Interferometric distillation and determination of unknown two-qubit entanglement

We propose a scheme for both distilling and quantifying entanglement, applicable to individual copies of an arbitrary unknown two-qubit state. It is realized in a usual two-qubit interferometry with local filtering. Proper filtering operation for the maximal distillation of the state is achieved, by erasing single-qubit interference, and then the concurrence of the state is determined directly from the visibilities of two-qubit interference. We compare the scheme with full state tomography

Spectator Behavior in a Quantum Hall Antidot with Multiple Bound Modes

We theoretically study Aharonov-Bohm resonances in an antidot system with multiple bound modes in the integer quantum Hall regime, taking capacitive interactions between the modes into account. We find the spectator behavior that the resonances of some modes disappear and instead are replaced by those of other modes, due to internal charge relaxation between the modes. This behavior is a possible origin of the features of previous experimental data which remain unexplained, spectator behavior in an antidot molecule and resonances in a single antidot with three modes.Comment: 4 pages, 3 figures, to be published in Physical Review Letter

Klein Tunneling and Berry Phase π\pi in Bilayer Graphene with a Band Gap

Klein tunneling in gapless bilayer graphene, perfect reflection of electrons injecting normal to a pn junction, is expected to disappear in the presence of energy band gap induced by external gates. We theoretically show that the Klein effect still exists in gapped bilayer graphene, provided that the gaps in the n and p regions are balanced such that the polarization of electron pseudospin has the same normal component to the bilayer plane in the regions. We attribute the Klein effect to Berry phase $\pi$ (rather than the conventional value $2 \pi$ of bilayer graphene) and to electron-hole and time-reversal symmetries. The Klein effect and the Berry phase $\pi$ can be identified in an electronic Veselago lens, an important component of graphene-based electron optics.Comment: Revised version; Main text (4 pages, 4 figures) + Supplemetal material (3 pages, 1 figure

Nonlocal Entanglement of 1D Thermal States Induced by Fermion Exchange Statistics

When two identical fermions exchange their positions, their wave function gains phase factor $-1$. We show that this distance-independent effect can induce nonlocal entanglement in one-dimensional (1D) electron systems having Majorana fermions at the ends. It occurs in the system bulk and has nontrivial temperature dependence. In a system having a single Majorana at each end, the nonlocal entanglement has a Bell-state form at zero temperature and decays as temperature increases, vanishing suddenly at certain finite temperature. In a system having two Majoranas at each end, it is in a cluster-state form and its nonlocality is more noticeable at finite temperature. By contrast, thermal states of corresponding 1D spins do not have nonlocal entanglement

Geometric phase at graphene edge

We study the scattering phase shift of Dirac fermions at graphene edge. We find that when a plane wave of a Dirac fermion is reflected at an edge of graphene, its reflection phase is shifted by the geometric phase resulting from the change of the pseudospin of the Dirac fermion in the reflection. The geometric phase is the Pancharatnam-Berry phase that equals the half of the solid angle on Bloch sphere determined by the propagation direction of the incident wave and also by the orientation angle of the graphene edge. The geometric phase is finite at zigzag edge in general, while it always vanishes at armchair edge because of intervalley mixing. To demonstrate its physical effects, we first connect the geometric phase with the energy band structure of graphene nanoribbon with zigzag edge. The magnitude of the band gap of the nanoribbon, that opens in the presence of the staggered sublattice potential induced by edge magnetization, is related to the geometric phase. Second, we numerically study the effect of the geometric phase on the Veselago lens formed in a graphene nanoribbon. The interference pattern of the lens is distinguished between armchair and zigzag nanoribbons, which is useful for detecting the geometric phase.Comment: 8 pages, 5 figure

Bilayer Graphene Interferometry : Phase Jump and Wave Collimation

We theoretically study the phase of the reflection amplitude of an electron (massive Dirac fermion) at a lateral potential step in Bernal-stacked bilayer graphene. The phase shows anomalous jump of $\pi$, as the electron incidence angle (relative to the normal direction to the step) varies to pass $\pm \pi/4$. The jump is attributed to the Berry phase associated with the pseudospin-1/2 of the electron. This Berry-phase effect is robust against the band gap opening due to the external electric gates generating the step. We propose an interferometry setup in which collimated waves can be generated and tuned. By using the setup, one can identify both the $\pi$ jump and the collimation angle.Comment: 4 pages, 6 figure

Capacitive interaction model for Aharonov-Bohm effects of a quantum Hall antidot

We derive a general capacitive interaction model for an antidot-based interferometer in the integer quantum Hall regime, and study Aharonov-Bohm resonances in a single antidot with multiple bound modes, as a function of the external magnetic field or the gate voltage applied to the antidot. The pattern of Aharonov-Bohm resonances is significantly different from the case of noninteracting electrons. The origin of the difference includes charging effects of excess charges, charge relaxation between the bound modes, the capacitive interaction between the bound modes and the extended edge channels nearby the antidot, and the competition between the single-particle level spacing and the charging energy of the antidot. We analyze the patterns for the case that the number of the bound modes is 2, 3, or 4. The results agree with recent experimental data.Comment: 9 pages, 6 figure