arXiv subjects

Jiangbin Gong

Publications and source records attributed to Jiangbin Gong.

At least 163 records · Page 9Linked to original sources

arXiv2014

Aspects of Floquet Bands and Topological Phase Transitions in a Continuously Driven Superlattice

Recently the creation of novel topological states of matter by a periodic driving field has attracted great attention. To motivate further experimental and theoretical studies, we investigate interesting aspects of Floquet bands and topological phase transitions in a continuously driven Harper model. In such a continuously driven system with an odd number of Floquet bands, the bands are found to have nonzero Chern numbers in general and topological phase transitions take place as we tune various system parameters, such as the amplitude or the period of the driving field. The nontrivial Floquet band topology results in a quantized transport of Wannier states in the lattice space. For certain parameter choices, very flat yet topologically nontrivial Floquet bands may also emerge, a feature that is potentially useful for the simulation of physics of strongly correlated systems. Some cases with an even number of Floquet bands may also have intriguing Dirac cones in the spectrum. Under open boundary conditions, anomalous counter-propagating chiral edge modes and degenerate zero modes are also found as the system parameters are tuned. These results should be of experimental interest because a continuously driven system is easier to realize than a periodically kicked system.

cond-mat.quant-gas↗

arXiv2014

Zeno and anti-Zeno effects on Dephasing

Quantum Zeno and anti-Zeno effects on pure dephasing are studied using exactly solvable microscopic models. The crossover between these two opposite effects is investigated. The case of a single two-level system undergoing dephasing is already different from the previously studied population decay problem, even without taking into account any back action from the environment. For many two-level systems interacting with a common environment, multiple transitions between Zeno and anti-Zeno regimes are predicted. Finally, if the system-environment coupling strength is not weak, we show that the nontrivial evolution of the environment between measurements can considerably alter the quantum Zeno and anti-Zeno effects.

quant-ph↗

arXiv2013

Boosting work characteristics and overall heat engine performance via shortcuts to adiabaticity: quantum and classical systems

Under a general framework, shortcuts to adiabatic processes are shown to be possible in classical systems. We then study the distribution function of the work done on a small system initially prepared at thermal equilibrium. It is found that the work fluctuations can be significantly reduced via shortcuts to adiabatic processes. For example, in the classical case probabilities of having very large or almost zero work values are suppressed. In the quantum case negative work may be totally removed from the otherwise non-positive-definite work values. We also apply our findings to a micro Otto-cycle-based heat engine. It is shown that the use of shortcuts, which directly enhances the engine output power, can also increase the heat engine efficiency substantially, in both quantum and classical regimes.

quant-ph↗

arXiv2013

Role of initial system-environment correlations: A master equation approach

In order to achieve practical implementations of emerging quantum technologies, it is important to have a firm understanding of the dynamics of realistic quantum open systems. Master equations provide a widely used tool in this regard. In this work, we first construct a master equation, valid for weak system-environment coupling, which explicitly takes into account the impact of preparing an initial system state from an equilibrium system-environment state that has system-environment correlations. We then investigate the role of initial system-environment correlations using this master equation for a system consisting of many two-level atoms interacting with a common environment. We show that, in general, due to the initial system-environment correlations before a state preparation, the quantum state of the system can evolve at a faster time-scale. Moreover, we also consider different initial state preparations, and demonstrate that the influence of state preparations depends on the initial states prepared. Our results can be of interest to many topics based on quantum open systems where system-environment correlation effects have been neglected before.

quant-ph↗

arXiv2013

Kicked-Harper model vs On-Resonance Double Kicked Rotor Model: From Spectral Difference to Topological Equivalence

Recent studies have established that, in addition to the well-known kicked Harper model (KHM), an on-resonance double kicked rotor model (ORDKR) also has Hofstadter's butterfly Floquet spectrum, with strong resemblance to the standard Hofstadter's spectrum that is a paradigm in studies of the integer quantum Hall effect. Earlier it was shown that the quasi-energy spectra of these two dynamical models (i) can exactly overlap with each other if an effective Planck constant takes irrational multiples of 2*pi and (ii) will be different if the same parameter takes rational multiples of 2*pi. This work makes some detailed comparisons between these two models, with an effective Planck constant given by 2*pi M/N, where M and N are coprime and odd integers. It is found that the ORDKR spectrum (with two periodic kicking sequences having the same kick strength) has one flat band and $N-1$ non-flat bands whose largest width decays in power law as K to the power of N+2, where K is a kicking strength parameter. The existence of a flat band is strictly proven and the power law scaling, numerically checked for a number of cases, is also analytically proven for a three-band case. By contrast, the KHM does not have any flat band and its band width scales linearly with K. This is shown to result in dramatic differences in dynamical behavior, such as transient (but extremely long) dynamical localization in ORDKR, which is absent in KHM. Finally, we show that despite these differences, there exist simple extensions of KHM and ORDKR (upon introducing an additional periodic phase parameter) such that the resulting extended KHM and ORDKR are actually topologically equivalent, i.e., they yield exactly the same Floquet-band Chern numbers and display topological phase transitions at the same kick strengths. A theoretical derivation of this topological equivalence is provided.

nlin.CD↗

arXiv2013

Time Dependent $\mathcal{PT}$-Symmetric Quantum Mechanics

The parity-time-reversal- ($\mathcal{PT}$) symmetric quantum mechanics (PTQM) has developed into a noteworthy area of research. However, to date most known studies of PTQM focused on the spectral properties of non-Hermitian Hamiltonian operators. In this work, we propose an axiom in PTQM in order to study general time-dependent problems in PTQM, e.g., those with a time-dependent $\mathcal{PT}$-symmetric Hamiltonian and with a time-dependent metric. We illuminate our proposal by examining a proper mapping from a time-dependent Schrödinger-like equation of motion for PTQM to the familiar time-dependent Schrödinger equation in conventional quantum mechanics. The rich structure of the proper mapping hints that time-dependent PTQM can be a fruitful extension of conventional quantum mechanics. Under our proposed framework, we further study in detail the Berry phase generation in a class of $\mathcal{PT}$-symmetric two-level systems. It is found that a closed path in the parameter space of PTQM is often associated with an open path in a properly mapped problem in conventional quantum mechanics. In one interesting case we further interpret the Berry phase as the flux of a continuously tunable fictitious magnetic monopole, thus highlighting the difference between PTQM and conventional quantum mechanics despite the existence of a proper mapping between them.

quant-ph↗

arXiv2013

Exponential Quantum Spreading in a Class of Kicked Rotor Systems near High-Order Resonances

Long-lasting quantum exponential spreading was recently found in a simple but very rich dynamical model, namely, an on-resonance double-kicked rotor model [J. Wang, I. Guarneri, G. Casati, and J. B. Gong, Phys. Rev. Lett. 107, 234104 (2011)]. The underlying mechanism, unrelated to the chaotic motion in the classical limit but resting on quasi-integrable motion in a pseudoclassical limit, is identified for one special case. By presenting a detailed study of the same model, this work offers a framework to explain long-lasting quantum exponential spreading under much more general conditions. In particular, we adopt the so-called "spinor" representation to treat the kicked-rotor dynamics under high-order resonance conditions and then exploit the Born-Oppenheimer approximation to understand the dynamical evolution. It is found that the existence of a flat-band (or an effectively flat-band) is one important feature behind why and how the exponential dynamics emerges. It is also found that a quantitative prediction of the exponential spreading rate based on an interesting and simple pseudoclassical map may be inaccurate. In addition to general interests regarding the question of how exponential behavior in quantum systems may persist for a long time scale, our results should motivate further studies towards a better understanding of high-order resonance behavior in delta-kicked quantum systems.

nlin.CD↗

arXiv2013

Speeding Up Classical and Quantum Adiabatic Processes: Implications for Work Functions and Heat Engine Designs

Adiabatic processes are important for studying the dynamics of a time-dependent system. Conventionally, the adiabatic processes can only be achieved by varying the system slowly. We speed up both classical and quantum adiabatic processes by adding control protocols. In classical systems, we work out the control protocols by analyzing the classical adiabatic approximation. In quantum systems, we follow the idea of transitionless driving by Berry [J. Phys. A: Math. Theor. Vol.42 365303 (2009)]. Such fast-forward adiabatic processes can be performed at arbitrary fast speed, and in the meanwhile reduce the work fluctuation. In both systems, we use a time-dependent harmonic oscillator model to work out explicitly the work function and the work fluctuation in three types of processes: fast-forward adiabatic processes, adiabatic processes, and non-adiabatic processes. We show the significant reduction on work fluctuation in fast-forward adiabatic process. We further illustrate how the fast-forward process improved the converging rate of the Jarzynski equality between the work function and the free energy. As an application, we show that the fast-forward process not only maximizes the output power but also improve the efficiency of a quantum engine.

quant-ph↗

arXiv2013

Generating Many Majorana Modes via Periodic Driving: A Superconductor Model

Realizing Majorana modes (MMs) in condensed-matter systems is of vast experimental and theoretical interests, and some signatures of MMs have been measured already. To facilitate future experimental observations and to explore further applications of MMs, generating many MMs at ease in an experimentally accessible manner has become one important issue. This task is achieved here in a one-dimensional $p$-wave superconductor system with the nearest- and next-nearest-neighbor interactions. In particular, a periodic modulation of some system parameters can induce an effective long-range interaction (as suggested by the Baker-Campbell-Hausdorff formula) and may recover time-reversal symmetry already broken in undriven cases. By exploiting these two independent mechanisms at once we have established a general method in generating many Floquet MMs via periodic driving.

cond-mat.mes-hall↗

arXiv2012

Amplification and suppression of system-bath correlation effects in an open many-body system

Understanding the rich dynamics of open quantum systems is of fundamental interest to quantum control and quantum information processing. By considering an open system of many identical two-level atoms interacting with a common bath, we show that effects of system-bath correlations are amplified in a many-body system via the generation of a short time scale inversely proportional to the number of atoms. Effects of system-bath correlations are therefore considerable even when each individual atom interacts with the bath weakly. We further show that correlation-induced dynamical effects may still be suppressed via the dynamical decoupling approach, but they present a challenge for quantum state protection as the number of atom increases.

quant-ph↗

arXiv2012

Intrinsic Dynamical Fluctuation Assisted Symmetry Breaking in Adiabatic Following

Classical adiabatic invariants in actual adiabatic processes possess intrinsic dynamical fluctuations. The magnitude of such intrinsic fluctuations is often thought to be negligible. This widely believed physical picture is contested here. For adiabatic following of a moving stable fixed-point solution facing a pitchfork bifurcation, we show that intrinsic dynamical fluctuations in an adiabatic process can assist in a deterministic and robust selection between two symmetry-connected fixed-point solutions, irrespective of the rate of change of adiabatic parameters. Using a classical model Hamiltonian also relevant to a two-mode quantum system, we further demonstrate the formation of an adiabatic hysteresis loop in purely Hamiltonian mechanics and the generation of a Berry phase via changing one single-valued parameter only.

quant-ph↗

arXiv2012

Statistical properties of power-law random banded unitary matrices in the delocalization-localization transition regime

Power-law random banded unitary matrices (PRBUM), whose matrix elements decay in a power-law fashion, were recently proposed to model the critical statistics of the Floquet eigenstates of periodically driven quantum systems. In this work, we numerically study in detail the statistical properties of PRBUM ensembles in the delocalization-localization transition regime. In particular, implications of the delocalization-localization transition for the fractal dimension of the eigenvectors, for the distribution function of the eigenvector components, and for the nearest neighbor spacing statistics of the eigenphases are examined. On the one hand, our results further indicate that a PRBUM ensemble can serve as a unitary analog of the power-law random Hermitian matrix model for Anderson transition. On the other hand, some statistical features unseen before are found from PRBUM. For example, the dependence of the fractal dimension of the eigenvectors of PRBUM upon one ensemble parameter displays features that are quite different from that for the power-law random Hermitian matrix model. Furthermore, in the time-reversal symmetric case the nearest neighbor spacing distribution of PRBUM eigenphases is found to obey a semi-Poisson distribution for a broad range, but display an anomalous level repulsion in the absence of time-reversal symmetry.

cond-mat.dis-nn↗

arXiv2012

Synthetic Spin-Orbit Coupling in Two-level Cold Atoms

Synthetic spin-orbit coupling (SOC) in controlled quantum systems such as cold atoms or trapped ions has been of great interest. Here we show, both theoretically and computationally, a simplest realization of SOC using two-level cold atoms interacting with only one laser beam. The underlying mechanism is based upon the non-adiabatic nature of laser-atom interaction, with the Rabi frequency and atom's kinetic energy being comparable to each other. We use the Zitterbewegung (ZB) oscillation to further illustrate the effects of the synthesized SOC on the quantum dynamics of the two-level cold atoms. We expect our proposal to be of experimental interest in quantum simulation of SOC-related physics.

cond-mat.quant-gas↗

arXiv2012

Non-Canonical Statistics of a Spin-Boson Model: Theory and Exact Monte-Carlo Simulations

Equilibrium canonical distribution in statistical mechanics assumes weak system-bath coupling (SBC). In real physical situations this assumption can be invalid and equilibrium quantum statistics of the system may be non-canonical. By exploiting both polaron transformation and perturbation theory in a spin-boson model, an analytical treatment is advocated to study non-canonical statistics of a two-level system at arbitrary temperature and for arbitrary SBC strength, yielding theoretical results in agreement with exact Monte-Carlo simulations. In particular, the eigen-representation of system's reduced density matrix is used to quantify non-canonical statistics as well as the quantumness of the open system. For example, it is found that irrespective of SBC strength, non-canonical statistics enhances as temperature decreases but vanishes at high temperature.

quant-ph↗

arXiv2012

Quantized Adiabatic Transport in Momentum Space

Though topological aspects of energy bands are known to play a key role in quantum transport in solid-state systems, the implications of Floquet band topology for transport in momentum space (i.e., acceleration) are not explored so far. Using a ratchet accelerator model inspired by existing cold-atom experiments, here we characterize a class of extended Floquet bands of one-dimensional driven quantum systems by Chern numbers, reveal topological phase transitions therein, and theoretically predict the quantization of adiabatic transport in momentum space. Numerical results confirm our theory and indicate the feasibility of experimental studies.

cond-mat.quant-gas↗

arXiv2012

2*2 random matrix ensembles with reduced symmetry: From Hermitian to PT-symmetric matrices

A possibly fruitful extension of conventional random matrix ensembles is proposed by imposing symmetry constraints on conventional Hermitian matrices or parity-time- (PT-) symmetric matrices. To illustrate the main idea, we first study 2*2 complex Hermitian matrix ensembles with O(2) invariant constraints, yielding novel level-spacing statistics such as singular distributions, half-Gaussian distribution, distributions interpolating between GOE (Gaussian Orthogonal Ensemble) distribution and half Gaussian distributions, as well as gapped-GOE distribution. Such a symmetry-reduction strategy is then used to explore 2*2 PT-symmetric matrix ensembles with real eigenvalues. In particular, PT-symmetric random matrix ensembles with U(2) invariance can be constructed, with the conventional complex Hermitian random matrix ensemble being a special case. In two examples of PT-symmetric random matrix ensembles, the level-spacing distributions are found to be the standard GUE (Gaussian Unitary Ensemble) statistics or "truncated-GUE" statistics.

quant-ph↗

arXiv2012

Protecting and Enhancing Spin Squeezing via Continuous Dynamical Decoupling

Realizing useful quantum operations with high fidelity is a two-task quantum control problem wherein decoherence is to be suppressed and desired unitary evolution is to be executed. The dynamical decoupling (DD) approach to decoherence suppression has been fruitful but synthesizing DD fields with certain quantum control fields may be experimentally demanding. In the context of spin squeezing, here we explore an unforeseen possibility that continuous DD fields may serve dual purposes at once. In particular, it is shown that a rather simple configuration of DD fields can suppress collective decoherence and yield a 1/N scaling of the squeezing performance (N is the number of spins), thus making spin squeezing more robust to noise and much closer to the so-called Heisenberg limit. The theoretical predictions should be within the reach of current spin squeezing experiments.

quant-ph↗

arXiv2012

Preferred States of Decoherence under Intermediate System-Environment Coupling

The notion that decoherence rapidly reduces a superposition state to an incoherent mixture implicitly adopts a special representation, namely, the representation of preferred (pointer) states (PS). For weak or strong system-environment coupling, PS is known to be the energy eigenstates of the system Hamiltonian or the eigenstates of the system-environment interaction Hamiltonian. Via a simple dynamical model that simulates a two-level system interacting with few other degrees of freedom as its environment, it is shown that even for intermediate system-environment coupling, approximate PS may still emerge from the coherent quantum dynamics of the whole system in the absence of any thermal averaging. The found PS can also continuously deform to expected limits for weak or strong system-environment coupling. Computational results are also qualitatively explained. The findings should be useful towards further understandings of decoherence and quantum thermalization processes.

quant-ph↗