The rovibrational state-selectivity in photoassociation (PA) is investigated for the ground electronic state of OH radical. The calculated results show that population can be transferred from continuum state to the ...The rovibrational state-selectivity in photoassociation (PA) is investigated for the ground electronic state of OH radical. The calculated results show that population can be transferred from continuum state to the target states through three-, four-, and nine-photon transitions by choosing suitable pulse parameters and initial collision energy. To control population transfer to a lower rovibrational state, a shorter pulse frequency has to be chosen and the photon number transferred to target state should be increased. In PA process, some associated OH radicals can be dissociated via intermediate and background states, which decreases the nal population of the target state.展开更多
The influence of multi-photon pulses on practical differcBtial-phase-shift quantum key distribution (DPS-Qt(D) is analysed. We have estimated the information which Eve obtained by PNS (photon-number splitting) at...The influence of multi-photon pulses on practical differcBtial-phase-shift quantum key distribution (DPS-Qt(D) is analysed. We have estimated the information which Eve obtained by PNS (photon-number splitting) attack and BS (beam splitting) attack. The result indicates that the PNS attack and BS attack will not limit the transmission distance as long as we select an appropriate mean photon number. Also, the maximum mean photon number under BS attack in practical DPS-QKD system and the set of practical assumptions about Eve's capabilities are presented.展开更多
The evolution of the electron phase orbits based on the multi-photon nonlinear Compton scattering with the high power laser-plasma is discussed by using Kroll-Morton-Rosenbluth theory. The random evolution of the un-c...The evolution of the electron phase orbits based on the multi-photon nonlinear Compton scattering with the high power laser-plasma is discussed by using Kroll-Morton-Rosenbluth theory. The random evolution of the un-captured electron phase orbits from periodicity to non-periodicity is found after the energy has been exchanged between the electron and photons. With the increase of the absorbed photon number n by an electron,this evolution will be more and more intense, while which is rapidly decreased with the enhancement of the collision non-flexibility ξ and their initial speeds of the electrons and photons,but this evolution is lower than that in the high power laser field. When the electrons are captured by the laser field,the evolution is finished,and the electrons will stably transport,and the photons don’t provide the energy for these electrons any more.展开更多
We demonstrate the controllable generation of multi-photon Fock states in circuit quantum electrodynamics (circuit QED). The external bias flux regulated by a counter can effectively adjust the bias time on each sup...We demonstrate the controllable generation of multi-photon Fock states in circuit quantum electrodynamics (circuit QED). The external bias flux regulated by a counter can effectively adjust the bias time on each superconducting flux qubit so that each flux qubit can pass in turn through the circuit cavity and thereby avoid the effect of decoherence. We further investigate the quantum correlation dynamics of coupling superconducting qubits in a Fock state. The results reveal that the lower the photon number of the light field in the number state, the stronger the interaction between qubits is, then the more beneficial to maintaining entanglement between qubits it will be.展开更多
It has been shown that the femtosecond laser polarization modulation is a very simple and well-established method to control the multi-photon absorption process by the light-matter interaction. Previous studies mainly...It has been shown that the femtosecond laser polarization modulation is a very simple and well-established method to control the multi-photon absorption process by the light-matter interaction. Previous studies mainly focused on the multi- photon absorption control in the weak field. In this paper, we further explore the polarization control behavior of multi- photon absorption process in the intermediate femtosecond laser field. In the weak femtosecond laser field, the second- order perturbation theory can well describe the non-resonant two-photon absorption process. However, the higher order nonlinear effect (e.g., four-photon absorption) can occur in the intermediate femtosecond laser field, and thus it is necessary to establish new theoretical model to describe the multi-photon absorption process, which includes the two-photon and four-photon transitions. Here, we construct a fourth-order perturbation theory to study the polarization control behavior of this multi-photon absorption under the intermediate femtosecond laser field excitation, and our theoretical results show that the two-photon and four-photon excitation pathways can induce a coherent interference, while the coherent interference is constructive or destructive that depends on the femtosecond laser center frequency. Moreover, the two-photon and four- photon transitions have the different polarization control efficiency, and the four-photon absorption can obtain the higher polarization control efficiency. Thus, the polarization control efficiency of the whole excitation process can be increased or decreased by properly designing the femtosecond laser field intensity and laser center frequency. These studies can provide a clear physical picture for understanding and controlling the multi-photon absorption process in the intermediate femtosecond laser field, and also can provide a theoretical guidance for the future experimental realization.展开更多
This paper proposes highly charged ions pumped by intense laser to produce very high order harmonics. Numerical simulations and full quantum theory of Ne^9+ ions driven by laser pulses at 1064 nm in the power range o...This paper proposes highly charged ions pumped by intense laser to produce very high order harmonics. Numerical simulations and full quantum theory of Ne^9+ ions driven by laser pulses at 1064 nm in the power range of 109 W/cm^2 1015 W/cm^2 show that the emission spectrum corresponds to the electronic transitions from the excited states to the ground state, which is very different from the spectrum of general high-order harmonic generation. In such situation, harmonic order as high as 1000 can be obtained without producing lower order harmonics and the energy conversion efficiency is close to general high order harmonic generation of hydrogen atom in the same laser field.展开更多
We study the interaction of a multi-photon three-level atom with a single mode field in a cavity, taking explicitly into account the existence of forms of nonlinearities of both the field and the intensity-dependent a...We study the interaction of a multi-photon three-level atom with a single mode field in a cavity, taking explicitly into account the existence of forms of nonlinearities of both the field and the intensity-dependent atom-field coupling. The analytical forms of the emission spectrum is calculated using the dressed states of the system. The effects of photon multiplicities, mean photon number, detuning, Kerr-like medium and the intensity-dependent coupling functional on the emission spectrum are analyzed.展开更多
Using the model of the inverse Compton scattering between high-energy electrons and heat-radiation photons, the influence of heat-radiating photons on multi-photon Compton scattering high-energy electrons is studied ....Using the model of the inverse Compton scattering between high-energy electrons and heat-radiation photons, the influence of heat-radiating photons on multi-photon Compton scattering high-energy electrons is studied . The results show that the energy loss, power loss, light resistance and light pressure of the high-energy electron formed by heat radiating are all proportional to the temperature T4 of the vacuum cavity of the electron,the Lorentz factor γ2 of the high-energy electrons, the scattering section of the electron and the number of photons acting at the same time with high-energy electrons. A good method for lessening the energy loss of the high-energy electron by using the one-photon Compton scattering between high-energy electrons and heat radiation photons is proposed.展开更多
Multi photon ionization (MPI) in plasma is examined in terms of optical metric, and the quantum Volkov state in curved space time is derived. The cross section of MPI is derived by virtue of the corrected Volkov sta...Multi photon ionization (MPI) in plasma is examined in terms of optical metric, and the quantum Volkov state in curved space time is derived. The cross section of MPI is derived by virtue of the corrected Volkov state within the framework of quantum electrodynamics (QED) formal scattering theory. It shows that the plasma medium acts as a suppression on MPI.展开更多
One of the challenges in the field of multi-photon 3D laser printing lies in further increasing the print speed in terms of voxels/s.Here,we present a setup based on a 7×7 focus array(rather than 3×3 in our ...One of the challenges in the field of multi-photon 3D laser printing lies in further increasing the print speed in terms of voxels/s.Here,we present a setup based on a 7×7 focus array(rather than 3×3 in our previous work)and using a focus velocity of about 1 m/s(rather than 0.5 m/s in our previous work)at the diffraction limit(40×/NA1.4 microscope objective lens).Combined,this advance leads to a ten times increased print speed of about 108 voxels/s.We demonstrate polymer printing of a chiral metamaterial containing more than 1.7×10^(12) voxels as well as millions of printed microparticles for potential pharmaceutical applications.The critical high-quality micro-optical components of the setup,namely a diffractive optical element generating the 7×7 beamlets and a 7×7 lens array,are manufactured by using a commercial two-photon grayscale 3D laser printer.展开更多
The construction of quantum networks requires long-distance teleportation of multi-qubit entangled states.Here,we investigate the entanglement dynamics of GHZ and W states in fiber channels.In a fiber channel,the two ...The construction of quantum networks requires long-distance teleportation of multi-qubit entangled states.Here,we investigate the entanglement dynamics of GHZ and W states in fiber channels.In a fiber channel,the two most important phenomena that affect polarization entanglement are polarization mode dispersion(PMD)and polarization-dependent loss(PDL).We theoretically characterize how PMD and PDL vectors affect three-qubit states.In particular,upon quantifying the entanglement at the output states using concurrence and entanglement witnesses,we reveal the occurrence of entanglement sudden death and the appearance of decoherence-free subspaces in tripartite systems.Finally,we explore the evolution of GHZ and W state with an arbitrary number of photons in a fiber network and discuss the decoherence mechanism of the 4-party cluster state.展开更多
The past few years witnessed extensive emergence of short-wavelength upconversion(UC) emission stimulated photoactivation studies. However, low efficiency of multi-photon process greatly limits further applications....The past few years witnessed extensive emergence of short-wavelength upconversion(UC) emission stimulated photoactivation studies. However, low efficiency of multi-photon process greatly limits further applications. Here, ultraviolet(UV) upconversion emissions originated from multi-photon process of Tm^3+ were studied with Nd^3+-sensitized NaGdF4:Yb,Tm@NaYF4:Nd,Yb core/shell nanoparticles. Crucial factors, including the contents of sensitizers Nd^3+, Yb^3+ and activator Tm^3+, as well as the excitation power density were investigated based on the UV emission. Spectral results showed that high contents of Nd^3+ in shell region up to 50%(molar fraction hereafter) and Yb^3+ of 10% were essential to mediate the energy transfer via the core/shell interface and facilitate multi-photon UV emissions. Compared with segregated activator and sensitizer, a core/shell strategy with isolated Nd^3+ in the shell was important for higher UV emission. Although the upconverting process was initiated with Nd^3+→Yb^3+, the short-wavelength emissions were intrinsically coming from four- and five-photon process. The optimized nanoparticles were found to be able to manipulate the configuration transition of azobenzene molecules, and it could be promising for near infrared(NIR) triggered optical switches applications.展开更多
Single-photon detectors are ubiquitous devices in quantum-photonic-based communication,computation,metrology,and sensing.In these applications,N-fold coincidence photon counting is often needed,for example,to characte...Single-photon detectors are ubiquitous devices in quantum-photonic-based communication,computation,metrology,and sensing.In these applications,N-fold coincidence photon counting is often needed,for example,to characterize entanglement.However,N-fold coincidence photon counting typically requires N individual singlephoton detectors and associated bias and readout electronics,and these resources could become prohibitive if N goes large and the detectors need to work at cryogenic temperatures.Here,to break this limit on N,we propose a device architecture based on N cascaded photosensitive superconducting nanowires and one wider nanowire that functions as a current reservoir.We show that by strategically designing the device,the network of these superconducting nanowires can work in a synergic manner as an n-photon detector,where n can be from 1 to N,depending on the bias conditions.We therefore name the devices of this type superconducting nanowire multi-photon detectors(SNMPDs).In addition to its simple one-port bias and readout circuitry,the coincidences are counted internally in the detector,eliminating the need for external multi-channel,time-correlated pulse counters.We believe that the SNMPDs proposed in this work could open avenues towards conveniently measuring high-order temporal correlations of light and characterizing multi-photon entanglement.展开更多
In recent years,multi-photon 3D laser printing has become a widely used tool for the fabrication of micro-and nanostructures for a large variety of applications.Typically,thorough sample characterisation is key for an...In recent years,multi-photon 3D laser printing has become a widely used tool for the fabrication of micro-and nanostructures for a large variety of applications.Typically,thorough sample characterisation is key for an efficient optimisation of the printing process.To date,three-dimensional microscopic inspection has usually been carried out on finished 3D printed microstructures,that is,using ex-situ approaches.In contrast,in-situ 3D characterization tools are desirable for quickly assessing the quality and properties of 3D printed microstructures.Along these lines,we present and characterise a Fourier-domain optical coherence tomography(FD-OCT)system that can be readily integrated into an existing 3D laser lithography setup.We demonstrate its capabilities by examining different 3D printed polymer microstructures immersed in a liquid photoresist.In such samples,local reflectivity arises from the(refractive-index)contrasts between the polymerised and non-polymerised regions.Thus,the refractive index of the printed material can be extracted.Furthermore,we demonstrate that the reflectivity of polymer-monomer transitions exhibits time-dependent behaviour after printing.Supported by transfer-matrix calculations,we explain this effect in terms of the time-dependent graded-index transition originating from monomer diffusion into the polymer matrix.Finally,we show exemplary 3D reconstructions of printed structures that can be readily compared with 3D computer designs.展开更多
We derive the adiabatic and non-adiabatic Berry phases in the generalized Jaynes-Cummings model of multi-photon process. The results show that the adiabatic Berry phase is kept a constant π independent of all the par...We derive the adiabatic and non-adiabatic Berry phases in the generalized Jaynes-Cummings model of multi-photon process. The results show that the adiabatic Berry phase is kept a constant π independent of all the parameters, while the non-adiabatic approximate Berry phase is parameter-dependent, proportional to the average photon number m, and tends to be constant with the increasing detuning. In the ease of exact n-photon resonance and an integer ratio of m/n, the two results coincide with each other, otherwise there appears an additional non-trivial phase factor.展开更多
基金This work is supported by the National Natural Science Foundation of China (No.11347012).
文摘The rovibrational state-selectivity in photoassociation (PA) is investigated for the ground electronic state of OH radical. The calculated results show that population can be transferred from continuum state to the target states through three-, four-, and nine-photon transitions by choosing suitable pulse parameters and initial collision energy. To control population transfer to a lower rovibrational state, a shorter pulse frequency has to be chosen and the photon number transferred to target state should be increased. In PA process, some associated OH radicals can be dissociated via intermediate and background states, which decreases the nal population of the target state.
文摘The influence of multi-photon pulses on practical differcBtial-phase-shift quantum key distribution (DPS-Qt(D) is analysed. We have estimated the information which Eve obtained by PNS (photon-number splitting) attack and BS (beam splitting) attack. The result indicates that the PNS attack and BS attack will not limit the transmission distance as long as we select an appropriate mean photon number. Also, the maximum mean photon number under BS attack in practical DPS-QKD system and the set of practical assumptions about Eve's capabilities are presented.
基金Natural Science Basic Research Project for Education Department of Henan Province(20011400006)
文摘The evolution of the electron phase orbits based on the multi-photon nonlinear Compton scattering with the high power laser-plasma is discussed by using Kroll-Morton-Rosenbluth theory. The random evolution of the un-captured electron phase orbits from periodicity to non-periodicity is found after the energy has been exchanged between the electron and photons. With the increase of the absorbed photon number n by an electron,this evolution will be more and more intense, while which is rapidly decreased with the enhancement of the collision non-flexibility ξ and their initial speeds of the electrons and photons,but this evolution is lower than that in the high power laser field. When the electrons are captured by the laser field,the evolution is finished,and the electrons will stably transport,and the photons don’t provide the energy for these electrons any more.
基金Project supported by the National Natural Science Foundation of China(Grant No.11264015)
文摘We demonstrate the controllable generation of multi-photon Fock states in circuit quantum electrodynamics (circuit QED). The external bias flux regulated by a counter can effectively adjust the bias time on each superconducting flux qubit so that each flux qubit can pass in turn through the circuit cavity and thereby avoid the effect of decoherence. We further investigate the quantum correlation dynamics of coupling superconducting qubits in a Fock state. The results reveal that the lower the photon number of the light field in the number state, the stronger the interaction between qubits is, then the more beneficial to maintaining entanglement between qubits it will be.
基金supported by the Program of Introducing Talents of Discipline to Universities(Grant No.B12024)the National Natural Science Foundation of China(Grant Nos.51132004,11474096,11547216,11547220,and 11604199)+1 种基金the Science Fund from the Science and Technology Commission of Shanghai Municipality(Grant No.14JC1401500)the Higher Education Key Program of He’nan Province of China(Grant Nos.17A140025 and 16A140030)
文摘It has been shown that the femtosecond laser polarization modulation is a very simple and well-established method to control the multi-photon absorption process by the light-matter interaction. Previous studies mainly focused on the multi- photon absorption control in the weak field. In this paper, we further explore the polarization control behavior of multi- photon absorption process in the intermediate femtosecond laser field. In the weak femtosecond laser field, the second- order perturbation theory can well describe the non-resonant two-photon absorption process. However, the higher order nonlinear effect (e.g., four-photon absorption) can occur in the intermediate femtosecond laser field, and thus it is necessary to establish new theoretical model to describe the multi-photon absorption process, which includes the two-photon and four-photon transitions. Here, we construct a fourth-order perturbation theory to study the polarization control behavior of this multi-photon absorption under the intermediate femtosecond laser field excitation, and our theoretical results show that the two-photon and four-photon excitation pathways can induce a coherent interference, while the coherent interference is constructive or destructive that depends on the femtosecond laser center frequency. Moreover, the two-photon and four- photon transitions have the different polarization control efficiency, and the four-photon absorption can obtain the higher polarization control efficiency. Thus, the polarization control efficiency of the whole excitation process can be increased or decreased by properly designing the femtosecond laser field intensity and laser center frequency. These studies can provide a clear physical picture for understanding and controlling the multi-photon absorption process in the intermediate femtosecond laser field, and also can provide a theoretical guidance for the future experimental realization.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10574030)
文摘This paper proposes highly charged ions pumped by intense laser to produce very high order harmonics. Numerical simulations and full quantum theory of Ne^9+ ions driven by laser pulses at 1064 nm in the power range of 109 W/cm^2 1015 W/cm^2 show that the emission spectrum corresponds to the electronic transitions from the excited states to the ground state, which is very different from the spectrum of general high-order harmonic generation. In such situation, harmonic order as high as 1000 can be obtained without producing lower order harmonics and the energy conversion efficiency is close to general high order harmonic generation of hydrogen atom in the same laser field.
文摘We study the interaction of a multi-photon three-level atom with a single mode field in a cavity, taking explicitly into account the existence of forms of nonlinearities of both the field and the intensity-dependent atom-field coupling. The analytical forms of the emission spectrum is calculated using the dressed states of the system. The effects of photon multiplicities, mean photon number, detuning, Kerr-like medium and the intensity-dependent coupling functional on the emission spectrum are analyzed.
基金Natural Science Foundation of Zhumadian City(058002)
文摘Using the model of the inverse Compton scattering between high-energy electrons and heat-radiation photons, the influence of heat-radiating photons on multi-photon Compton scattering high-energy electrons is studied . The results show that the energy loss, power loss, light resistance and light pressure of the high-energy electron formed by heat radiating are all proportional to the temperature T4 of the vacuum cavity of the electron,the Lorentz factor γ2 of the high-energy electrons, the scattering section of the electron and the number of photons acting at the same time with high-energy electrons. A good method for lessening the energy loss of the high-energy electron by using the one-photon Compton scattering between high-energy electrons and heat radiation photons is proposed.
文摘Multi photon ionization (MPI) in plasma is examined in terms of optical metric, and the quantum Volkov state in curved space time is derived. The cross section of MPI is derived by virtue of the corrected Volkov state within the framework of quantum electrodynamics (QED) formal scattering theory. It shows that the plasma medium acts as a suppression on MPI.
基金funding by the Deutsche Forschungsgemeinschaft(DFG,German Research Foundation)under Germany’s Excellence Strategy for the Excellence Cluster“3D Matter Made to Order”(2082/1-390761711)by the Carl Zeiss Foundation,and by the Helmholtz program Materials Systems Engineering.
文摘One of the challenges in the field of multi-photon 3D laser printing lies in further increasing the print speed in terms of voxels/s.Here,we present a setup based on a 7×7 focus array(rather than 3×3 in our previous work)and using a focus velocity of about 1 m/s(rather than 0.5 m/s in our previous work)at the diffraction limit(40×/NA1.4 microscope objective lens).Combined,this advance leads to a ten times increased print speed of about 108 voxels/s.We demonstrate polymer printing of a chiral metamaterial containing more than 1.7×10^(12) voxels as well as millions of printed microparticles for potential pharmaceutical applications.The critical high-quality micro-optical components of the setup,namely a diffractive optical element generating the 7×7 beamlets and a 7×7 lens array,are manufactured by using a commercial two-photon grayscale 3D laser printer.
基金supported by the National Key R&D Program of China[Grant No.2017YFE0301303]。
文摘The construction of quantum networks requires long-distance teleportation of multi-qubit entangled states.Here,we investigate the entanglement dynamics of GHZ and W states in fiber channels.In a fiber channel,the two most important phenomena that affect polarization entanglement are polarization mode dispersion(PMD)and polarization-dependent loss(PDL).We theoretically characterize how PMD and PDL vectors affect three-qubit states.In particular,upon quantifying the entanglement at the output states using concurrence and entanglement witnesses,we reveal the occurrence of entanglement sudden death and the appearance of decoherence-free subspaces in tripartite systems.Finally,we explore the evolution of GHZ and W state with an arbitrary number of photons in a fiber network and discuss the decoherence mechanism of the 4-party cluster state.
基金Project supported by National Natural Science Foundation of China(21425101,21331001,21371011)Ministry of Science and Technology of China(2014CB643800)
文摘The past few years witnessed extensive emergence of short-wavelength upconversion(UC) emission stimulated photoactivation studies. However, low efficiency of multi-photon process greatly limits further applications. Here, ultraviolet(UV) upconversion emissions originated from multi-photon process of Tm^3+ were studied with Nd^3+-sensitized NaGdF4:Yb,Tm@NaYF4:Nd,Yb core/shell nanoparticles. Crucial factors, including the contents of sensitizers Nd^3+, Yb^3+ and activator Tm^3+, as well as the excitation power density were investigated based on the UV emission. Spectral results showed that high contents of Nd^3+ in shell region up to 50%(molar fraction hereafter) and Yb^3+ of 10% were essential to mediate the energy transfer via the core/shell interface and facilitate multi-photon UV emissions. Compared with segregated activator and sensitizer, a core/shell strategy with isolated Nd^3+ in the shell was important for higher UV emission. Although the upconverting process was initiated with Nd^3+→Yb^3+, the short-wavelength emissions were intrinsically coming from four- and five-photon process. The optimized nanoparticles were found to be able to manipulate the configuration transition of azobenzene molecules, and it could be promising for near infrared(NIR) triggered optical switches applications.
基金National Natural Science Foundation of China(11527808,61505141)Natural Science Foundation of Tianjin City(15JCYBJC52500,19JCYBJC16900)。
文摘Single-photon detectors are ubiquitous devices in quantum-photonic-based communication,computation,metrology,and sensing.In these applications,N-fold coincidence photon counting is often needed,for example,to characterize entanglement.However,N-fold coincidence photon counting typically requires N individual singlephoton detectors and associated bias and readout electronics,and these resources could become prohibitive if N goes large and the detectors need to work at cryogenic temperatures.Here,to break this limit on N,we propose a device architecture based on N cascaded photosensitive superconducting nanowires and one wider nanowire that functions as a current reservoir.We show that by strategically designing the device,the network of these superconducting nanowires can work in a synergic manner as an n-photon detector,where n can be from 1 to N,depending on the bias conditions.We therefore name the devices of this type superconducting nanowire multi-photon detectors(SNMPDs).In addition to its simple one-port bias and readout circuitry,the coincidences are counted internally in the detector,eliminating the need for external multi-channel,time-correlated pulse counters.We believe that the SNMPDs proposed in this work could open avenues towards conveniently measuring high-order temporal correlations of light and characterizing multi-photon entanglement.
基金This work was funded by the Deutsche Forschungsgemeinschaft(DFG,German Research Foundation)under Germany’s Excellence Strategy 2082/1-390761711(Excellence Cluster“3D Matter Made to Order”).
文摘In recent years,multi-photon 3D laser printing has become a widely used tool for the fabrication of micro-and nanostructures for a large variety of applications.Typically,thorough sample characterisation is key for an efficient optimisation of the printing process.To date,three-dimensional microscopic inspection has usually been carried out on finished 3D printed microstructures,that is,using ex-situ approaches.In contrast,in-situ 3D characterization tools are desirable for quickly assessing the quality and properties of 3D printed microstructures.Along these lines,we present and characterise a Fourier-domain optical coherence tomography(FD-OCT)system that can be readily integrated into an existing 3D laser lithography setup.We demonstrate its capabilities by examining different 3D printed polymer microstructures immersed in a liquid photoresist.In such samples,local reflectivity arises from the(refractive-index)contrasts between the polymerised and non-polymerised regions.Thus,the refractive index of the printed material can be extracted.Furthermore,we demonstrate that the reflectivity of polymer-monomer transitions exhibits time-dependent behaviour after printing.Supported by transfer-matrix calculations,we explain this effect in terms of the time-dependent graded-index transition originating from monomer diffusion into the polymer matrix.Finally,we show exemplary 3D reconstructions of printed structures that can be readily compared with 3D computer designs.
基金Supported by the National Natural Science Foundation of China under Grants Nos.11075099,11047167,and 11105087
文摘We derive the adiabatic and non-adiabatic Berry phases in the generalized Jaynes-Cummings model of multi-photon process. The results show that the adiabatic Berry phase is kept a constant π independent of all the parameters, while the non-adiabatic approximate Berry phase is parameter-dependent, proportional to the average photon number m, and tends to be constant with the increasing detuning. In the ease of exact n-photon resonance and an integer ratio of m/n, the two results coincide with each other, otherwise there appears an additional non-trivial phase factor.