arXiv subjects

Choo Hiap Oh

Publications and source records attributed to Choo Hiap Oh.

4 recordsLinked to original sources

arXiv2025

Exactly Solvable Quantum Model with Spin-Dependent Coulomb Interaction

In this work, we report an exactly solvable quantum model featuring a spin-dependent Coulomb interaction, described by the spin vector potential $\vec{\mathcal{A}} = k (\vec{r} \times \vec{S}) / r^2$ together with a Coulomb-type scalar potential $\varphi = \kappa / r$ . The model is governed by the Schr\"odinger-type Hamiltonian $\mathcal{H}_{\rm S} = \vec{\Pi}^2 / (2M) + q \varphi$ in nonrelativistic quantum mechanics and by the Dirac-type Hamiltonian $\mathcal{H}_{\rm D} = c \vec{\alpha} \cdot \vec{\Pi} + \beta M c^2 + q \varphi$ in relativistic quantum mechanics, where $\vec{\Pi} = \vec{p} - (q/c)\vec{\mathcal{A}}$ is the canonical momentum. We demonstrate two main results: (i) Just as the Coulomb-type scalar potential $\mathcal{S}_{\rm Maxwell} = \{\vec{\mathcal{A}} = 0,\ \varphi = \kappa / r\}$ is a local exact solution of Maxwell's equations on $r\neq0$, the gauge potential $\mathcal{S}_{\rm YM} = \{\vec{\mathcal{A}} = k (\vec{r} \times \vec{S}) / r^2,\ \varphi = \kappa / r\}$ constitutes a local exact solution of the Yang--Mills equations on the punctured region $r\neq0$. (ii) Both Hamiltonians $\mathcal{H}_{\rm S}$ and $\mathcal{H}_{\rm D}$ can be solved exactly in the presence of this spin-dependent Coulomb interaction. The resulting energy spectra are derived, and they naturally reduce to those of the ordinary hydrogen atom when the spin-dependent terms are neglected. Finally, we clarify the quantization conditions and the fixed-background interpretation of the model.

quant-ph↗

arXiv2025

Electric-Type Stern-Gerlach Effect

The Stern-Gerlach (SG) experiment is a fundamental experiment for revealing the existence of ``spin''. In such an experiment, beams of silver atoms were sent through inhomogeneous magnetic fields to observe their deflection. Thus, the conventional SG experiment can be actually viewed as a magnetic-type spin effect. In this work, we successfully generalize the SG effect from magnetic-type to electric-type by solving Dirac's equation with a potential barrier, thus revealing an extraordinary spin effect. Beams of Dirac's particles can be regarded as matter waves. Based on Dirac's equation, we obtain the explicit forms of the incident, reflected, and transmitted waves. The electric-type SG effect shows that the reflected and transmitted waves can have notable spatial shifts, which depend on the spin direction and the incident angle of incident wave. The electric-type SG effect has potential applications to separating Dirac's particles with different spin directions and to estimating the spin direction of Dirac's particles. Some discussions related to the interaction between spin and electric field are also made.

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arXiv2024

Revealing the Boundary between Quantum Mechanics and Classical Model by EPR-Steering Inequality

In quantum information, the Werner state is a benchmark to test the boundary between quantum mechanics and classical models. There have been three well-known critical values for the two-qubit Werner state, i.e., $V_{\rm c}^{\rm E}=1/3$ characterizing the boundary between entanglement and separable model, $V_{\rm c}^{\rm B}=1/K_G(3)$ characterizing the boundary between Bell's nonlocality and the local-hidden-variable model, while $V_{\rm c}^{\rm S}=1/2$ characterizing the boundary between Einstein-Podolsky-Rosen (EPR) steering and the local-hidden-state model. So far, the problem of $V_{\rm c}^{\rm E}=1/3$ has been completely solved by an inequality involving in the positive-partial-transpose criterion, while how to reveal the other two critical values by the inequality approach are still open. In this work, we focus on EPR steering, which is a form of quantum nonlocality intermediate between entanglement and Bell's nonlocality. By proposing the optimal $N$-setting linear EPR-steering inequalities, we have successfully obtained the desired value $V_{\rm c}^{\rm S}=1/2$ for the two-qubit Werner state, thus resolving the long-standing problem.

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arXiv2003

An experimental observation of geometric phases for mixed states using NMR interferometry

Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently fault-tolerant quantum computation. This, however, requires to deal with geometric phases in the presence of noise and interactions between different physical subsystems. Despite the wealth of literature on the subject of geometric phases very little is known about this very important case. Here we report the first experimental study of geometric phases for mixed quantum states. We show how different they are from the well understood, noiseless, pure-state case.

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