In conventional superfluid hydrodynamics the velocity field v_s is irrotational except at the cores of quantized vortices, implying a single scalar phase field. We propose that in addition to the ordinary superfluid velocity there exists a hidden rotational mode represented by an effective vorticity field Omega_h that is not directly observable through conventional probes. This hidden mode emerges naturally from the multi-component order parameter structure when internal symmetries are spontaneously broken. By constructing a generalized Ginzburg–Landau functional that includes both the conventional phase gradient and an auxiliary vector potential associated with internal gauge fields, we derive coupled equations of motion that reveal the coexistence of a standard mass current and a hidden rotational current. The hidden vorticity Omega_h satisfies a conservation law analogous to Kelvin's theorem but is confined to subspaces of the internal symmetry group, thereby evading direct detection. We analyze the stability conditions for such hidden modes, showing that they are energetically favorable in regimes of rapid rotation or strong spin–orbit coupling, typical of ultracold atomic gases. The existence of Omega_h implies an additional set of collective excitations—hidden Kelvin waves—that modify the low-energy spectrum of the superfluid. We discuss how these excitations influence the response to external perturbations and outline potential signatures in density–density correlation functions and in the dynamical structure factor. Our theoretical framework provides a unified description of hidden rotational degrees of freedom in superfluid systems and opens a pathway for discovering new quantum fluid phases with exotic angular momentum textures.
In conventional superfluid hydrodynamics the velocity field v_s is irrotational except at the cores of quantized vortices, implying a single scalar phase field. We propose that in addition to the ordinary superfluid velocity there exists a hidden rotational mode represented by an effective vorticity field Omega_h that is not directly observable through conventional probes. This hidden mode emerges naturally from the multi-component order parameter structure when internal symmetries are spontaneously broken. By constructing a generalized Ginzburg–Landau functional that includes both the conventional phase gradient and an auxiliary vector potential associated with internal gauge fields, we derive coupled equations of motion that reveal the coexistence of a standard mass current and a hidden rotational current. The hidden vorticity Omega_h satisfies a conservation law analogous to Kelvin's theorem but is confined to subspaces of the internal symmetry group, thereby evading direct detection. We analyze the stability conditions for such hidden modes, showing that they are energetically favorable in regimes of rapid rotation or strong spin–orbit coupling, typical of ultracold atomic gases. The existence of Omega_h implies an additional set of collective excitations—hidden Kelvin waves—that modify the low-energy spectrum of the superfluid. We discuss how these excitations influence the response to external perturbations and outline potential signatures in density–density correlation functions and in the dynamical structure factor. Our theoretical framework provides a unified description of hidden rotational degrees of freedom in superfluid systems and opens a pathway for discovering new quantum fluid phases with exotic angular momentum textures.
Vortices are essential to angular momentum in quantum systems such as ultracold atomic gases. The existence of quantized vorticity in bosonic systems stimulated the development of the Gross-Pitaevskii mean-field approximation. However, the true dynamics of angular momentum in finite, interacting many-body systems like trapped Bose-Einstein condensates is enriched by the emergence of quantum correlations whose description demands more elaborate methods. Herein we theoretically investigate the full many-body dynamics of the acquisition of angular momentum by a gas of ultracold bosons in two dimensions using a standard rotation procedure. We demonstrate the existence of a novel mode of quantized vorticity, which we term the phantom vortex. Contrary to the conventional mean-field vortex, can be detected as a topological defect of spatial coherence, but not of the density. We describe previously unknown many-body mechanisms of vortex nucleation and show that angular momentum is hidden in phantom vortices modes which so far seem to have evaded experimental detection. This phenomenon is likely important in the formation of the Abrikosov lattice and the onset of turbulence in superfluids.
Rotating supersolids challenge the conventional notion of superfluid flow: quantized vortices coexist with crystalline order arising from the system's intrinsic density modulation. Drawing on concepts developed in the context of superfluid helium, this seemingly paradoxical state is often described phenomenologically in terms of a dual response, combining superfluid flow with rigid-body-like motion. Here we show that these apparently distinct behaviors emerge from a single microscopic velocity field, globally constrained by irrotationality. By applying a Helmholtz decomposition, we disentangle a divergence-free incompressible component, which carries vortex circulation, from a curl-free compressible component generated by the intrinsic density modulation. In absence of vortices, the response is entirely encoded in the compressible field: the droplets co-rotate with the external drive, while the interstitial fluid develops an oppositely directed counterflow that preserves vanishing circulation. Above the vortex nucleation threshold, the incompressible component carries the usual quantized circulation, whereas the compressible field counteracts the vortex-induced angular momentum, reducing the total jump with respect to an unmodulated condensate. Our results recast supersolid rotation in terms of a flow-counterflow response, providing a microscopic interpretation of the phenomenological rigid/superfluid partitioning.
Vortices are essential to angular momentum in quantum systems such as ultracold atomic gases. The existence of quantized vorticity in bosonic systems stimulated the development of the Gross-Pitaevskii mean-field approximation. However, the true dynamics of angular momentum in finite, interacting many-body systems like trapped Bose-Einstein condensates is enriched by the emergence of quantum correlations whose description demands more elaborate methods. Herein we theoretically investigate the full many-body dynamics of the acquisition of angular momentum by a gas of ultracold bosons in two dimensions using a standard rotation procedure. We demonstrate the existence of a novel mode of quantized vorticity, which we term the phantom vortex that, contrary to the conventional mean-field vortex, can be detected as a topological defect of spatial coherence, but not of the density. We describe previously unknown many-body mechanisms of vortex nucleation and show that angular momentum is hidden in phantom vortex modes which so far seem to have evaded experimental detection.
Supersolids are states of matter that spontaneously break two continuous symmetries: translational invariance due to the appearance of a crystal structure and phase invariance due to phase locking of single-particle wave functions, responsible for superfluid phenomena. While originally predicted to be present in solid helium, ultracold quantum gases provided a first platform to observe supersolids, with particular success coming from dipolar atoms. Phase locking in dipolar supersolids has been probed through e.g. measurements of the phase coherence and gapless Goldstone modes, but quantized vortices, a hydrodynamic fingerprint of superfluidity, have not yet been observed. Here, with the prerequisite pieces at our disposal, namely a method to generate vortices in dipolar gases and supersolids with two-dimensional crystalline order, we report on the theoretical investigation and experimental observation of vortices in the supersolid phase. Our work reveals a fundamental difference in vortex seeding dynamics between unmodulated and modulated quantum fluids. This opens the door to study the hydrodynamic properties of exotic quantum systems with multiple spontaneously broken symmetries, in disparate domains such as quantum crystals and neutron stars.
Abstract We determine the hydrodynamic modes of the superfluid analog of a smectic-A liquid crystal phase, i.e., a state in which both gauge invariance and translational invariance along a single direction are spontaneously broken. Such a superfluid smectic provides an idealized description of the incommensurate supersolid state realized in Bose–Einstein condensates with strong dipolar interactions as well as of the stripe phase in Bose gases with spin–orbit coupling. We show that the presence of a finite normal fluid density in the ground state of these systems gives rise to a well-defined second-sound type mode even at zero temperature. It replaces the diffusive permeation mode of a normal smectic phase and is directly connected with the classic description of supersolids by Andreev and Lifshitz in terms of a propagating defect mode. An analytic expression is derived for the two sound velocities that appear in the longitudinal excitation spectrum. It only depends on the low-energy parameters associated with the two independent broken symmetries, which are the effective layer compression modulus and the superfluid fraction.
This doctoral thesis consists of experimental studies on rotating superfluid helium-3 at millikelvin temperatures. Superfluid 3He provides an example of ordered systems where quantum phenomena are visible on a macroscopic scale. The order parameter is described by a 3x3 complex matrix leading to different superfluid phases with different properties. The A and B phases support topologically different kinds of defects, most notably vortex lines. Vortex lines are most easily created and studied in uniform rotation. Because of quantum nature, the circulation around the vortices is quantized in units of κ0 = h/2m3.\n\nIn superfluid 3He nuclear magnetic resonance (NMR) provides a means to distinguish between different types of vortices and count them one by one. During the course of this work the sensitivity of the NMR spectrometer was improved by an order of magnitude, which enabled the direct measurement of the circulation of a vortex in the A phase that carries two circulation quanta (2κ0). Up to now the circulation of the known quantized vortex types in other quantum fluids, which include superfluid 4He, superconductors, and Bose-Einstein -condensates, has been singly quantized.\n\nOther NMR experiments reported in the thesis are: (1) The first qualitative measurements of vortex annihilation in the A and B phases of 3He. These measurements tell the lowest rotation velocity that stabilizes an array of vortex lines with a given number of vortices, and how it depends on the type of the defect. (2) Studies of vortex arrays with both singly and doubly quantized A phase vortex lines coexisting in the experimental container. 3He-A provides a unique system in which this kind of arrangement can be done. (3) In order to improve the vortex detection sensitivity in the B phase even further, the response of different nonlinear spin precession modes to superfluid-normal fluid counterflow was studied. A new mode, where the orbital angular momentum is oriented transverse to the external magnetic field, was found.