Luca Salasnich, Fabio Sattin
In this paper we prove a recent conjecture [Robnik M and Salasnich L 1997 J. Phys. A: Math. Gen. 30 1719] about the convergence of the WKB series for the angular momentum operator. We demonstrate that the WKB algorithm for the angular momentum gives the exact quantization formula if all orders are summed.
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A Bohr-Sommerfeld quantization rule is generalized for the case of the deformed commutation relation leading to minimal uncertainties in both coordinate and momentum operators. The correctness of the rule is verified by comparing obtained results with exact expressions for corresponding spectra.
As a model for the semiclassical analysis of quantum-mechanical systems with both potentials and boundary conditions, we construct the WKB propagator for a linear potential sloping away from an impenetrable boundary. First, we find all classical paths from point $y$ to point $x$ in time $t$ and calculate the corresponding action and amplitude functions. A large part of space-time turns out to be classically inaccessible, and the boundary of this region is a caustic of an unusual type, where the amplitude vanishes instead of diverging. We show that this curve is the limit of caustics in the usu…
We present an analytic calculation of the semiclassical electron-positron pair creation rate by time-dependent electrical fields. We use two methods, first the imaginary time method in the WKB-approximation and second the world-line instanton approach. The analytic tools for both methods are generalized to time-dependent electric fields with more than one component. For the WKB method an expansion of the momentum spectrum of produced pairs around the canonical momentum $\vec{P}=0$ is presented which simplifies the computation of the pair creation rate. We argue that the world-line instanton me…
Spin is an important quantum degree of freedom in relativistic quantum information theory. This paper provides a first-principles derivation of the observable corresponding to a Stern-Gerlach measurement with relativistic particle velocity. The specific mathematical form of the Stern-Gerlach operator is established using the transformation properties of the electromagnetic field. To confirm that this is indeed the correct operator we provide a detailed analysis of the Stern-Gerlach measurement process. We do this by applying a WKB approximation to the minimally coupled Dirac equation describin…
The nature of intrinsic/extrinsic character of angular momentum is defined in terms of the kind of the associated rotational energy of the light. The salient features of the spin energy of light and photon are highlighted. Spin angular momentum is intrinsic while orbital angular momentum possesses quasi-intrinsicness only if the vortex-like singularities are present. The claimed spin to orbital angular momentum conversion is interpreted in terms of spin redirection geometric phase. It is pointed out that this interpretation validates our angular momentum holonomy conjecture.
Angular momentum in classical and quantum mechanics is carried out beyond textbooks frames. We compare angular distribution of particle position with classical probabilistic approach. Addition of angular momenta is also discussed together with approximation to Clebsh-Gordan coefficients.
We consider the angular momentum of a charge q rotating in a homogeneous magnetic field and study the role of the electromagnetic quantum vacuum. Its orbital angular momentum is caused by the recoil of energetic vacuum photons that grows as n^2, i.e. faster than the kinetic angular momentum -2n\hbar of a Landau level.
Excitation exchange between identical atoms having arbitrary angular momentum
该论文推导了任意角动量下两相同原子间激发交换的运动方程，为相关量子过程提供了理论描述。
A simple approach for understanding the quantum nature of angular momentum and its reduction to the classical limit is presented based on Schwinger's coupled-boson representation. This approach leads to a straightforward explanation of why the square of the angular momentum in quantum mechanics is given by j(j+1) instead of just j^2, where j is the angular momentum quantum number.
We study the generalized uncertainty principle (GUP) modified simple harmonic oscillator (SHO) in the operator formalism by considering the appropriate form of the creation and annihilation operators $ A, A^\dagger $. The angular momentum algebra is then constructed using Schwinger's model of angular momentum with two independent GUP modified SHOs. With the GUP modified angular momentum algebra, we discuss coupling of angular momentum for a two-particle composite system. Further, we calculate the Clebsch-Gordan (CG) coefficients for a two-particle system explicitly. Our results show that the C…
A comprehensive theory of the Weyl-Wigner formalism for the canonical pair angle-angular momentum is presented. Special attention is paid to the problems linked to rotational periodicity and angular-momentum discreteness.
Optical modes with different orbital angular momentums (OAMs) per photon may be sorted by Mach-Zehnder interferometers incorporated with beam rotators, without resorting to OAM mode converters.
Photon Angular Momentum and Zero-Point Oscillations
本文通过单个光子电偶极辐射这一最简单情形，证明经典电动力学无法解释的辐射角动量来源于偶极源未激发态的零点振荡。
In the spirit of Quantum Non-Demolition Measurements, we show that exploiting suitable vibronic couplings and repeatedly measuring the atomic population of a confined ion, it is possible to distill center of mass vibrational states with well defined square of angular momentum or, alternatively, angular momentum projection Schrödinger cat states.
Quasiclassical solution of the three-dimensional Schredinger's equation is given. The existence of nonzero minimal angular momentum M_0 = \hbar /2 is shown, which corresponds to the quantum fluctuations of the angular momentum and contributes to the energy of the ground state.
We develop the quantum theory of transverse angular momentum of light beams. The theory applies to paraxial and quasi-paraxial photon beams in vacuum, and reproduces the known results for classical beams when applied to coherent states of the field. Both the Poynting vector, alias the linear momentum, and the angular momentum quantum operators of a light beam are calculated including contributions from first-order transverse derivatives. This permits a correct description of the energy flow in the beam and the natural emergence of both the spin and the angular momentum of the photons. We show …
Bound states of quasiparticles with quartic dispersion in an external potential: WKB approach
本文通过WKB方法研究了具有四次动量 dispersion 的准粒子束缚态，推导了包含非微扰修正的量子化条件，适用于二次和四次势的情况。
Many methods now exist to prepare free electrons into orbital angular momentum states, and the predicted applications of these electron states as probes of materials and scattering processes are numerous. The development of electron orbital angular momentum measurement techniques has lagged behind. We show that coupling between electron orbital angular momentum and a spatially varying magnetic field produces an angular momentum-dependent focusing effect. We propose a design for an orbital angular momentum measurement device built on this principle. As the method of measurement is non-interfero…
Photon carries linear momentum and angular momentum simultaneously. Within the light-matter interaction process, exchange of linear momentum results in optical forces, whereas exchange of angular momentum leads to optical torques. Use of optical forces (light pressure or damping) have been long and wide in quantum optomechanics, however, those of optical torque and optical angular momentum are not. Here we propose a theoretical framework based on optical angular momentum and optical torques to derive the Hamiltonians of cavity orbital and spin angular momentum optomechanical systems, respectiv…
The angular momentum density and flux of light in a dispersive, rotationally symmetric medium are derived from Noether's theorem. Optical angular momentum in a dispersive medium has no simple relation to optical linear momentum, even if the medium is homogeneous. A circularly polarized monochromatic beam in a homogeneous, dispersive medium carries a spin angular momentum of $\pm\hbar$ per energy $\hbarω$, as in vacuum. This result demonstrates the non-trivial interplay of dispersive contributions to optical angular momentum and energy.
We address the problem of angular momentum decomposition of a free photon. We propose a natural and physical scheme for separating the total angular momentum operator for a free photon into an orbital part and a spin part with the hope that it solves this long-standing problem and it could provide a natural basis for further study of the problem of angular momentum decomposition of a gauge field system.
We propose to use an acoustic surface wave as a memory for a photon carrying orbital angular momentum. We clarify the physical mechanism that enables the transfer of information, derive the angular momentum selection rule that must be obeyed in the process, and show how to optimize the optoacoustic coupling. We theoretically demonstrate that high fidelities can be achieved, using realistic parameters, for the transfer of a coherent optical Laguerre-Gaussian state, associated with large angular momentum, to a mechanical shear mode. Our results add a significant possibility to the ongoing effort…
Angular Momentum Quantization of a Charge-flux Composite: Quantum Electrodynamic Approach
研究二维电荷 - 磁通复合体角动量量子化问题，采用量子电动力学方法结合诺特定理，揭示电荷与磁通相互作用产生的角动量补偿了动能角动量分数部分，使净角动量严格量子化，阐明传统分数自旋及经典定义失效原因。
We give an explicit and general description of the energy, linear momentum, angular momentum and boost momentum of a molecule to order $1/c^2$, where it necessary to take account of kinetic contributions made by the electrons and nuclei as well as electromagnetic contributions made by the intramolecular field. A wealth of interesting subtleties are encountered that are not seen at order $1/c^0$, including relativistic Hall shifts, anomalous velocities and hidden momenta. Some of these have well known analogues in solid state physics.
We investigate the nonlinear dynamics of two coupled annular Bose-Einstein condensates (BECs). For certain values of the coupling strength the nonrotating ground state is unstable with respect to fluctuations in the higher angular momentum modes. The two branched Bogoliubov spectrum exhibits distinct regions of instability enabling one to selectively occupy certain angular momentum modes. For sufficiently long evolution times angular momentum Josephson oscillations spontaneously appear, breaking the initial chiral symmetry of the BECs.
We study theoretically by means of quantum electrodynamics the vortex radiation of a relativistic electron in a uniform magnetic field. The exact expressions for the probability of emission of a photon with a certain angular momentum are found. The classical asymptotics $\hbar\to 0$ of this probability does not match the angular momentum flux density calculated by the classical method using the symmetrized energy-momentum tensor. Although the flux of angular momentum integrated over the radiation directions is the same in both cases. We found the angular momentum flux of the radiation field us…
We discuss a type of measurement in which a macroscopically large angular momentum (spin) is "created" nonlocally by the measurement of just a few atoms from a double Fock state. This procedure apparently leads to a blatant nonconservation of a macroscopic variable - the local angular momentum. We argue that while this gedankenexperiment provides a striking illustration of several counter-intuitive features of quantum mechanics, it does not imply a non-local violation of the conservation of angular momentum.
Stated simply the paradox is as follows: it is clear that the orbital angular momentum of a light beam in its direction of propagation is an intrinsic quantity, and therefore has the same value everywhere in the beam. How then can a Gaussian beam, with precisely zero orbital angular momentum, drive a (single-photon) quadrupole transition which requires the transfer of angular momentum 2$\hbar$ to an absorbing atom?
Inspired by the electromagnetic duality, we propose an approach to realize the fractional angular momentum by using a cold atom which possesses a permanent magnetic dipole momentum. This atom interacts with two electric fields and is trapped by a harmonic potential which enable the motion of the atom to be planar and rotationally symmetric. We show that eigenvalues of the canonical angular momentum of the cold atom can take fractional values when the atom is cooled down to its lowest kinetic energy level. The fractional part of canonical angular momentum is dual to that of the fractional angul…
We study angular momentum of phonons in a magnetic crystal. In the presence of a spin-phonon interaction, we obtain a nonzero angular momentum of phonons, which is an odd function of magnetization. At zero temperature, phonon has a zero-point angular momentum besides a zero-point energy. With increasing temperature, the total phonon angular momentum diminishes and approaches to zero in the classical limit. The nonzero phonon angular momentum can have a significant impact on the Einstein-de Haas effect. To obtain the change of angular momentum of electrons, the change of phonon angular momentum…
This is the third part of our series "Quasiclassical and Quantum Systems of Angular Momentum". In two previous parts we have discussed the methods of group algebras in formulation of quantum mechanics and certain quasiclassical problems. Below we specify to the special case of the group ${\rm SU}(2)$ and its quotient ${\rm SO}(3,\mathbb{R})$, and discuss just our main subject in this series, i.e., angular momentum problems. To be more precise, this is the purely ${\rm SU}(2)$-treatment, so formally this might also apply to isospin. However. it is rather hard to imagine realistic quasiclassical…
In this note, we show that the methodology and conclusions of "Schwinger's Model of Angular Momentum with GUP" [arxiv:1808.00766] are flawed and that the conclusions of "Generalized Uncertainty Principle and angular momentum" (P. Bosso and S. Das) [arxiv:1607.01083] remain valid.
We study angular momentum of the electron stored in its electric and magnetic fields. We use for this purpose quantum electrodynamics in the covariant gauge. We show that a finite one-loop result for such angular momentum can be obtained without invoking any renormalization procedure. We compare it to the classical estimation relying on a short-distance cutoff.
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