Schwinger, Pegg and Barnett and a relationship between angular and Cartesian quantum descriptions

Pegg-Barnett与Paul量子相位框架之间的形式关系

Formal relation between Pegg-Barnett and Paul quantum phase frameworks

本文通过证明结合量子受限放大器信道可将Pegg-Barnett形式精确推导出Paul形式的相位概率分布，建立了两种量子相位框架间的明确联系，表明Paul框架是Pegg-Barnett方法的半经典极限。

Barnett-Pegg formalism of angle operators, revivals, and flux lines

We use the Barnett-Pegg formalism of angle operators to study a rotating particle with and without a flux line. Requiring a finite dimensional version of the Wigner function to be well defined we find a natural time quantization that leads to classical maps from which the arithmetical basis of quantum revivals is seen. The flux line, that fundamentally alters the quantum statistics, forces this time quantum to be increased by a factor of a winding number and determines the homotopy class of the path. The value of the flux is restricted to the rational numbers, a feature that persists in the in…

Leggett-Garg inequalities with deformed Pegg-Barnett phase observables

We investigate the Leggett-Garg inequalities (LGIs) for a boson system whose observables are given by deforming the Pegg-Barnett phase operators. We consider two observables and show that the quantum Fourier transform is useful in the realization of the required measurements. Deriving explicit forms for the LGIs using the coherent state $|α\rangle$ as the initial state, we explore the regimes where they are violated when the time difference between observations of the phase operators is varied. We show that the system remains nonclassical in the large amplitude limit without dissipation, howev…

Schwinger, Pegg and Barnett approaches and a relationship between angular and Cartesian quantum descriptions II: Phase Spaces

Following the discussion -- in state space language -- presented in a preceding paper, we work on the passage from the phase space description of a degree of freedom described by a finite number of states (without classical counterpart) to one described by an infinite (and continuously labeled) number of states. With that it is possible to relate an original Schwinger idea to the Pegg and Barnett approach to the phase problem. In phase space language, this discussion shows that one can obtain the Weyl-Wigner formalism, for both Cartesian {\em and} angular coordinates, as limiting elements of t…

Wigner函数、负值体积与Pegg-Barnett相算符本征态的实验生成

Wigner functions, negativity volumes, and experimental generation of Pegg-Barnett phase-operator eigenstates

本文研究了Pegg-Barnett相可观测量本征态的非高斯性，通过计算Wigner函数确认其在相空间特定区域取负值，并探讨了本征态的负值体积与希尔伯特空间维度的关系，同时提出量子光学电路生成本征态并分析单光子探测对其非高斯性的影响。

Intermediate coherent-phase(PB) states of radiation fields and their nonclassical properties

Intermediate states interpolating coherent states and Pegg-Barnett phase states are investigated using the ladder operator approach. These states reduce to coherent and Pegg-Barnett phase states in two different limits. Statistical and squeezing properties are studied in detail.

Phase shift operator and cyclic evolution in finite dimensional Hilbert space

We address the problem of phase shift operator acting as time evolution operator in Pegg-Barnett formalism. It is argued that standard shift operator is inconsistent with the behaviour of the state vector under cyclic evolution. We consider a generally deformed oscillator algebra at q-root of unity, as it yields the same Pegg-Barnett operator and show that shift operator meets our requirement.

On the Quantum Phase Operator for Coherent States

In papers by Lynch [Phys. Rev. A41, 2841 (1990)] and Gerry and Urbanski [Phys. Rev. A42, 662 (1990)] it has been argued that the phase-fluctuation laser experiments of Gerhardt, Büchler and Lifkin [Phys. Lett. 49A, 119 (1974)] are in good agreement with the variance of the Pegg-Barnett phase operator for a coherent state, even for a small number of photons. We argue that this is not conclusive. In fact, we show that the variance of the phase in fact depends on the relative phase between the phase of the coherent state and the off-set phase $ϕ_0$ of the Pegg-Barnett phase operator. This off-set…

On the quantum phase problem

We present a phase formalism that passes the Barnett-Pegg acid test, i.e. phase fluctuations for a number state are the expected value $π^2/3$ which are the fluctuations for a classical random phase distribution. The formalism is shown to have consistency subjected to different approaches.

Quantum Formulation of Fractional Orbital Angular Momentum

The quantum theory of rotation angles (S. M. Barnett and D. T. Pegg, Phys. Rev. A, 41, 3427-3425 (1990)) is generalised to non-integer values of the orbital angular momentum. This requires the introduction of an additional parameter, the orientation of a phase discontinuity associated with fractional values of the orbital angular momentum. We apply our formalism to the propagation of light modes with fractional orbital angular momentum in the paraxial and non-paraxial regime.

Quantum phase properties of nonlinear optical phenomena

We review some quantum-phase descriptions of optical fields. We focus on real fields that can be generated in practice in various nonlinear optical processes. Thus, we rather avoid discussions of phase formalisms as such and try to exploit their practical applicability in the description of optical fields. In the description of the phase properties we use two different, though related formalisms: the Pegg-Barnett Hermitian phase formalism and the formalism based on $s$-parametrized phase distributions.

Is the Deformation Parameter in q-Rotor Model Really Phenomenological ?

We cast the $q$-rotor in the framework of Barnett-Pegg theory for rotation angle, whose underlying algebra is $SU_q(2)$. A new method to fix the deformation parameter from the theory is suggested. We test our ideas by fitting rotational spectra in deformed even-even and superdeformed nuclei. The results are in good agreement with the previous phenomenological applications of $q$-rotor model.

Reduction of Quantum Phase Fluctuations in Intermediate States

Recently we have shown that the reduction of the Carruthers-Nieto symmetric quantum phase fluctuation parameter (U) with respect to its coherent state value corresponds to an antibunched state, but the converse is not true. Consequently reduction of U is a stronger criterion of nonclassicality than the lowest order antibunching. Here we have studied the possibilities of reduction of $U$ in intermediate states by using the Barnett Pegg formalism. We have shown that the reduction of phase fluctuation parameter U can be seen in different intermediate states, such as binomial state, generalized bi…

通过N体角动量耦合实现量子位多控制酉算子和超图态的实现与表示

Implementation and representation of qudit multi-controlled unitaries and hypergraph states by N-body angular momentum couplings

研究通过N体角动量耦合实现量子位多控制酉算子及超图态的表示，在三量子位特殊情况阐述要点，将三量子位三方控制酉算子按二体角动量耦合分解，给出光学系统实现示例并定义新的角动量超图态。