influence of dissipation on the scheme in both the resonant atom-field interaction case and the large detuning case. We numerically analyze the success probability and the transferring fidelity. It is shown that the resonant case is a preferable choice for the technique of the stimulated Raman adiabatic passage (STIRAP) due to the shorter operation time and the smaller probability of dissipation.展开更多
Using the time-dependent multilevel approach, we have calculated the coherent population transfer between the quantum states of potassium atom by a single frequency-chirped laser pulse. The result shows that a pair of...Using the time-dependent multilevel approach, we have calculated the coherent population transfer between the quantum states of potassium atom by a single frequency-chirped laser pulse. The result shows that a pair of sequential 'broadband' frequency-chirped laser pulses can efficiently transfer population from the initial state of the ladder system to the target state. It is also found that the population can be efficiently transferred to a target state and trapped there by using an 'intuitive' or a 'counterintuitive' frequency sweep laser pulse in the case of 'narrowband' frequency-chirped laser pulse. Our research shows that the complete population transfer is related to the pulse duration, chirp rate, and amplitude of the laser pulse.展开更多
Based on adiabatic passage, we propose a scheme for implementing the quantum transfer of an unknown atomic state. In our scheme, we utilize photons for ideal quantum transmission between two cavities with the successf...Based on adiabatic passage, we propose a scheme for implementing the quantum transfer of an unknown atomic state. In our scheme, we utilize photons for ideal quantum transmission between two cavities with the successful probability being about 1. Meanwhile, the scheme is robust against the effects of atomic spontaneous emission. It may be useful for transferring quantum information among spatially distant atoms.展开更多
This paper considers a scheme for the preparation of two-qutrit entangled states via adiabatic passage in iontrapped system. In the proposal, the two three-level V-type ions are initially cooled to the ground states a...This paper considers a scheme for the preparation of two-qutrit entangled states via adiabatic passage in iontrapped system. In the proposal, the two three-level V-type ions are initially cooled to the ground states and need not be separately addressed. Moreover, only the ionic states act as memory and the system evolves in the dark space during the whole procedure, which makes the system robust against the decoherence and the fluctuation of the laser pulse.展开更多
Combining adiabatic passage and Rydberg antiblockade, we propose a scheme to implement a two-qubit phase gate between two Rydberg atoms. Detuning parameters between frequencies of atomic transitions and those of the c...Combining adiabatic passage and Rydberg antiblockade, we propose a scheme to implement a two-qubit phase gate between two Rydberg atoms. Detuning parameters between frequencies of atomic transitions and those of the corresponding driving lasers are carefully chosen to offset the blockade effect of two Rydberg atoms, so that an effective Hamiltonian,representing a single-photon detuning L-type three-level system and concluding the quantum state of two Rydberg atoms excited simultaneously, is obtained. The adiabatic-passage technique, based on the effective Hamiltonian, is adopted to implement a two-atom phase gate by using two time-dependent Rabi frequencies. Numerical simulations indicate that a high-fidelity two-qubit p-phase gate is constructed and its operation time does not have to be controlled accurately. Besides,owing to the long coherence time of the Rydberg state, the phase gate is robust against atomic spontaneous emission.展开更多
This paper proposes a scheme for implementing teleportation of an entangled state of two trapped atoms through adiabatic passage and photonic interference. The scheme is robust against certain noise such as atomic spo...This paper proposes a scheme for implementing teleportation of an entangled state of two trapped atoms through adiabatic passage and photonic interference. The scheme is robust against certain noise such as atomic spontaneous emission and the detector inefficiency.展开更多
A scheme is proposed to generate W state with qubits of superconducting quantum interference devices (SQUIDs), based on adiabatic passage along dark state. Taking advantages of adiabatic passage, the scheme is very ...A scheme is proposed to generate W state with qubits of superconducting quantum interference devices (SQUIDs), based on adiabatic passage along dark state. Taking advantages of adiabatic passage, the scheme is very robust against decoherence, and it does not need to control the classical field and the interaction time accurately. Because of the achievable strong coupling between SQUID qubits and cavity, W state can be generated with high successful probability.展开更多
We propose a scheme for the deterministic generation of qutrit entanglement for two atoms trapped in an optical cavity. Taking advantage of the adiabatic passage, the operation is immune to atomic spontaneous emission...We propose a scheme for the deterministic generation of qutrit entanglement for two atoms trapped in an optical cavity. Taking advantage of the adiabatic passage, the operation is immune to atomic spontaneous emission as the atomic excited states are never populated; under certain conditions, the probability that the cavity is excited is negligible. We also study the influences of the dissipation due to the atomic spontaneous emission and cavity decay.展开更多
We describe a scheme for the generation of W states and implementation of phase-covariant cloning for n trapped ions. The scheme does not use the vibational mode as the memory and works beyond the Lamb-Dicke regime. T...We describe a scheme for the generation of W states and implementation of phase-covariant cloning for n trapped ions. The scheme does not use the vibational mode as the memory and works beyond the Lamb-Dicke regime. The procedure is robust against moderate fluctuations of experimental parameters by using adiabatic passage.展开更多
We proposed an efficient scheme for constructing a quantum controlled phase-shift gate and generating thecluster states with rf superconducting quantum interference devices (SQUIDs)coupled to a microwave cavity throug...We proposed an efficient scheme for constructing a quantum controlled phase-shift gate and generating thecluster states with rf superconducting quantum interference devices (SQUIDs)coupled to a microwave cavity throughadiabatic evolution of dark eigenstates.During the operation,the spontaneous emission is suppressed since the rf SQUIDsare always in the three lowest flux states.Considering the influence from the cavity decay with achievable experimentalparameters,we numerically analyze the success probability and the fidelity for generating the two-SQUID maximallyentangled state and the controlled phase-shift gate by adiabatic passage.展开更多
A scheme is proposed to generate W state of N atoms trapped in a cavity,based on adiabatic passage alongdark state.Taking advantage of adiabatic passage,the atoms have no probability of being excited and thus the atom...A scheme is proposed to generate W state of N atoms trapped in a cavity,based on adiabatic passage alongdark state.Taking advantage of adiabatic passage,the atoms have no probability of being excited and thus the atomicspontaneous emission is suppressed.The scheme is simple.It does not need to adjust the interaction time accurately,anddoes not need to prepare the cavity field in one-photon state.Numerical simulation shows that the successful probabilityof the scheme increases with the increasing of the atom number.展开更多
We propose a scheme to produce quantum phase gates for trapped ions. Taking advantage of the adiabatic evolution, the operation is insensitive to small fluctuations of experimental parameters. Furthermore, the sponta...We propose a scheme to produce quantum phase gates for trapped ions. Taking advantage of the adiabatic evolution, the operation is insensitive to small fluctuations of experimental parameters. Furthermore, the spontaneous emission is suppressed since the ions have no probability of being populated in the electronic excited states.展开更多
We propose two schemes for generating Greenberger-Horne-Zeilinger and W states of three distant atoms. In the present schemes, the atoms are individually trapped in three spatially separated optical cavities coupled b...We propose two schemes for generating Greenberger-Horne-Zeilinger and W states of three distant atoms. In the present schemes, the atoms are individually trapped in three spatially separated optical cavities coupled by two optical fibres. Performing an adiabatic passage along dark states, the population of cavities and fibres excited is negligible under certain conditions. In addition, the spontaneous decay of atoms is also efficiently suppressed based on our proposals. Furthermore, the discussion about the entanglement fidelity is given and we point out that our schemes work robustly with small fluctuations of experimental parameters.展开更多
A scheme is proposed for generating a three-dimensional entangled state for two atoms trapped in a cavity by one step via adiabatic passage. In the scheme, the two atoms are always in ground states and the field mode ...A scheme is proposed for generating a three-dimensional entangled state for two atoms trapped in a cavity by one step via adiabatic passage. In the scheme, the two atoms are always in ground states and the field mode of the cavity excited is negligible under a certain condition. Therefore, the scheme is very robust against decoherence. Furthermore, it needs neither the exact control of all parameters nor the accurate control of the interaction time. It is shown that qutrit entanglement can be generated with a high fidelity.展开更多
We propose a scheme to generate a Greenberger-Horn-Zeilinger (GHZ) state of four atoms trapped in a two-mode optical cavity via an adiabatic passage. The scheme is robust against moderate fluctuations of the experim...We propose a scheme to generate a Greenberger-Horn-Zeilinger (GHZ) state of four atoms trapped in a two-mode optical cavity via an adiabatic passage. The scheme is robust against moderate fluctuations of the experimental parameters. Numerical calculations show that the excited probabilities of both the cavity modes and the atoms are tiny and depend on the pulse peaks of the classical laser fields. For certain decoherence due to the atomic spontaneous emission and the cavity decay, there exits a range of pulse peaks to get a high fidelity.展开更多
This paper presents a direct implementation scheme of the non-local multi-qubit controlled phase gate by using optical fibres and adiabatic passage. The smaller operation number for implementing the multi-qubit contro...This paper presents a direct implementation scheme of the non-local multi-qubit controlled phase gate by using optical fibres and adiabatic passage. The smaller operation number for implementing the multi-qubit controlled phase gate and needlessness for addressing individually save physical resource and lower the difficulties of experiment. Mean- while, the scheme is immune from some decoherence effects such as the atomic spontaneous emission and fibre loss. In principle, it is scalable.展开更多
The time-dependent multilevel approach(TDMA) and B-spline expansion technique are used to study the coherent population transfer between the quantum states of a potassium atom by a single frequency-chirped microwave...The time-dependent multilevel approach(TDMA) and B-spline expansion technique are used to study the coherent population transfer between the quantum states of a potassium atom by a single frequency-chirped microwave pulse.The Rydberg potassium atom energy levels of n=6-15,l=0-5 states in zero field are calculated and the results are in good agreement with other theoretical values.The time evolutions of the population transfer of the six states from n=70 to n=75 in different microwave fields are obtained.The results show that the coherent control of the population transfer from the lower states to the higher ones can be accomplished by optimizing the microwave pulse parameters.展开更多
We extend the idea of laser cooling with adiabatic passage to multi-level type-Ⅱ transitions.We find the cooling force can be significantly enhanced when a proper magnetic field is applied.That is because the magneti...We extend the idea of laser cooling with adiabatic passage to multi-level type-Ⅱ transitions.We find the cooling force can be significantly enhanced when a proper magnetic field is applied.That is because the magnetic field decomposes the multi-level system into several two-level sub-systems,hence the stimulated absorption and stimulated emission can occur in order,allowing for the multiple photon momentum transfer.We show that this scheme also works on the laser-coolable molecules with a better cooling effect compared to the conventional Doppler cooling.A reduced dependence on spontaneous emission based on our scheme is observed as well.Our results suggest this scheme is very feasible for laser cooling of polar molecules.展开更多
Stimulated adiabatic passage has been extensively studied to achieve robust and selective population transfer in quantum systems. Recently, the quantum-classic analogy has been rapidly developing and can be considered...Stimulated adiabatic passage has been extensively studied to achieve robust and selective population transfer in quantum systems. Recently, the quantum-classic analogy has been rapidly developing and can be considered responsible for the implementation of the adiabatic transfer of sound energy in cavity chain systems. In this article, we investigate the adiabatic transfer of sound energy between two topological end states in the Su-Schrieffer-Heeger(SSH) cavity chain, which can be considered to be the acoustic analog of the quantum chirped-pulse excitation. The topological adiabatic passage in SSH cavity chain has two categories. When the single-cavity resonance frequencies on the sublattices A and B in the SSH cavity chain do not switch their spectrum positions, the topologically protected adiabatic evolution results in the returning passage of the sound excited in one end cavity. When a level crossing with single-cavity resonance frequencies on the sublattices A and B exhibits switch in the frequency spectrum, acoustic energy is observed to be topologically pumped between the two end cavities of the SSH chain.展开更多
A scheme for creating an arbitrary coherent superposition of two atomic states in serial multi-A-type system is proposed. This technique with the application of a control field is based on the existence of two degener...A scheme for creating an arbitrary coherent superposition of two atomic states in serial multi-A-type system is proposed. This technique with the application of a control field is based on the existence of two degenerate dark states and their interaction. The mixing of the dark states can be controlled by changing the relative delay time of the control pulse. One can get any desired superposition by changing the delay time of the control pulse.展开更多
文摘Recently, Zhou et al. [Phys. Rev. A 79 (2009) 044304] proposed a scheme for transferring three-dimensional quantum states between remote atomic qubits confined in cavities connected by fibers through adiabatic passage. In order to avoid the decoherence due to spontaneous emission, Zhou et al. utilized the large detuning atom-field interaction. In the present paper, we discuss the influence of dissipation on the scheme in both the resonant atom-field interaction case and the large detuning case. We numerically analyze the success probability and the transferring fidelity. It is shown that the resonant case is a preferable choice for the technique of the stimulated Raman adiabatic passage (STIRAP) due to the shorter operation time and the smaller probability of dissipation.
文摘Using the time-dependent multilevel approach, we have calculated the coherent population transfer between the quantum states of potassium atom by a single frequency-chirped laser pulse. The result shows that a pair of sequential 'broadband' frequency-chirped laser pulses can efficiently transfer population from the initial state of the ladder system to the target state. It is also found that the population can be efficiently transferred to a target state and trapped there by using an 'intuitive' or a 'counterintuitive' frequency sweep laser pulse in the case of 'narrowband' frequency-chirped laser pulse. Our research shows that the complete population transfer is related to the pulse duration, chirp rate, and amplitude of the laser pulse.
基金Project supported by the Funds of Educational Committee of Fujian Province (Grant No JB05334), the National Natural Science Foundation of China (Grant No10574022), and the Fujian Provincial Natural Science Foundation (Grant No A0410016).
文摘Based on adiabatic passage, we propose a scheme for implementing the quantum transfer of an unknown atomic state. In our scheme, we utilize photons for ideal quantum transmission between two cavities with the successful probability being about 1. Meanwhile, the scheme is robust against the effects of atomic spontaneous emission. It may be useful for transferring quantum information among spatially distant atoms.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60878059)the Science Foundation of the Educational Committee of Fujian Province of China (Grant No. JA09041)Fujian Normal University (Grant Nos. 2008100220and BKL2009-010)
文摘This paper considers a scheme for the preparation of two-qutrit entangled states via adiabatic passage in iontrapped system. In the proposal, the two three-level V-type ions are initially cooled to the ground states and need not be separately addressed. Moreover, only the ionic states act as memory and the system evolves in the dark space during the whole procedure, which makes the system robust against the decoherence and the fluctuation of the laser pulse.
基金Project supported by the National Natural Science Foundation of China(Grant No.11464046)
文摘Combining adiabatic passage and Rydberg antiblockade, we propose a scheme to implement a two-qubit phase gate between two Rydberg atoms. Detuning parameters between frequencies of atomic transitions and those of the corresponding driving lasers are carefully chosen to offset the blockade effect of two Rydberg atoms, so that an effective Hamiltonian,representing a single-photon detuning L-type three-level system and concluding the quantum state of two Rydberg atoms excited simultaneously, is obtained. The adiabatic-passage technique, based on the effective Hamiltonian, is adopted to implement a two-atom phase gate by using two time-dependent Rabi frequencies. Numerical simulations indicate that a high-fidelity two-qubit p-phase gate is constructed and its operation time does not have to be controlled accurately. Besides,owing to the long coherence time of the Rydberg state, the phase gate is robust against atomic spontaneous emission.
基金Protect supported by the National Natural Science Foundation of China (Grant No 10574022), the Natural Science Foundation of Fujian Province, China (Grant Nos A0410016 and 2006J0230) and the Funds of Educational Committee of Fujian Province, China (Grant No JB05334 and JB05340).
文摘This paper proposes a scheme for implementing teleportation of an entangled state of two trapped atoms through adiabatic passage and photonic interference. The scheme is robust against certain noise such as atomic spontaneous emission and the detector inefficiency.
基金Supported by the Foundation of Educational Committee of Fujian Province under Grant Nos.JB09012 and JB09013
文摘A scheme is proposed to generate W state with qubits of superconducting quantum interference devices (SQUIDs), based on adiabatic passage along dark state. Taking advantages of adiabatic passage, the scheme is very robust against decoherence, and it does not need to control the classical field and the interaction time accurately. Because of the achievable strong coupling between SQUID qubits and cavity, W state can be generated with high successful probability.
基金supported by the National Natural Science Foundation of China (Grant Nos.10674025 and 10974028)the Fujian Natural Science Foundation of China (Grant No.2009J06002)+2 种基金the Doctoral Foundation of the Ministry of Education of China(Grant Nos.20070386002 and 20093514110009)the Funds from State Key Laboratory Breeding Base of Photocatalysis,Fuzhou Universitythe Funds from the Education Department of Fujian Province of China (Grant No.JB08010)
文摘We propose a scheme for the deterministic generation of qutrit entanglement for two atoms trapped in an optical cavity. Taking advantage of the adiabatic passage, the operation is immune to atomic spontaneous emission as the atomic excited states are never populated; under certain conditions, the probability that the cavity is excited is negligible. We also study the influences of the dissipation due to the atomic spontaneous emission and cavity decay.
基金supported by the National Natural Science Foundation of China under Grant No.10674025
文摘We describe a scheme for the generation of W states and implementation of phase-covariant cloning for n trapped ions. The scheme does not use the vibational mode as the memory and works beyond the Lamb-Dicke regime. The procedure is robust against moderate fluctuations of experimental parameters by using adiabatic passage.
文摘We proposed an efficient scheme for constructing a quantum controlled phase-shift gate and generating thecluster states with rf superconducting quantum interference devices (SQUIDs)coupled to a microwave cavity throughadiabatic evolution of dark eigenstates.During the operation,the spontaneous emission is suppressed since the rf SQUIDsare always in the three lowest flux states.Considering the influence from the cavity decay with achievable experimentalparameters,we numerically analyze the success probability and the fidelity for generating the two-SQUID maximallyentangled state and the controlled phase-shift gate by adiabatic passage.
基金Supported by the Science Foundation of Educational Committee of Fujian Province under Grant No.JB09011
文摘A scheme is proposed to generate W state of N atoms trapped in a cavity,based on adiabatic passage alongdark state.Taking advantage of adiabatic passage,the atoms have no probability of being excited and thus the atomicspontaneous emission is suppressed.The scheme is simple.It does not need to adjust the interaction time accurately,anddoes not need to prepare the cavity field in one-photon state.Numerical simulation shows that the successful probabilityof the scheme increases with the increasing of the atom number.
基金The project supported by National Natural Science Foundation of China under Grant No. 10674025 and the Funds from Fuzhou University
文摘We propose a scheme to produce quantum phase gates for trapped ions. Taking advantage of the adiabatic evolution, the operation is insensitive to small fluctuations of experimental parameters. Furthermore, the spontaneous emission is suppressed since the ions have no probability of being populated in the electronic excited states.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 90503010,10874050,10975054,91021011 and 11005057)National Basic Research Program of China (Grant No. 2005CB724508)the Foundation from the Ministry of Education of China (Grant No. 200804870051)
文摘We propose two schemes for generating Greenberger-Horne-Zeilinger and W states of three distant atoms. In the present schemes, the atoms are individually trapped in three spatially separated optical cavities coupled by two optical fibres. Performing an adiabatic passage along dark states, the population of cavities and fibres excited is negligible under certain conditions. In addition, the spontaneous decay of atoms is also efficiently suppressed based on our proposals. Furthermore, the discussion about the entanglement fidelity is given and we point out that our schemes work robustly with small fluctuations of experimental parameters.
基金supported by the Science Foundation of Educational Committee of Fujian Province of China (Grant Nos. JB09012 and JB09013)
文摘A scheme is proposed for generating a three-dimensional entangled state for two atoms trapped in a cavity by one step via adiabatic passage. In the scheme, the two atoms are always in ground states and the field mode of the cavity excited is negligible under a certain condition. Therefore, the scheme is very robust against decoherence. Furthermore, it needs neither the exact control of all parameters nor the accurate control of the interaction time. It is shown that qutrit entanglement can be generated with a high fidelity.
基金Project supported by the National Basic Research Program of China (Grant No. 2012CB921601)the National Natural Science Foundation of China (Grant No. 10974028)the Doctoral Foundation of the Ministry of Education of China (Grant No. 20093514110009)
文摘We propose a scheme to generate a Greenberger-Horn-Zeilinger (GHZ) state of four atoms trapped in a two-mode optical cavity via an adiabatic passage. The scheme is robust against moderate fluctuations of the experimental parameters. Numerical calculations show that the excited probabilities of both the cavity modes and the atoms are tiny and depend on the pulse peaks of the classical laser fields. For certain decoherence due to the atomic spontaneous emission and the cavity decay, there exits a range of pulse peaks to get a high fidelity.
基金Project supported by the National Natural Science Foundation of China (Grant No 10574022)Natural Science Foundation of Fujian Province of China (Grant Nos 2007J0002 and 2006J0230)Foundation for Universities in Fujian Province (Grant No 2007F5041)
文摘This paper presents a direct implementation scheme of the non-local multi-qubit controlled phase gate by using optical fibres and adiabatic passage. The smaller operation number for implementing the multi-qubit controlled phase gate and needlessness for addressing individually save physical resource and lower the difficulties of experiment. Mean- while, the scheme is immune from some decoherence effects such as the atomic spontaneous emission and fibre loss. In principle, it is scalable.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10774039)the Natural Science Foundation of Education Bureau of Henan Province,China (Grant Nos. 2010C140002 and 2010A140006)the Research Planning Project of Basic and Advanced Technology of Henan Province,China (Grant No. 112300410025)
文摘The time-dependent multilevel approach(TDMA) and B-spline expansion technique are used to study the coherent population transfer between the quantum states of a potassium atom by a single frequency-chirped microwave pulse.The Rydberg potassium atom energy levels of n=6-15,l=0-5 states in zero field are calculated and the results are in good agreement with other theoretical values.The time evolutions of the population transfer of the six states from n=70 to n=75 in different microwave fields are obtained.The results show that the coherent control of the population transfer from the lower states to the higher ones can be accomplished by optimizing the microwave pulse parameters.
基金the Natural Science Foundation of Zhejiang Province under Grant No.LZ18A040001the National Key R&D Program of China under Grant No.2018YFA0307200+2 种基金the National Natural Science Foundation of China under Grant No.12074337Zhejiang Province Plan for Science and Technology No.2020C01019the Fundamental Research Funds for the Central Universities.
文摘We extend the idea of laser cooling with adiabatic passage to multi-level type-Ⅱ transitions.We find the cooling force can be significantly enhanced when a proper magnetic field is applied.That is because the magnetic field decomposes the multi-level system into several two-level sub-systems,hence the stimulated absorption and stimulated emission can occur in order,allowing for the multiple photon momentum transfer.We show that this scheme also works on the laser-coolable molecules with a better cooling effect compared to the conventional Doppler cooling.A reduced dependence on spontaneous emission based on our scheme is observed as well.Our results suggest this scheme is very feasible for laser cooling of polar molecules.
基金supported by the National Natural Science Foundation of China (Grant Nos.11674119,11774297,11690030,and 11690032)support from the General Research Fund of Hong Kong Research Grants Council (Grant No.15205219)。
文摘Stimulated adiabatic passage has been extensively studied to achieve robust and selective population transfer in quantum systems. Recently, the quantum-classic analogy has been rapidly developing and can be considered responsible for the implementation of the adiabatic transfer of sound energy in cavity chain systems. In this article, we investigate the adiabatic transfer of sound energy between two topological end states in the Su-Schrieffer-Heeger(SSH) cavity chain, which can be considered to be the acoustic analog of the quantum chirped-pulse excitation. The topological adiabatic passage in SSH cavity chain has two categories. When the single-cavity resonance frequencies on the sublattices A and B in the SSH cavity chain do not switch their spectrum positions, the topologically protected adiabatic evolution results in the returning passage of the sound excited in one end cavity. When a level crossing with single-cavity resonance frequencies on the sublattices A and B exhibits switch in the frequency spectrum, acoustic energy is observed to be topologically pumped between the two end cavities of the SSH chain.
文摘A scheme for creating an arbitrary coherent superposition of two atomic states in serial multi-A-type system is proposed. This technique with the application of a control field is based on the existence of two degenerate dark states and their interaction. The mixing of the dark states can be controlled by changing the relative delay time of the control pulse. One can get any desired superposition by changing the delay time of the control pulse.