arXiv subjects

Longwen Zhou

Publications and source records attributed to Longwen Zhou.

At least 55 records · Page 3Linked to original sources

arXiv2020

Floquet higher-order topological phases in momentum space

Higher-order topological phases (HOTPs) are characterized by symmetry-protected bound states at the corners or hinges of the system. In this work, we reveal a momentum-space counterpart of HOTPs in time-periodic driven systems, which are demonstrated in a two-dimensional extension of the quantum double-kicked rotor. The found Floquet HOTPs are protected by chiral symmetry and characterized by a pair of topological invariants, which could take arbitrarily large integer values with the increase of kicking strengths. These topological numbers can also be measured from the chiral dynamics of wave packets. Under open boundary conditions, multiple quartets Floquet corner modes with zero and $π$ quasienergies emerge in the system and coexist with delocalized bulk states at the same quasienergies, forming second-order Floquet topological bound states in continuum. The numbers of these corner modes are further counted by the bulk topological invariants according to the relation of bulk-corner correspondence. Our findings thus extend the study HOTPs to momentum-space lattices, and further uncover the richness of HOTPs and corner-localized bound states in continuum in Floquet driven systems.

quant-ph↗

arXiv2020

Super-exponential diffusion in nonlinear non-Hermitian systems

We investigate the quantum diffusion of a periodically kicked particle subjecting to both nonlinearity induced self-interactions and $\mathcal{PT}$-symmetric potentials. We find that, due to the interplay between the nonlinearity and non-Hermiticity, the expectation value of mean square of momentum scales with time in a super-exponential form $\langle p^2(t)\rangle\propto\exp[β\exp(αt)]$, which is faster than any known rates of quantum diffusion. In the $\mathcal{PT}$-symmetry-breaking phase, the intensity of a state increases exponentially with time, leading to the exponential growth of the interaction strength. The feedback of the intensity-dependent nonlinearity further turns the interaction energy into the kinetic energy, resulting in a super-exponential growth of the mean energy. These theoretical predictions are in good agreement with numerical simulations in a $\cal{PT}$-symmetric nonlinear kicked particle. Our discovery establishes a new mechanism of diffusion in interacting and dissipative quantum systems. Important implications and possible experimental observations are discussed.

nlin.CD↗

arXiv2020

Dual topological characterization of non-Hermitian Floquet phases

Non-Hermiticity is expected to add far more physical features to the already rich Floquet topological phases of matter. Nevertheless, a systematic approach to characterize non-Hermitian Floquet topological matter is still lacking. In this work we introduce a dual scheme to characterize the topology of non-Hermitian Floquet systems in momentum space and in real space, using a piecewise quenched nonreciprocal Su-Schrieffer-Heeger model for our case studies. Under the periodic boundary condition, topological phases are characterized by a pair of experimentally accessible winding numbers that make jumps between integers and half-integers. Under the open boundary condition, a Floquet version of the so-called open boundary winding number is found to be integers and can predict the number of pairs of zero and $π$ Floquet edge modes coexisting with the non-Hermitian skin effect. Our results indicate that a dual characterization of non-Hermitian Floquet topological matter is necessary and also feasible because the formidable task of constructing the celebrated generalized Brillouin zone for non-Hermitian Floquet systems with multiple hopping length scales can be avoided. This work hence paves a way for further studies of non-Hermitian physics in non-equilibrium systems.

cond-mat.mes-hall↗

arXiv2020

Non-Hermitian Floquet second order topological insulators in periodically quenched lattices

Higher-order topological phases are characterized by protected states localized at the corners or hinges of the system. By applying time-periodic quenches to a two-dimensional lattice with balanced gain and loss, we obtain a rich variety of non-Hermitian Floquet second order topological insulating phases. Each of the phases is characterized by a pair of integer topological invariants, which predict the numbers of Floquet corner modes at zero and $π$ quasienergies. We establish the topological phase diagram of the model, and find a series of non-Hermiticity induced transitions between different Floquet second order topological phases. We further generalize the mean chiral displacement to two-dimensional non-Hermitian systems, and use it to extract the topological invariants of our model dynamically. This work thus extend the study of higher-order topological matter to more generic nonequilibrium settings, in which the interplay between Floquet engineering and non-Hermiticity yields fascinating new phases.

cond-mat.mes-hall↗

arXiv2020

Non-Hermitian Floquet phases with even-integer topological invariants in a periodically quenched two-leg ladder

Periodically driven non-Hermitian systems could possess exotic nonequilibrium phases with unique topological, dynamical and transport properties. In this work, we introduce an experimentally realizable two-leg ladder model subjecting to both time-periodic quenches and non-Hermitian effects, which belongs to an extended CII symmetry class. Due to the interplay between drivings and nonreciprocity, rich non-Hermitian Floquet topological phases emerge in the system, with each of them been characterized by a pair of even-integer topological invariants $(w_{0},w_π)\in2\mathbb{Z}\times2\mathbb{Z}$. Under the open boundary condition, these invariants further predict the number of zero- and $π$-quasienergy modes localized around the edges of the system. We finally construct a generalized version of the mean chiral displacement, which could be employed as a dynamical probe to the topological invariants of non-Hermitian Floquet phases in the CII symmetry class. Our work thus introduces a new type of non-Hermitian Floquet topological matter, and further reveals the richness of topology and dynamics in driven open systems.

quant-ph↗

arXiv2020

Interband coherence induced correction to Thouless pumping: possible observation in cold-atom systems

In Thouless pump, the charge transport in a one-dimensional insulator over an adiabatic cycle is topologically quantized. For nonequilibrium initial states, however, interband coherence will induce a previously unknown contribution to Thouless pumping. Though not geometric in nature, this contribution is independent of the time scale of the pumping protocol. In this work, we perform a detailed analysis of our previous finding [Phys. Rev. B 91, 085420 (2015)] in an already available cold-atom setup. We show that initial states with interband coherence can be obtained via a quench of the system's Hamiltonian. Adiabatic pumping in the post-quench system are then examined both theoretically and numerically, in which the interband coherence is shown to play an important role and can hence be observed experimentally. By choosing adiabatic protocols with different switching-on speeds, we also show that the contribution of interband coherence to adiabatic pumping can be tuned. It is further proposed that the interband coherence induced correction to Thouless pumping may be useful in capturing a topological phase transition point. All our results have direct experimental interests.

cond-mat.mes-hall↗

arXiv2020

Non-Hermitian Floquet topological phases in the double-kicked rotor

Dynamical kicking systems possess rich topological structures. In this work, we study Floquet states of matter in a non-Hermitian extension of double kicked rotor model. Under the on-resonance condition, we find various non-Hermitian Floquet topological phases, with each being characterized by a pair of topological winding numbers. A generalized mean chiral displacement is introduced to detect these winding numbers dynamically in two symmetric time frames. Furthermore, by mapping the system to a periodically quenched lattice model, we obtain the topological edge states and unravel the bulk-edge correspondence of the non-Hermitian double kicked rotor. These results uncover the richness of Floquet topological states in non-Hermitian dynamical kicking systems.

quant-ph↗

arXiv2020

Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder

Floquet engineering has the advantage of generating new phases with large topological invariants and many edge states by simple driving protocols. In this work, we propose an approach to obtain Floquet edge states with fourfold degeneracy and even-integer topological characterizations in a spinful Creutz ladder model, which is realizable in current experiments. Putting the ladder under periodic quenches, we found rich Floquet topological phases in the system, which belong to the symmetry class CII. Each of these phases is characterized by a pair of even integer topological invariants $(w_{0},w_π) \in 2\mathbb{Z} \times 2 \mathbb{Z}$, which can take arbitrarily large values with the increase of driving parameters. Under the open boundary condition, we further obtain multiple quartets of topological edge states with quasienergies zero and $π$ in the system. Their numbers are determined by the bulk topological invariants $(w_{0},w_π)$ due to the bulk-edge correspondence. Finally, we propose a way to dynamically probe the Floquet topological phases in our system by measuring a generalized mean chiral displacement. Our findings thus enrich the family of Floquet topological matter, and put forward the detection of their topological properties.

cond-mat.mes-hall↗

arXiv2020

Dynamical characterization of non-Hermitian Floquet topological phases in one-dimension

Non-Hermitian topological phases in static and periodically driven systems have attracted great attention in recent years. Finding dynamical probes for these exotic phases would be of great importance in the detection and application of their topological properties. In this work, we propose a systematic approach to dynamically characterize non-Hermitian Floquet topological phases in one-dimension with chiral symmetry. We show that the topological invariants of a chiral symmetric Floquet system can be fully determined by measuring the winding angles of its time-averaged spin textures. We further purpose a piecewise quenched lattice model with rich non-Hermitian Floquet topological phases, in which our theoretical predictions are numerically demonstrated and compared with another approach utilizing the mean chiral displacement of a wavepacket.

cond-mat.mes-hall↗

arXiv2020

Non-Hermitian Floquet topological superconductors with multiple Majorana edge modes

Majorana edge modes are candidate elements of topological quantum computing. In this work, we purpose a Floquet engineering approach to generate arbitrarily many non-Hermitian Majorana zero and $π$ modes at the edges of a one-dimensional topological superconductor. Focusing on a Kitaev chain with periodically kicked superconducting pairings and gain/losses in the chemical potential or nearest neighbor hopping terms, we found rich non-Hermitian Floquet topological superconducting phases, which are originated from the interplay between drivings and non-Hermitian effects. Each of the phases is characterized by a pair of topological winding numbers, which can in principle take arbitrarily large integer values thanks to the applied driving fields. Under open boundary conditions, these winding numbers also predict the number of degenerate Majorana edge modes with quasienergies zero and $π$. Our findings thus expand the family of Floquet topological phases in non-Hermitian settings, with potential applications in realizing environmentally robust Floquet topological quantum computations.

cond-mat.mes-hall↗

arXiv2019

Revealing many-body effects on interband coherence through adiabatic charge pumping

The adiabatic charge pumping of a non-equilibrium state of spinless fermions in a one-dimensional lattice is investigated, with an emphasis placed on its usefulness in revealing many-body interaction effects on interband coherence. For a non-interacting system, the pumped charge per adiabatic cycle depends not only on the topology of the occupied bands but also on the interband coherence in the initial state. This insight leads to an interesting opportunity for quantitatively observing how quantum coherence is affected by many-body interaction that is switched on for a varying duration prior to adiabatic pumping. In particular, interband coherence effects can be clearly observed by adjusting the switch-on rates with different adiabatic pumping protocols and by scanning the duration of many-body interaction prior to adiabatic pumping. The time dependence of single-particle interband coherence in the presence of many-body interaction can then be examined in detail. As a side but interesting result, for relatively weak interaction strength, it is found that the difference in the pumped charges between different pumping protocols vanishes if a coherence measure defined from the single-particle density matrix in the sublattice representation reaches its local minima. Our results hence provide an interesting means to quantitatively probe the dynamics of quantum coherence in the presence of many-body interaction (e.g., in a thermalization process).

cond-mat.mes-hall↗

arXiv2019

Coupled-wire construction of static and Floquet second-order topological insulators

Second-order topological insulators (SOTI) exhibit protected gapless boundary states at their hinges or corners. In this paper, we propose a generic means to construct SOTIs in static and Floquet systems by coupling one-dimensional topological insulator wires along a second dimension through dimerized hopping amplitudes. The Hamiltonian of such SOTIs admits a Kronecker sum structure, making it possible for obtaining its features by analyzing two constituent one-dimensional lattice Hamiltonians defined separately in two orthogonal dimensions. The resulting topological corner states do not rely on any delicate spatial symmetries, but are solely protected by the chiral symmetry of the system. We further utilize our idea to construct Floquet SOTIs, whose number of topological corner states is arbitrarily tunable via changing the hopping amplitudes of the system. Finally, we propose to detect the topological invariants of static and Floquet SOTIs constructed following our approach in experiments by measuring the mean chiral displacements of wavepackets.

cond-mat.mes-hall↗

arXiv2019

Floquet dynamical quantum phase transitions

Dynamical quantum phase transitions (DQPTs) are manifested by time-domain nonanalytic behaviors of many-body systems.Introducing a quench is so far understood as a typical scenario to induce DQPTs.In this work, we discover a novel type of DQPTs, termed "Floquet DQPTs", as intrinsic features of systems with periodic time modulation.Floquet DQPTs occur within each period of continuous driving, without the need for any quenches.In particular, in a harmonically driven spin chain model, we find analytically the existence of Floquet DQPTs in and only in a parameter regime hosting a certain nontrivial Floquet topological phase. The Floquet DQPTs are further characterized by a dynamical topological invariant defined as the winding number of the Pancharatnam geometric phase versus quasimomentum.These findings are experimentally demonstrated with a single spin in diamond.This work thus opens a door for future studies of DQPTs in connection with topological matter.

quant-ph↗

arXiv2018

Non-Hermitian Floquet topological phases with arbitrarily many real-quasienergy edge states

Topological states of matter in non-Hermitian systems have attracted a lot of attention due to their intriguing dynamical and transport properties. In this study, we propose a periodically driven non-Hermitian lattice model in one-dimension, which features rich Floquet topological phases. The topological phase diagram of the model is derived analytically. Each of its non-Hermitian Floquet topological phases is characterized by a pair of integer winding numbers, counting the number of real 0- and π-quasienergy edge states at the boundaries of the lattice. Non-Hermiticity induced Floquet topological phases with unlimited winding numbers are found, which allow arbitrarily many real 0- and π-quasienergy edge states to appear in the complex quasienergy bulk gaps in a well-controlled manner. We further suggest to probe the topological winding numbers of the system by dynamically imaging the stroboscopic spin textures of its bulk states.

cond-mat.mes-hall↗

arXiv2018

Experimental Observation of a Generalized Thouless Pump with a Single Spin

Adiabatic cyclic modulation of a one-dimensional periodic potential will result in quantized charge transport, which is termed the Thouless pump. In contrast to the original Thouless pump restricted by the topology of the energy band, here we experimentally observe a generalized Thouless pump that can be extensively and continuously controlled. The extraordinary features of the new pump originate from interband coherence in nonequilibrium initial states, and this fact indicates that a quantum superposition of different eigenstates individually undergoing quantum adiabatic following can also be an important ingredient unavailable in classical physics. The quantum simulation of this generalized Thouless pump in a two-band insulator is achieved by applying delicate control fields to a single spin in diamond. The experimental results demonstrate all principal characteristics of the generalized Thouless pump. Because the pumping in our system is most pronounced around a band-touching point, this work also suggests an alternative means to detect quantum or topological phase transitions.

quant-ph↗

arXiv2018

Recipe for creating an arbitrary number of Floquet chiral edge states

Floquet states of periodically driven systems could exhibit rich topological properties. Many of them are absent in their static counterparts. One such example is the chiral edge states in anomalous Floquet topological insulators, whose description requires a new topological invariant and a novel type of bulk-edge correspondence. In this work, we propose a prototypical quenched lattice model, whose two Floquet bands could exchange their Chern numbers periodically and alternatively via touching at quasienergies 0 and $π$ under the change of a single system parameter. This process in principle allows the generation of as many Floquet chiral edge states as possible in a highly controllable manner. The quantized transmission of these edge states are extracted from the Floquet scattering matrix of the system. The flexibility in controlling the number of topological edge channels provided by our scheme could serve as a starting point for the engineering of robust Floquet transport devices.

cond-mat.mes-hall↗

arXiv2018

Floquet topological phases in a spin-1/2 double kicked rotor

The double kicked rotor model is a physically realizable extension of the paradigmatic kicked rotor model in the study of quantum chaos. Even before the concept of Floquet topological phases became widely known, the discovery of the Hofstadter butterfly spectrum in the double kicked rotor model [J. Wang and J. Gong, Phys. Rev. A 77, 031405 (2008)] already suggested the importance of periodic driving to the generation of unconventional topological matter. In this work, we explore Floquet topological phases of a double kicked rotor with an extra spin-1/2 degree of freedom. The latter has been experimentally engineered in a quantum kicked rotor recently by loading Rb87 condensates into a periodically pulsed optical lattice. Under the on-resonance condition, the spin-1/2 double kicked rotor admits fruitful topological phases due to the interplay between its external and internal degrees of freedom. Each of these topological phases is characterized by a pair of winding numbers, whose combination predicts the number of topologically protected 0 and π-quasienergy edge states in the system. Topological phases with arbitrarily large winding numbers can be easily found by tuning the kicking strength. We discuss an experimental proposal to realize this model in kicked Rb87 condensates, and suggest to detect its topological invariants by measuring the mean chiral displacement in momentum space.

cond-mat.quant-gas↗

arXiv2017

Dynamical quantum phase transitions in non-Hermitian lattices

In closed quantum systems, a dynamical phase transition is identified by nonanalytic behaviors of the return probability as a function of time. In this work, we study the nonunitary dynamics following quenches across exceptional points in a non-Hermitian lattice realized by optical resonators. Dynamical quantum phase transitions with topological signatures are found when an isolated exceptional point is crossed during the quench. A topological winding number defined by a real, noncyclic geometric phase is introduced, whose value features quantized jumps at critical times of these phase transitions and remains constant elsewhere, mimicking the plateau transitions in quantum Hall effects. This work provides a simple framework to study dynamical and topological responses in non-Hermitian systems.

cond-mat.stat-mech↗