Asymmetric transmission through a flux-controlled non-Hermitian scattering center

We study the possibility of asymmetric transmission induced by a non-Hermitian scattering center embedded in a one-dimensional waveguide, motivated by the aim of realizing quantum diode in a non-Hermitian system. It is shown that a $\mathcal{PT}$ symmetric non-Hermitian scattering center always has symmetric transmission although the dynamics within the isolated center can be unidirectional, especially at its exceptional point. We propose a concrete scheme based on a flux-controlled non-Hermitian scattering center, which comprises a non-Hermitian triangular ring threaded by an Aharonov-Bohm flux. The analytical solution shows that such a complex scattering center acts as a diode at the resonant energy level of the spectral singularity, exhibiting perfect unidirectionality of the transmission. The connections between the phenomena of the asymmetric transmission and reflectionless absorption are also discussed.Comment: 6 pages, 5 figure

Geometric phase and phase diagram for non-Hermitian quantum XY model

We study the geometric phase for the ground state of a generalized one-dimensional non-Hermitian quantum XY model, which has transverse-field-dependent intrinsic rotation-time reversal symmetry. Based on the exact solution, this model is shown to have full real spectrum in multiple regions for the finite size system. The result indicates that the phase diagram or exceptional boundary, which separates the unbroken and broken symmetry regions corresponds to the divergence of the Berry curvature. The scaling behaviors of the groundstate energy and Berry curvature are obtained in an analytical manner for a concrete system.Comment: 6 pages, 3 figure

Momentum-independent reflectionless transmission in the non-Hermitian time-reversal symmetric system

We theoretically study the non-Hermitian systems, the non-Hermiticity of which arises from the unequal hopping amplitude (UHA) dimers. The distinguishing features of these models are that they have full real spectra if all of the eigenvectors are time-reversal (T) symmetric rather than parity-time-reversal (PT) symmetric, and that their Hermitian counterparts are shown to be an experimentally accessible system, which have the same topological structures as that of the original ones but modulated hopping amplitudes within the unbroken region. Under the reflectionless transmission condition, the scattering behavior of momentum-independent reflectionless transmission (RT) can be achieved in the concerned non-Hermitian system. This peculiar feature indicates that, for a certain class of non-Hermitian systems with a balanced combination of the RT dimers, the defects can appear fully invisible to an outside observer.Comment: 9 pages, 4 figures. arXiv admin note: text overlap with arXiv:1008.5306 by other author

Non-Hermitian anisotropic XY model with intrinsic rotation-time reversal symmetry

We systematically study the non-Hermitian version of the one-dimensional anisotropic XY model, which in its original form, is a unique exactly solvable quantum spin model for understanding the quantum phase transition. The distinguishing features of this model are that it has full real spectrum if all the eigenvectors are intrinsic rotation-time reversal (RT) symmetric rather than parity-time reversal (PT) symmetric, and that its Hermitian counterpart is shown approximately to be an experimentally accessible system, an isotropic XY spin chain with nearest neighbor coupling. Based on the exact solution, exceptional points which separated the unbroken and broken symmetry regions are obtained and lie on a hyperbola in the thermodynamic limit. It provides a nice paradigm to elucidate the complex quantum mechanics theory for a quantum spin system.Comment: 7 pages, 3 figure

Partial topological Zak phase and dynamical confinement in non-Hermitian bipartite system

Unlike a Chern number in $2$D and $3$D topological system, Zak phase takes a subtle role to characterize the topological phase in $1$D. On the one hand, it is not a gauge invariant, on the other hand, the Zak phase difference between two quantum phases can be used to identify the topological phase transitions. A non-Hermitian system may inherit some characters of a Hermitian system, such as entirely real spectrum, unitary evolution, topological energy band, etc. In this paper, we study the influence of non-Hermitian term on the Zak phase for a class of non-Hermitian systems. We show exactly that the real part of the Zak phase remains unchanged in a bipartite lattice. In a concrete example, $1$D Su-Schrieffer-Heeger (SSH) model, we find that the real part of Zak phase can be obtained by an adiabatic process. To demonstrate this finding, we investigate a scattering problem for a time-dependent scattering center, which is a magnetic-flux-driven non-Hermitian SSH ring. Owing to the nature of the Zak phase, the intriguing features of this design are the wave-vector independence and allow two distinct behaviors, perfect transmission or confinement, depending on the timing of a flux impulse threading the ring. When the flux is added during a wavepacket travelling within the ring, the wavepacket is confined in the scatter partially. Otherwise, it exhibits perfect transmission through the scatter. Our finding extends the understanding and broaden the possible application of geometric phase in a non-Hermitian system.Comment: 11 pages, 7 figure

EPR pairing dynamics in Hubbard model with resonant UU

We study the dynamics of the collision between two fermions in Hubbard model with on-site interaction strength $U$. The exact solution shows that the scattering matrix for two-wavepacket collision is separable into two independent parts, operating on spatial and spin degrees of freedom, respectively. The S-matrix for spin configuration is equivalent to that of Heisenberg-type pulsed interaction with the strength depending on $U$ and relative group velocity $\upsilon _{r}$. This can be applied to create distant EPR pair, through a collision process for two fermions with opposite spins in the case of $\left\vert \upsilon _{r}/U\right\vert =1$,\ without the need for temporal control and measurement process. Multiple collision process for many particles is also discussed.Comment: 7 pages, 3 figure

The sinusoidal periodicity nature for M>=5 global earthquakes

By using the M>=5 global earthquake data for Jan. 1950 to Dec. 2015, we performed statistical analyses for the parameters magnitude, time, and depth on a yearly scale. The magnitude spectrum, which is the earthquake number accumulated at different magnitudes, had an exponential distribution. For the first time, we report a very significant characteristic of the sinusoidal periodic variation in the spectral index. The cycle of the sine function fitting was 30.98 years. The concept of annual equivalent total magnitude (AETM) of total released energy for each year was introduced and the trend variation of AETM year by year was studied. Overall, the global AETM of earthquakes with M>=5 displayed a certain upward trend as the years elapsed. At the same time, the change of the average epicenter depth of the global earthquakes (M>=5) in each year was analyzed

Improving quantum dense key distribution

The capacity of the quantum dense key distribution (QDKD) [Phys. Rev. A69, 032310 (2004)] is doubled by introducing the dense coding. The security of the improved QDKD against eavesdropping is pointed out to be easily proven. In both the original QDKD and the present improved QDKD, a strategy to double the efficiency of generating the secret key with given length is proposed. In addition, we point out a leak of security of the original QDKD and fix it

Deterministic secure direct communication by using swapping quantum entanglement and local unitary operations

A deterministic direct quantum communication protocol by using swapping quantum entanglement and local unitary operations is proposed in this paper. A set of ordered EPR pairs in one of the four Bell states is used. For each pair, each of the two legitimate users owns a photon of the entangled pair via quantum channel. The pairs are divided into two types of group, i.e., the checking groups and the encoding-decoding groups. In the checking groups, taking advantage of the swapping quantum entanglement and Alice's (the message sender's) public announcement, the eavesdropping can be detected provided that the number of the checking groups is big enough. After insuring the security of the quantum channel, Alice encodes her bits via the local unitary operations on the encoding-decoding groups. Then she performs her Bell measurements on her photons and publicly announces her measurement results. After her announcement, the message receiver Bob performs his Bell measurements on his photons and directly extracts the encoding bits by using the property of the quantum entanglement swapping. The security of the present scheme is also discussed: under the attack scenarios to our best knowledge, the scheme is secure

Generalizing Several Theoretical Deterministic Secure Direct Bidirectional Communications to Improve Their Capacities

Several theoretical Deterministic Secure Direct Bidirectional Communication protocols are generalized to improve their capacities by introducing the superdense-coding in the case of high-dimension quantum states