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Topological phase transition for a quantum rotor Bose-Einstein condensate

Piotr Szulim, Marek Trippenbach, Y. B. Band, Mariusz Gajda, Mirosław Brewczyk

Published May 26, 2021• 0 citations
OpenAlex

Abstract

We investigate the properties of a Bose-Einstein condensate (BEC) of $F=1$ $^{87}$Rb atoms in a 2D spin-dependent optical lattice potential generated by intersecting laser beams with a superposition of polarizations. For $^{87}$Rb, where the total electronic angular momentum is $J = 1/2$, the effective interaction of an atom with the electromagnetic field contains a scalar potential $V$ and a vector potential (often called fictitious magnetic field). The Rb atoms behave as a quantum rotor (QR) with angular momentum given by the sum of the atomic motion rotational angular momentum around the lattice minima and the atomic hyperfine spin $F$. Properties of the QR are strongly affected when an external magnetic field perpendicular to the plane of QR motion is applied. A topological phase transition occurs as the ratio of the external transverse magnetic field to fictitious magnetic field exceeds critical value. At such a quantum phase transition the symmetry of the ground state changes and is expressed in the change of the spin texture.

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We investigate the properties of a Bose-Einstein condensate (BEC) of F=1F=1F=1 87^{87}87Rb atoms in a 2D spin-dependent optical lattice potential generated by intersecting laser beams with a superposition of polarizations. For 87^{87}87Rb, where the total electronic angular momentum is J=1/2J = 1/2J=1/2, the effective interaction of an atom with the electromagnetic field contains a scalar potential VVV and a vector potential (often called fictitious magnetic field). The Rb atoms behave as a quantum rotor (QR) with angular momentum given by the sum of the atomic motion rotational angular momentum around the lattice minima and the atomic hyperfine spin FFF. Properties of the QR are strongly affected when an external magnetic field perpendicular to the plane of QR motion is applied. A topological phase transition occurs as the ratio of the external transverse magnetic field to fictitious magnetic field exceeds critical value. At such a quantum phase transition the symmetry of the ground state changes and is expressed in the change of the spin texture.
Abstract We investigate a Bose–Einstein condensate of F = 187Rb atoms in a 2D spin-dependent optical lattice generated by intersecting laser beams with a superposition of polarizations. For 87Rb the effective interaction of an atom with the electromagnetic field contains scalar and vector (called a fictitious magnetic field, B fic) potentials. The Rb atoms behave as a quantum rotor (QR) with angular momentum given by the sum of the atomic rotational motion angular momentum and the hyperfine spin. The ground state of the QR is affected upon applying an external magnetic field, B ext, perpendicular to the plane of QR motion and a sudden change of its topology occurs as the ratio B ext/B fic exceeds a critical value. It is shown that the change of topology of the QR ground state is a result of combined action of Zeeman and Einstein–de Haas effects. The first transfers atoms to the largest hyperfine component to polarize the sample along the field as the external magnetic field is increased. The second sweeps spin to rotational angular momentum, modifying the kinetic energy of the atoms.
We investigate the properties of a Bose-Einstein condensate (BEC) of F=1 rubidium 87 atoms in a 2D spin-dependent optical lattice potential generated by intersecting laser beams with a superposition of polarizations. The Rb atoms behave as a quantum rotor (QR) with rotor angular momentum given by the sum of the atomic motion rotational angular momentum around the lattice minima and the atomic hyperfine spin FFF. Properties of the QR are strongly affected when an external magnetic field perpendicular to the plane of QR motion is applied. We observe a topological phase transition as the strength of the external transverse magnetic field is varied. We determine the spin texture of the QR BEC. At such a quantum phase transition the symmetry of the ground state changes. This transition is a result of the interplay between the Zeeman and rotational-kinetic energies in different eigenstates of the QR as the external magnetic field is increased.
We investigate the combined effects of spin-orbit coupling and rotation on the topological vortical phase transition in F=2F=2F=2 Bose-Einstein condensates. We find that the spin-orbit coupling can precisely manipulate the canonical atom current which is generated in the opposite direction of the gauge atom current and causes both a continuous and a discontinuous canonical angular momentum. We apply the canonical angular momentum and magnetization to reveal the emergence of novel topological excitations, such as the Anderson-Toulouse vortex as well as the vortex--dipole lattice. Especially, strong spin-orbit coupling can induce two perpendicular vortex chains. We also find that both the first-order and the second-order phase transition can be characterized by the canonical angular momentum and the magnetization. Differently from the spin singlet-pairing interaction, the spin-exchange interaction can adjust the canonical angular momentum and control the phase transition well. The topological vortical phase transition in an F=2F=2F=2 cold-atom system is compatible with the current experiment and can be detected by the spin polarization procedure.
Following a novel experimental arrangement which can rotate a two-dimensional optical lattice at frequencies up to several kilohertz we discuss the ground state of the two-dimensional Bose-Hubbard Hamiltonian, relevant for rotating gaseous Bose-Einstein condensates, by employing U(1) quantum rotor approach and the topologically constrained path integral.Ultracold atoms in such a rotating lattice can be used for the direct quantum simulation of strongly correlated systems under large effective magnetic fields.We derive an effective quantum action for the Bose-Hubbard model, which enables a non-perturbative treatment of the zero-temperature phase transition in the rotating frame.We calculate the ground-state phase diagram, analytically deriving maximum repulsive energy for several rational values of the frustration rotation parameter f = 0, 1/2, 1/3, 1/4, and 1/6 for the square and triangular lattice.Performed calculations revealed strong non-monotonical dependence of the critical ratio of the kinetic energy to the repulsive on-site energy, that separates the global coherent from the insulating state, on topology of the lattice.
In a cold atom gas subject to a two-dimensional spin-dependent optical lattice potential with hexagonal symmetry, trapped atoms execute circular motion around the potential minima. Such atoms are elementary quantum rotors. The theory of such quantum rotors is developed. Wave functions, energies, and degeneracies are determined for both bosonic and fermionic atoms, and magnetic dipole transitions between quantum rotor states are elucidated. Quantum rotors in optical lattices with precisely one atom per unit cell can be used as extremely high sensitivity rotation sensors, accelerometers, and magnetometers.
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.