Nonlinear optical studies of the transient coherence in the Quantum Hall system

We review recent investigations of the femtosecond nonlinear optical response of the two-dimensional electron gas (2DEG) in a strong magnetic field. We probe the Quantum Hall (QH) regime for filling factors ν∼1. Our focus is on the transient coherence induced via optical excitation and on its time evolution during early femtosecond timescales. We simultaneously study the interband and intraband coherence in this system by using a nonlinear spectroscopic technique, transient three-pulse four wave mixing optical spectroscopy, and a many-body theory. We observe striking differences in the temporal and spectral profile of the nonlinear optical signal between a modulation doped quantum well system (with the 2DEG) and a similar undoped quantum well (without a 2DEG). We attribute these qualitative differences to Coulomb correlations between the photoexcited electron-hole pairs and the 2DEG. We show, in particular, that intraband many-particle coherences assisted by the inter-Landau-level magnetoplasmon excitations of the 2DEG dominate the femtosecond nonlinear optical response. The most striking effect of these exciton-magnetoplasmon coherences is a large off-resonant four-wave-mixing signal in the case of very low photoexcited carrier densities, not observed in the undoped system, with strong temporal oscillations and unusually symmetric temporal profile.     

Minigap plasmons in a two-dimensional electron gas subjected to a one-dimensional periodic potential

We investigate the plasmon excitations in a two-dimensional electron gas subjected to a one-dimensional weak periodic potential. We derive and discuss the dispersion relations for both intrasubband and intersubband excitations within the framework of Bohm-Pines' random-phase approximation. For such an anisotropic system with spatially modulated charge density, we observe a splitting of the 2D plasmon dispersion. The splitting is caused by the superlattice effect of the charge-density modulation on the collective excitation spectrum. We also discuss how the tunneling and the potential amplitude affect the plasmon excitations.     

Emergence of electromagnetically induced absorption in a perturbation solution of optical Bloch equations

We study phenomenon of electromagnetically induced absorption (EIA) in the Hanle configuration by applying a perturbative method to solve linear system of optical Bloch equations (OBEs) for the case of closed F _g = 1 → F _e = 2 transition. The method is applied assuming stationary case and a weak laser fields (Ω ≪ Γ, i.e., Rabi frequency small compared to spontaneous emission rate). This way, we calculate (both numerically and analytically) higher order corrections to density matrix. Odd corrections give contributions to optical coherences, while even corrections contribute to populations and Zeeman coherences. The method gives insight into mechanism of transfer of coherences and transfer of populations between Zeeman sublevels. We have found that the ground-state coherences (2nd correction to coherences) are crucial for the 4th correction to the change of populations which brings EIA type behavior of the Hanle spectrum. Using exact analytical expressions we further discuss further the role of decoherence of the ground-state sublevels when forming EIA.     

Homogeneous broadenings in 2D solid-state NMR of half-integer quadrupolar nuclei

The question of the homogeneous broadening that occurs in 2D solid-state NMR experiments is examined. This homogeneous broadening is mathematically introduced in a simple way, versus the irreversible decay rates related to the coherences that are involved during t1 and t2. We give the pulse sequences and coherence transfer pathways that are used to measure these decay rates. On AlPO4 berlinite, we have measured the 27Al echo-type relaxation times of the central and satellite transitions on 1Q levels, so that of coherences that are situated on 2Q, 3Q, and 5Q levels. We compare the broadenings that can be deduced from these relaxation times to those directly observed on the isotropic projection of berlinite with multiple-quantum magic-angle spinning (MAS), or satellite-transition MAS. We show that the choice of the high-resolution method, should be done according to the spin value and the corresponding homogeneous broadening.     

One-dimensional band-edge absorption in a doped quantum wire

Low-temperature photoluminescence-excitation spectra are studied in an n-type modulation-doped T-shaped single quantum wire with a gate to tune electron densities. With a nondegenerate one-dimensional (1D) electron gas, the band-edge absorption exhibits a sharp peak structure induced by the 1D density of states. When the dense 1D electron gas is degenerate at a low temperature, we observe a Fermi-edge absorption onset without many-body modifications.     

Radio-frequency spectroscopy of a strongly interacting two-dimensional Fermi gas

We realize and study a strongly interacting two-component atomic Fermi gas confined to two dimensions in an optical lattice. Using radio-frequency spectroscopy we measure the interaction energy of the strongly interacting gas. We observe the confinement-induced Feshbach resonance on the attractive side of the 3D Feshbach resonance and find the existence of confinement-induced molecules in very good agreement with theoretical predictions.     

Magnetic field studies of the frictional drag between coupled two-dimensional electronic systems – Coulomb versus phonon coupling

The coupling between systems of two spatially separated two-dimensional (2D) electron gases and between systems of a separated 2D electron gas and a 2D hole gas is studied as a function of magnetic field . The small barrier (30 nm) separated coupled electron gases showed a transition from a phonon dominated interaction at to a Coulomb dominated one at quantising fields. For large barriers (190 nm) phonons have been found to be the dominant coupling mechanism both at zero and finite fields. However, for all barriers investigated we could observe novel screening effects manifested in a suppression of the coupling at half-filled Landau levels. For the coupled electron–hole gases we have investigated samples with large barriers ( ) so that the coupling is both in zero and finite fields dominated by phonon mediated processes. The enhanced screening effects could not be observed in those samples possibly due to the less pronounced quantisation of the hole gas.     

Photon-induced vanishing of magnetoconductance in 2D electrons on liquid helium

We report on a novel transport phenomenon realized by optical pumping in surface state electrons on helium subjected to perpendicular magnetic fields. The electron dynamics is governed by the photon-induced excitation and scattering-mediated transitions between electric subbands. In a range of magnetic fields, we observe vanishing longitudinal conductivity σ(xx)→0. Our result suggests the existence of radiation-induced zero-resistance states in the nondegenerate 2D electron system.     

Fractional magnetization plateaus and magnetic order in the Shastry-Sutherland magnet TmB4

We investigate the phase diagram of TmB4, an Ising magnet on a frustrated Shastry-Sutherland lattice, by neutron diffraction and magnetization experiments. At low temperature we find Néel order at low field, ferrimagnetic order at high field, and an intermediate phase with magnetization plateaus at fractional values M/M_(sat)=1/7,1/8,1/9,... and spatial stripe structures. Using an effective S=1/2 model and its equivalent two-dimensional fermion gas we suggest that the magnetic properties of TmB4 are related to the fractional quantum Hall effect of a 2D electron gas.     

Coherence Evolution and Transfer Supplemented by Sender’s Initial-State Restoring

The evolution of quantum coherences comes with a set of conservation laws provided that the Hamiltonian governing this evolution conserves the spin-excitation number. At that, coherences do not intertwist during the evolution. Using the transmission line and the receiver in the initial ground state we can transfer the coherences to the receiver without interaction between them, although the matrix elements contributing to each particular coherence intertwist in the receiver’s state. Therefore we propose a tool based on the unitary transformation at the receiver side to untwist these elements and thus restore (at least partially) the structure of the sender’s initial density matrix. A communication line with two-qubit sender and receiver is considered as an example of implementation of this technique.     

Obtaining absorptive line shapes in two-dimensional infrared vibrational correlation spectra

Absorptive line shapes in two-dimensional infrared (2D IR) vibrational spectra are important for an intuitive interpretation of molecular structure and dynamics. We obtain an absorptive 2D IR correlation spectrum by summing complementary spectra from experiments sampling vibrational coherences that oscillate with conjugate frequencies in the initial evolution time period. The 2D correlation spectrum of a coupled vibrational system reveals certain spectral features with tilted line shapes that are explained in terms of unequal contributions of Liouville-space pathways.     

MR imaging with phase encoding of intermolecular multiple quantum coherences

Novel 2D and 3D pulse sequences producing images through the phase encoding of intermolecular multiple quantum coherences (i-MQCs) are presented. The signal acquired with these sequences is free from intermolecular zero quantum coherences (i-ZQCs) which are not phase encoded and additional phase cycling eliminates artifacts. Phase encoding during the n-quantum evolution period provides n times the resolution expected from equivalent phase encoding of the reconverted single quantum coherences. These sequences have potential applications for producing i-MQC images of biological tissues as well as nonbiological materials with substantial amounts of water.     

Microwave-induced giant oscillations of the magnetoconductivity in 2D electronic corbino disks with capacitance contacts

Using Corbino disks with capacitance contacts, the microwave photoconductivity of the 2D electron gas in selectively doped GaAs/AlAs heterostructures has been studied at 4.2 K in magnetic fields up to 0.6 T. The giant oscillations of the magnetoconductivity have been revealed in the samples exposed to microwave radiation at high filling factors similar to those earlier discovered in the 2D Corbino disks with ohmic contacts. The results demonstrate that the presence of ohmic contacts is of no importance for the observation of the microwave-induced giant oscillations of the magnetoconductivity in the 2D electron system.     

Multiple Quantum Coherences (MQ) NMR and Entanglement Dynamics in the Mixed-Three-Spin XXX Heisenberg Model with Single-Ion Anisotropy

We analytically investigate Multiple Quantum (MQ) NMR dynamics in a mixed-three-spin (1/2,1,1/2) system with XXX Heisenberg model at the front of an external homogeneous magnetic field B. A single-ion anisotropy property ζ is considered for the spin-1. The intensities dependence of MQ NMR coherences on their orders (zeroth and second orders) for two pairs of spins (1,1/2) and (1/2,1/2) of the favorite tripartite system are obtained. It is also investigated dynamics of the pairwise quantum entanglement for the bipartite (sub)systems (1,1/2) and (1/2,1/2) permanently coupled by, respectively, coupling constants J₁ and J₂, by means of concurrence and fidelity. Then, some straightforward comparisons are done between these quantities and the intensities of MQ NMR coherences and ultimately some interesting results are reported. We also show that the time evolution of MQ coherences based on the reduced density matrix of the pair spins (1,1/2) is closely connected with the dynamics of the pairwise entanglement. Finally, we prove that one can introduce MQ coherence of the zeroth order corresponds to the pair spins (1,1/2) as an entanglement witness at some special time intervals.     

Topological Hall effect and Berry phase in magnetic nanostructures

We discuss the anomalous Hall effect in a two-dimensional electron gas subject to a spatially varying magnetization. This topological Hall effect does not require any spin-orbit coupling and arises solely from Berry phase acquired by an electron moving in a smoothly varying magnetization. We propose an experiment with a structure containing 2D electrons or holes of diluted magnetic semiconductor subject to the stray field of a lattice of magnetic nanocylinders. The striking behavior predicted for such a system (of which all relevant parameters are well known) allows one to observe unambiguously the topological Hall effect and to distinguish it from other mechanisms.     

Phonon images of crystals

Using the pair of coupled Boltzmann kinetic equations for 2D electron gas and bulk acoustic phonons we derive the explicit formula for the phonon drag voltage induced by a pulsed phonon beam. A point source producing very short bursts of monoenergetic phonons is considered. The time integrated signal of the phonon drag voltage is calculated numerically for 2D electron gas lying in a {001} plane. For the raster scanned source of phonons the pattern of induced voltage is obtained and compared to the suitable experimental pattern and to the calculated quasimomentum focusing image. For several phonon propagation directions the dependency of induced voltage on the phonon energy is studied and compared with the experimental results. The ratio of the strength of piezo-electric coupling to the deformation potential constant and the localization length of 2D electrons are fitted.     

Observation of the presuperfluid regime in a two-dimensional Bose gas

In complementary images of coordinate-space and momentum-space density in a trapped 2D Bose gas, we observe the emergence of presuperfluid behavior. As phase-space density ρ increases toward degenerate values, we observe a gradual divergence of the compressibility κ from the value predicted by a bare-atom model, κ(ba). κ/κ(ba) grows to 1.7 before ρ reaches the value for which we observe the sudden emergence of a spike at p = 0 in momentum space. Momentum-space images are acquired by means of a 2D focusing technique. Our data represent the first observation of non-mean-field physics in the presuperfluid but degenerate 2D Bose gas.     

Effects of intersubband coupling on Friedel oscillations in quasi-two-dimensional electron systems

We have studied the effect of screening on an ionized impurity and Freidel oscillations in a quasi-two-dimensional (Q2D) electron system in which multisubbands are occupied. The screening effects of the Q2D electron gas are investigated within the random-phase approximation. We show that in a quantum well in which two subbands are occupied, the intersubband coupling significantly deepens the first minimum in the Friedel oscillation.     

Two-dimensional NMR spectroscopy in Earth's magnetic field

We demonstrate the first two-dimensional correlation NMR (COSY) spectra obtained at ultra low frequencies (ULF) using the Earth's magnetic field. Using a specially developed spectrometer with multiple audio-frequency pulses under controlled pulse phase, we observe magnetisation transfer arising from heteronuclear J-couplings in trifluoroethanol and para-difluorobenzene. The 2D COSY spectra exhibit all diagonal and off-diagonal multiplets consistent with known J-couplings in these molecules.     

Interface states in two-dimensional electron systems with spin-orbital interaction

Interface states at a boundary between regions with different spin-orbit interactions (SOIs) in two-dimensional (2D) electron systems are investigated within the one-band effective mass method with generalized boundary conditions for envelope functions. We have found that the interface states unexpectedly exist even if the effective interface potential equals zero. Depending on the system parameters, the energy of these states can lie in either or both forbidden and conduction bands of bulk states. The interface states have chiral spin texture similar to that of the edge states in 2D topological insulators. However, their energy spectrum is more sensitive to the interfacial potential, the largest effect being produced by the spin-dependent component of the interfacial potential. We have also studied the size quantization of the interface states in a strip of 2D electron gas with SOI and found an unusual (non-monotonic) dependence of the quantization energy on the strip width.