Optical amplification and spatial multiplexing technologies have important applications in quantum communication, quantum networks, and optical information processing. In this paper, based on the non-reciprocal amplification of a pair of co-propagating conjugate four-wave mixing (FWM) signals induced by a one-way pump field in a double-Λ-type hot atomic system, we demonstrate spatially multiplexed multiple FWM processes by introducing a counter-propagating collinear pump field. This configuration enables simultaneous amplification of bidirectional four-channel FWM signals. Furthermore, when the injected signal and pump beams are modulated to Laguerre-Gaussian beams carrying different optical orbital angular momentum (OAM), the OAM of the pump beam is transferred to each amplified field. Through the tilted lens method, we experimentally demonstrate that the OAM of the amplified signal light remains identical to that of the original injected signal light. In contrast, the OAM of the other three newly generated FWM fields is governed by the angular momentum conservation law of their respective FWM processes, which enables the precise manipulation of the OAM for the other generated amplified fields. Theoretical analysis of the dynamical transport equation for the density operator in light-matter interaction processes fully corroborates the experimental results. These findings establish a robust framework for developing OAM-compatible optical non-reciprocal devices based on complex structured light.
Optical amplification and spatial multiplexing technologies have important applications in quantum communication, quantum networks, and optical information processing. In this paper, based on the non-reciprocal amplification of a pair of co-propagating conjugate four-wave mixing (FWM) signals induced by a one-way pump field in a double-Λ-type hot atomic system, we demonstrate spatially multiplexed multiple FWM processes by introducing a counter-propagating collinear pump field. This configuration enables simultaneous amplification of bidirectional four-channel FWM signals. Furthermore, when the injected signal and pump beams are modulated to Laguerre-Gaussian beams carrying different optical orbital angular momentum (OAM), the OAM of the pump beam is transferred to each amplified field. Through the tilted lens method, we experimentally demonstrate that the OAM of the amplified signal light remains identical to that of the original injected signal light. In contrast, the OAM of the other three newly generated FWM fields is governed by the angular momentum conservation law of their respective FWM processes, which enables the precise manipulation of the OAM for the other generated amplified fields. Theoretical analysis of the dynamical transport equation for the density operator in light-matter interaction processes fully corroborates the experimental results. These findings establish a robust framework for developing OAM-compatible optical non-reciprocal devices based on complex structured light.
Magnet-free optical nonreciprocity has significant applications in quantum communication, quantum networks, and optical information processing. In this research, considering a degenerate two-level thermal atomic system with the Doppler effect of thermal atoms, the nonreciprocal amplification (NRA) of dual-path degenerate four-wave mixing (FWM) signals is achieved under the action of a co-propagating pumping field. On this basis, spatially multiplexed multiple FWM processes are formed by introducing another counter-propagating pumping field, thereby achieving the reciprocal amplification (RA) of the dual-channel FWM signals. Furthermore, by using multiple sets of spiral phase plates to load spiral phases on the signal light and the pumping light respectively, higher-order Laguerre-Gaussian vortex beams carrying different optical orbital angular momentum (OAM) are generated and participate in the FWM process, achieving the transfer of the OAM of the pumping light to the amplified FWM fields. Simultaneously, using the Mach-Zehnder interferometer, the conservation characteristics of the OAM of each FWM signal in the NRA-RA conversion are further analyzed. Furthermore, experimental results demonstrate that in the multiple FWM process induced by a pair of counter-propagating pump fields, the OAM of the amplified FWM signal in each channel varies with that of the pump field. However, the overall process maintains the OAM conservation. This study provides a feasible solution for expanding the channel capacity using OAM based on NRA-RA system, showing that the OAM has potential application prospects in achieving high-capacity optical communication and multi-channel signal processing.
Optical nonreciprocity plays an important role in optical communication and quantum networks. In this research, we propose and demonstrate a conversion scheme of magnetic-free dual-channel optical reciprocal amplification (RA) and nonreciprocal amplification (NRA) based on the multiple degenerate four-wave mixing (FWM) process in hot atoms. In our experiment, the dual-channel NRA works with the action of a single pump field based on the establishment of FWM in the same direction and breaking in the opposite direction. Based on stable ground-state Zeeman coherence, by introducing a counter-propagating pump field again, NRA can be changed to RA in the opposite direction of the two original amplified conjugate signals. Moreover, the frequencies of RA signals are very dependent on those of co-propagating pump fields. The experimental realization of NRA-RA conversion may have applications for multichannel angular momentum spatial multiplexing and quantum gate manipulation.
In this work we present a series of results on four-wave mixing (FWM) processes induced by structured light in atomic media. We start with a theoretical study focusing on a cascade FWM process in rubidium vapor, generating a blue light field at 420 nm. In this setting, we show that in the extended-medium regime the Hermite-Gaussian basis presents a unique property of optical structure transfer. We then exploit this result to show that, by carefully tailoring the structure of the pump beams, one can obtain desired spatial modes with cylindrical and elliptical symmetries with high fidelity at the blue light output. Following that, we consider an experimental configuration where two degenerate FWM signals are generated in different directions of space by the same pump fields. In this setup, we present results in heated rubidium vapor evidencing the simultaneous conservation of orbital angular momentum (OAM) in the two FWM processes. We show that the two-channel setting allows to encode the OAM content of the input beams onto the OAM carried by the two FWM signals. Next, we explore the transverse mode dynamics in the context of optical modes contained in the so-called orbital angular momentum Poincaré sphere (PS). Defined in analogy with a general polarization state, this family of modes is parametrized in terms of polar and azimuthal angles. We show that the two FWM signals can also be described as belonging to Poincaré spheres, and that the angles on the output PS are related to those on the input PS by well-defined symmetries. The predicted FWM intensity profiles, as well as the consequences of the symmetry properties, are in good agreement with our experimental results. We also explore interesting scenarios, such as combinations of different PS modes and the fulfillment of one of the symmetry relations in each sphere independently, and restrictions that arise in the extended-medium regime. In the last part, we study the correlations between the light fields participating in the two-channel FWM configuration. Following our recent work on cold atoms, we investigate the correlations originating from the conversion of phase-noise to amplitude-noise as a result of the light-atom interaction, and discuss our attempts to discriminate transverse spatial dependencies on these correlations. Finally, we outline the quantum theory of FWM, exploring the multi-spatial-mode nature of the generated light state and the associated spatial correlations.
Abstract We study various coherent optical properties, e.g., two-photon electromagnetically induced transparency (EIT) and three-photon electromagnetically induced transparency and absorption (TPEIT/TPEIA), in a four-level ladder (Ξ)-type system of 87Rb atoms, where the probe and control fields are Gaussian-shaped laser beams and the pump field is structured laser beam. Additionally, the generated four-wave mixing (FWM) signal has been studied. Interestingly, it is found that the generated FWM signal is spatially structured along with the azimuthal phase, which carries the orbital angular momentum (OAM) of light. It is also observed that the coherent optical responses (EIT, TPEIT/TPEIA, and FWM signals) can be manipulated by utilizing the OAM number of the pump beam as a control knob.
Nondegenerate four-wave mixing (FWM) process based on a double-Λ scheme in hot alkali metal vapor is a versatile tool in quantum state engineering, quantum imaging, and quantum precision measurements. In this Letter, we investigate the generation of quantum correlated twin beams which carry nonzero orbital angular momentums (OAMs) based on the FWM process in hot cesium vapor. The amplified probe beam and the newly generated conjugate beam in the FWM process have the same and opposite topological charge as the seed beam, respectively. We also explore the FWM process operated in a nonamplifying regime where quantum correlated twin beams carrying OAMs can still be generated. In this regime, the FWM process plays the role of quantum beam splitter for the OAM of light; that is, a device that can split a coherent light beam carrying OAM into quantum-correlated twin beams carrying OAMs. More generally, our setup can be used as a quantum beam splitter of images.
Detuning Tunable OAM Generation via Double-Λ Four-Wave Mixing in Hot Rubidium Vapor
We demonstrate detuning-tunable generation of orbital-angular-momentum (OAM) light using a double Lambda four-wave-mixing (FWM) process in Doppler broadened rubidium vapor. Two near-resonant pumps on the D1 line drive non degenerate FWM that produces bright probe conjugate beams whose transverse modes evolve with pump detuning. A paraxial density-matrix model coupled to split-step propagation predicts detuning-dependent spatial gain shaping that sets the OAM content; experiments with a mode cleaned pump laser and a 12-mm AR-coated vapor cell validate these predictions. We quantify mode formation by imaging, spectroscopy, and power measurements, and verify OAM conservation between the generated beams. The results establish resonant atomic vapor as a compact, tunable platform for structured-light generation with applications to high-dimensional quantum communications and imaging.