arXiv subjects

Z. Song

Publications and source records attributed to Z. Song.

At least 145 records · Page 8Linked to original sources

arXiv2016

Majorana charges, winding numbers and Chern numbers in quantum Ising models

Mapping a many-body state on a loop in parameter space is a simple way to characterize a quantum state. The connections of such a geometrical representation to the concepts of Chern number and Majorana zero mode are investigated based on a generalized quantum spin system with short and long-range interactions. We show that the topological invariants, the Chern numbers of corresponding Bloch band is equivalent to the winding number in the auxiliary plane, which can be utilized to characterize the phase diagram. We introduce the concept of Majorana charge, the magnitude of which is defined by the distribution of Majorana fermion probability in zero-mode states, and the sign is defined by the type of Majorana fermion. By direct calculations of the Majorana modes we analytically and numerically verify that the Majorana charge is equal to Chern numbers and winding numbers.

quant-ph↗

arXiv2016

Reciprocal and unidirectional scattering of parity-time symmetric structures

Parity-time (PT) symmetry is of great interest. The reciprocal and unidirectional features are intriguing besides the PT symmetry phase transition. Recently, the reciprocal transmission, unidirectional reflectionless and invisibility are intensively studied. Here, we show the reciprocal reflection/transmission in PT -symmetric system is closely related to the type of PT symmetry, that is, the axial (reflection) PT symmetry leads to reciprocal reflection (transmission). The results are further elucidated by studying the scattering of rhombic ring form coupled resonators with enclosed synthetic magnetic flux. The nonreciprocal phase shift induced by the magnetic flux and gain/loss break the parity (P) and time-reversal (T) symmetry but keep the parity-time (PT) symmetry. The reciprocal reflection (transmission) and unidirectional transmission (reflection) are found in the axial (reflection) PT-symmetric ring center. The explorations of symmetry and asymmetry from PT symmetry may shed light on novel one-way optical devices and application of PT metamaterials.

quant-ph↗

arXiv2015

Topological Characterization of Extended Quantum Ising Models

We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic XY model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model corresponds to a circle and the XY model corresponds to an ellipse, while other models yield cardioid, limacon, hypocycloid, and Lissajous curves etc. It is shown that the variation of the ground state energy density, which is a function of the loop, experiences a nonanalytical point when the winding number of the corresponding loop changes. The winding number can serve as a topological quantum number of the quantum phases in the extended quantum Ising model, which sheds some light upon the relation between quantum phase transition and the geometrical order parameter characterizing the phase diagram.

quant-ph↗

arXiv2015

Amplitude control of a quantum state in a non-Hermitian Rice-Mele model driven by an external field

In the Hermitian regime, a Berry phase is always the real number. It may be imaginary for a non-Hermitian system, which leads to amplitude amplification or attenuation of an evolved quantum state. We study the dynamics of the non-Hermitian Rice-Mele model driven by a time-dependent external field. The exact results show that it can have full real spectrum for any value of the field. Several rigorous results are presented for the Berry phase with respect to the varying field. We show that the Berry phase is the same complex constant for any initial state in a single sub-band. Numerical simulation indicates that the amplitude control of a state can be accomplished by a quasi-adiabatic process within a short time.

quant-ph↗

arXiv2015

EPR pairing dynamics in Hubbard model with resonant $U$

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.

quant-ph↗

arXiv2015

Quench field sensitivity of two-particle correlation in a Hubbard model

Short-range interaction can give rise to particle pairing with a short-range correlation, which may be destroyed in the presence of an external field. We study the transition between correlated and uncorrelated particle states in the framework of one-dimensional Hubbard model driven by a field. We show that the long time-scale transfer rate from an initial correlated state to final uncorrelated particle states is sensitive to the quench field strength and exhibits a periodic behavior. This process involves an irreversible energy transfer from the field to particles, leading to a quantum electrothermal effect.

quant-ph↗

arXiv2015

Quantum-state transfer between atom and cavity field in Jaynes-Cummings model

We present a scheme for transferring quantum state between atom and cavity field in Jaynes-Cummings model. It is based on the fact that the atom in a cavity can induce the generation of modified coherent states, which can be shown to be macroscopically distinguishable. The application on two-cavity system provides an alternative scheme for preparation of non-local superpositions of quasi-classical light states. Numerical simulation shows that the proposed schemes are efficient.

quant-ph↗

arXiv2015

Transmission phase lapse in the non-Hermitian Aharonov-Bohm interferometer near the spectral singularity

We study the effect of PT-symmetric imaginary potentials embedded in the two arms of an Aharonov-Bohm interferometer on the transmission phase by finding an exact solution for a concrete tight-binding system. It is observed that the spectral singularity always occurs at k=${\pm}$π/2 for a wide range of fluxes and imaginary potentials. Critical behavior associated with the physics of the spectral singularity is also investigated. It is demonstrated that the quasi-spectral singularity corresponds to a transmission maximum and the transmission phase jumps abruptly by π when the system is swept through this point. Moreover, We find that there exists a pulse-like phase lapse when the imaginary potential approaches the boundary value of the spectral singularity.

quant-ph↗

arXiv2015

Sudden death of particle-pair Bloch oscillation and unidirectional propagation in a one-dimensional driven optical lattice

We study the dynamics of bound pairs in the extended Hubbard model driven by a linear external field. It is shown that two interacting bosons or singlet fermions with nonzero on-site and nearest-neighbor interaction strengths can always form bound pairs in the absence of an external field. There are two bands of bound pairs, one of which may have incomplete wave vectors when it has an overlap with the scattering band, referred to as an imperfect band. In the presence of the external field, the dynamics of the bound pair in the perfect band exhibits distinct Bloch-Zener oscillation (BZO), while in the imperfect band the oscillation presents a sudden death. The pair becomes uncorrelated after the sudden death and the BZO never comes back. Such dynamical behaviors are robust even for the weak-coupling regime and thus can be used to characterize the phase diagram of the bound states.

quant-ph↗

arXiv2015

An impurity-induced gap system as a quantum data bus for quantum state transfer

We introduce a tight-binding chain with a single impurity to act as a quantum data bus for perfect quantum state transfer. Our proposal is based on the weak coupling limit of the two outermost quantum dots to the data bus. First show that the data bus has an energy gap between the ground and first-excited states in the single-particle case induced by the impurity in the single particle case. By connecting two quantum dots to two sites of the data bus, the system can accomplish a high-fidelity and long-distance quantum state transfer. Numerical simulations were performed for a finite system; the results show that the numerical and analytical results of the effective coupling strength agree well with each other. Moreover, we study the robustness of this quantum communication protocol in the presence of disorder in the couplings between the nearest-neighbor quantum dots. We find that the gap of the system plays an important role in robust quantum state transfer.

quant-ph↗

arXiv2014

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.

quant-ph↗

arXiv2014

Conventional quantum phase transition driven by complex parameter in non-Hermitian PT-symmetric Ising model

A conventional quantum phase transition (QPT) can be accessed by varying a real parameter at absolute zero temperature. Motivated by the discovery of the pseudo-Hermiticity of non-Hermitian systems, we explore the QPT in non-Hermitian PT-symmetric Ising model, which is driven by a staggered complex transverse field. Exact solution shows that the Laplacian of the groundstate energy density, with respect to real and imaginary components of the transverse field, diverges on the boundary in the complex plane. The phase diagram indicate that the imaginary transverse field has the effect of shrinking the paramagnet phase. In addition, we also investigate the connection between the geometric phase and the QPT.

quant-ph↗

arXiv2014

Complete particle-pair annihilation as a dynamical signature of the spectral singularity

Motivated by the physical relevance of a spectral singularity of interacting many-particle system, we explore the dynamics of two bosons as well as fermions in one-dimensional system with imaginary delta interaction strength. Based on the exact solution, it shows that the two-particle collision leads to amplitude-reduction of the wave function. For fermion pair, the amplitude-reduction depends on the spin configuration of two particles. In both cases, the residual amplitude can vanish when the relative group velocity of two single-particle Gaussian wave packets with equal width reaches the magnitude of the interaction strength, exhibiting complete particle-pair annihilation at the spectral singularity.

quant-ph↗

arXiv2013

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.

quant-ph↗

arXiv2013

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.

quant-ph↗

arXiv2013

Perfect State Transfer in PT-symmetric Non-Hermitian Networks

We systematically study the parity- and time-reversal (PT) symmetric non-Hermitian version of a quantum network proposed in the paper of Christandl et al. [Phys. Rev. Lett. 92, 187902 (2004)]. The nature of this model shows that it is a paradigm to demonstrate the complex relationship between the pseudo-Hermitian Hamiltonian and its Hermitian counterpart as well as a candidate in the experimental realization to simulate PT-symmetry breaking. We also show that this model allows a conditional perfect state transfer within the unbroken PT-symmetry region but not an arbitrary one. This is due to the fact that the evolution operator at a certain period is equivalent to the PT operator for the real-valued wave function in the elaborate PT-symmetric Hilbert space.

quant-ph↗

arXiv2013

Self-sustained emission in semi-infinite non-Hermitian systems at the exceptional point

Complex potential and non-Hermitian hopping amplitude are building blocks of a non-Hermitian quantum network. Appropriate configuration, such as PT-symmetric distribution, can lead to the full real spectrum. To investigate the underlying mechanism of this phenomenon, we study the phase diagram of a semi-infinite non-Hermitian system. It consists of a finite non-Hermitian cluster and a semi-infinite lead. Based on the analysis of the solution of the concrete systems, it is shown that it can have the full real spectrum without any requirements on the symmetry and the wave function within the lead becomes a unidirectional plane wave at the exceptional point. This universal dynamical behavior is demonstrated as the persistent emission and reflectionless absorption of wave packets in the typical non-Hermitian systems containing the complex on-site potential and non-Hermitian hopping amplitude.

quant-ph↗

arXiv2012

Scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard system

We study scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard model. In the free interaction case, using both analytical and numerical approaches, the metric operator for many-particle is constructed. The derived properties of the metric operator, similarity matrix and equivalent Hamiltonian reflect the fact that all the matrix elements change dramatically with diverging derivatives near the exceptional point. In the nonzero interaction case, it is found that even small on-site interaction can break the PT symmetry drastically. It is demonstrated that the scaling law can be established for the exceptional point in both small and large interaction limit. Based on perturbation and numerical methods, we also find that the phase diagram shows rich structure: there exist multiple regions of unbroken PT symmetry.

cond-mat.stat-mech↗