arXiv subjects

Z. C. Shi

Publications and source records attributed to Z. C. Shi.

13 recordsLinked to original sources

arXiv2017

Engineering the coupling between Majorana bound states

We study the coupling between Majorana bound states (CMBS), which is mediated by a topologically trivial chain in the presence of pairing coupling and long-range coupling. The results show that CMBS can be enhanced by the pairing coupling and long-range coupling of the trivial chain. When driving the trivial chain by periodic driving field, we deduce the analytical expressions of CMBS in the high-frequency limit, and demonstrate that CMBS can be modulated by the frequency and amplitude of driving field. Finally we exhibit the application of tunable CMBS in realizing quantum logic gates.

quant-ph↗

arXiv2017

The influence of localization transition on dynamical properties for an extended Aubry-André-Harper model

We show the localization transition and its effect on two dynamical processes for an extended Aubry-André-Harper model with incommensurate on-site and hopping potentials. After specifying an extended Aubry-André-Harper model, we check the localization transition for all the eigenstates and eigenenergy band splitting behavior versus a system parameter. To examine the effect of localization transition on dynamical processes, firstly, the slowly pumping of the edge states are examined. In the dynamical processes, the system acts as conductor for the excitation in the nonlocal region and insulator in the localized region. Then by quantum Lyapunov control method with different control Hamiltonians, we prepare an edge localized state which exists in the nonlocal region. Compared to that in the nonlocal region, the control effect is suppressed in the localized region. Then we employ the entropy and occupation imbalance between even and odd sites to indicate the localization transition further. Finally, the experimental schemes based on cold atoms trapped quasiperiodic optical lattice and coupled optical waveguide arrays are suggested.

cond-mat.dis-nn↗

arXiv2017

Optical Schrödinger Cat States in One Mode and two Coupled-Modes Subject to Environments

Taking the decoherence into account, we investigate nonclassical features of the optical Schrödinger cat states in one mode and two coupled-modes systems with two-photon driving. In the one mode system, the relationship between the Schrödinger cat states and the system parameters is derived. We observe that in the presence of single-photon decay the steady states would be a mixture of Schrödinger cats. The dynamics and steady states of such a cat versus single-photon decay are examined. In the two coupled-modes cases with linear and nonlinear couplings, the dynamics of entanglement and mutual information are examined with two different initial states and single-photon decay. Compared to the linear coupling case, more complicated structure appears in the Wigner function in the nonlinear coupling case. The joint quadrature distributions are also explored. Such nonclassical states can be used not only in exploring the boundary between the classical and the quantum worlds but also in quantum metrology and quantum information processing.

quant-ph↗

arXiv2017

Effect of loss on the topological features of dimer chain described by the extended Aubry-André-Harper model

By introducing loss to one sublattice of a dimer chain described by the extended Aubry-André or Harper (AAH) model, we study the topological features including the edge states, spectrum and winding number of the chain. We find that the parameter region for the system to have real band-gap-closing is increased due to the loss, and the average displacement of the single excitation can still witness the topological features of the chain in the presence of loss. The robustness of the zero energy eigenstate against four kinds of disorders is also examined. A feasible experiment setup based on coupled waveguides to observe the prediction of this paper is proposed.

cond-mat.quant-gas↗

arXiv2016

Edge state preparation in one dimensional lattice by quantum Lyapunov control

Quantum Lyapunov control uses a feedback control methodology to determine control fields which are applied to control quantum systems in an open-loop way. In this work, we adopt two Lyapunov control schemes to prepare an edge state for a fermionic chain consisted of cold atoms loaded in an optical lattice. Such a chain can be described by the Harper model. Corresponding to the two schemes, state distance and state error Lyapunov functions are considered. The results show that both the schemes are effective to prepare the edge state within a wide range of parameters. We found that the edge state can be prepared with high fidelity even \textbf{if} there are moderate fluctuations in on-site or hopping potentials. Both control schemes can be extended to similar chains (3$m+d$, $d$=2) of different lengths. Since regular amplitude control field is easier to apply in practice, amplitude-modulated control fields are used to replace the unmodulated one to prepare the edge state. Such control approaches provide tools to explore edge states for one dimensional topological materials.

cond-mat.quant-gas↗

arXiv2016

Entangled states of two quantum dots mediated by Majorana fermions

With the assistance of a pair of Majorana fermions, we propose schemes to entangle two quantum dots by Lyapunov control in the charge and spin degrees of freedom. Four different schemes are considered, i.e., the teleportation scheme, the crossed Andreev reflection scheme, the intradot spin flip scheme, and the scheme beyond the intradot spin flip. We demonstrate that the entanglement can be generated by modulating the chemical potential of quantum dots with square pulses, which is easily realized in practice. In contrast to Lyapunov control, the preparation of entangled states by adiabatic passage is also discussed. There are two advantages in the scheme by Lyapunov control, i.e., it is flexible to choose a control Hamiltonian, and the control time is much shorter with respect to the scheme by adiabatic passage. Furthermore, we find that the results are quite different by different adiabatic passages in the scheme beyond the intradot spin flip, which can be understood as an effect of quantum destructive interference.

quant-ph↗

arXiv2016

Population transfer driven by far-off-resonant fields

For a two-level system, it is believed that a far-off-resonant driving can not help coherent population transfer between the states. In this work, we propose a scheme to implement the coherent transfer with far-off-resonant driving. The scheme works well with both constant driving and Gaussian driving. The total time to finish population transfer is also minimized by optimizing the detuning and coupling constants. We find that the scheme is sensitive to spontaneous emission much more than dephasing. It might find potential applications in X-ray quantum optics and population transfer in Rydberg atoms as well.

quant-ph↗

arXiv2016

Preparation of edge states by shaking boundaries

Preparing topological states of quantum matter, such as edge states, is one of the most important directions in condensed matter physics. In this work, we present a proposal to prepare edge states in Aubry-Andr$\acute{\textrm{e}}$-Harper (AAH) model with open boundaries, which takes advantage of Lyapunov control to design operations. We show that edge states can be obtained with almost arbitrary initial states. A numerical optimalization for the control is performed and the dependence of control process on the system size is discussed. The merit of this proposal is that the shaking exerts only on the boundaries of the model. As a by-product, a topological entangled state is achieved by elaborately designing the shaking scheme.

quant-ph↗

arXiv2015

Floquet theorem for open systems and its applications

For a closed system with periodic driving, Floquet theorem tells that the time evolution operator can be written as $ U(t,0)\equiv P(t)e^{\frac{-i}{\hbar}H_F t}$ with $P(t+T)=P(t)$, and $H_F$ is Hermitian and time-independent called Floquet Hamiltonian. In this work, we extend the Floquet theorem from closed systems to open systems described by a Lindblad master equation that is periodic in time. Lindbladian expansion in powers of $\frac 1 ω$ is derived, where $ω$ is the driving frequency. Two examples are presented to illustrate the theory. We find that appropriate trace preserving time-independent Lindbladian of such a periodically driven system can be constructed by the application of open system Floquet theory, and it agrees well with the exact dynamics in the high frequency limit.

quant-ph↗

arXiv2015

Hall conductance of two-band systems in a quantized field

Kubo formula gives a linear response of a quantum system to external fields, which are classical and weak with respect to the energy of the system. In this work, we take the quantum nature of the external field into account, and define a Hall conductance to characterize the linear response of a two-band system to the quantized field. The theory is then applied to topological insulators. Comparisons with the traditional Hall conductance are presented and discussed.

cond-mat.mes-hall↗

arXiv2015

Preparation of topological modes by Lyapunov control

By Lyapunov control, we present a proposal to drive quasi-particles into a topological mode in quantum systems described by a quadratic Hamiltonian. The merit of this control is the individual manipulations on the boundary sites. We take the Kitaev's chain as an illustration for Fermi systems and show that an arbitrary excitation mode can be steered into the Majorana zero mode by manipulating the chemical potential of the boundary sites. For Bose systems, taking the noninteracting Su-Schrieffer-Heeger (SSH) model as an example, we illustrate how to drive the system into the edge mode. The sensitivity of the fidelity to perturbations and uncertainties in the control fields and initial modes is also examined. The experimental feasibility of the proposal and the possibility to replace the continuous control field with square wave pulses is finally discussed.

quant-ph↗

arXiv2015

Quantum gates by periodic driving

Topological quantum computation has been extensively studied due to its robustness against decoherence. A conventional way to realize it is by adiabatic operations---it requires relatively long time to accomplish so that the speed of quantum computation slows down. In this work, we present a method to realize topological quantum computation by periodic driving. Compared to the adiabatic evolution, the total operation time can be regulated arbitrarily by the amplitude and frequency of the periodic driving. For the sinusoidal driving, we give an expression for the total operation time in the high-frequency limit. For the square wave driving, we derive an exact analytical expression for the evolution operator without any approximations, and show that the amplitude and frequency of driving field depend on its period and total operation time. This could provide a new direction in regulations of the operation time in topological quantum computation.

cond-mat.mes-hall↗

arXiv2015

Robust state transfer with high fidelity in spin-1/2 chains by Lyapunov control

Based on the Lyapunov control, we present a scheme to realize state transfer with high fidelity by only modulating the boundary spins in a quantum spin-1/2 chain. Recall that the conventional transmission protocols aim at nonstationary state (or information) transfer from the first spin to the end spin at a fixed time. The present scheme possesses the following advantages. First, the scheme does not require precise manipulations of the control time. Second, it is robust against uncertainties in the initial states and fluctuations in the control fields. Third, the controls are exerted only on the boundary sites of the chain. It works for variable spin-1/2 chains with different periodic structures and has good scalability. The feasibility to replace the control fields by square pules is explored, which simplifies the realization in experiments.

quant-ph↗