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arXiv:2610.16976

Vortex structures in momentum distributions from multi-pair production

Z. L. Li, R. Z. Jiang

hep-phquant-phSubmitted Oct 12, 2026• Announced Oct 13, 2026
arXivHTMLPDF

Abstract

The vortex structures in the momentum distributions of multiple particle-antiparticle pairs produced from the vacuum by a spatially uniform, time-varying electric field with arbitrary polarization are investigated using the Bogoliubov transformation. For linearly polarized fields, as the field strength increases, the nodal lines in the multi-pair momentum distribution break up into vortex-antivortex pairs in both the bosonic and fermionic cases. Each vortex carries a topological charge that is an integer multiple of the single-pair vortex topological charge. For circular polarization, a central vortex appears at all field strengths. For bosons, its topological charge is an integer multiple of the single-pair vortex topological charge; for fermions, it is an integer multiple of the vortex topological charge for single-pair production with zero total spin projection along the field propagation direction. For elliptical polarization with suitable ellipticity, discrete vortices coexist with a central vortex. In this case, however, the integer-multiple relation for fermions generally fails because the two-pair production amplitude is a determinant and spin-channel contributions are separated in momentum space. These results provide a theoretical basis for understanding the vortex topology of multi-pair production in strong-field QED and for its potential control.

Comments
14 pages, 7 figures

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The vortex structures in the momentum distributions of multiple particle-antiparticle pairs produced from the vacuum by a spatially uniform, time-varying electric field with arbitrary polarization are investigated using the Bogoliubov transformation. For linearly polarized fields, as the field strength increases, the nodal lines in the multi-pair momentum distribution break up into vortex-antivortex pairs in both the bosonic and fermionic cases. Each vortex carries a topological charge that is an integer multiple of the single-pair vortex topological charge. For circular polarization, a central vortex appears at all field strengths. For bosons, its topological charge is an integer multiple of the single-pair vortex topological charge; for fermions, it is an integer multiple of the vortex topological charge for single-pair production with zero total spin projection along the field propagation direction. For elliptical polarization with suitable ellipticity, discrete vortices coexist with a central vortex. In this case, however, the integer-multiple relation for fermions generally fails because the two-pair production amplitude is a determinant and spin-channel contributions are separated in momentum space. These results provide a theoretical basis for understanding the vortex topology of multi-pair production in strong-field QED and for its potential control.
We investigate spin-resolved momentum distributions and phase vortices in multiphoton electron-positron pair production within a modified two-level model. This model retains the diagonal spinor inner-product terms neglected in the adiabatic approximation, thereby inducing spin-resolved transverse asymmetries in the momentum distribution. For a circularly polarized pulse, the handedness determines the winding direction of the quantized vortices, whereas for a linearly polarized pulse, the phase distribution exhibits nodal lines rather than quantized vortices. For two time-delayed circularly polarized pulses, the time delay introduces a relative phase that governs the multiphoton interference, which in turn drives the vortex evolution in each spin configuration. These results demonstrate that pulse polarization and time delay enable coherent control over vortex topology in pair production.
We investigate the multiphoton pair production in circularly polarized field via two level model. There appears obvious discrete ring structures in the momentum distribution of the created particles, in which the ring radius is mainly controlled by the number of the photons absorbed in the creation with the energy conservation and could also be modulated by the spin of the created pair. These multiphoton rings become narrower when both of the pair particles' spin are aligned with the direction of the field rotation, and become broader if both spin are antiparallel to that direction. This spin-modulation can be simply understood with the angular momentum conservation, as less orbital angular momentum from the absorbed photons would be transferred to the created particles if their spins are aligned with the field rotation. The orbital angular momentum of the created particles is manifested as the vortex structure in the phase of the momentum distribution, and valued as the topological charge of this phase vortex. We also study the spin entanglement between the created particles, and reveal that the entanglement becomes stronger with the increase of the particles' transverse momentum, and gets sharp peak in the transition between different multiphoton rings, where the topological charge of the phase vortex is changed.
We investigate the spin resolved vortex properties of electron positron pairs created from vacuum in time delayed, two color electromagnetic fields. By treating the temporal delay G as a continuous tuning parameter, we reveal a dynamic transition from interference-dominated domain patterns at G=0 to the nucleation of quantized vortex lattices at G=0.5. These topological structures exhibit a staggered arrangement analogous to von Karman vortex streets in fluid dynamics. We demonstrate that the momentum-space morphology is strictly governed by spin orbit selection rules, i.e., parallel spin configurations enforce a dipole-like connectivity, while anti-parallel configurations resolve into distinct quadrupole structures. This difference originates from the conservation of total angular momentum Jz, where the spin projection determines the required orbital angular momentum Lz of the created pairs. At large delays (G greater than 1), macroscopic vortex coherence dissolves into a chaotic phase landscope due to multi-channel interference, yet the spin-dependent nodal geometries remain robust. Our findings suggest that these topological signatures provide a high-fidelity diagnostic for the quantum dynamics of vacuum excitations in strong field QED.
The fundamental mode of rotation in quantum fluids is given by a vortex whose quantized value yields the orbital angular momentum (OAM) per particle. If the vortex is displaced (off-centered) from the reference point for rotation, the angular momentum is reduced and becomes fractional. Such displaced vortices can further exhibit a peculiar dynamics in the presence of confining potentials or couplings to other fields. We study analytically a number of 2D systems where displaced vortices exhibit a noteworthy dynamics, including time-varying self-sustained oscillation of the OAM, complex reshaping of their morphology with possible creation of vortex–antivortex pairs, and peculiar trajectories for the vortex core with sequences of strong accelerations and decelerations that can even send the core to infinity and bring it back. Interestingly, these do not have to occur conjointly, with complex time dynamics of the vortex core and/or their wavepacket morphology possibly taking place without affecting the total OAM. Our results generalize to simple and fundamental systems a phenomenology recently reported with Rabi-coupled bosonic fields, showing their wider relevance and opening prospects for new types of control and structuring of the angular momentum of light and/or quantum fluids.
When vortices are displaced in Bose-Einstein condensates (BECs), the Magnus force gives the system a momentum transverse in the direction to the displacement. We show that BECs in long channels with vortices exhibit a quantization of the current response with respect to the spatial vortex distribution. The quantization originates from the well-known topological property of the phase around a vortex; it is an integer multiple of $2\ensuremath{\pi}$. In a way similar to that of the integer quantum Hall effect, the current along the channel is related to this topological phase and can be extracted from two experimentally measurable quantities: the total momentum of the BEC and the spatial distribution. The quantization is in units of m/2hm/2hm/2h, where mmm is the mass of the atoms and hhh is Planck's constant. We derive an exact vortex momentum-displacement relation for BECs in long channels under general circumstances. Our results present the possibility that the configuration described here can be used as a novel way of measuring the mass of the atoms in the BEC using a topological invariant of the system. If an accurate determination of the plateaus are experimentally possible, this gives the possibility of a topological quantum mass standard and precise determination of the fine structure constant.
The global spin polarization of hadrons in heavy ion collisions has been measured in the solenoidal tracker at relativistic heavy ion collider experiments, which opens up a new window in the study of the hottest, least viscous, and most vortical fluid that has ever been produced in the laboratory. We present a different approach to spin polarization from conventional ones: a topological realization of spin polarization through quantum vortex formation in collisions of Bose–Einstein condensates. This approach is based on the observation that the vortex is a topological excitation in a superfluid in the presence of local orbital angular momentum and is an analog of spin degrees of freedom. The formation processes of vortices and vortex–antivortex pairs are investigated by solving the Gross–Pitaevskii equation with a large-scale parallel algorithm on a graphics processing unit to very high precision. In a rotating environment, the primary vortex with winding number one is stable against perturbation, which has minimal energy and fixed orbital angular momentum (OAM), but the vortices with larger winding numbers are unstable and will decay into primary vortices through a redistribution of the energy and vorticity. The injection of OAM can also be realized in non-central collisions of self-interacting condensates, part of the OAM of the initial state will induce the formation of vortices through concentration of energy and vorticity density around topological defects. Different from a hydrodynamical description, the interference of the wave function plays an important role in the transport of energy and vorticity, reflecting the quantum nature of the vortex formation process. The study of the vortex formation may shed light on the nature of particle spin and spin–orbit couplings in strong interaction matter produced in heavy-ion collisions.