Narrow Results

Taking inspiration from F. Bloch’s seminal work (PRA 7, 2187 (1973)), we investigate the quantum many-body states of superfluid ⁴He, unveiling a novel characteristic in the system’s energy levels. Below the transition temperature, the thermally active low-energy levels exhibit a distinctive grouping behavior, with each level belonging exclusively to a single group. In a superflow state, the system establishes thermal equilibrium with its surroundings on a group-specific basis. Specifically, the levels within a chosen group, initially populated, undergo thermal redistribution, while the remaining groups of levels stay vacant due to absence of transitions between groups. The macroscopic properties of the system, such as its superflow velocity and thermal energy density, are statistically determined by the thermal distribution of the occupied group. Additionally, we infer that the thermal energy of a superflow has an unusual relationship with flow velocity, such that the larger the flow velocity, the smaller the thermal energy. This relationship is responsible for a range of intriguing phenomena, including the mechano-caloric effect and the fountain effect, which demonstrate a fundamental coupling between the thermal motion and hydrodynamic motion of the system. Furthermore, we present experimental evidence of a self-heating effect in ⁴He superflows, confirming that a ⁴He superflow carries significant thermal energy related to its velocity.

Quantum condensates in nuclear matter are treated beyond the mean-field approximation, with the inclusion of cluster formation. The occurrence of a separate binding pole in the four-particle propagator in nuclear matter is investigated with respect to the formation of a condensate of α-like particles (quartetting), which is dependent on temperature and density. Due to Pauli blocking, the formation of an α-like condensate is limited to the low-density region. Consequences for finite nuclei are considered. In particular, excitations of self-conjugate 2n-Z–2n-N nuclei near the n-α-breakup threshold are candidates for quartetting. We review some results and discuss their consequences. Exploratory calculations are performed for the density dependence of the α condensate fraction at zero temperature to address the suppression of the four-particle condensate below nuclear-matter density.

A possible resolution of the incompatibility of quantum mechanics and general relativity is that the relativity principle is emergent. I show that the central paradox of black holes also occurs at a liquid-vapor critical surface of a bose condensate but is resolved there by the phenomenon of quantum criticality. I propose that real black holes are actually phase boundaries of the vacuum analogous to this, and that the Einstein field equations simply fail at the event horizon the way quantum hydrodynamics fails at a critical surface. This can occur without violating classical general relativity anywhere experimentally accessible to external observers. Since the low-energy effects that occur at critical points are universal, it is possible to make concrete experimental predictions about such surfaces without knowing much, if anything about the true underlying equations. Many of these predictions are different from accepted views about black holes — in particular the absence of Hawking radiation and the possible transparency of cosmological black hole surfaces.

In a fermionic quantum vacuum, the parameters k_μ of a CPT-violating Chern–Simons-like action term induced by CPT-violating parameters of the fermionic sector depend on the universality class of the system. As a concrete example, we consider the Dirac Hamiltonian of a massive fermionic quasiparticle and add a particular term with purely-spacelike CPT-violating parameters b_μ = (0, b). A quantum phase transition separates two phases, one with a fully-gapped fermion spectrum and the other with topologically-protected Fermi points (gap nodes). The emergent Chern–Simons "vector" k_μ = (0, k) now consists of two parts. The regular part, k^reg, is an analytic function of |b| across the quantum phase transition and may be nonzero due to explicit CPT violation at the fundamental level. The anomalous (nonanalytic) part, k^anom, comes solely from the Fermi points and is proportional to their splitting. In the context of condensed-matter physics, the quantum phase transition may occur in the region of the BEC–BCS crossover for Cooper pairing in the p-wave channel. For elementary particle physics, the splitting of Fermi points may lead to neutrino oscillations, even if the total electromagnetic Chern–Simons-like term cancels out.

The exact renormalization group method is applied to many-fermion systems with short-range attractive forces. The strength of the attractive fermion-fermion interaction is determined from the vacuum scattering length. A set of approximate flow equations is derived including fermionic bosonic fluctations. The numerical solutions show a phase transition to a gapped phase. The inclusion of bosonic fluctuations is found to be significant only in the small-gap regime.

We generalize the big bang model in a previous paper by extending the real vacuum scalar field to a complex vacuum scalar field, within the FLRW framework. The phase dynamics of the scalar field, which makes the universe a superfluid, is described in terms of a density of quantized vortex lines, and a tangle of vortex lines gives rise to quantum turbulence. We propose that all the matter in the universe was created in the turbulence, through reconnection of vortex lines, a process necessary for the maintenance of the vortex tangle. The vortex tangle grows and decays, and its lifetime is the era of inflation. These ideas are implemented in a set of closed cosmological equations that describe the cosmic expansion driven by the scalar field on the one hand, and the vortex–matter dynamics on the other. We show how these two aspects decouple from each other, due to a vast difference in energy scales. The model is not valid beyond the inflation era, but the universe remains a superfluid afterwards. This gives rise to observable effects in the present universe, including dark matter, galactic voids, nonthermal filaments, and cosmic jets.

The vacuum is filled with complex scalar fields, such as the Higgs field. These fields serve as order parameters for superfluidity (quantum phase coherence over macroscopic distances), making the entire universe a superfluid. We review a mathematical model consisting of two aspects: (a) emergence of the superfluid during the big bang; (b) observable manifestations of superfluidity in the present universe. The creation aspect requires a self-interacting scalar field that is asymptotically free, i.e. the interaction must grow from zero during the big bang, and this singles out the Halpern–Huang potential, which has exponential behavior for large fields. It leads to an equivalent cosmological constant that decays like a power law, and this gives dark energy without "fine-tuning." Quantum turbulence (chaotic vorticity) in the early universe was able to create all the matter in the universe, fulfilling the inflation scenario. In the present universe, the superfluid can be phenomenologically described by a nonlinear Klein–Gordon equation. It predicts halos around galaxies with higher superfluid density, which is perceived as dark matter through gravitational lensing. In short, dark energy is the energy density of the cosmic superfluid, and dark matter arises from local fluctuations of the superfluid density.

The ordered state and the elementary excitations are theoretically studied in an interacting dilute quasi-two-dimensional Bose gas of excitons in a type-II quantum well. This system is advantageous for studying the macroscopic quantum phenomena because those excitons have a long lifetime of the order of 10^-6 s, and their transport mechanism can be directly studied in experiments by observing electric current since the excitons consist of spatially separated electron-hole pairs. Using the obtained dispersion relations for excitations, we examine the Landau criterion for exciton superflow and the temperature dependence of the off-diagonal long-range order which characterizes the quasi-Bose-Einstein condensation in two-dimensional systems.

We review the topic of quantized vortices in multicomponent Bose–Einstein condensates of dilute atomic gases, with an emphasis on the two-component condensates. First, we review the fundamental structure, stability and dynamics of a single vortex state in a slowly rotating two-component condensates. To understand recent experimental results, we use the coupled Gross–Pitaevskii equations and the generalized nonlinear sigma model. An axisymmetric vortex state, which was observed by the JILA group, can be regarded as a topologically trivial skyrmion in the pseudospin representation. The internal, coherent coupling between the two components breaks the axisymmetry of the vortex state, resulting in a stable vortex molecule (a meron pair). We also mention unconventional vortex states and monopole excitations in a spin-1 Bose–Einstein condensate. Next, we discuss a rich variety of vortex states realized in rapidly rotating two-component Bose–Einstein condensates. We introduce a phase diagram with axes of rotation frequency and the intercomponent coupling strength. This phase diagram reveals unconventional vortex states such as a square lattice, a double-core lattice, vortex stripes and vortex sheets, all of which are in an experimentally accessible parameter regime. The coherent coupling leads to an effective attractive interaction between two components, providing not only a promising candidate to tune the intercomponent interaction to study the rich vortex phases but also a new regime to explore vortex states consisting of vortex molecules characterized by anisotropic vorticity. A recent experiment by the JILA group vindicated the formation of a square vortex lattice in this system.

Extensive Path Integral Monte Carlo simulations of two-dimensional para-Hydrogen embedded in a crystalline matrix of Alkali atoms, show no evidence of superfluid behavior at low temperature. Rather, the system is observed to form a commensurate (non superfluid) crystal.

The recent observation of non-classical rotational inertia in solid ⁴He for temperatures T < 200 mk, and the continued non-observation of unusual flow associated with "zero-point defectons", favors the Leggett picture of Non-Classical Rotational Inertia over the Andreev-Lifshitz zero-point defecton picture of possible superflow in this system. We discuss the nature of the wavefunction, the Leggett one-body phase function upper bound for the superfluid fraction, and more complex forms for the phase-function and how this affects the net momentum density of this many-body system. The general properties of quantum vortices in such a system are briefly discussed.

We present quantum Monte Carlo calculations of the effective rotational constant B of several cromophore molecules embedded in He clusters, as a function of the cluster size. The predictive power of the computed B values is demonstrated not only by their agreement with available measurements, but also by their use in the assignment of several lines in both infrared and microwave spectra. The simulation results complement and extend the experimental information, offering insight into the relationship between structural and dynamical properties and the onset of superfluidity. The range of cluster sizes studied in our simulations includes systems of several tens particles, intermediate between the small-cluster and the nanodroplet regimes. In this size range we find unexpected trends for the evolution of B towards its asymptotic nano-droplet value.

We have performed a fully non-perturbative calculation of the thermal properties of a system of spin 1/2 fermions in 3D in the unitary regime. We have determined the critical temperature for the superfluid-normal phase transition. The thermodynamic behavior of this system presents a number of unexpected features, and we conclude that spin 1/2 fermions in the BCS-BEC crossover should be classified as a new type of superfluid.

In this paper, we study the structure of vortex lattices in a trapped superfluid Fermi gas in the unitary region near the superfluid transition temperature. A phenomenological approach based on the Ginzburg-Landau theory is used. Two types of stable triangular vortex lattices are found numerically at the same rotation frequency. In type (A), the trap center is occupied by a vortex; in type (B), there are three vortices closest to the trap center which is unoccupied. The lattice structures at different rotation frequencies and temperatures are analyzed. The vortex density increases linearly with the rotation frequency, very close to the analytical estimation. The superfluid and type-(B) vortex lattice do not disappear together. At high rotation frequencies, the vortex lattice disappears, but there exists a localized superfluid state near the trap center. The superfluid vanishes at a critical rotation frequency consistent with the theory for the upper critical magnetic field of type-II superconductors.

The Bogolyubov model of liquid helium is considered. The validity of substituting a c-number for the k = 0 mode operator â₀ is established rigorously. The domain of stability of the Bogolyubov's Hamiltonian is found. We derive sufficient conditions which ensure an appearance of the Bose condensate in the model. For some temperatures and some positive values of the chemical potential, there is the gapless Bogolyubov spectrum of elementary excitations, leading to the proper microscopic interpretation of the superfluidity.

In this review we will discuss the experimental and theoretical progresses in studying spin–orbit coupled degenerate atomic gases during the last two years. We shall first review a series of pioneering experiments in generating synthetic gauge potentials and spin–orbit coupling in atomic gases by engineering atom-light interaction. Realization of spin–orbit coupled quantum gases opens a new avenue in cold atom physics, and also brings out a lot of new physical problems. In particular, the interplay between spin–orbit coupling and inter-atomic interaction leads to many intriguing phenomena. By reviewing recent theoretical studies of both interacting bosons and fermions with isotropic Rashba spin–orbit coupling, the key message delivered here is that spin–orbit coupling can enhance the interaction effects, and make the interaction effects much more dramatic even in the weakly interacting regime.

We study a system of spatially separated electrons and holes, assuming the carriers are confined to two parallel planes. The existence of the superfluid state of electron–hole pairs between two critical temperatures is predicted for such system in a case of electron–hole asymmetry caused by the difference in the carrier masses and their chemical potentials. The stability of the superfluid state is studied with respect to the changes of the asymmetry between electrons and holes. It is found that one type of the asymmetry can compensate another one, so the superfluid state is possible in a wide range of the asymmetry parameters when they satisfy a simple linear equation.

The spectacular properties of liquid helium at low temperature are generally accepted as the signature of the bosonic nature of this system. Particularly the superfluid phase is identified with a Bose–Einstein condensed fluid. However, the relationship between the superfluidity and the Bose–Einstein condensation is still largely unknown. Studying a perturbed liquid ⁴He system would provide information on the relationship between the two phenomena. Liquid ⁴He confined in porous media provides an excellent example of a boson system submitted to disorder and finite-size effects.

Much care should be paid to the sample preparation, particularly the confining condition should be defined quantitatively. To achieve homogeneous confinement conditions, firstly a suitable porous sample should be selected, the experiments should then be conducted at a lower pressure than the saturated vapor pressure of bulk helium.

Several interesting effects have been shown in confined ⁴He samples prepared as described above. Particularly we report the observation of the separation of the superfluid-normal fluid transition temperature, T_c, from the temperature at which the Bose–Einstein condensation is believed to start, T_BEC, the existence of metastable densities for the confined liquid accessible to the bulk system as a short-lived metastable state only and strong clues for a finite lifetime of the elementary excitations at temperatures as low as 0.4 K.

We show that the suppression of light scattering off a Bose Einstein Condensate is equivalent to the Landau argument for superfluidity and thus is a consequence of the Principle of Superfluidity. The superfluid ground state of a BEC contains nonseparable, nontrivial correlations between the bosons that make up the system, i.e., it is entangled. The correlations in the ground state entangle the bosons into a coherent state for the lowest energy state. The entanglement is so extreme that the bosons that make up the system cannot be excited at long wavenumbers. Their existence at low energies is impossible. Only quantum sound can be excited, i.e. the excitations are Bogolyubov quasiparticles which do not resemble free bosons whatsoever at low energies. This means that the system is superfluid by the Landau argument and the superfluidity is ultimately the reason for suppressed scattering at low wavelengths.

We review a natural universal theoretical framework of superfluidity and its analogues, superconductivity and supersolidity. This framework has the potential to describe all physical properties of superfluids to a high level of satisfaction. A unified description of both the "intrinsic" and "extrinsic" critical velocity of liquid ⁴He is suggested. A recent clarification of the so-call pseudogap phase of a superconductor based on this framework is introduced. This paper reflects the current author's views of superfluidity, rather than being an attempt to review on a vast literature on this subject.