Ultra-thin single-layer transparent geometrical phase gradient metasurface and its application to high-gain circularly-polarized lens antenna

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.

Geometric Phase in General Relativity

We study the transport of a small wave packet in the embedding of the Stueckelberg-Horwitz-Piron relativistic quantum theory into the manifold of general relativity around the Schwarzschild solution using a semiclassical approximation. We find that the parallel transport of the momentum leads to a geometrical (Berry type) phase.

On the geometric phase in the spatial equilibria of nonlinear rods

Geometric phases have natural manifestations in large deformations of geometrically exact rods. The primary concerns of this article are the physical implications and observable consequences of geometric phases arising from the deformed patterns exhibited by a rod subjected to end moments. This mechanical problem is classical and has a long tradition dating back to Kirchhoff. However, the perspective from geometric phases seems to go more deeply into relations between local strain states and global geometry of shapes, and infuses genuinely new insights and better understanding, which enable one to describe this kind of deformation in a neat and elegant way. On the other hand, visual representations of these deformations provide beautiful illustrations of geometric phases and render the meaning of the abstract concept of holonomy more direct and transparent.

A scheme for the implementation of unconventional geometric phase gates with trapped ions

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.

Experimental Observation of the Ground-State Geometric Phase of Three-Spin XY Model

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.

Implementing remote controlled-NOT gates and entanglement swapping via geometric phase gates in ion-trap systems

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.

Induced modification of the geometric phase of a qubit coupled to an XY spin chain by Dzyaloshinsky-Moriya interaction

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.

Unconventional geometric phase gate and multiqubit entanglement for hot ions with a frequency-modulated field

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.

Geometric Phases for Mixed States in Trapped Ions

The generalization of geometric phase from the pure states to the mixed states may have potential applications in constructing geometric quantum gates. We here investigate the mixed state geometric phases and visibilities of the trapped ion system in both non-degenerate and degenerate cases. In the proposed quantum system, the geometric phases are determined by the evolution time, the initial states of trapped ions, and the initial states of photons. Moreover, special periods are gained under which the geometric phases do not change with the initial states changing of photon parts in both non-degenerate and degenerate cases. The high detection efficiency in the ion trap system implies that the mixed state geometric phases proposed here can be easily tested.

Critical Property of the Geometric Phase in the Dicke Model with the Dipole-dipole Interactions

We obtained the ground-state energy level and associated geometric phase in the Dicke model with the dipoledipole interactions analytically by the Holstein-Primakoff transformation and the boson expansion approach in the thermodynamic limit. The nonadiabatic geometric phase induced by the photon field was derived with the time-dependent unitary transformation. It is shown that dipole-dipole interactions have a deep influence on scaled behavior of the geometric phase at the critical point.

Berry phase in a generalized nonlinear two-level system

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.

Critical entanglement and geometric phase of a two-qubit model with Dzyaloshinski-Moriya anisotropic interaction

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.

Implementation of Controlled Geometric Phase Gate for Two Trapped Neutral Atoms

We propose a scheme for realizing a controlled geometric phase gate for two neutral atoms.We apply thestimulated Raman adiabatic passage to transfer atoms from their ground states into Rydberg excited states, and use theRydberg interaction induced energy shifts to generate geometric phase and construct quantum gates.

Influence of Bipartite Qubit Coupling on Geometric Phase

The geometric phase of the bipartite Heisenberg spin-1/2 system with one spin driven by rotating magnetic field is investigated. It is found that in the one-site drive case, the intersubsystem coupling can be equivalent to a static quasi-magnetic field in the parameter space. This perspective has satisfactorily explained the irregular asymptote effect of geometric phase. We discuss the property of the two-site magnetic drive spin system and discover that a stationary state with no geometric phase shift is generated.

Fidelity susceptibility and geometric phase in critical phenomenon

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）.

Aharonov-Anandan Phases in Lipkin-Meskov-Glick Model

In the system of several interacting spins,geometric phases have been researched intensively.However,the studies are mainly focused on the adiabatic case (Berry phase),so it is necessary for us to study the non-adiabaticcounterpart (Aharonov and Anandan phase).In this paper,we analyze both the non-degenerate and degenerate geometricphase of Lipkin-Meskov-Glick type model,which has many application in Bose-Einstein condensates and entanglementtheory.Furthermore,in order to calculate degenerate geometric phases,the Floquet theorem and decomposition ofoperator are generalized.And the general formula is achieved.

Spatial-Variant Geometric Phase of Hybrid-Polarized Vector Optical Fields

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.

Geometric phases and quantum phase transitions in inhomogeneous XY spin-chains:Effect of the Dzyaloshinski-Moriya interaction

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.

Geometric phase under the Unruh effect with intermediate statistics

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.

Observation of geometric phase in a dispersively coupled resonator-qutrit system

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.