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arXiv:2606.28766 · Physical Review A

Linear and nonlinear optical torque in multi-level atomic systems driven by counter-rotating orbital angular momentum fields

Dharma P. Permana, Mažena Mackoit Sinkevičienė, Viačeslav Kudriašov, Julius Ruseckas, Gediminas Juzeliünas, Hamid R. Hamedi

quant-phSubmitted Jun 27, 2026• Announced Jun 30, 2026• 0 citations
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Abstract

We investigate the generation of optical torque in coherently prepared multi-level atomic media driven by a vector vortex beam composed of two counter-rotating components carrying opposite orbital angular momenta, $+l\hbar$ and $-l\hbar$. We consider a three-level $Λ$ configuration and a four-level tripod configuration. Using a perturbative steady-state solution of the optical Bloch equations, we obtain analytical expressions for both linear and nonlinear contributions to the optical torque. The results show that the torque is strongly controlled by atomic coherence, including the initial population imbalance and the relative phase between the vortex components. Nonvanishing torque can arise even when the two components have equal amplitudes, due to coherence-induced asymmetry in the atomic response. In the tripod configuration, the presence of a strong control field leads to electromagnetically induced transparency, which suppresses the torque near resonance and shifts the dominant response to finite detunings. These results establish a route for controlling light-induced rotational dynamics in atomic media using vector vortex fields, with potential applications in coherent optical manipulation and angular-momentum-based control in quantum systems.

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We investigate the generation of optical torque in coherently prepared multi-level atomic media driven by a vector vortex beam composed of two counter-rotating components carrying opposite orbital angular momenta, +lℏ+l\hbar+lℏ and −lℏ-l\hbar−lℏ. We consider a three-level ΛΛΛ configuration and a four-level tripod configuration. Using a perturbative steady-state solution of the optical Bloch equations, we obtain analytical expressions for both linear and nonlinear contributions to the optical torque. The results show that the torque is strongly controlled by atomic coherence, including the initial population imbalance and the relative phase between the vortex components. Nonvanishing torque can arise even when the two components have equal amplitudes, due to coherence-induced asymmetry in the atomic response. In the tripod configuration, the presence of a strong control field leads to electromagnetically induced transparency, which suppresses the torque near resonance and shifts the dominant response to finite detunings. These results establish a route for controlling light-induced rotational dynamics in atomic media using vector vortex fields, with potential applications in coherent optical manipulation and angular-momentum-based control in quantum systems.
We investigate a phase-controllable mechanism for generating optical torque in a five-level double-tripod (DT) atom-light coupling scheme interacting with four strong coherent control fields as well as two weak optical vortex probe beams carrying orbital angular momentum (OAM). The spatial phase gradients of the OAM-carrying probes induce a quantized torque that is transferred to the atoms, rotating them and generating a directed atomic flow within an annular geometry. Analytical solutions of the optical Bloch equations under steady-state conditions show that the induced torque and resulting rotational motion exhibit high sensitivity to phase variations. We show that the DT system coherently reconfigures into either coupled Λ or double-Λ schemes depending on the relative phases, with each configuration exhibiting distinct quantized torque characteristics. This enables precise phase control of the atomic current flow, with potential applications in quantum control, precision measurement, and quantum information processing.
This paper investigates the manipulation of induced torque on a four-level tripod atom system through the interaction with two vortex probe beams featuring spatial inhomogeneity, along with a non-vortex control beam. The study explores both the linear and nonlinear regimes of torque induction. In the linear regime, where the intensity of the vortex beams is weaker than that of the control field, effective control over the induced torque is demonstrated by adjusting parameters such as magnetic field strength, control field intensity, detuning, and dephasing terms between relevant atomic levels. The analysis highlights the significant contribution of the Zeeman shift-induced magnetic field, which enhances the torque and exhibits a distinct sharp peak. Furthermore, higher-order contributions to the induced torque are discussed as the intensity of the probe fields approaches that of the control field, resulting in further enhancement of the induced torque. These findings offer opportunities for precise control over the rotational motion of atoms within the system, with potential applications in precision measurement, quantum information processing, and quantum control.
We investigate the propagation of optical vector vortices of slow light in a coherently prepared four-level tripod atomic system. The vector vortex consists of superposed pulse pairs with opposite circular polarizations and orbital angular momentum (OAM) charges ±l\pm l±l, weakly interacting with an atomic medium initially prepared in a coherent superposition of two ground states. A third unoccupied state is coupled to a stronger control laser without OAM, creating a phase-dependent configuration. In the linear regime, the vortex OAM is mapped onto the medium, producing symmetrical azimuthally structured absorption patterns, with losses significantly reduced by the control field. For small detunings, complementary spatially dependent amplification and absorption occur for the two circular polarization components. This OAM-structured coherence induces a dynamical anisotropy, affecting both the intensity and polarization of the slow-light vortex. Polarization states evolve periodically between left-circular, linear, and right-circular polarizations during propagation. Once the beam reaches a stationary regime, the ring-shaped intensity transforms into a petal-like structure, and the final polarization states stabilize according to the initial superposition. The rate of polarization transitions is tunable via the control field strength, demonstrating flexible control over slow-light vector vortex dynamics.
We investigate the propagation of an optical vector vortex weakly interacting with a coherently prepared atomic medium (phaseonium) in a three-level ΛΛΛ configuration. The vector beam consists of vortex pulse pairs with right- and left-circular polarizations, corresponding to opposite spin angular momentum (SAM), and carrying opposite orbital angular momentum (OAM) charges ±l\pm l±l. We show that during the propagation of the vortex pairs, analytically obtained in the linear regime, the medium inherits the topology of the vortex pair, mapping the OAM onto a spatially structured atomic coherence. This mapping produces 2∣l∣−2|l|-2∣l∣−fold azimuthal transparency structures that reshape the beam intensity from a ring into a petal-like pattern. The OAM-structured atomic coherence induces a corresponding optical anisotropy within the medium, which feeds back into the propagating vector beam, resulting in optical spin-orbit coupling manifested as SAM exchange, rotation, and evolution of polarization textures. Depending on the initial ground-state population of the phaseonium, the polarization state evolves between left-circular, linear, and right-circular polarizations.
This paper explores the propagation of optical vortices of slow light inside a four-level tripod atomic light-matter coupling system. Initially, the system is prepared in a coherent superposition of two out of the three lower levels by, for example, coherent population trapping, while the third lower state remains unoccupied. The unoccupied state is coupled to a strong control laser field with a constant Rabi frequency, lacking orbital angular momentum (OAM). Simultaneously, one of the remaining lower states interacts with a weak vortex beam. The third lower state has no initial coupling to any field. This arrangement effectively closes the level transitions, resulting in a phase-dependent configuration. By solving the Maxwell-Schr\"odinger equations, we provide analytical evidence that the application of a strong control field can generate an additional optical vortex of slow light. This vortex possesses the same OAM as the incident vortex beam. Furthermore, we explore the matching of optical vortices at different propagation distances, contingent upon the intensity of the control field. Additionally, our analysis extends to a more complex five-level tripod and $\mathrm{\ensuremath{\Lambda}}$ scheme, where we introduce two additional strong control fields to prepare the atoms in a coherent superposition of two lower levels.
We study the manipulation of slow light with an orbital angular momentum propagating in a cloud of cold atoms. Atoms are affected by four co-propagating control laser beams in a double tripod configuration of the atomic energy levels involved, allowing us to minimize the losses at the vortex core of the control beams. In such a situation the atomic medium is transparent for a pair of co-propagating probe fields, leading to the creation of two-component (spinor) slow light. We study the interaction between the probe fields when two control beams carry optical vortices of opposite helicity. As a result, a transfer of the optical vortex takes place from the control to the probe fields without switching off and on the control beams. This feature is missing in a single tripod scheme where the optical vortex can be transferred from the control to the probe field only during either the storage or retrieval of light.