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Physical Review A

Creating atomic Stokes vortices with spin-1 atomic wave functions

Maitreyi Jayaseelan, Joseph D. Murphree, Justin T. Schultz, N. P. Bigelow

Published Sep 14, 2023• 0 citations
Publisher

Abstract

The formal correspondences between pseudo-spin-1/2 systems in optics and in atomic physics have provided fertile ground for exploring polarization in atom optics. Previous experimental results demonstrated atomic polarimetry techniques for two-level wave functions and explored wave-field singularities in the multicomponent wave function of a spinor Bose-Einstein condensate using visualization techniques developed in optics [J. T. Schultz, A. Hansen, and N. P. Bigelow, Opt. Lett. 39, 4271 (2014); A. Hansen, J. T. Schultz, and N. P. Bigelow, Optica 3, 355 (2016)]. Here we further this discussion, reexamining the atomic Stokes parameters and Stokes polarimetry in the context of spin-1 systems where the tensor moments of the higher-spin system enrich the physics considerably. We show that our atomic polarimetry methods provide tools to engineer the multipole tensor moments of the higher-spin atomic wave function, and to realize nontrivial couplings between these multipole moments and an atomic center-of-mass orbital angular momentum. The different forms of coupling between internal tensor moments and external angular momenta can be used to realize a variety of topological structures in the atomic wave field. We identify these $\ensuremath{\pi}$- and $2\ensuremath{\pi}$-symmetric features in the streamlines of the atomic Stokes fields constructed in analogy with singular optics.

DOI
10.1103/physreva.108.033311

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Spinor Bose–Einstein condensates (BECs) and singular optical systems have both recently served as sandboxes to create and study analogs of phenomena from other fields of physics that are otherwise difficult to create and control experimentally. Interfacing singular optics and spinor BECs allows us to take advantage of and build on the foundations of singular optics to create and describe complex spin textures in BECs that serve as analogs of other systems. Here, the complete BEC wavefunctions are precisely engineered via a two-photon Raman interaction to contain π-symmetric (lemon, star) or 2π-symmetric (saddle, spiral) C-point singularities. The optical Raman beams are singular optical beams that contain these singularities and transfer them to the condensate, thereby creating vector-vortex spin textures—the spinor counterparts to scalar vortices—in pseudo-spin-1/2 BECs. With a version of atom-optic polarimetry, we can measure the Stokes parameters of the atomic cloud and characterize the singularities by the patterns present in their ellipse fields or by the C-point index. In the low density limit, these spin textures are analogs of optical vector vortices and should have dynamics driven by a matter-wave Gouy phase. With precise tuning of Raman beam parameters, we can create full Bloch BECs that contain every possible superposition between two states in the atomic cloud. Full Bloch BECs are similar to topologically stable magnetic skyrmions such as those created in thin metal films and nanowires, which may prove useful for atom-spintronics and topological quantum processes.
Abstract Atom optics demonstrates optical phenomena with coherent matter waves, providing a foundational connection between light and matter. Significant advances in optics have followed the realization of structured light fields hosting complex singularities and topologically non-trivial characteristics. However, analogous studies are still in their infancy in the field of atom optics. Here, we investigate and experimentally create knotted quantum wavefunctions in spinor Bose–Einstein condensates which display non-trivial topologies. In our work we construct coordinated orbital and spin rotations of the atomic wavefunction, engineering a variety of discrete symmetries in the combined spin and orbital degrees of freedom. The structured wavefunctions that we create map to the surface of a torus to form torus knots, Möbius strips, and a twice-linked Solomon’s knot. In this paper we demonstrate close connections between the symmetries and underlying topologies of multicomponent atomic systems and of vector optical fields—a realization of topological atom-optics.
The physics of optical vortices, also known as twisted light, is now a well-established and a growing branch of optical physics with a number of important applications and significant interdisciplinary connections.Optical vortex fields of widely varying forms and degrees of complexity can be realised in the laboratory by a host of different means.The interference between such beams with designated orbital angular momenta and optical spins (the latter is associated with wave polarisations) can be structured to conform to various geometrical arrangements.The focus of this review is on how such tailored forms of light can exert a controllable influence on atoms with which they interact.The main physical effects involve atoms in motion due to application of optical forces.The now mature area of atom optics has had notable successes both of fundamental nature and in applications such as atom lasers, atom guides and Bose-Einstein condensates.The concepts in atom optics encompass not only atomic beams interacting with light, but atomic motion in general as influenced by optical and other fields.Our primary concern in this review is on atoms in structured light where, in particular, the twisted nature of the light is made highly complex with additional features due to wave polarisation.These features bring to the fore a variety of physical phenomena not realisable in the context of atomic motion in more conventional forms of laser light.Atoms near resonance with such structured light fields become subject to electromagnetic fields with complex polarisation and phase distributions, as well as intricately structured intensity gradients and radiative forces.From the combined effect of optical spin and orbital angular momenta, atoms may also experience forces and torques involving an interplay between the internal and centre of mass degrees of freedom.Such interactions lead to new forms of processes including scattering, trapping and rotation and, as a result, they exhibit characteristic new features at the micro-scale and below.A number of distinctive properties involving angular momentum exchange between the light and the atoms are highlighted, and prospective applications are discussed.Comparison is made between the theoretical predictions in this area and the corresponding experiments that have been reported to date.
An effective spin-orbit coupling can be generated in a cold atom system by engineering atom-light interactions. In this Letter we study spin-1/2 and spin-1 Bose-Einstein condensates with Rashba spin-orbit coupling, and find that the condensate wave function will develop nontrivial structures. From numerical simulation we have identified two different phases. In one phase the ground state is a single plane wave, and often we find the system splits into domains and an array of vortices plays the role of a domain wall. In this phase, time-reversal symmetry is broken. In the other phase the condensate wave function is a standing wave, and it forms a spin stripe. The transition between them is driven by interactions between bosons. We also provide an analytical understanding of these results and determine the transition point between the two phases.
The (pseudo)spin degrees of freedom greatly enriches the physics of cold atoms. This is particularly so for systems with high spins (i.e., spin quantum number larger than 1/2). For example, one can construct not only the rank-1 spin vector, but also the rank-2 spin tensor in high spin systems. Here we propose a simple scheme to couple the spin tensor and the center-of-mass orbital angular momentum in a spin-1 cold atom system and show that this leads to a new quantum phase of the matter: the spin-nematic vortex state that features vorticity in an SU(2) spin-nematic tensor subspace. Under proper conditions, such states are characterized by quantized topological numbers. Our work opens up new avenues of research in topological quantum matter with high spins.
Abstract A coherent two-photon optical Raman interaction in a pseudo-spin-1/2 Bose–Einstein condensate (BEC) serves as a q -plate for atoms, converting spin to orbital angular momentum. This Raman q -plate has a singular pattern in its polarization distribution in analogy to the singular birefringent q -plates used in singular optics. The vortex winding direction and magnitude as well as the final spin state of the BEC depend on the initial spin state and the topology of the optical Raman q -plate beams. Drawing on the mathematical and geometric foundations of singular optics, we derive the equivalent Jones matrix for this Raman q -plate and use it to create and characterize atomic spin singularities in the BEC that are analogous to optical C -point singularities in polarization. By tuning the optical Raman parameters, we can generate a coreless vortex spin texture which contains every possible superposition in a two-state system. We identify this spin texture as a full-Bloch BEC since every point on the Bloch sphere is represented at some point in the cross section of the atomic cloud. This spin–orbit interaction and the spin textures it generates may allow for the observation of interesting geometric phases in matter waves and lead to schemes for topological quantum computation with spinor BECs.