We propose a scheme for the realization of unconventional geometric two-qubit phase gates with two identical two-level ions, In the present scheme, the two ions are simultaneously illuminated by a standing-wave laser ...We propose a scheme for the realization of unconventional geometric two-qubit phase gates with two identical two-level ions, In the present scheme, the two ions are simultaneously illuminated by a standing-wave laser pulse with its pulse frequency being tuned to the ionic transition. The gate operation time can be much shorter, making the system robust against decoherence. In addition, we choose the appropriate experimental parameters to construct the geometric phase gate in one step, and thus avoid implementing the pure geometric single qubit operation.展开更多
The geometric phase has become a fundamental concept in many fields of physics since it was revealed. Recently, the study of the geometric phase has attracted considerable attention in the context of quantum phase tra...The geometric phase has become a fundamental concept in many fields of physics since it was revealed. Recently, the study of the geometric phase has attracted considerable attention in the context of quantum phase transition, where the ground state properties of the system experience a dramatic change induced by a variation of an external parameter. In this work, we experimentally measure the ground-state geometric phase of the three-spin XY model by utilizing the nuclear magnetic resonance technique. The experimental results indicate that the geometric phase could be used as a fingerprint of the ground-state quantum phase transition of many-body systems.展开更多
We propose a scheme for the implementation of remote controlled-NOT gates and entanglement swapping via geometric phase gates in ion-trap systems. The proposed scheme uses the two ground states of the A-type ions as m...We propose a scheme for the implementation of remote controlled-NOT gates and entanglement swapping via geometric phase gates in ion-trap systems. The proposed scheme uses the two ground states of the A-type ions as memory instead of the vibrational mode. And the system is robust against the spontaneous radiation and the dephasing.展开更多
We consider a qubit symmetrically and transversely coupled to an XY spin chain with Dzyaloshinsky-Moriya（DM） interaction in the presence of a transverse magnetic field.An analytical expression for the geometric phas...We consider a qubit symmetrically and transversely coupled to an XY spin chain with Dzyaloshinsky-Moriya（DM） interaction in the presence of a transverse magnetic field.An analytical expression for the geometric phase of the qubit is obtained in the weak coupling limit.We find that the modification of the geometrical phase induced by the spin chain environment is greatly enhanced by DM interaction in the weak coupling limit around the quantum phase transition point of the spin chain.展开更多
We present an alternative scheme for implementing the unconventional geometric two-qubit phase gate and prepar- ing multiqubit entanglement by using a frequency-modulated laser field to simultaneously illuminate all i...We present an alternative scheme for implementing the unconventional geometric two-qubit phase gate and prepar- ing multiqubit entanglement by using a frequency-modulated laser field to simultaneously illuminate all ions. Selecting the index of modulation yields selective mechanisms for coupling and decoupling between the internal and the external states of the ions. By the selective mechanisms, we obtain the unconventional geometric two-qubit phase gate, multiparticle Greenberger-Horne-Zeilinger states and highly entangled cluster states. Our scheme is insensitive to the thermal motion of the ions.展开更多
We consider a two-qubit system described by the Heisenberg XY model with Dzyaloshinski Moriya （DM） anisotropic interaction in a perpendicular magnetic field to investigate the relation between entanglement, geometri...We consider a two-qubit system described by the Heisenberg XY model with Dzyaloshinski Moriya （DM） anisotropic interaction in a perpendicular magnetic field to investigate the relation between entanglement, geometric phase and quantum phase transition （QPT）. It is shown that the DM interaction has an effect on the critical boundary. The combination of entanglement and geometric phase may characterize QPT completely. Their jumps mean that the occurrence of QPT and inversely the QPT at the critical point at least corresponds to a jump of one of them.展开更多
Motivated by recent developments in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshko...Motivated by recent developments in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshkov Glick model. We obtain the fidelity susceptibilities for SU（2） and SU（1, 1） algebraic structure models. From this relation, the validity of the fidelity susceptibility to signal for the quantum phase transition is also verified in these two systems. At the same time, we obtain the geometric phases in these two systems by calculating the fidelity susceptibility. In addition, the new method of calculating fidelity susceptibility is used to explore the two-dimensional XXZ model and the Bose-Einstein condensate （BEC）.展开更多
We study geometric phases of the ground states of inhomogeneous XY spin chains in transverse fields with Dzyaloshinski--Moriya （DM） interaction, and investigate the effect of the DM interaction on the quantum phase ...We study geometric phases of the ground states of inhomogeneous XY spin chains in transverse fields with Dzyaloshinski--Moriya （DM） interaction, and investigate the effect of the DM interaction on the quantum phase transition （QPT） of such spin chains. The results show that the DM interaction could influence the distribution of the regions of QPTs but could not produce new critical points for the spin-chain. This study extends the relation between geometric phases and QPTs.展开更多
We investigate a novel spatial geometric phase of hybrid-polarized vector fields consisting of linear, elliptical and circular polarizations by Young＇s two-slit interferometer instead of the widely used Mach-Zehnder ...We investigate a novel spatial geometric phase of hybrid-polarized vector fields consisting of linear, elliptical and circular polarizations by Young＇s two-slit interferometer instead of the widely used Mach-Zehnder interferometer. This spatial geometric phase can be manipulated by engineering the spatial configuration of hybrid polarizations, and is directly related to the topological charge, the local states of polarization and the rotational symmetry of hybrid-polarized vector optical fields. The unique feature of geometric phase has implications in quantum information science as well as other physical systems such as electron vortex beams.展开更多
Utilizing the geometric phase(GP)acquired in a quantum evolution,we manifest the thermality and quantum nature of the Unruh effect of an accelerating detector.We consider an UDW detector coupling to a conformal field ...Utilizing the geometric phase(GP)acquired in a quantum evolution,we manifest the thermality and quantum nature of the Unruh effect of an accelerating detector.We consider an UDW detector coupling to a conformal field in Minkowski spacetime,whose response spectrum exhibits an intermediate statistics of(1+1)anyon field.We find that comparing to an inertial moving detector,the GP in accelerating frame is modified after the nonunitary evolution of the detector due to the Unruh effect.We show that such modification can distinguish the different thermalizing ways of the detector,which depends on the scaling dimension of the conformal primary field.Finally,we estimate the difference between the GP under the Unruh radiation and that in a thermal bath for a static observer,which reveals the quantum origin of the Unruh effect rather than a conventional thermal noise.展开更多
We present an experiment of observing the geometric phase in a superconducting circuit where the resonator and the qutrit energy levels are dispersively coupled. The drive applied to the resonator displaces its state ...We present an experiment of observing the geometric phase in a superconducting circuit where the resonator and the qutrit energy levels are dispersively coupled. The drive applied to the resonator displaces its state components associated with the qutrit＇s ground state and first-excited state along different circular trajectories in phase space. We identify the resonator＇s phase-space trajectories by Wigner tomography using an ancilla qubit, following which we observe the difference between the geometric phases associated with these trajectories using Ramsey interferometry. This geometric phase is further used to construct the single-qubit It-phase gate with a process fidelity of 0.851± 0.001.展开更多
In this work we investigated the geometric phases of a qubit-oscillator system beyond the conventional rotating- wave approximation. We find that in the limiting of weak coupling the results coincide with that obtaine...In this work we investigated the geometric phases of a qubit-oscillator system beyond the conventional rotating- wave approximation. We find that in the limiting of weak coupling the results coincide with that obtained under rotating-wave approximation while there exists an increasing difference with the increase of coupling constant. It was shown that the geometric phase is symmetric with respect to the sign of the detuning of the quantized field from the one-photon resonance under the conventional rotating-wave approximation while a red-blue detuning asymmetry occurs beyond the conventional rotating-wave approximation.展开更多
We study theoretically the nonadiabatic geometric phase of a doubly driven two-level system with an additional relative phase between the two driving modes introduced in. It is shown that the time evolution of the sys...We study theoretically the nonadiabatic geometric phase of a doubly driven two-level system with an additional relative phase between the two driving modes introduced in. It is shown that the time evolution of the system strongly depends on this relative phase. The condition for the system returning to its initial state after a single period is given by the means of the Landau–Zener–Stückelberg–Majorana destructive interference. The nonadiabatic geometric phase accompanying a cyclic evolution is shown to be related to the Stokes phase as well as this relative phase. By controlling the relative phase, the geometric phase can characterize two distinct phases in the adiabatic limit.展开更多
With the help of the time-dependent gauge transformation technique, we have studied the geometric phase of a spin-half particle in a rotating magnetic field. We have found that the slow but finite frequency of the rot...With the help of the time-dependent gauge transformation technique, we have studied the geometric phase of a spin-half particle in a rotating magnetic field. We have found that the slow but finite frequency of the rotating magnetic field will make the difference between the adiabatic geometric phase and the exact geometric phase. When the frequency is much smaller than the energy space and the adiabatic condition is perfectly guaranteed, the adiabatic approximation geometric phase is exactly consistent with the adiabatic geometric phase. A simple relation for the accuracy of the adiabatic approximation is given in terms of the changing rate of the frequency of the rotating magnetic field and the energy level space.展开更多
A new method to design an ultra-thin high-gain circularly-polarized antenna system with high efficiency is proposed based on the geometrical phase gradient metasurface（GPGM）.With an accuracy control of the transmiss...A new method to design an ultra-thin high-gain circularly-polarized antenna system with high efficiency is proposed based on the geometrical phase gradient metasurface（GPGM）.With an accuracy control of the transmission phase and also the high transmission amplitude,the GPGM is capable of manipulating an electromagnetic wave arbitrarily.A focusing transmission lens working at Ku band is well optimized with the F /D of 0.32.A good focusing effect is demonstrated clearly by theoretical calculation and electromagnetic simulation.For further application,an ultra-thin single-layer transmissive lens antenna based on the proposed focusing metasurface operating at 13 GHz is implemented and launched by an original patch antenna from the perspective of high integration,simple structure,and low cost.Numerical and experimental results coincide well,indicating the advantages of the antenna system,such as a high gain of 17.6 d B,the axis ratio better than 2 d B,a high aperture efficiency of 41%,and also a simple fabrication process based on the convenient print circuit board technology.The good performance of the proposed antenna indicates promising applications in portable communication systems.展开更多
A scheme to perfectly preserve an initial qubit state in geometric quantum computation is proposed for a single- qubit geometric quantum gate in a nuclear magnetic resonance system. At first, by adjusting some magneti...A scheme to perfectly preserve an initial qubit state in geometric quantum computation is proposed for a single- qubit geometric quantum gate in a nuclear magnetic resonance system. At first, by adjusting some magnetic field parameters, one can let the dynamic phase be proportional to the geometric phase. Then, by controlling the azimuthal angle in the initial state, we may realize a geometric quantum gate whose fidelity is equal to one under cyclic evolution. This means that the quantum information is no distortion in the process of geometric quantum computation.展开更多
In this paper, we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field. Both the field...In this paper, we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field. Both the field nonlinearity and the atom-field coupling nonlinearity are considered. We find that the geometric phase depends on whether the index k is an odd number or an even number in the resonant case. In addition, we also find that the geometric phase may be easily observed when the field nonlinearity is not considered. The fractional statistical phenomenon appears in this system if the strong nonlinear atom-field coupling is considered. We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.展开更多
The photonic spin Hall effect(SHE)refers to the transverse spin separation of photons with opposite spin angular momentum,after the beam passes through an optical interface or inhomogeneous medium,manifested as the sp...The photonic spin Hall effect(SHE)refers to the transverse spin separation of photons with opposite spin angular momentum,after the beam passes through an optical interface or inhomogeneous medium,manifested as the spin-dependent splitting.It can be considered as an analogue of the SHE in electronic systems:the light’s right-circularly polarized and left-circularly polarized components play the role of the spin-up and spin-down electrons,and the refractive index gradient replaces the electronic potential gradient.Remarkably,the photonic SHE originates from the spin-orbit interaction of the photons and is mainly attributed to two different geometric phases,i.e.,the spin-redirection Rytov-Vlasimirskii-Berry in momentum space and the Pancharatnam-Berry phase in Stokes parameter space.The unique properties of the photonic SHE and its powerful ability to manipulate the photon spin,gradually,make it a useful tool in precision metrology,analog optical computing and quantum imaging,etc.In this review,we provide a brief framework to describe the fundamentals and advances of photonic SHE,and give an overview on the emergent applications of this phenomenon in different scenes.展开更多
A new type of quantum theory known as time-dependent𝒫PT-symmetric quantum mechanics has received much attention recently.It has a conceptually intriguing feature of equipping the Hilbert space of a𝒫PT-...A new type of quantum theory known as time-dependent𝒫PT-symmetric quantum mechanics has received much attention recently.It has a conceptually intriguing feature of equipping the Hilbert space of a𝒫PT-symmetric system with a time-varying inner product.In this work,we explore the geometry of time-dependent𝒫𝒯PT-symmetric quantum mechanics.We find that a geometric phase can emerge naturally from the cyclic evolution of a PT-symmetric system,and further formulate a series of related differential-geometry concepts,including connection,curvature,parallel transport,metric tensor,and quantum geometric tensor.These findings constitute a useful,perhaps indispensible,tool to investigate geometric properties of𝒫PT-symmetric systems with time-varying system’s parameters.To exemplify the application of our findings,we show that the unconventional geometric phase[Phys.Rev.Lett.91187902(2003)],which is the sum of a geometric phase and a dynamical phase proportional to the geometric phase,can be expressed as a single geometric phase unveiled in this work.展开更多
We propose a method for generating double-ring-shaped vector beams. A step phase introduced by a spatial light modulator（SLM） first makes the incident laser beam have a nodal cycle. This phase is dynamic in nature b...We propose a method for generating double-ring-shaped vector beams. A step phase introduced by a spatial light modulator（SLM） first makes the incident laser beam have a nodal cycle. This phase is dynamic in nature because it depends on the optical length. Then a Pancharatnam–Berry phase（PBP） optical element is used to manipulate the local polarization of the optical field by modulating the geometric phase. The experimental results show that this scheme can effectively create double-ring-shaped vector beams. It provides much greater flexibility to manipulate the phase and polarization by simultaneously modulating the dynamic and the geometric phases.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No 10574022）, and the Funds of the Natural Science of Fujian Province, China （Grant Nos Z0512006 and A0210014）.
文摘We propose a scheme for the realization of unconventional geometric two-qubit phase gates with two identical two-level ions, In the present scheme, the two ions are simultaneously illuminated by a standing-wave laser pulse with its pulse frequency being tuned to the ionic transition. The gate operation time can be much shorter, making the system robust against decoherence. In addition, we choose the appropriate experimental parameters to construct the geometric phase gate in one step, and thus avoid implementing the pure geometric single qubit operation.
基金Supported by the National Key Basic Research Program under Grant Nos 2013CB921800 and 2014CB848700the National Science Fund for Distinguished Young Scholars under Grant No 11425523+4 种基金the National Natural Science Foundation of China under Grant Nos 11375167,11227901,91021005 and 11575173the Strategic Priority Research Program(B)of the Chinese Academy of Sciences under Grant No XDB01030400the Research Fund for the Doctoral Program of Higher Education of China under Grant No 20113402110044the China Postdoctoral Science Foundationthe Fundamental Research Funds for the Central Universities
文摘The geometric phase has become a fundamental concept in many fields of physics since it was revealed. Recently, the study of the geometric phase has attracted considerable attention in the context of quantum phase transition, where the ground state properties of the system experience a dramatic change induced by a variation of an external parameter. In this work, we experimentally measure the ground-state geometric phase of the three-spin XY model by utilizing the nuclear magnetic resonance technique. The experimental results indicate that the geometric phase could be used as a fingerprint of the ground-state quantum phase transition of many-body systems.
基金Project supported by the National Natural Science Foundation (Grant Nos 10574022 and 10575022)the Funds of the Natural Science of Fujian Province, China (Grant No Z0512006)
文摘We propose a scheme for the implementation of remote controlled-NOT gates and entanglement swapping via geometric phase gates in ion-trap systems. The proposed scheme uses the two ground states of the A-type ions as memory instead of the vibrational mode. And the system is robust against the spontaneous radiation and the dephasing.
基金Project supported by the National Basic Research Program of China (Grant No. 2010CB923102)the Special Prophase Project on the National Basic Research Program of China (Grant No. 2011CB311807)the National Natural Science Foundation of China (Grant No. 11074199)
文摘We consider a qubit symmetrically and transversely coupled to an XY spin chain with Dzyaloshinsky-Moriya（DM） interaction in the presence of a transverse magnetic field.An analytical expression for the geometric phase of the qubit is obtained in the weak coupling limit.We find that the modification of the geometrical phase induced by the spin chain environment is greatly enhanced by DM interaction in the weak coupling limit around the quantum phase transition point of the spin chain.
基金Project supported by the National Basic Research Program of China (Grant No. 2005CB724508)the Scientific Research Foundation of Jiangxi Provincial Department of Education,China (Grant No. GJJ10133)the Foundation of Talent of Jinggangof Jiangxi Province,China (Grant No. 2008DQ00400)
文摘We present an alternative scheme for implementing the unconventional geometric two-qubit phase gate and prepar- ing multiqubit entanglement by using a frequency-modulated laser field to simultaneously illuminate all ions. Selecting the index of modulation yields selective mechanisms for coupling and decoupling between the internal and the external states of the ions. By the selective mechanisms, we obtain the unconventional geometric two-qubit phase gate, multiparticle Greenberger-Horne-Zeilinger states and highly entangled cluster states. Our scheme is insensitive to the thermal motion of the ions.
基金Project supported by the Natural Science Foundation for Young Scientists of Shanxi Province of China (Grant No. 2007021001)the Science and Technology Key Item of Chinese Ministry of Education (Grant No. 207017)+1 种基金National Fundamental Fund of Personnel Training (Grant No. J0730317)the National Natural Science Foundation of China (Grant No. 10774094)
文摘We consider a two-qubit system described by the Heisenberg XY model with Dzyaloshinski Moriya （DM） anisotropic interaction in a perpendicular magnetic field to investigate the relation between entanglement, geometric phase and quantum phase transition （QPT）. It is shown that the DM interaction has an effect on the critical boundary. The combination of entanglement and geometric phase may characterize QPT completely. Their jumps mean that the occurrence of QPT and inversely the QPT at the critical point at least corresponds to a jump of one of them.
基金supported by the National Natural Science Foundation of China (Grant No. 11075101)the Shanghai Leading Academic Discipline Project,China (Grant No. S30105)the Shanghai Research Foundation,China (Grant No. 07d222020)
文摘Motivated by recent developments in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshkov Glick model. We obtain the fidelity susceptibilities for SU（2） and SU（1, 1） algebraic structure models. From this relation, the validity of the fidelity susceptibility to signal for the quantum phase transition is also verified in these two systems. At the same time, we obtain the geometric phases in these two systems by calculating the fidelity susceptibility. In addition, the new method of calculating fidelity susceptibility is used to explore the two-dimensional XXZ model and the Bose-Einstein condensate （BEC）.
基金Project supported by National Natural Science Foundation of China (Grant Nos. 10847108 and 10775023)
文摘We study geometric phases of the ground states of inhomogeneous XY spin chains in transverse fields with Dzyaloshinski--Moriya （DM） interaction, and investigate the effect of the DM interaction on the quantum phase transition （QPT） of such spin chains. The results show that the DM interaction could influence the distribution of the regions of QPTs but could not produce new critical points for the spin-chain. This study extends the relation between geometric phases and QPTs.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11534006,11674184 and 11374166the Natural Science Foundation of Tianjin under Grant No 16JC2DJC31300Collaborative Innovation Center of Extreme Optics
文摘We investigate a novel spatial geometric phase of hybrid-polarized vector fields consisting of linear, elliptical and circular polarizations by Young＇s two-slit interferometer instead of the widely used Mach-Zehnder interferometer. This spatial geometric phase can be manipulated by engineering the spatial configuration of hybrid polarizations, and is directly related to the topological charge, the local states of polarization and the rotational symmetry of hybrid-polarized vector optical fields. The unique feature of geometric phase has implications in quantum information science as well as other physical systems such as electron vortex beams.
基金Project supported by the National Natural Science Foundation of China(Grant No.12075178)Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2018JM1049)。
文摘Utilizing the geometric phase(GP)acquired in a quantum evolution,we manifest the thermality and quantum nature of the Unruh effect of an accelerating detector.We consider an UDW detector coupling to a conformal field in Minkowski spacetime,whose response spectrum exhibits an intermediate statistics of(1+1)anyon field.We find that comparing to an inertial moving detector,the GP in accelerating frame is modified after the nonunitary evolution of the detector due to the Unruh effect.We show that such modification can distinguish the different thermalizing ways of the detector,which depends on the scaling dimension of the conformal primary field.Finally,we estimate the difference between the GP under the Unruh radiation and that in a thermal bath for a static observer,which reveals the quantum origin of the Unruh effect rather than a conventional thermal noise.
基金Project supported by the National Basic Research Program of China(Grant No.2014CB921201)the National Natural Science Foundation of China(Grant Nos.11434008 and 11574380)
文摘We present an experiment of observing the geometric phase in a superconducting circuit where the resonator and the qutrit energy levels are dispersively coupled. The drive applied to the resonator displaces its state components associated with the qutrit＇s ground state and first-excited state along different circular trajectories in phase space. We identify the resonator＇s phase-space trajectories by Wigner tomography using an ancilla qubit, following which we observe the difference between the geometric phases associated with these trajectories using Ramsey interferometry. This geometric phase is further used to construct the single-qubit It-phase gate with a process fidelity of 0.851± 0.001.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11075099, 11047167, and 11105087)the Programme of State Key Laboratory of Quantum Optics and Quantum Optics Devices (Grant No. KF201002)+1 种基金the National Fundamental Fund of Personnel Training (Grant No. J1103210)the Youth Science Foundation of Shanxi Province of China (Grant No. 2010021003-2)
文摘In this work we investigated the geometric phases of a qubit-oscillator system beyond the conventional rotating- wave approximation. We find that in the limiting of weak coupling the results coincide with that obtained under rotating-wave approximation while there exists an increasing difference with the increase of coupling constant. It was shown that the geometric phase is symmetric with respect to the sign of the detuning of the quantized field from the one-photon resonance under the conventional rotating-wave approximation while a red-blue detuning asymmetry occurs beyond the conventional rotating-wave approximation.
基金the Special Foundation for theoretical physics Research Program of China (Grant No. 11647165)the China Postdoctoral Science Foundation Funded Project (Project No. 2020M673118)+3 种基金the funding from the National Natural Science Foundation of China (Grant No. 11874247)the National Key Research and Development Program of China (Grant No. 2017YFA0304500)the Program of State Key Laboratory of Quantum Optics and Quantum Optics Devices, China (Grant No. KF201703)the support from Guangdong Provincial Key Laboratory (Grant No. 2019B121203002)。
文摘We study theoretically the nonadiabatic geometric phase of a doubly driven two-level system with an additional relative phase between the two driving modes introduced in. It is shown that the time evolution of the system strongly depends on this relative phase. The condition for the system returning to its initial state after a single period is given by the means of the Landau–Zener–Stückelberg–Majorana destructive interference. The nonadiabatic geometric phase accompanying a cyclic evolution is shown to be related to the Stokes phase as well as this relative phase. By controlling the relative phase, the geometric phase can characterize two distinct phases in the adiabatic limit.
基金Project supported by the State Key Development Program for Basic Research of China （Grant No 2006CB921603）, the National Natural Science Foundation of China （Grant Nos 10444002 and 10674087）7 the Natural Science Foundation of Shanxi Province （Grant No 2006011004）7 the Shanxi Provincial Foundation for Returned Scholars the Scientific Research Foundation of the State Human Resource Ministry for Returned Chinese Scholars, and the Scientific Research Foundation for the Returned 0verseas Chinese Scholars, Ministry of Education of China.
文摘With the help of the time-dependent gauge transformation technique, we have studied the geometric phase of a spin-half particle in a rotating magnetic field. We have found that the slow but finite frequency of the rotating magnetic field will make the difference between the adiabatic geometric phase and the exact geometric phase. When the frequency is much smaller than the energy space and the adiabatic condition is perfectly guaranteed, the adiabatic approximation geometric phase is exactly consistent with the adiabatic geometric phase. A simple relation for the accuracy of the adiabatic approximation is given in terms of the changing rate of the frequency of the rotating magnetic field and the energy level space.
基金Project supported by the National Natural Science Foundation of China(Grant No.61372034)
文摘A new method to design an ultra-thin high-gain circularly-polarized antenna system with high efficiency is proposed based on the geometrical phase gradient metasurface（GPGM）.With an accuracy control of the transmission phase and also the high transmission amplitude,the GPGM is capable of manipulating an electromagnetic wave arbitrarily.A focusing transmission lens working at Ku band is well optimized with the F /D of 0.32.A good focusing effect is demonstrated clearly by theoretical calculation and electromagnetic simulation.For further application,an ultra-thin single-layer transmissive lens antenna based on the proposed focusing metasurface operating at 13 GHz is implemented and launched by an original patch antenna from the perspective of high integration,simple structure,and low cost.Numerical and experimental results coincide well,indicating the advantages of the antenna system,such as a high gain of 17.6 d B,the axis ratio better than 2 d B,a high aperture efficiency of 41%,and also a simple fabrication process based on the convenient print circuit board technology.The good performance of the proposed antenna indicates promising applications in portable communication systems.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10864002)
文摘A scheme to perfectly preserve an initial qubit state in geometric quantum computation is proposed for a single- qubit geometric quantum gate in a nuclear magnetic resonance system. At first, by adjusting some magnetic field parameters, one can let the dynamic phase be proportional to the geometric phase. Then, by controlling the azimuthal angle in the initial state, we may realize a geometric quantum gate whose fidelity is equal to one under cyclic evolution. This means that the quantum information is no distortion in the process of geometric quantum computation.
基金Project supported partially by the National Natural Science Foundation of China (Grant Nos 10575040 and 10634060)
文摘In this paper, we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field. Both the field nonlinearity and the atom-field coupling nonlinearity are considered. We find that the geometric phase depends on whether the index k is an odd number or an even number in the resonant case. In addition, we also find that the geometric phase may be easily observed when the field nonlinearity is not considered. The fractional statistical phenomenon appears in this system if the strong nonlinear atom-field coupling is considered. We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.
基金supports from the National Natural Science Foundation of China(Grant No.12174097)the Natural Science Foundation of Hunan Province(Grant No.2021JJ10008).
文摘The photonic spin Hall effect(SHE)refers to the transverse spin separation of photons with opposite spin angular momentum,after the beam passes through an optical interface or inhomogeneous medium,manifested as the spin-dependent splitting.It can be considered as an analogue of the SHE in electronic systems:the light’s right-circularly polarized and left-circularly polarized components play the role of the spin-up and spin-down electrons,and the refractive index gradient replaces the electronic potential gradient.Remarkably,the photonic SHE originates from the spin-orbit interaction of the photons and is mainly attributed to two different geometric phases,i.e.,the spin-redirection Rytov-Vlasimirskii-Berry in momentum space and the Pancharatnam-Berry phase in Stokes parameter space.The unique properties of the photonic SHE and its powerful ability to manipulate the photon spin,gradually,make it a useful tool in precision metrology,analog optical computing and quantum imaging,etc.In this review,we provide a brief framework to describe the fundamentals and advances of photonic SHE,and give an overview on the emergent applications of this phenomenon in different scenes.
基金supported by Singapore Ministry of Education Academic Research Fund Tier I(WBS No.R-144-000-353-112)by the Singapore NRF Grant No.NRFNRFI2017-04(WBS No.R-144-000-378-281)supported by Singapore Ministry of Education Academic Research Fund Tier I(WBS No.R-144-000-352-112)。
文摘A new type of quantum theory known as time-dependent𝒫PT-symmetric quantum mechanics has received much attention recently.It has a conceptually intriguing feature of equipping the Hilbert space of a𝒫PT-symmetric system with a time-varying inner product.In this work,we explore the geometry of time-dependent𝒫𝒯PT-symmetric quantum mechanics.We find that a geometric phase can emerge naturally from the cyclic evolution of a PT-symmetric system,and further formulate a series of related differential-geometry concepts,including connection,curvature,parallel transport,metric tensor,and quantum geometric tensor.These findings constitute a useful,perhaps indispensible,tool to investigate geometric properties of𝒫PT-symmetric systems with time-varying system’s parameters.To exemplify the application of our findings,we show that the unconventional geometric phase[Phys.Rev.Lett.91187902(2003)],which is the sum of a geometric phase and a dynamical phase proportional to the geometric phase,can be expressed as a single geometric phase unveiled in this work.
基金Project supported by the National Natural Science Foundation of China(Grant No.11547017)the Hubei Engineering University Research Foundation,China(Grant No.z2014001)the Natural Science Foundation of Hubei Province,China(Grant No.2014CFB578)
文摘We propose a method for generating double-ring-shaped vector beams. A step phase introduced by a spatial light modulator（SLM） first makes the incident laser beam have a nodal cycle. This phase is dynamic in nature because it depends on the optical length. Then a Pancharatnam–Berry phase（PBP） optical element is used to manipulate the local polarization of the optical field by modulating the geometric phase. The experimental results show that this scheme can effectively create double-ring-shaped vector beams. It provides much greater flexibility to manipulate the phase and polarization by simultaneously modulating the dynamic and the geometric phases.
