Superfluidity and superconductivity have been widely studied since the last century in many different contexts ranging from nuclear matter to atomic quantum gases. The rigidity of these systems with respect to external perturbations results in frictionless motion for superfluids and resistance-free electric current flow in superconductors. This peculiar behaviour is lost when external perturbations overcome a critical threshold, i.e. above a critical magnetic field or a critical current for superconductors. In superfluids, such as liquid helium or ultracold gases, the corresponding quantities are a critical rotation rate and a critical velocity respectively. Enhancing the critical values is of great fundamental and practical value. Here we demonstrate that superfluidity can be completely restored for specific, arbitrarily large flow velocities above the critical velocity through quantum interference-induced resonances providing a nonlinear counterpart of the Ramsauer-Townsend effect occurring in ordinary quantum mechanics. We illustrate the robustness of this phenomenon through a thorough analysis in one dimension and prove its generality by showing the persistence of the effect in non-trivial 2d systems. This has far reaching consequences for the fundamental understanding of superfluidity and superconductivity and opens up new application possibilities in quantum metrology, e.g. in rotation sensing.
Superfluidity and superconductivity have been widely studied since the last century in many different contexts ranging from nuclear matter to atomic quantum gases. The rigidity of these systems with respect to external perturbations results in frictionless motion for superfluids and resistance-free electric current flow in superconductors. This peculiar behaviour is lost when external perturbations overcome a critical threshold, i.e. above a critical magnetic field or a critical current for superconductors. In superfluids, such as liquid helium or ultracold gases, the corresponding quantities are a critical rotation rate and a critical velocity respectively. Enhancing the critical values is of great fundamental and practical value. Here we demonstrate that superfluidity can be completely restored for specific, arbitrarily large flow velocities above the critical velocity through quantum interference-induced resonances providing a nonlinear counterpart of the Ramsauer-Townsend effect occurring in ordinary quantum mechanics. We illustrate the robustness of this phenomenon through a thorough analysis in one dimension and prove its generality by showing the persistence of the effect in non-trivial 2d systems. This has far reaching consequences for the fundamental understanding of superfluidity and superconductivity and opens up new application possibilities in quantum metrology, e.g. in rotation sensing.
We discuss the general interplay between the uncertainty principle and the onset of dissipationless transport phenomena such as superconductivity and superfluidity. We argue that these phenomena are possible because of the robustness of many-body quantum states with respect to the external environment, which is directly related to the uncertainty principle as applied to coordinates and momenta of the carriers. In the case of superconductors, this implies relationships between macroscopic quantities such as critical temperature and critical magnetic field, and microscopic quantities such as the amount of spatial squeezing of a Cooper pair and its correlation time. In the case of ultracold atomic Fermi gases, this should be paralleled by a connection between the critical temperature for the onset of superfluidity and the corresponding critical velocity. Tests of this conjecture are finally sketched with particular regard to the understanding of the behaviour of superconductors under external pressures or mesoscopic superconductors, and the possibility to mimic these effects in ultracold atomic Fermi gases using Feshbach resonances and atomic squeezed states.
We discuss the general interplay between the uncertainty principle and the onset of dissipationless transport phenomena such as superconductivity and superfluidity. We argue that these phenomena are possible because of the robustness of many-body quantum states with respect to the external environment, which is directly related to the uncertainty principle as applied to coordinates and momenta of the carriers. In the case of superconductors, this implies relationships between macroscopic quantities such as critical temperature and critical magnetic field, and microscopic quantities such as the amount of spatial squeezing of a Cooper pair and its correlation time. In the case of ultracold atomic Fermi gases, this should be paralleled by a connection between the critical temperature for the onset of superfluidity and the corresponding critical velocity. Tests of this conjecture are finally sketched with particular regard to the understanding of the behaviour of superconductors under external pressures or mesoscopic superconductors, and the possibility to mimic these effects in ultracold atomic Fermi gases using Feshbach resonances and atomic squeezed states.
What is a superfluid? The word “superfluid” was coined to describe a qualitatively different state of a fluid that can occur at low temperatures, in which the resistance to flow is identically zero, so that flow round a closed path lasts for ever – a persistent current. Superfluidity can occur either for uncharged particles such as helium atoms or for charged particles such as the electrons in a metal. In the latter case the flow constitutes an electric current and we have a superconductor. Since an electric current is accompanied by a magnetic field, it is much easier to demonstrate the presence of a persistent current in a superconductor than in a neutral superfluid. In this chapter I shall describe the properties of superfluids, starting with the simplest and working up to more complicated examples. But in this introductory section I shall depart from the historical order even further by turning to the last page of the detective story so as to catch a glimpse of the conclusion from almost a century of experimental and theoretical research; we shall then have an idea of where we are heading. The conclusion is that superfluidity is more than just flow without resistance. It is an example of a transition to a more ordered state as the temperature is lowered, like the transition to ferromagnetism. At such a transition new macroscopically measurable quantities appear: in the case of a ferromagnet, the spontaneous magnetization. Such new measurable quantities are known as the order parameter of the low-temperature phase. The new quantities in the case of a superfluid are more subtle and more surprising: the amplitude and phase of the de Broglie wave associated with the motion of the superfluid particles. A superfluid can therefore exhibit quantummechanical effects on a macroscopic scale.
We consider the changes in the spectrum of elementary excitations of a flowing superfluid that result when a weak external perturbing potential is added. As a specific application, we study the critical velocity of superfluid flow in a slightly distorted, tight, toroidal trap for atoms. The critical velocity is not accurately predicted by the argument that the flow turns dissipative when the local flow velocity exceeds the local speed of sound somewhere in the fluid. The unusual critical velocity probably reflects the essentially one-dimensional physics of the model.
Superfluidity and superconductivity are striking examples of how quantum mechanics can affect the collective behaviour of large numbers of identical particles. When the temperature of a many-particle fluid is lowered below a critical threshold, thermal fluctuations are no longer able to prevent it from collapsing into a purely quantum state. If the particles are electrically neutral, like helium–3 and helium–4 atoms, such a 'coherent' state can flow without friction and is known as a superfluid. If, on the other hand, the particles are charged, the coherent state loses its resistance to electrical current and becomes a superconductor.
The difference between normal systems and superfinid systems is perhaps most strikingly manifested in their current flow. Superfluid current flow displays very special features, both in its structure and in its response to external probes. We now focus our attention on these characteristic “superfluid” properties at zero-temperature. The generalization of the theory to finite temperatures is postponed until Chapter 6 . Two fundamental features of superfluid flow are the following: Superfluid flow is irrotational This property may be viewed in a number of ways. In the language of a two-fluid model, it is expressed by the equation: ∇ × v s = 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429495717/2cc6e3e4-f702-48c8-b407-59783ef3d6a6/content/eq89_v2.tif"/> where v s is the superfluid velocity, which we shall define more precisely in Chapter 5 . More conveniently, we may say that it is impossible to set up rotational currents on a macroscopic scale in a superfluid. It follows that when a transverse probe is applied to the fluid, the latter does not respond. For example, let us imagine a simple experiment, in which a bucket of helium is rotated at a constant angular velocity ω . In a frame of reference which rotates along with the walls, the fluid feels a Coriolis force, which acts as a transverse probe applied to the system. A normal liquid would respond to such a probe; at equilibrium, the liquid would be dragged by the walls and rotate at the same angular velocity ω . In a homogeneous superfluid at T = 0, the liquid does not respond to the 50 Coriolis force; it stays at rest while the walls are rotating. In an actual superfluid, we shall see that matters are more complicated, in that vortices may appear in the rotating bucket. As a result, one does not encounter the dramatic manifestation of superfluid behavior predicted for a homogeneous superfluid. Nevertheless, the above fictitious experiment is conceptually very important, as it illustrates an essential feature of superfluids, namely their rigidity against transverse probes. The physical importance of such a concept is even more obvious in superconductors, since in that case it corresponds to the Meissner effect. Superfluid flow is resistance free: when a superfluid flows in a thin capillary, it is not slowed down by the walls. The flow thus persists without any pressure head applied to the end of the capillary.