Quasiparticle scattering by quantum phase slips in one-dimensional superfluids

Quantum phase slips (QPS) in narrow superfluid channels generate momentum by unwinding the supercurrent. In a uniform Bose gas, this momentum needs to be absorbed by quasiparticles (phonons). We show that this requirement results in an additional exponential suppression of the QPS rate (compared to the rate of QPS induced by a sharply localized perturbation). In BCS-paired fluids, momentum can be transferred to fermionic quasiparticles, and we find an interesting interplay between quasiparticle scattering on QPS and on disorder.     

Strong-coupling topological Josephson effect in quantum wires

We investigate the Josephson effect for a setup with two lattice quantum wires featuring Majorana zero energy boundary modes at the tunnel junction. In the weak-coupling regime, the exact solution reproduces the perturbative result for the energy containing a contribution ～ ± cos(?/2) relative to the tunneling of paired Majorana fermions. As the tunnel amplitude g grows relative to the hopping amplitude w, the gap between the energy levels gradually diminishes until it closes completely at the critical value gc [Formula: see text]. At this point the Josephson energies have the principal values [Formula: see text], where m =- 1,0,1 and σ =± 1, a result not following from perturbation theory. It represents a transparent regime where three Bogoliubov states merge, leading to additional degeneracies of the topologically nontrivial ground state with an odd number of Majorana fermions at the end of each wire. We also obtain the exact tunnel currents for a fixed parity of the eigenstates. The Josephson current shows the characteristic 4π periodicity expected for a topological Josephson effect. We discuss the additional features of the current associated with a closure of the energy gap between the energy levels.     

Evolution of edge states in topological superfluids during the quantum phase transition

The quantum phase transition between topological and nontopological insulators or between fully gapped superfluids/superconductors can occur without closing the gap. We consider the evolution of the Majorana edge states on the surface of topological superconductor during transition to the topologically trivial superconductor on example of non-interacting Hamiltonian describing spin-triplet superfluid ³He-B. In conventional situation when the gap is nullified at the transition, the spectrum of Majorana fermions shrinks and vanishes after the transition to the trivial state. If the topological transition occurs without the gap closing, the Majorana fermion spectrum disappears by escaping to ultraviolet, where the Green’s function approaches zero. This demonstrates the close connection between the topological transition without closing the gap and zeroes in the Green’s function. Similar connection takes place in interacting systems where zeroes may occur due to interaction.     

Macroscopic quantum phenomena in superfluids and superconductors

In this paper I will discuss the common macroscopic quantum phenomena in the three superfluid systems known in condensed matter, the superconducting state of a metal, the superfluid phase of liquid⁴He, and the superfluid phases of liquid³He. The discussed phenomena will be persistent currents and their decay, critical velocities and critical magnetic fields, quantization of magnetic flux and of circulation, the two-dimensional flux and vortex lattices, and eventually the Josephson effects.Invited paper at the International Conference on Macroscopic Quantum Phenomena, Smolenice Castle, Czechoslovakia, September 18–22, 1989.     

Interlayer phase coherence and Josephson effects in bilayer quantum Hall systems

When an electron is confined within the lowest Landau level, its position is described solely by the guiding center, whose X and Y coordinates do not commute with one another. The equations of motion do not follow from the kinetic Hamiltonian but from the noncommutative property of the space. Based on this microscopic theory, we analyze the bilayer QH system at the filling factor ?? = 1, and show that there develops an interlayer phase coherence. It is interpreted that the phase coherence occurs due to the Bose-Einstein condensation of composite bosons, which are single electrons bound to magnetic flux quanta. The phase coherence can induce the Josephson inplane current as well as the Josephson tunneling current, which are dissipationless as in superconductor. We demonstrate that the Josephson inplane current provokes anomalous behaviors in the Hall resistance in counterflow and drag experiments. Furthermore, we investigate the condition on the input current for the tunneling current to be coherent and dissipationless. We predict also how the condition changes when the sample is tilted in the magnetic field.     

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.     

Dynamics of quantum phase transition in an array of Josephson junctions

We study the dynamics of the Mott insulator-superfluid quantum phase transition in a periodic 1D array of Josephson junctions. We show that crossing the critical point at a finite rate with a quench time tau(Q) induces finite quantum fluctuations of the current around the loop proportional to tau(-1/6)(Q). This scaling could be experimentally verified with an array of weakly coupled Bose-Einstein condensates or superconducting grains.     

Vortex dynamics in superfluids and the Berry phase

There is a close analogy between the dynamics of electrons in a strong magnetic field and the dynamics of quantized vortices in superfluids and superconductors. In both systems an important part is played by a term in the Lagrangian linear in velocity that corresponds to a Berry phase in the quantum theory. This Berry phase can be calculated from the usual trial wave function for a vortex. This has important consequences for quantum tunneling of vortices, and leads unambiguously to the form of the Magnus force in a superconductor.     

Josephson effect without superconductivity: realization in quantum Hall bilayers

We show that a quantum Hall bilayer with the total filling nu = 1 should exhibit a dynamical regime similar to the flux flow in large Josephson junctions. This analogy may explain a conspicuous peak in the interlayer tunneling conductance [Phys. Rev. Lett. 84, 5808 (2000)]. The flux flow is likely to be spatiotemporally chaotic at low-bias voltage, which will manifest itself through broadband noise. The peak position can be controlled by an in-plane magnetic field.     

量子微结构中的Josephson 效应

文章为纪念Josephson 效应发现50周年而作.文章介绍了当前关于几种量子微结构中Josephson 效应的理论研究,涉及Josephson 效应的基本物理现象和它在某些热点材料中的独特表现,如单层石墨纳米条带中的0-π转变,二维拓扑绝缘体中的手征性边态超导电流,以及半导体微腔中激子极化激元凝聚体之间的Josephson 效应和直流-交流Josephson 电流的转变.     

BEC-BCS crossover, phase transitions and phase separation in polarized resonantly-paired superfluids

We study resonantly-paired s-wave superfluidity in a degenerate gas of two species (hyperfine states labeled by ↑, ↓) of fermionic atoms when the numbers N_↑ and N_↓ of the two species are unequal, i.e., the system is “polarized.” We find that the continuous crossover from the Bose-Einstein condensate (BEC) limit of tightly-bound diatomic molecules to the Bardeen-Cooper-Schrieffer (BCS) limit of weakly correlated Cooper pairs, studied extensively at equal populations, is interrupted by a variety of distinct phenomena under an imposed population difference ΔN ≡ N_↑ − N_↓. Our findings are summarized by a “polarization” (ΔN) versus Feshbach-resonance detuning (δ) zero-temperature phase diagram, which exhibits regions of phase separation, a periodic FFLO superfluid, a polarized normal Fermi gas and a polarized molecular superfluid consisting of a molecular condensate and a fully polarized Fermi gas. We describe numerous experimental signatures of such phases and the transitions between them, in particular focusing on their spatial structure in the inhomogeneous environment of an atomic trap.     

约瑟夫森器件中的宏观量子现象及超导量子计算

超导体中的电子结成库珀对，凝聚到可以用一个宏观波函数来描绘的能量基态，该波函数的位相是代表了成百万库珀对集体运动的宏观变量．以约瑟夫森结为基础元件的超导约瑟夫森器件，使人们能够控制并测量一个超导体的位相和库珀对数目，因此是研究宏观量子现象的理想系统．文章回顾了约瑟夫森器件中的宏观量子现象研究的发展历程，介绍了当前超导约瑟夫森器件在量子计算中的重要应用，并对它们的未来作了简要的展望．     

A geometrical quantum phase effect

A localized change in the spatial boundary conditions of a propagating quanton in shown to modify the phase of its outgoing wavefunction. This elementary effect is in principle observable by neutron interferometry, and gives rise to a purely geometrical analog of the Aharonov-Bohm effect, which puts into full light the nonlocal character of quantum behaviour.     

A flow phase diagram for helium superfluids

The existence of the flow phase diagram predicted by Volovik [JETP Lett. 78, 553 (2003)] is discussed based on the available experimental data for He II and ³He-B. The effective temperature-dependent but scale-independent Reynolds number Re_eff≡1/q≡(1?α′)/α, where α and α′ are the mutual friction parameters, and the superfluid Reynolds number characterizing the circulation of the superfluid component in units of the circulation quantum are used as the dynamic parameters. In particular, the flow diagram permits the identification of the experimentally observed turbulent states I and II in counterflowing He II with the classical and quantum turbulent regimes suggested by Volovik.