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arXiv:2104.10591 · Physical Review A

Multipolar Fermi-surface deformation in a Rydberg-dressed Fermi gas with long-range anisotropic interactions

Yijia Zhou, Rejish Nath, Haibin Wu, Igor Lesanovsky, Weibin Li

Published Dec 20, 2021• 4 citations
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Abstract

We study theoretically the deformation of the Fermi surface (FS) of a three-dimensional gas of Rydberg-dressed $^{6}\mathrm{Li}$ atoms. The laser dressing to high-lying Rydberg $D$ states results in angle-dependent soft-core-shaped interactions whose anisotropy is described by multiple spherical harmonics. We show that this can drastically modify the shape of the FS and that its deformation depends on the interplay between the Fermi momentum ${k}_{F}$ and the reciprocal momentum $\overline{k}$ corresponding to the characteristic soft-core radius of the dressing-induced potential. When ${k}_{F}<\overline{k}$, the dressed interaction stretches a spherical FS into an ellipsoid. When ${k}_{F}\ensuremath{\gtrsim}\overline{k}$, complex deformations are encountered which exhibit multipolar characteristics. We analyze the formation of Cooper pairs around the deformed FS and show that they occupy large orbital angular momentum states ($p, f$, and $h$ wave) coherently. Our study demonstrates that Rydberg dressing to high angular momentum states may pave a route toward the investigation of unconventional Fermi gases and multiwave superconductivity.

DOI
10.1103/physreva.104.l061302

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We study theoretically the deformation of the Fermi surface (FS) of a three-dimensional gas of Rydberg-dressed 6Li^{6}\mathrm{Li}6Li atoms. The laser dressing to high-lying Rydberg DDD states results in angle-dependent soft-core-shaped interactions whose anisotropy is described by multiple spherical harmonics. We show that this can drastically modify the shape of the FS and that its deformation depends on the interplay between the Fermi momentum kF{k}_{F}kF​ and the reciprocal momentum k‾\overline{k}k corresponding to the characteristic soft-core radius of the dressing-induced potential. When kF<k‾{k}_{F}<\overline{k}kF​<k, the dressed interaction stretches a spherical FS into an ellipsoid. When kF\ensuremath≳k‾{k}_{F}\ensuremath{\gtrsim}\overline{k}kF​\ensuremath≳k, complex deformations are encountered which exhibit multipolar characteristics. We analyze the formation of Cooper pairs around the deformed FS and show that they occupy large orbital angular momentum states (p,fp, fp,f, and hhh wave) coherently. Our study demonstrates that Rydberg dressing to high angular momentum states may pave a route toward the investigation of unconventional Fermi gases and multiwave superconductivity.
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Many-body dipolar effects in Fermi gases are quite subtle as they energetically compete with the large kinetic energy at and below the Fermi surface (FS). Recently it was experimentally observed that its FS is deformed from a sphere to an ellipsoid due to the presence of the anisotropic and long-range dipole-dipole interaction. Moreover, it was suggested that, when the dipoles are rotated by means of an external field, the Fermi surface follows their rotation, thereby keeping the major axis of the momentum-space ellipsoid parallel to the dipoles. Here we generalise a previous Hartree-Fock mean-field theory to systems confined in an elongated triaxial trap with an arbitrary orientation of the dipoles relative to the trap. With this we study for the first time the effects of the dipoles' arbitrary orientation on the ground-state properties of the system. Furthermore, taking into account the geometry of the system, we show how the ellipsoidal FS deformation can be reconstructed, assuming ballistic expansion, from the experimentally measurable real-space aspect ratio after a free expansion. We compare our theoretical results with new experimental data measured with erbium Fermi gas for various trap parameters and dipole orientations. The observed remarkable agreement demonstrates the ability of our model to capture the full angular dependence of the FS deformation. Moreover, for systems with even higher dipole moment, our theory predicts an additional unexpected effect: the FS does not simply follow rigidly the orientation of the dipoles but softens showing a change in the aspect ratio depending on the dipoles' orientation relative to the trap geometry, as well as on the trap anisotropy itself. Our theory provides the basis for understanding and interpreting phenomena in which the investigated physics depends on the underlying structure of the FS, such as fermionic pairing and superfluidity.
Abstract We theoretically analyze the interactions and decay rates for atoms dressed by multiple laser fields to strongly interacting Rydberg states using a quantum master equation approach. In this framework a comparison of two-level and three-level Rydberg-dressing schemes is presented. We identify a resonant enhancement of the three-level dressed interaction strength which originates from cooperative multiphoton couplings as well as small distance dependent decay rates. In this regime the soft-core shape of the potential is independent of the sign of the bare Rydberg–Rydberg interaction, while its sign can be repulsive or attractive depending on the intermediate state detuning. As a consequence, near-resonant Rydberg dressing in three-level atomic systems may enable the realization of laser driven quantum fluids with long-range and anisotropic interactions and with controllable dissipation.
Many-body dipolar effects in Fermi gases are quite subtle as they energetically compete with the large kinetic energy at and below the Fermi surface (FS).Recently it was experimentally observed in a sample of erbium atoms that its FS is deformed from a sphere to an ellipsoid due to the presence of the anisotropic and long-range dipole-dipole interaction Aikawa et al (2014 Science 345 1484).Moreover, it was suggested that, when the dipoles are rotated by means of an external field, the FS follows their rotation, thereby keeping the major axis of the momentum-space ellipsoid parallel to the dipoles.Here we generalise a previous Hartree-Fock mean-field theory to systems confined in an elongated triaxial trap with an arbitrary orientation of the dipoles relative to the trap.With this we study for the first time the effects of the dipoles' arbitrary orientation on the ground-state properties of the system.Furthermore, taking into account the geometry of the system, we show how the ellipsoidal FS deformation can be reconstructed, assuming ballistic expansion, from the experimentally measurable real-space aspect ratio after a free expansion.We compare our theoretical results with new experimental data measured with erbium Fermi gas for various trap parameters and dipole orientations.The observed remarkable agreement demonstrates the ability of our model to capture the full angular dependence of the FS deformation.Moreover, for systems with even higher dipole moment, our theory predicts an additional unexpected effect: the FS does not simply follow rigidly the orientation of the dipoles, but softens showing a change in the aspect ratio depending on the dipoles' orientation relative to the trap geometry, as well as on the trap anisotropy itself.Our theory provides the basis for understanding and interpreting phenomena in which the investigated physics depends on the underlying structure of the FS, such as fermionic pairing and superfluidity.
We present a theoretical investigation into the expansion dynamics of Rydberg-dressed ultracold Fermi gases. The effective interaction potential induced by Rydberg dressing significantly modifies the intrinsic properties and dynamical behavior of the quantum gas. The strength and range of these interactions can be precisely tuned by varying the intensity and detuning of the applied laser field. By employing mean-field theory and utilizing the density distribution of the atomic cloud to describe the quantum system dynamics, we theoretically describe the time-dependent evolution of the atomic cloud during the free expansion process, encompassing both non-interacting and unitary Fermi gases. Notably, the specific quantum states of the ground-state atoms play a pivotal role in shaping the effective interaction potential within the Rydberg-dressed quantum system. We elucidate how the interaction potential influences the rate and mode of the atom cloud’s expansion by hydrodynamic expansion arising from Rydberg-dressed atoms in distinct spin hyperfine states. This investigation may deepen our understanding of the behavior and interactions in quantum many-body systems and offer broad potential for future applications like the exploration of novel quantum phase transitions and emergent phenomena.
We study the superfluid pairing in a two-species gas of heteronuclear fermionic molecules with equal density. The interplay of the isotropic sss-wave interaction and anisotropic long-range dipolar interaction reveals rich physics. We find that the single-particle momentum distribution has a characteristic ellipsoidal shape that can be reasonably represented by a deformation parameter $\ensuremath{\alpha}$ defined similarly to the normal phase. Interesting momentum-dependent features of the order parameter are identified. We calculate the critical temperatures of both the singlet and triplet superfluids, suggesting a possible pairing symmetry transition by tuning the sss-wave or dipolar interaction strength.