Landau-Zener Research Articles

Genetic optimization of quantum annealing

The study of optimal control of quantum annealing by modulating the pace of evolution and by introducing a counterdiabatic potential has gained significant attention in recent times. In this work, we present a numerical approach based on genetic algorithms to improve the performance of quantum annealing, which evades the Landau-Zener transitions to navigate to the ground state of the final Hamiltonian with high probability. We optimize the annealing schedules starting from polynomial ansatz by treating their coefficients as chromosomes of the genetic algorithm. We also explore shortcuts to adiabaticity by computing a practically feasible $k$-local optimal driving operator, showing that even for $k=1$ we achieve substantial improvement of the fidelity over the standard annealing solution. With these genetically optimized annealing schedules and/or optimal driving operators, we are able to perform quantum annealing in relatively short time-scales and with larger fidelity compared to traditional approaches.

A multiple time step algorithm for trajectory surface hopping simulations.

A multiple time step (MTS) algorithm for trajectory surface hopping molecular dynamics has been developed, implemented, and tested. The MTS scheme is an extension of the ab initio implementation for Born-Oppenheimer molecular dynamics presented in the work of Liberatore et al. [J. Chem. Theory Comput. 14, 2834 (2018)]. In particular, the MTS algorithm has been modified to enable the simulation of non-adiabatic processes with the trajectory surface hopping (TSH) method and Tully's fewest switches algorithm. The specificities of the implementation lie in the combination of Landau-Zener and Tully's transition probabilities during the inner MTS time steps. The new MTS-TSH method is applied successfully to the photorelaxation of protonated formaldimine, showing that the important characteristics of the process are recovered by the MTS algorithm. A computational speed-up between 1.5 and 3 has been obtained compared to standard TSH simulations, which is close to the ideal values that could be obtained with the computational settings considered.

Tunneling dynamics of tunable spin-orbit coupled Bose-Einstein condensates

We theoretically study the band structure, tunneling dynamics, and tunneling probability of tunable spin-orbit-coupled Bose-Einstein condensates under the periodic driving of Raman coupling. The time-independent Floquet Hamiltonian is obtained in the high-frequency approximation. It is found that the periodic driving can effectively tune spin-orbit coupling and nonlinear interaction. The system is mapped to a standard nonlinear two-level model, and the critical condition for the appearance of the loop in energy band structure and the width of the loop are obtained analytically. When the interspecies atomic interaction is equal to the intraspecies atomic interaction, there is no loop. However, when the intraspecies atomic interaction is smaller (larger) than the interspecies atomic interaction, the loop appears in the lower (upper) energy band. In this case, both spin-orbit coupling and Raman coupling will suppress the appearance of loop. In particular, the critical condition for the appearance of loop structure can be controlled by adjusting external driving. We also study the tunneling dynamics of Bose-Einstein condensate with tunable spin-orbit coupling. More importantly, by tuning the periodic driving, the tunneling dynamics of the system and the location of nonlinear Landau-Zener tunneling can be controlled. We also find that the spin components of the system can be reversed. Finally, the Landau-Zener tunneling probability of the system is calculated. The research shows that the periodic driving can effectively change the tunneling probability of the system.

The hierarchy of Davydov's Ansätze and its applications

AbstractThis review provides a bird's eye view over the development of the hierarchy of Davydov's Ansätze and its applications in a variety of problems in computational physical chemistry. Davydov's original solitons appeared in the 1970s as a candidate for vibrational energy carriers in proteins, thanks to their association with the Fröhlich Hamiltonian and the Holstein molecular crystal model. Momentum‐space projection of those solitary waves emerged to be great approximations to the ground‐state wave functions of the extended Holstein Hamiltonian, lending unambiguous evidence to the absence of formal quantum phase transitions in those systems. The multiple Davydov Ansätze are introduced, with increasing multiplicity, as incremental improvements of their corresponding single‐Ansatz parents. The time‐dependent variational formalism of Davydov's Ansätze is discussed in great detail, and the relative deviation of the Ansätze is constructed to quantify how faithfully they follow the Schrödinger equation, a quantity that is shown to vanish in the limit of large multiplicities. Three approaches to finite‐temperature variational dynamics of Davydov's Ansätze are demonstrated, namely, the Monte Carlo importance sampling, the method of thermo‐field dynamics, and the method of displaced number states. Applications of Davydov's Ansätze are given to variants of the spin‐boson model, the Landau–Zener transition, the Holstein Hamiltonian, energy transfer in light‐harvesting, and singlet fission in organic photovoltaics. As an example, simulation of multidimensional spectroscopic signals via Davydov's Ansätze is fully implemented for the finite‐temperature fission process in crystalline rubrene.This article is categorized under: Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics Software > Simulation Methods Theoretical and Physical Chemistry > Spectroscopy

Thirty Years in Silicon Photonics: A Personal View

Silicon Photonics, the technology where optical devices are fabricated by the mainstream microelectronic processing technology, was proposed almost 30 years ago. I joined this research field at its start. Initially, I concentrated on the main issue of the lack of a silicon laser. Room temperature visible emission from porous silicon first, and from silicon nanocrystals then, showed that optical gain is possible in low-dimensional silicon, but it is severely counterbalanced by nonlinear losses due to free carriers. Then, most of my research focus was on systems where photons show novel features such as Zener tunneling or Anderson localization. Here, the game was to engineer suitable dielectric environments (e.g., one-dimensional photonic crystals or waveguide-based microring resonators) to control photon propagation. Applications of low-dimensional silicon raised up in sensing (e.g., gas-sensing or bio-sensing) and photovoltaics. Interestingly, microring resonators emerged as the fundamental device for integrated photonic circuit since they allow studying the hermitian and non-hermitian physics of light propagation as well as demonstrating on-chip heavily integrated optical networks for reconfigurable switching applications or neural networks for optical signal processing. Finally, I witnessed the emergence of quantum photonic devices, where linear and nonlinear optical effects generate quantum states of light. Here, quantum random number generators or heralded single-photon sources are enabled by silicon photonics. All these developments are discussed in this review by following my own research path.

Polaron dynamics of Bloch–Zener oscillations in an extended Holstein model

Recent developments in qubit engineering make circuit quantum electrodynamics devices promising candidates for the study of Bloch oscillations (BOs) and Landau–Zener (LZ) transitions. In this work, a hybrid circuit chain with alternating site energies under external electric fields is employed to study Bloch–Zener oscillations (BZOs), i.e. coherent superpositions of BOs and LZ transitions. We couple each of the tunable qubits in the chain to dispersionless optical phonons and build an extended Holstein polaron model with the purpose of investigating vibronic effects in the BZOs. We employ an extension of the Davydov ansatz in combination with the Dirac–Frenkel time-dependent variational principle to simulate the dynamics of the qubit chain under the influence of high-frequency quantum harmonic oscillators. Band gaps emerge due to energy differences in site energies at alternating qubit sites, and are shown to play key roles in tuning band structures and time periodic reconstructions of the wave patterns. In the absence of qubit–phonon interactions, the qubits undergo either standard BZOs or breathing modes, depending on whether the initial wave packet is formed by a broad or narrow Gaussian wave packet, respectively. The BZOs can get localized in space if the band gaps are sufficiently large. In the presence of qubit–phonon coupling, the periodic behavior of BZOs can be washed out and undergo dynamic localization. The influence of an ohmic bath on the dynamics of BZOs is investigated by means of a Markovian master equation approach. Finally, we calculate the von Neumann entropy as a measure of the entanglement between qubits and phonons.

Time-domain Landau-Zener-Stückelberg-Majorana interference in an optical lattice clock

The interference between a sequence of Landau-Zener (LZ) transitions can produce Rabi oscillations(LZROs). This phenomenon is a kind of time-domain Landau-Zener-Stuckelberg-Majorana (LZSM) interference. However, experimental demonstrations of this LZSM interference induced Rabi oscillation are extremely hard due to the short coherence time of the driven quantum system. Here, we study theoretically the time-domain LZSM interference between the clock transition in one-dimensional (1D) Sr-87 optical lattice clock (OLC) system. With the help of both the adiabatic-impulse model and Floquet numerical simulation method, the LZROs with special step-like structure are clearly found both in fast- and slow-passage limit in the real experiment parameter regions. In addition, the dephasing effect caused by the system temperature can be suppressed with destructive interference in the slow-passage limit. Finally, we discuss the possible Bloch-Siegert shift while the pulse time is away from the half-integer and integer periods. Our work provides a clear roadmap to observe the LZROs on the OLC platform.

Disentangling 4f -radical coupling and dissipative Landau-Zener quantum tunneling in a continuously measured single-ion magnet spin transistor

Both radical-lanthanide exchange coupling and crystal-field tunnel splitting are responsible for the ground to first-excited Kramers doublet energy gap $\mathrm{\ensuremath{\Delta}}{E}_{\text{KD}}$ in an Ising $4f$ single-ion magnet coupled to a noninnocent ligand. However, these two mechanisms cannot be easily disentangled via spectroscopy alone because their interplay results in a single absorption line. Here we present a microscopic theory for the continuous measurement of the dissipative Landau-Zener transitions recently discussed for a ${\mathrm{TbPc}}_{2}$ spin transistor [Phys. Rev. Lett. 118, 257701 (2017)] and show how this quantum transport experiment can be used to disentangle the magnetic coupling and the tunnel splitting contributions to $\mathrm{\ensuremath{\Delta}}{E}_{\text{KD}}$. In addition, our model elucidates the microscopic origin of the decoherent spin tunneling observed in the ${\mathrm{TbPc}}_{2}$ spin transistor, by explicitly exposing the role played by phonon-mediated spin relaxation and sequential electron transport through the noninnocent ligand, in a time-dependent magnetic field.

Bloch oscillations in the spin- 12 XXZ chain

Under a perfect periodic potential, the electric current density induced by a constant electric field may exhibit nontrivial oscillations, so-called Bloch oscillations, with an amplitude that remains nonzero in the large system size limit. Such oscillations have been well studied for nearly noninteracting particles and observed in experiments. In this work we revisit Bloch oscillations in strongly interacting systems. By analyzing the spin-$\frac{1}{2}$ XXZ chain, we demonstrate that the current density at special values of the anisotropy parameter $\mathrm{\ensuremath{\Delta}}=\ensuremath{-}cos(\ensuremath{\pi}/p)$ $(p=3,4,5,\ensuremath{\cdots})$ in the ferromagnetic gapless regime behaves qualitatively the same as in the noninteracting case $(\mathrm{\ensuremath{\Delta}}=0)$ even in the weak electric field limit. When $\mathrm{\ensuremath{\Delta}}$ deviates from these values, the amplitude of the oscillation under a weak electric field is suppressed by a factor of the system size. We estimate the strength of the electric field required to observe such a behavior using the Landau-Zener formula.

Band evolution and Landau-Zener Bloch oscillations in strained photonic rhombic lattices.

We investigate band evolution of chiral and non-chiral symmetric flatband photonic rhombic lattices by applying a strain along the diagonal direction, and thereby demonstrating Landau-Zener Bloch (LZB) oscillations in the presence of a refractive index gradient. The chiral and non-chiral symmetric rhombic lattices are obtained by adding a detuning to uniform lattices. For the chiral symmetric lattices, the middle flatband is perturbed due to the chiral symmetry breaking while a nearly flatband appears as the bottom band with the increase of strain-induced next-nearest-neighbor hopping. Consequently, LZB oscillations exhibit intriguing characteristics such as asymmetric energy transitions and almost complete suppression of the oscillations. Nevertheless, for the non-chiral symmetric lattices, flatband persists owing to the retained particle-hole symmetry and evolves into the bottom band. Remarkably, the band gap can be readily tuned, which allows controlling of the amplitude of Landau-Zener tunneling (LZT) rate and may lead to thorough LZT. Our analysis provides an alternative perspective on the generation of tunable flatband and may also bring insight to study the symmetry and topological characterization of the flatband.

Topological Bloch–Zener oscillations in non-Hermitian graphene plasmonic waveguide arrays

We investigate the topological Bloch–Zener oscillations for surface plasmon polaritons (SPPs) propagating in a Su–Schrieffer–Heeger plasmonic system, which composed of graphene dimer arrays with a potential gradient. The topological trivial and non-trivial band gaps are achieved to investigate the topological effect to plasmonic Bloch oscillations. The topological transition from trivial phase to non-trivial one through the exceptional point is realized by alternating the gain and loss in the graphene waveguide arrays. Zener tunneling of the SPP beam was observed in the parity-time (PT) symmetric region, which was prohibited in the PT-symmetric broken region. The numerical calculations demonstrated reasonable agreements with theoretical tight-binding model. Furthermore, a single dynamically stable zero-energy edge state was also found in these non-Hermitian plasmonic waveguide arrays.

Stability of superconducting resonators: Motional narrowing and the role of Landau-Zener driving of two-level defects.

Frequency instability of superconducting resonators and qubits leads to dephasing and time-varying energy loss and hinders quantum processor tune-up. Its main source is dielectric noise originating in surface oxides. Thorough noise studies are needed to develop a comprehensive understanding and mitigation strategy of these fluctuations. We use a frequency-locked loop to track the resonant frequency jitter of three different resonator types—one niobium nitride superinductor, one aluminum coplanar waveguide, and one aluminum cavity—and we observe notably similar random telegraph signal fluctuations. At low microwave drive power, the resonators exhibit multiple, unstable frequency positions, which, for increasing power, coalesce into one frequency due to motional narrowing caused by sympathetic driving of two-level system defects by the resonator. In all three devices, we identify a dominant fluctuator whose switching amplitude (separation between states) saturates with increasing drive power, but whose characteristic switching rate follows the power law dependence of quasi-classical Landau-Zener transitions.

Adiabaticity parameters for the categorization of light-matter interaction: From weak to strong driving

We investigate theoretically and numerically the light-matter interaction in a two-band system (TBS) as a model system for excitation in a solid-state band structure. We identify five clearly distinct excitation regimes, categorized with well-known adiabaticity parameters: (1) the perturbative multiphoton absorption regime for small driving field strengths, and four light-field-driven regimes, where intraband motion becomes important (2) the impulsive Landau-Zener (LZ) regime, (3) the nonimpulsive LZ regime, (4) the adiabatic regime, and (5) the adiabatic-impulsive regime for large electric field strengths. This categorization is tremendously helpful to understand the highly complex excitation dynamics in solids, in particular, when the driving field strength varies, and this categorization naturally connects Rabi physics with Landau-Zener physics. In addition, we find an insightful analytical expression for the photon orders connecting the perturbative multiphoton regime with the light-field-driven regimes. Moreover, in the adiabatic-impulsive regime, adiabatic motion and impulsive LZ transitions are equally important, leading to a broken symmetry of the TBS and a residual current when applying few-cycle laser pulses of broken temporal symmetry. This categorization allows a deep understanding of strong-field excitation in solids, including current and high-harmonic generation in a large variety of settings, and will help to find optimal driving parameters for a given purpose.

Geometrical Rabi oscillations and Landau-Zener transitions in non-Abelian systems

Topological phases of matter became a new standard to classify quantum systems in many cases, yet key quantities like the quantum geometric tensor providing local information about topological properties are still experimentally hard to access. In non-Abelian systems this accessibility to geometric properties can be even more restrictive due to the degeneracy of the states. We propose universal protocols to determine quantum geometric properties in non-Abelian systems. First, we show that for a weak resonant driving of the local parameters the coherent Rabi oscillations are related to the quantum geometric tensor. Second, we derive that in a Landau-Zener-like transition the final probability of an avoided energy crossing is proportional to elements of the non-Abelian quantum geometric tensor. Our schemes suggest a way to prepare eigenstates of the quantum metric, a task that is difficult otherwise in a degenerate subspace.

Room-temperature Bloch oscillations and interminiband Zener tunneling in a GaAs-based narrow-minigap superlattice

We investigate peculiar Bloch oscillations and interminiband Zener tunneling in a GaAs-based narrow-minigap superlattice up to room temperature, by using terahertz emission spectroscopy under dc bias electric fields. The Bloch oscillations observed previously with a π/2 phase shift at 10 K under relatively low bias fields are found to survive even at 300 K, where thermal energy kT exceeds the relevant minigap (k: Boltzmann constant, T: temperature). Furthermore, the interminiband Zener tunneling under high bias fields leads to a monocyclic terahertz signal with a temperature-dependent subsequent bumpy tail, indicating its occurrence at a few different occasions for Bloch oscillating electrons.

Floquet-Bloch Oscillations and Intraband Zener Tunneling in an Oblique Spacetime Crystal.

We study an oblique spacetime crystal realized by a monoatomic crystal in which a sound wave propagates, and analyze its quasienergy band structure starting from a tight-binding Bloch band for the static crystal. We investigate Floquet-Bloch oscillations under an external field, which show different characteristics for different band topologies. We also discover intraband Zener tunneling beyond the adiabatic limit, which effectively converts between different band topologies. Our results indicate the possibility of energy conversion between the sound wave and a dc electric field.

Nonadiabatic dynamics across a first-order quantum phase transition: Quantized bubble nucleation

Metastability is a quintessential feature of first-order quantum phase transitions, which is lost either by dynamical instability or by nucleating bubbles of a true vacuum through quantum tunneling. By considering a drive across the first-order quantum phase transition in the quantum Ising chain in the presence of both transverse and longitudinal fields, we reveal multiple regions in the parameter space where the initial metastable state loses its metastability in successive stages. The mechanism responsible is found to be semidegenerate resonant tunnelings to states with specific bubble sizes. We show that such dynamics of quantized bubble nucleations can be understood in terms of Landau-Zener transitions, which provide quantitative predictions of nucleation probabilities for different bubble sizes.

Wave redirection, localization, and non-reciprocity in a dissipative nonlinear lattice by macroscopic Landau–Zener tunneling: Experimental results

Nonlinear lattices and the nonlinear acoustics they support have a broad impact on shock and vibration mitigation, sound isolation, and acoustic logic devices. In this work, we experimentally study wave redirection, localization, and non-reciprocity in an asymmetric network of two nonlinear lattices with weak linear inter-lattice coupling. We report on the design, fabrication, and system identification of coupled lattices with essentially nonlinear next-neighbor intra-lattice coupling and on their unusual nonlinear acoustics. By weakly coupling the lattices and introducing structural disorder in one of them, we experimentally prove the realization of irreversible breather redirection between lattices governed by a macroscopic analog of the quantum Landau–Zener tunneling effect. In the experiments performed, the input energy is applied by impulse (broadband) excitation, and the resulting acoustical mechanism for wave redirection is in the form of propagating breathers, that is, localized oscillating wave packets formed by the synergy of nonlinearity and dispersion. Moreover, we study the non-reciprocal acoustics of the experimental lattice system by applying separate impulses at each of its four terminals and investigate the tunability with the energy of the resulting acoustic non-reciprocity by systematically varying the impulse intensity. The reported experimental results show that the weakly coupled, disordered, and nonlinear lattice system has wave tailoring properties that are tunable with energy. Altogether, the experimental results agree well with theoretical predictions reported in a companion work based on reduced-order numerical models and prove the efficacy of the system for applications, providing a path for applying these advanced concepts in future structures and devices.

Spatial Bloch oscillations in acoustic waveguide arrays

We designed a type of acoustic waveguide supported by spoof acoustic surface waves. The effective refractive index of acoustic waveguide can be effectively tuned by tailoring the waveguide width to control the propagation of spoof acoustic surface waves. Based on the advantage of the tunable refractive index, we construct a discrete waveguide array with transverse refractive index gradients to simulate the time evolution of the probability waves of electron in a tight-binding lattice under an external electric field. Based on numerical simulations and experiments, we discuss the relationship between the spatial Bloch oscillations period and the transverse refractive index gradient. Furthermore, we also investigate the influence of the interval between waveguides on the amplitude of the Bloch oscillations. Our acoustic waveguide array maybe provides a versatile testbed to explore analogous quantum mechanical effects, such as Zener tunneling, Anderson localization, and massless Dirac dynamics in acoustic system.

Nonlinear electric conductivity and THz-induced charge transport in graphene

Based on the quantum master equation approach, the nonlinear electric conductivity of graphene is investigated under static electric fields for various chemical potential shifts. The simulation results show that, as the field strength increases, the effective conductivity is firstly suppressed, reflecting the depletion of effective carriers due to the large displacement in the Brillouin zone caused by the strong field. Then, as the field strength exceeds 1 MV m−1, the effective conductivity increases, overcoming the carrier depletion via the Landau–Zener tunneling process. Based on the nonlinear behavior of the conductivity, the charge transport induced by few-cycle THz pulses is studied to elucidate the ultrafast control of electric current in matter.