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1.
We use the quantum kinematic approach to revisit geometric phases associated with polarizing processes of a monochromatic light wave. We give the expressions of geometric phases for any, unitary or non-unitary, cyclic or non-cyclic transformations of the light wave state. Contrarily to the usually considered case of absorbing polarizers, we found that a light wave passing through a polarizer may acquire in general a nonzero geometric phase. This geometric phase exists despite the fact that initial and final polarization states are in phase according to the Pancharatnam criterion and cannot be measured using interferometric superposition. Consequently, there is a difference between the Pancharatnam phase and the complete geometric phase acquired by a light wave passing through a polarizer. We illustrate our work with the particular example of total reflection based polarizers. 相似文献
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3.
The geometric phase of the quantum systems with slow but finite
rate of the external time-dependent field
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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. 相似文献
4.
We study the geometric curvature and phase of the Rabi model. Under the rotating-wave approximation (RWA), we apply the gauge independent Berry curvature over a surface integral to calculate the Berry phase of the eigenstates for both single and two-qubit systems, which is found to be identical with the system of spin-1/2 particle in a magnetic field. We extend the idea to define a vacuum-induced geometric curvature when the system starts from an initial state with pure vacuum bosonic field. The induced geometric phase is related to the average photon number in a period which is possible to measure in the qubit–cavity system. We also calculate the geometric phase beyond the RWA and find an anomalous sudden change, which implies the breakdown of the adiabatic theorem and the Berry phases in an adiabatic cyclic evolution are ill-defined near the anti-crossing point in the spectrum. 相似文献
5.
Using the quantum kinematic approach of Mukunda and Simon, we propose a geometric phase in Bohmian mechanics. A reparametrization and gauge invariant geometric phase is derived along an arbitrary path in configuration space. The single valuedness of the wave function implies that the geometric phase along a path must be equal to an integer multiple of 2π. The nonzero geometric phase indicates that we go through the branch cut of the action function from one Riemann sheet to another when we locally travel along the path. For stationary states, quantum vortices exhibiting the quantized circulation integral can be regarded as a manifestation of the geometric phase. The bound-state Aharonov-Bohm effect demonstrates that the geometric phase along a closed path contains not only the circulation integral term but also an additional term associated with the magnetic flux. In addition, it is shown that the geometric phase proposed previously from the ensemble theory is not gauge invariant. 相似文献
6.
Rajendra Bhandari 《Physics letters. A》2011,375(41):3562-3569
Generalizing an earlier definition of the noncyclic geometric phase [R. Bhandari, Phys. Lett. A 157 (1991) 221], a nonmodular topological phase is defined with reference to a generic time-dependent two-slit interference experiment involving particles with N internal states in which the internal state of both the beams undergoes unitary evolution. A simple proof of the shorter geodesic rule for closure of the open path is presented and several useful new insights into the behavior of the dynamical and geometrical components of the phase shift presented. An effective Hamiltonian interpretation of the observable phase shifts is also presented. 相似文献
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G. F. Brand 《International Journal of Infrared and Millimeter Waves》1997,18(9):1655-1662
A millimeter-wave interferometer operating purely on the geometric phase is presented. Like its optical counterpart described
by Hariharan and Roy, this system uses two circular polarizers with a half-wave section in between. The geometric phase of
each signal is determined by the orientation of the half-wave section. 相似文献
9.
We propose a relaxation rate or dissipative cavity-based parameters that can be used as indicators of the stationary limit of a mixed state geometric phase. We perform our considerations for the system of a superconducting qubit in an open transmission line or interacting with a dissipative cavity. This system is very useful for performing an effective quantum computation by exhibiting the long collapse time of the geometric phase. It is shown that the geometric phase in the stationary limit does not depend on interaction time if the decay time exceeds an upper bound. 相似文献
10.
Critical entanglement and geometric phase of a two-qubitmodel with Dzyaloshinski--Moriya anisotropic interaction
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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. 相似文献
11.
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. 相似文献
12.
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. 相似文献
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15.
评注了《大学物理》21 23一文关于量子几何相位与Lewis相位论述与《物理学报》48 2018一文的结论有极大不同.指出前者对Lewis导出的相位与量子几何相位关系的错误陈述,而后者的结论是正确的.
关键词:
量子几何相位
不变量方法
Lewis-Riesenfeld相位 相似文献
16.
We study theoretically the geometric phase of a double-quantum-dot(DQD) system measured by a quantum point contact(QPC) in the pure dephasing and dissipative environments, respectively. The results show that in these two environments, the coupling strength between the quantum dots has an enhanced impact on the geometric phase during a quasiperiod. This is due to the fact that the expansion of the width of the tunneling channel connecting the two quantum dots accelerates the oscillations of the electron between the quantum dots and makes the length of the evolution path longer.In addition, there is a notable near-zero region in the geometric phase because the stronger coupling between the system and the QPC freezes the electron in one quantum dot and the solid angle enclosed by the evolution path is approximately zero,which is associated with the quantum Zeno effect. For the pure dephasing environment, the geometric phase is suppressed as the dephasing rate increases which is caused only by the phase damping of the system. In the dissipative environment,the geometric phase is reduced with the increase of the relaxation rate which results from both the energy dissipation and phase damping of the system. Our results are helpful for using the geometric phase to construct the fault-tolerant quantum devices based on quantum dot systems in quantum information. 相似文献
17.
The geometric phase of light has been demonstrated in various platforms of the linear optical regime, raising interest both for fundamental science as well as applications, such as flat optical elements. Recently, the concept of geometric phases has been extended to nonlinear optics, following advances in engineering both bulk nonlinear photonic crystals and nonlinear metasurfaces. These new technologies offer a great promise of applications for nonlinear manipulation of light. In this review, we cover the recent theoretical and experimental advances in the field of geometric phases accompanying nonlinear frequency conversion. We first consider the case of bulk nonlinear photonic crystals, in which the interaction between propagating waves is quasi-phase-matched, with an engineerable geometric phase accumulated by the light. Nonlinear photonic crystals can offer efficient and robust frequency conversion in both the linearized and fully-nonlinear regimes of interaction, and allow for several applications including adiabatic mode conversion, electromagnetic nonreciprocity and novel topological effects for light. We then cover the rapidly-growing field of nonlinear Pancharatnam-Berry metasurfaces, which allow the simultaneous nonlinear generation and shaping of light by using ultrathin optical elements with subwavelength phase and amplitude resolution. We discuss the macroscopic selection rules that depend on the rotational symmetry of the constituent meta-atoms, the order of the harmonic generations, and the change in circular polarization. Continuous geometric phase gradients allow the steering of light beams and shaping of their spatial modes. More complex designs perform nonlinear imaging and multiplex nonlinear holograms, where the functionality is varied according to the generated harmonic order and polarization. Recent advancements in the fabrication of three dimensional nonlinear photonic crystals, as well as the pursuit of quantum light sources based on nonlinear metasurfaces, offer exciting new possibilities for novel nonlinear optical applications based on geometric phases. 相似文献
18.
Das R Kumar SK Kumar A 《Journal of magnetic resonance (San Diego, Calif. : 1997)》2005,177(2):318-328
Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of error. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using the non-adiabatic geometric phase we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system. 相似文献
19.
Guo-Qiang Zhu 《Central European Journal of Physics》2007,5(4):463-470
The geometric phase of a bi-particle model is discussed. One can drive the system to evolve by applying an external magnetic
field, thereby controlling the geometric phase. The model has degenerate lowest-energy eigenvectors. The initial state is
assumed to be the linear superposition or mixture of the eigenvectors. The relationship between the geometric phase and the
structures of the initial state is considered, and the results are extended to a more general model.
相似文献
20.
We derive a geometric phase using the quantum kinematic approach within the complex quantum Hamilton-Jacobi formalism. The single valuedness of the wave function implies that the geometric phase along an arbitrary path in the complex plane must be equal to an integer multiple of 2π. The nonzero geometric phase indicates that we travel along the path through the branch cut of the phase function from one Riemann sheet to another. 相似文献