1,207 research outputs found
A new quasi-exactly solvable problem and its connection with an anharmonic oscillator
The two-dimensional hydrogen with a linear potential in a magnetic field is
solved by two different methods. Furthermore the connection between the model
and an anharmonic oscillator had been investigated by methods of KS
transformation
Aharonov-Anandan phase 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-adiabatic
counterpart (Aharonov and Anandan phase). In this paper, we analyze both the
non-degenerate and degenerate geometric phase of Lipkin-Meskov-Glick type
model, which has many application in Bose-Einstein condensates and entanglement
theory. Furthermore, in order to calculate degenerate geometric phases, the
Floquet theorem and decomposition of operator are generalized. And the general
formula is achieved
Geometric phase for nonlinear coherent and squeezed state
The geometric phases for standard coherent states which are widely used in
quantum optics have attracted a large amount of attention. Nevertheless, few
physicists consider about the counterparts of non-linear coherent states, which
are useful in the description of the motion of a trapped ion. In this paper,
the non-unitary and non-cyclic geometric phases for two nonlinear coherent and
one squeezed states are formulated respectively. Moreover, some of their common
properties are discussed respectively, such as gauge invariance, non-locality
and non-linear effects. The non-linear functions have dramatic impacts on the
evolution of the corresponding geometric phases. They speed the evolution up or
down. So this property may have application in controlling or measuring
geometric phase. For the squeezed case, when the squeezed parameter r ->
\infinity, the limiting value of the geometric phase is also determined by
non-linear function at a given time and angular velocity. In addition, the
geometric phases for standard coherent and squeezed states are obtained under a
particular condition. When the time evolution undergoes a period, their
corresponding cyclic geometric phases are achieved as well. And the distinction
between the geometric phases of the two coherent states maybe regarded as a
geometric criterion
Demonstrating Additional Law of Relativistic Velocities based on Squeezed Light
Special relativity is foundation of many branches of modern physics, of which
theoretical results are far beyond our daily experience and hard to realized in
kinematic experiments. However, its outcomes could be demonstrated by making
use of convenient substitute, i.e. squeezed light in present paper. Squeezed
light is very important in the field of quantum optics and the corresponding
transformation can be regarded as the coherent state of SU(1; 1). In this
paper, the connection between the squeezed operator and Lorentz boost is built
under certain conditions. Furthermore, the additional law of relativistic
velocities and the angle of Wigner rotation are deduced as well
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