Quantum oscillations in confined and degenerate Fermi gases. I. Half-vicinity model

We propose an analytical model for the prediction and accurate calculation of size and density dependent quantum oscillations in thermodynamic and transport properties of confined and degenerate Fermi gases. Our model considers only half-vicinity states of Fermi level. We show that the half-vicinity model quite accurately estimates quantum oscillations depending on confinement and degeneracy. Periods of quantum oscillations are even analytically expressed for one-dimensional case. Furthermore, similarities between functional behaviors of total occupancy variance and conventional density of states functions at Fermi level are discussed.     

Discrete nature of thermodynamics in confined ideal Fermi gases

Intrinsic discrete nature in thermodynamic properties of Fermi gases appears under strongly confined and degenerate conditions. For a rectangular confinement domain, thermodynamic properties of an ideal Fermi gas are expressed in their exact summation forms. For 1D, 2D and 3D nano domains, variations of both number of particles and internal energy per particle with chemical potential are examined. It is shown that their relation with chemical potential exhibits a discrete nature which allows them to take only some definite values. Furthermore, quasi-irregular oscillatory-like sharp peaks are observed in heat capacity. New nano devices can be developed based on these behaviors.     

Quantum phase transitions in Bose–Fermi systems

Quantum phase transitions in a system of N bosons with angular momentum L = 0, 2 (s, d) and a single fermion with angular momentum j are investigated both classically and quantum mechanically. It is shown that the presence of the odd fermion strongly influences the location and nature of the phase transition, especially the critical value of the control parameter at which the phase transition occurs. Experimental evidence for the U(5)–SU(3) (spherical to axially-deformed) transition in odd–even nuclei is presented.     

BCS-BEC crossover and topological phase transition in 3D spin-orbit coupled degenerate Fermi gases

We investigate the BCS-BEC crossover in three-dimensional degenerate Fermi gases in the presence of spin-orbit coupling (SOC) and Zeeman field. We show that the superfluid order parameter destroyed by a large Zeeman field can be restored by the SOC. With increasing strengths of the Zeeman field, there is a series of topological quantum phase transitions from a nontopological superfluid state with fully gapped fermionic spectrum to a topological superfluid state with four topologically protected Fermi points (i.e., nodes in the quasiparticle excitation gap) and then to a second topological superfluid state with only two Fermi points. The quasiparticle excitations near the Fermi points realize the long-sought low-temperature analog of Weyl fermions of particle physics. We show that the topological phase transitions can be probed using the experimentally realized momentum-resolved photoemission spectroscopy.     

Spin-orbit coupling in Bose-Einstein condensate and degenerate Fermi gases

We review our recent experimental realization and investigation of a spin orbit （SO） coupled Bose Einstein condensate （BEC） and quantum degenerate Fermi gas. By using two counter-propagathlg Ranlan lasers and controlling the different frequency of two R,aman lasers to engineer the atom light interaction, we first study the SO coupling in BEC. Then we study SO coupling in Fermi gas. We, observe the spin dephasing in spin dynamics and momentum distribution asymmetry of the equilibrium state as halhnarks of SO coupling in a Fermi gas. To clearly reveal the, property of SO coupling Fermi gas, we also study the momentmn-resolved radio-frequency spectroscopy which characterizes the energy momentum dispersion and spin composition of the quantum states. We observe the change of errmion surfaces in different helieity branches with different atomic density, which indicates that a Lifshitz transition of the Fermi surface topology change can be found by further cooling the system. At last, we study the momentum-resolved Raman spectroscopy of an ultracoht Fermi gas.     

The macroscopic quantum phase of ultracold degenerate gases in the asymmetrical two-dimensional magnetic lattice

We investigate the existence of the macroscopic quantum phase in trapped ultracold quantum degenerate gases in an asymmetrical two-dimensional magnetic lattice. We show the key to adiabatically control the tunneling in the new two-dimensional magnetic lattice by means of external magnetic bias fields. In solving the system of coupled time-dependent differential equations, described here by the Boson Josephson Junctions (BJJs), we used an order parameter that includes both time-dependent variational parameters to describe the fractional population at each lattice site and the phase difference to quantify the macroscopic quantum phase signature. A dynamical oscillation of the fractional population and the phase difference at each individual lattice site is observed when solving the BJJs system.     

Quantum phase transition in the generalized single-mode superradiant model

In this paper we reveal a zero-temperature quantum phase transition for the single-mode superradiant model with the form A² from the normal to superradiant phase by mean of the Holstein-Primakoff transformation. In the thermodynamic limit, in which the numbers of atoms becomes infinite, the ground state energy and corresponding wavefunctions of both the normal and superradiant phases are obtained and therefore the scaling behavior near the critical transition point is derived.     

Dynamics and phase behaviour of materials in confined geometry

Phase transitions and dynamics of the liquid crystal MBBA [N-( p-methoxybenzylidene)-p-n-butylaniline] microconfined within porous glasses of average pore diameters: 82 and 337 Å were investigated by ¹H Nuclear Magnetic Resonance (NMR). Confinement is found to favour the depression of phase transition temperatures below the corresponding transitions of bulk MBBA. Confinement induces further effects for the molecular dynamics related to the phase investigated. The correlation times of the molecular motions were obtained and the results are discussed by making comparison with the bulk analysis.     

Quantum phase transition of alkaline-earth fermionic atoms confined in an optical superlattice

Using the density matrix renormalization group method, we evaluate the spin and charge gaps of alkaline-earth fermionic atoms in a periodic one-dimensional optical superlattice. The number of delocalized atoms is equal to the lattice size and we consider an antiferromagnetic coupling between delocalized and localized atoms. We found a quantum phase transition from a Kondo insulator spin liquid state without confining potential to a charge-gapped antiferromagnetic state with nonzero potential. For each on-site coupling, there is a critical potential point for which the spin gap vanishes and its value increases linearly with the local interaction.     

Water confined in two-dimensions: Fundamentals and applications

The behavior of water in close proximity to other materials under ambient conditions is of great significance due to its importance in a broad range of daily applications and scientific research. The structure and dynamics of water at an interface or in a nanopore are often significantly different from those of its bulk counterpart. Until recently, experimental access to these interfacial water structures was difficult to realize. The advent of two-dimensional materials, especially graphene, and the availability of various scanning probe microscopies were instrumental to visualize, characterize and provide fundamental knowledge of confined water. This review article summarizes the recent experimental and theoretical progress in a better understanding of water confined between layered Van der Waals materials. These results reveal that the structure and stability of the hydrogen bonded networks are determined by the elegant balance between water-surface and water-water interactions. The water-surface interactions often lead to structures that differ significantly from the conventional bilayer model of natural ice. Here, we review the current knowledge of water adsorption in different environments and intercalation within various confinements. In addition, we extend this review to cover the influence of interfacial water on the two-dimensional material cover and summarize the use of these systems in potential novel applications. Finally, we discuss emerged issues and identify some flaws in the present understanding.     

Collective excitations of a degenerate Fermi vapour in a magnetic trap

We evaluate the small-amplitude excitations of a spin-polarized vapour of Fermi atoms confined inside a harmonic trap. The dispersion law is obtained for the vapour in the collisional regime inside a spherical trap of frequency , with n the number of radial nodes and the orbital angular momentum. The low-energy excitations are also treated in the case of an axially symmetric harmonic confinement. The collisionless regime is discussed with main reference to a Landau-Boltzmann equation for the Wigner distribution function: this equation is solved within a variational approach allowing an account of non-linearities. A comparative discussion of the eigenmodes of oscillation for confined Fermi and Bose vapours is presented in an Appendix. Received 23 February 1999 and Received in final form 21 April 1999     

Quantum kinetic theory of confined electrons in a strong time dependent field

A gauge-invariant Green’s function approach to the quantum transport of spatially confined electrons in strong electromagnetic fields is presented. The theory includes mean field and exchange effects, as well as collisions and initial correlations. It allows for a self-consistent treatment of spectral properties and collective effects (plasmons), on one hand, and nonlinear field phenomena, such as harmonic generation and multiphoton absorption, on the other. It is equally applicable to electrons in quantum dots, ultracold ions in traps and valence electrons of metal clusters.     

Probability density tomography of microcavity polaritons confined in cylindrical traps of various sizes

We present the optical tomography of the probability density of microcavity polaritons, confined in three dimensions by cylindrical traps of various sizes. Collecting the photoluminescence emitted by the quasimodes under continuous nonresonant laser excitation, we reconstruct a three dimensional mapping of the photoluminescence, from which we can extract the spatial distribution of the confined states at any energy. We discuss the impact of the confinement shape and size on the probability density patterns.     

Studies of diffusion coefficients in disordered porous matrices confined in a slit-pore

We present a series of molecular dynamics simulations to study the structure of porous matrices confined in a slit-pore. The matrices were prepared by two different methods. In the first method we used direct simulations of a fluid at a fixed density and the matrix was taken from the last configuration of its particles. In the second method we simulated a binary mixture where one of the components served as a template material and the final porous matrix configuration was obtained by removing template particles from the mixture. In both methods the matrices were confined by two parallel walls (slit-pore) modeled by continuous solid surfaces. The results show that the matrix structure and porosity were affected by the method of preparation of the porous matrices. Moreover, we found smaller void cavities in these matrices than in matrices prepared without walls. Finally, diffusion of a fluid inside the matrices was investigated and it was found that the diffusion coefficient did not decrease with the fluid density, and presented a maximum at certain values of the fluid density.     

Quantum phase transition in the anisotropic one-dimensional XY model with long-range interactions

In this paper we study the one-dimensional XY model with single ion anisotropy and long-range interaction that decay as a power law. The model has a quantum phase transition, at zero temperature, at a critical value D_c of the anisotropy parameter D. For values of D below D_c we use a self-consistent harmonic approximation. We have found that the critical temperature increases with D for small values of this parameter. For values of D above D_c we use the bond operator technique and calculate the gap as a function of D, at zero temperature.     

Quantum chaos and magnetotransport in lateral superlattices: The transition from weak to strong modulation potential

Magnetotransport in lateral superlattices covers a variety of apparently different physics dependent on the amplitude of the modulation potential relative to the Fermi energy ranging from the weakly modulated 2DEG to the antidot lattice. Here we investigate the transition between weak modulation and antidots within the quantum-mechanical theory by studying (i) the single-particle spectrum with respect to quantum signatures of classical chaos and (ii) the change of characteristic features in the magnetoresistance starting from the Kubo formula.     

Reprint of : Quantum interference in a Cooper pair splitter: The three sites model

New generation of Cooper pair splitters defined on hybrid nanostructures are devices with high tunable coupling parameters. Transport measurements through these devices revealed clear signatures of interference effects and motivated us to introduce a new model, called the 3-sites model. These devices provide an ideal playground to tune the Cooper pair splitting (CPS) efficiency on demand, and displays a rich variety of physical phenomena. In the present work we analyze theoretically the conductance of the 3-sites model in the linear and non-linear regimes and characterize the most representative features that arise by the interplay of the different model parameters. In the linear regime we find that the local processes typically exhibit Fano-shape resonances, while the CPS contribution exhibits Lorentzian-shapes. Remarkably, we find that under certain conditions, the transport is blocked by the presence of a dark state. In the non-linear regime we established a hierarchy of the model parameters to obtain the conditions for optimal efficiency.     

Quantum phase transitions in antiferromagnets and superfluids

We present a general introduction to the non-zero temperature dynamic and transport properties of low-dimensional systems near a quantum phase transition. Basic results are reviewed in the context of experiments on the spin-ladder compounds, insulating two-dimensional antiferromagnets, and double-layer quantum Hall systems. Recent large N computations on an extended t–J model (Phys. Rev. Lett. 83 (1999) 3916) motivate a global scenario of the quantum phases and transitions in the high-temperature superconductors, and connections are made to numerous experiments.