We investigate the relation between the canonical model of quantum optics, the Jaynes-Cummings Hamiltonian and Dirac fermions in quantizing magnetic field. We demonstrate that Rabi oscillations are observable in the optical response of graphene, providing us with a transparent picture about the structure of optical transitions. While the longitudinal conductivity reveals chaotic Rabi oscillations, the Hall component measures coherent ones. This opens up the possibility of investigating a microscopic model of a few quantum objects in a macroscopic experiment with tunable parameters.
Under resonant conditions, a long sequence of landau-zener transitions can lead to Rabi oscillations. Using a nitrogen-vacancy (NV) center spin in diamond, we investigated the interference between more than 100 Landau-Zener processes. We observed the new type of Rabi oscillations of the electron spin resulting from the interference between successive Landau-Zener processes in various regimes, including both slow and fast passages. The combination of the control techniques and the favorable coherent properties of NV centers provides an excellent experimental platform to study a variety of quant…
We have studied the interplay of an Anderson impurity in Landau quantized graphene, with special emphasis on the influence of the chemical potential. Within the slave-boson mean-field theory, we found reentrant Kondo behaviour by varying the chemical potential or gate voltage. Between Landau levels, the density of states is suppressed, and by changing the graphene's Fermi energy, we cross from metallic to semiconducting regions. Hence, the corresponding Kondo behaviour is also influenced. The f-level spectral function reveals both the presence of Landau levels in the conduction band and the Ko…
The dissipative response of a quantum system upon a time-dependent drive can be exploited as a probe of its geometric and topological properties. In this work, we explore the implications of such phenomena in the context of two-dimensional gases subjected to a uniform magnetic field. It is shown that a filled Landau level exhibits a quantized circular dichroism, which can be traced back to its underlying non-trivial topology. Based on selection rules, we find that this quantized circular dichroism can be suitably described in terms of Rabi oscillations, whose frequencies satisfy simple quantiz…
We investigate quantum interference effects in a superconducting Cooper-pair box by taking into account the possibility of tunneling processes involving one and two Cooper pairs. The quantum dynamics is analysed in a framework of three-level model. We compute Landau-Zener probabilities for a linear sweep of the gate charge and investigate Rabi oscillations in a periodically driven three-level system under in- and off- resonance conditions. It was shown that the Landau-Zener probabilities reveal two different patterns: "step" and "beats"-like behaviours associated with the quantum interference …
We study the dynamic behaviour of a quantum two-level system with periodically varying parameters by solving the master equation for the density matrix. Two limiting cases are considered: multiphoton Rabi oscillations and Landau-Zener transitions. The approach is applied to the description of the dynamics of superconducting qubits. In particular, the case of the interferometer-type charge qubit with periodically varying parameters (gate voltage or magnetic flux) is investigated. The time-averaged energy level populations are calculated as funtions of the qubit's control parameters.
We perform numerical studies to determine if the fractional quantum Hall state observed at filling nu=5/2 is the Moore-Read wavefunction or its particle hole conjugate, the so-called AntiPfaffian. Using a truncated Hilbert space approach we find that for realistic interactions, including Landau-level mixing, the ground state remains fully polarized and the AntiPfaffian is strongly favored.
We present results of extensive numerical calculations on the ground state of electrons in the first excited (n=1) Landau level with Coulomb interactions, and including non-zero thickness effects, for filling factors 12/5 and 13/5 in the torus geometry. In a region that includes these experimentally-relevant values, we find that the energy spectrum and the overlaps with the trial states support the previous hypothesis that the system is in the non-Abelian k = 3 liquid phase we introduced in a previous paper.
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 quan…
We describe the spin-dependent quantum conductance in a wire where a magnetic field is spatially modulated. The change in direction and intensity of the magnetic field acts as a perturbation that mixes spin projections. This is exemplified by a ferromagnetic nanowire. There the local field varies smoothly its direction generating a domain wall (DW) as described by the well-known Cabrera-Falicov model. Here, we generalize this model to include also a strength modulation. We identify two striking diabatic regimes that appear when such magnetic inhogeneity occurs. 1) If the field strength at the …
We present a quantized model of harmonically confined dot atom with inherent damping in the presence of a transverse magnetic field. The model leads to a non hermitian Hamiltonian in real coordinate. We have analytically studied the effects that damping has on the Rabi type oscillations of the system. The model explains the decoherence of Rabi oscillation in a Josephson Junction.
The observation of new insulating phases of two-dimensional electrons in the first excited Landau level is reported. These states, which are manifested as re-entrant integer quantized Hall effects, exist alongside well-developed even-denominator fractional quantized Hall states at nu=7/2 and 5/2 and new odd-denominator states at nu=3+1/5 and 3+4/5.
We study nonlinear optical response of Landau quantized graphene to an intense electromagnetic wave. In particular, we consider high harmonic generation process. It is shown that one can achieve efficient generation of high harmonics with strong radiation fields -- when the work of the wave electric field on the magnetic length is larger than pump photon energy. At that high harmonics generation process takes place for a wide range of the pump wave frequencies and intensities even for significant broadening of Landau levels because of impurities in graphene.
This work addresses the statistical thermodynamic features of a Landau-quantized T-3 Dice lattice in a normal magnetic field in the nondegenerate statistical regime. Our study includes analyses of the Grand Potential, magnetic moment, entropy and specific heat at constant volume, with explicit determination of their temperature and magnetic field dependencies. In this, we find that the specific heat at constant volume is negative in the nondegenerate regime, for the Landau-quantized Dice lattice.
Scanning tunneling microscopy and spectroscopy in magnetic field was used to study Landau quantization in graphene and its dependence on charge carrier density. Measurements were carried out on exfoliated graphene samples deposited on a chlorinated SiO2 thermal oxide which allowed observing the Landau level sequences characteristic of single layer graphene while tuning the density through the Si backgate. Upon changing the carrier density we find abrupt jumps in the Fermi level after each Landau level is filled. Moreover, the Landau level spacing shows a marked increase at low doping levels, c…
We develop a rigorous quantum-mechanical theory of the nonlinear optical process of difference frequency generation of surface plasmon-polaritons in Landau-quantized graphene. Although forbidden in the electric-dipole approximation, the second-order susceptibility is surprisingly high, equivalent to the bulk magnitude above $10^{-3}$ m/V. We consider the graphene monolayer as a nonlinear optical component of a monolithic photonic chip with integrated pump fields. The nonlinear power conversion efficiency of the order of tens $μ$W/W$^2$ is predicted from structures of $10-100$ $μ$m size. We inv…
Detailed measurements of the longitudinal thermopower of two-dimensional electrons in the first excited Landau level are reported. Clear signatures of numerous fractional quantized Hall states, including those at $ν= 5/2$ and 7/3, are observed in the magnetic field and temperature dependence of the thermopower. An abrupt collapse of the thermopower is observed below about $T= 40$ mK at those filling factors where re-entrant insulating electronic states have been observed in conventional resistive transport studies. The thermopower observed at $ν= 5/2$ is discussed in the context of recent theo…
We present nonlocal resistance measurements in an ultra high mobility two dimensional electron gas. Our experiments show that even at weak magnetic fields classical guiding along edges leads to a strong non local resistance on macroscopic distances. In this high Landau level regime the transport along edges is dissipative and can be controlled by the amplitude of the voltage drop along the edge. We report resonances in the nonlocal transport as a function of this voltage that are interpreted as escape and formation of edge channels.
We identify an unusual mechanism for quantum oscillations in nodal semimetals, driven by a single pair of Landau levels periodically closing their gap at the Fermi energy as a magnetic field is varied. These `zero Landau level' quantum oscillations (ZQOs) appear in the nodal limit where the zero-field Fermi volume vanishes, and have distinctive periodicity and temperature dependence. We link the Landau spectrum of a two-dimensional (2D) nodal semimetal to the Rabi model, and show by exact solution that across the entire Landau fan, pairs of opposite-parity Landau levels are intertwined in a `s…
In this work the role of magnetic Landau quantization in the dynamics and spectrum of Diced Lattice charge carriers is studied in terms of the associated pseudospin 1 Green's function. The equations of motion for the 9 matrix elements of this Green's function are formulated in position/frequency representation and are solved explicitly in terms of a closed form integral representation involving only elementary functions. The latter is subsequently expanded in a Laguerre eigenfunction series whose frequency poles identify the discretized energy spectrum for the Landau-quantized Diced Lattice as…
We consider massless Dirac fermions in a graphene monolayer subject to both a perpendicular magnetic field $B$ and a proximity-induced pairing gap $Δ$. When the chemical potential is at the Dirac point, our exact solution of the Bogoliubov-de Gennes equation yields $Δ$-independent relativistic Landau levels. Since eigenstates depend on $Δ$, many observables nevertheless are sensitive to pairing, e.g., the local density of states or the edge state spectrum. By solving the problem with an additional in-plane electric field, we also discuss how snake states are influenced by a pairing gap.
This work addresses the temperature dependence of the statistical thermodynamic functions of the Group VI Dichalcogenides in a quantizing magnetic field. These functions include the grand partition function, the ordinary partition function, the Helmholtz Free Energy and the entropy: Their dependencies on temperature and magnetic field strength are carefully examined, particularly in the degenerate regime and the approach to zero temperature, also in the nondegenerate regime. The joint dependence on magnetic field and temperature is also examined in the Dichalcogenide magnetic moment in both st…
We discuss selection rules and intensities of photocurrent of a two-dimensional electron gas in a strong magnetic field via absorptions of orbital angular momentum carried by obliquely irradiated optical vortex beams. By angular deflection, optical vortex beams on the two-dimensional electron gas interface can be seen as a superposition of the various orbital angular momentum states. As a result, it is demonstrated that it is yielded that the angular momentum selection rules and induced currents are modified from the case of vertical incidence.
We theoretically investigate multiphonons resonance Raman scattering between the Landau levels in graphene on the polar substrate using the Huang-Rhys's model. We not only present the single and multiple surface optical (SO) phonons scattering, but also propose the combined multiphonons scattering (CMS), which is composed of the SO phonon and longitudinal acoustic phonon. We find that the CMS has a blue-shift behavior with increasing the magnetic field, differing from these SO phonon resonance scattering at a special magnetic field. This behavior may be used to explain the changing shoulder of…
Non-equilibrium dynamics of strongly correlated systems constitutes a fascinating problem of condensed matter physics with many open questions. Here we investigate the relaxation dynamics of Landau-quantized electron system into spin-valley polarized ground state in a gate-tunable MoSe$_2$ monolayer subjected to a strong magnetic field. The system is driven out of equilibrium with optically injected excitons that depolarize the electron spins and the subsequent electron spin-valley relaxation is probed in time-resolved experiments. We demonstrate that the relaxation rate at millikelvin tempera…
We study edges states of graphene ribbons in the quantized Hall regime, and show that they can be described within a continuum model (the Dirac equation) when appropriate boundary conditions are adopted. The two simplest terminations, zigzag and armchair edges, are studied in detail. For zigzag edges, we find that the lowest Landau level states terminate in two types of edge states, dispersionless and current-carrying surface states. The latter involve components on different sublattices that may be separated by distances far greater than the magnetic length. For armchair edges, the boundary c…
Landau level lasers have the advantage of tunability of the laser frequency by means of the external magnetic field. The crucial prerequisite of such a laser is a population inversion between optically coupled Landau levels. Efficient carrier-carrier and carrier-phonon scattering generally suppresses this effect in conventional materials. Based on microscopic calculations, we predict for the first time the occurrence of a long-lived population inversion in Landau-quantized graphene and reveal the underlying many-particle mechanisms. To guide the experimental demonstration, we present optimal c…
We demonstrate coherent control of cyclotron resonance (CR) in a two-dimensional electron gas (2DEG). We use a sequence of terahertz pulses to control the amplitude of CR oscillations in an arbitrary fashion via phase-dependent coherent interactions. We observe a self-interaction effect, where the 2DEG interacts with the terahertz field emitted by itself within the decoherence time, resulting in a revival and collapse of quantum coherence. These observations are accurately describable using {\em single-particle} optical Bloch equations, showing no signatures of electron-electron interactions, …
An optical vortex beam carries orbital angular momentum $\ell$ in addition to spin angular momentum $σ$. We demonstrate that a Landau-quantized two dimensional electron system absorbs the optical vortex beam through modified selection rules, reflecting two kinds of angular momenta. The lowest Landau level electron absorbs the optical vortex beams with $σ=1$ (positive helicity) and $\ell=0$ or $σ=-1$ (negative helicity) and $\ell=2$ in the electric dipole transition. The induced electric currents survive only along the edge of the sample, due to cancellation of the bulk currents. Thus, the magn…
In recent years, control of group velocity of light has attracted enormous interest. One of the main challenges is to realize an absorption-free fast or slow light propagation. Here, we study dispersion and absorption properties of a weak probe field in a Landau-quantized graphene and report a gain-assisted superluminal light propagation. Moreover, an attempt is made to develop an analytical expression and necessary parameters for switching the group velocity of the probe field from subluminal to superluminal. It's worth mentioning that large dephasing rate in graphene offers feasibility of su…
The Landau level laser has been proposed a long time ago as a unique source of monochromatic radiation, widely tunable in the THz and infrared spectral ranges using an externally applied magnetic field. In spite of decades of efforts, this appealing concept never resulted in the design of a reliable device. This is due to efficient Auger scattering of Landau-quantized electrons, which is an intrinsic non-radiative recombination channel that eventually gains over cyclotron emission in all materials studied so far: in conventional semiconductors with parabolic bands, but also in graphene with ma…
We investigate Landau-quantized excitonic absorption and luminescence of monolayer WSe$_2$ under magnetic field. We observe gate-dependent quantum oscillations in the bright exciton and trions (or exciton-polarons) as well as the dark trions and their phonon replicas. Our results reveal spin- and valley-polarized Landau levels (LLs) with filling factors $n = +0, +1$ in the bottom conduction band and $n = -0$ to $-6$ in the top valence band, including the Berry-curvature-induced $n = \pm0$ LLs of massive Dirac fermions. The LL filling produces periodic plateaus in the exciton energy shift accom…
The frictional drag between parallel two-dimensional electron systems has been measured in a regime of strong interlayer correlations. When the bilayer system enters the excitonic quantized Hall state at total Landau level filling factor ν_T=1 the longitudinal component of the drag vanishes but a strong Hall component develops. The Hall drag resistance is observed to be accurately quantized at h/e^2.
In three-dimensional topological insulators (TIs), the nontrivial topology in their electronic bands casts a gapless state on their solid surfaces, using which dissipationless TI edge devices based on the quantum anomalous Hall (QAH) effect and quantum Hall (QH) effect have been demonstrated. Practical TI devices present a pair of parallel-transport topological surface states (TSSs) on their top and bottom surfaces. However, due to the no-go theorem, the two TSSs always appear as a pair and are expected to quantize synchronously. Quantized transport of a separate Dirac channel is still desirab…
We study theoretically the two-dimensional topological electric state in a single band semiconductor with strong spin-orbit interactions under harmonic scalar electrostatic potentials. The electronic states described by the spin Landau levels are insulating in the bulk and host gapless edge states in the presence of time-reversal symmetry. Such topological states show the properties of the quantized electric conductivity and the quantized spin Hall conductivity characterized by the spin Chern number $\mathbb{Z}$. The quantization of the two conductivities are robust under various perturbations…
The 2D semimetal consisting of heavy holes and light electrons is studied. The consideration is based on assumption that electrons are quantized by magnetic field while holes remain classical. We assume also that the interaction between components is weak and the conversion between components is absent. The kinetic equation for holes colliding with quantized electrons is utilized. It has been stated that the inter-component friction and corresponding correction to the dissipative conductivity $σ_{xx}$ {\it do not vanish at zero temperature} due to degeneracy of the Landau levels. This correcti…
The Rabi model considers a two-level system (or spin-1/2) coupled to a quantized harmonic oscillator and describes the simplest interaction between matter and light. The recent experimental progress in solid-state circuit quantum electrodynamics has engendered theoretical efforts to quantitatively describe the mathematical and physical aspects of the light-matter interaction beyond the rotating wave approximation. We develop a stochastic Schrödinger equation approach which enables us to access the strong-coupling limit of the Rabi model and study the effects of dissipation, and AC drive in an …
We study generation and dynamics of an exchange spin qubit encoded in three coherently coupled quantum dots with three electrons. For two geometries of the system a linear and a triangular one, the creation and coherent control of the qubit states are performed by the Landau--Zener transitions. In the triangular case both the qubit states are equivalent and can be easily generated for particular symmetries of the system. If one of the dots is smaller than the others one can observe Rabi oscillations, that can be used for coherent manipulation of the qubit states. The linear system is easier to…
The quantum Hall effect (QHE) with quantized Hall resistance of h/νe2 starts the research on topological quantum states and lays the foundation of topology in physics. Afterwards, Haldane proposed the QHE without Landau levels, showing nonzero Chern number |C|=1, which has been experimentally observed at relatively low temperatures. For emerging physics and low-power-consumption electronics, the key issues are how to increase the working temperature and realize high Chern numbers (C>1). Here, we report the experimental discovery of high-Chern-number QHE (C=2) without Landau levels and C=1 Cher…
The motion of micro- and nanomechanical resonators can be coupled to electromagnetic fields. Such optomechanical setups allow one to explore the interaction of light and matter in a new regime at the boundary between quantum and classical physics. We propose an approach to investigate non-equilibrium photon dynamics driven by mechanical motion in a recently developed setup with a membrane between two mirrors, where photons can be shuttled between the two halves of the cavity. For modest driving strength we predict the possibility to observe an Autler-Townes splitting indicative of Rabi dynamic…
We report ultra-low temperature experiments on the obscure fractional quantum Hall effect (FQHE) at Landau level filling factor $ν$=5/2 in a very high mobility specimen of $μ=1.7 \times 10^7$ cm$^2$/Vs. We achieve an electron temperature as low as $\sim$ 4~mK, where we observe vanishing $R_{xx}$ and, for the first time, a quantized Hall resistance, $R_{xy}=h/(5/2e^2)$ to within 2 ppm. $R_{xy}$ at the neighboring odd-denominator states $ν$=7/3 and 8/3 is also quantized. The temperature dependences of the $R_{xx}$-minima at these fractional fillings yield activation energy gaps $Δ_{5/2}$=0.11K, …
Delayed Formation of Landau Polaritons in Phase-Resolved THz Spectroscopy
Centera Labs, Institute of High Pressure Physics, Polish Academy of Sciences（波兰科学院高压物理研究所）；Centera, Cezamat, Warsaw University of Technology（华沙理工大学）；Weitzman Institute of Science（魏茨曼科学研究所）；Faculty of Physics, University of Warsaw（华沙大学物理学院）
We present an analytical approach to the problem of the multiphoton absorption and Rabi oscillations in an armchair graphene nanoribbon (AGNR) in the presence of a time-oscillating strong electric field induced by a light wave directed parallel to the ribbon axis. The two-dimensional Dirac equation for the massless electron subject to the ribbon confinement is employed. In the resonant approximation the electron-hole pair production rate, associated with the electron transitions between the valence and conduction size-quantized subbands, the corresponding multiphoton absorption coefficient and…
We propose a cavity QED approach to describe light-matter interaction between an individual anharmonic molecular vibration and an infrared cavity field. Starting from a generic Morse oscillator with quantized nuclear motion, we derive a multi-level quantum Rabi model to study vibrational polaritons beyond the rotating-wave approximation. We analyze the spectrum of vibrational polaritons in detail and compare with available experiments. For high excitation energies, the spectrum exhibits a dense manifold of true and avoided level crossings as the light-matter coupling strength and cavity freque…
We review low and high field magnetotransport in 80 nm-thick strained HgTe, a material that belongs to the class of strong three-dimensional topological insulators. Utilizing a top gate, the Fermi level can be tuned from the valence band via the Dirac surface states into the conduction band and allows studying Landau quantization in situations where different species of charge carriers contribute to magnetotransport. Landau fan charts, mapping the conductivity $ σ_{xx}(V_g, B) $ in the whole magnetic field - gate voltage range, can be divided into six areas, depending on the state of the parti…
Using the Landauer formulation of transport theory, we predict that dielectric quantum wires should exhibit quantized thermal conductance at low temperatures in a ballistic phonon regime. The quantum of thermal conductance is universal, independent of the characteristics of the material, and equal to $π^2 k^2_B T /3h$ where $k_B$ is the Boltzmann constant, h is Planck's constant and T is the temperature. Quantized thermal conductance should be experimentally observable in suspended nanostructures adiabatically coupled to reservoirs, devices that can be realized at the present time.
The optical emission spectrum of a quantum dot in strong coupling with the single mode of a microcavity is obtained in the nonlinear regime. We study how exciton-exciton interactions alter the emission spectrum of the system, bringing the linear Rabi doublet into a multiplet structure that is strongly dependent on the cavity-exciton energy detuning. We emphasise how nonlinearity can be used to evidence the genuine quantum nature of the coupling by producing satellites peaks of the Rabi doublet that originate from the quantized energy levels of the interactions.
Motivated by recent experiments demonstrating intricate quantum Hall physics on the surface of elemental bismuth, we consider proximity coupling an $s$-wave superconductor to a two-dimensional electron gas with strong Rashba spin-orbit interactions in the presence of a strong perpendicular magnetic field. We focus on the high-field limit so that the superconductivity can be treated as a perturbation to the low-lying Landau levels. In the clean case, wherein the superconducting order parameter takes the form of an Abrikosov vortex lattice, we show that a lattice of hybridized Majorana modes eme…
We study the relaxation dynamics of the electron system in graphene flakes under Landau quantization regime using a novel approach of time-resolved Raman scattering. The non-resonant character of the experiment allows us to analyze the field dependence of the relaxation rate. Our results clearly evidence sharp increase in the relaxation rate upon the resonance between the energy of the Landau transition and the G-band and shed new light on relaxation mechanism of the Landau-quantized electrons in graphene beyond the previously studied Auger scattering.
On the level of single atoms and photons, the coupling between atoms and the electromagnetic field is typically very weak. By employing a cavity to confine the field, the strength of this interaction can be increased many orders of magnitude to a point where it dominates over any dissipative process. This strong-coupling regime of cavity quantum electrodynamics has been reached for real atoms in optical cavities, and for artificial atoms in circuit QED and quantum-dot systems. A signature of strong coupling is the splitting of the cavity transmission peak into a pair of resolvable peaks when a…
We study the current and charge distribution of a two dimensional electron gas under strong perpendicular magnetic fields within the linear response regime. We show within a self-consistent screening theory that incompressible strips with integer values of local Landau-level filling factor exist for finite intervals of the magnetic field strength $B$. Within an essentially local conductivity model, we find that the current density in these $B$ intervals is confined to the incompressible strips of vanishing local longitudinal resistivity. This leads to vanishing longitudinal and exactly quantiz…
We propose that the electronic structure of twisted bilayer graphene (TBG) can be understood as Dirac fermions coupled with opposite pseudo magnetic fields generated by the moiré pattern. The two low-energy flat bands from each monolayer valley originate from the two zeroth pseudo Landau levels of Dirac fermions under such opposite effective magnetic fields, which have opposite sublattice polarizations and carry opposite Chern numbers $\pm1$, giving rise to helical edge states in the gaps below and above the low-energy bulk bands near the first magic angle. We argue that small Coulomb interact…
