General N-level Research Articles

Modeling and Analysis of Shutdown Dynamics in Flying Capacitor Multilevel Converters

This work explores the dynamic behavior of the flying capacitor multilevel (FCML) converter during unplanned shutdown. A model for a general N-level FCML converter is developed, which captures capacitor non-linearities, component leakage paths, and body diode behavior. This work highlights how switch voltage ratings may be exceeded during unplanned shutdown, and proposes several mitigation strategies. Using a ten-level FCML converter hardware prototype, the time-domain behavior of the model is verified, and a successful hardware mitigation strategy is demonstrated which ensures safe and rapid converter shutdown.

GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls

The GRadient Ascent Pulse Engineering (GRAPE) method is widely used for optimization in quantum control. GRAPE is gradient search method based on exact expressions for gradient of the control objective. It has been applied to various coherently controlled closed and open quantum systems. In this work, we adopt the GRAPE method for optimizing objective functionals in open quantum systems driven by both coherent and incoherent controls. In our case, a tailored or engineered environment acts on the controlled system as control via time-dependent decoherence rates or, equivalently, via spectral density of the environment. To develop the GRAPE approach for this problem, we compute gradient of various objectives for general N-level open quantum systems for the piecewise constant class of control. The case of a single qubit is considered in details and solved analytically. For this case, an explicit analytical expression for evolution and objective gradient is obtained via diagonalization of a matrix determining the system’s dynamics in the Bloch ball. The diagonalization is obtained by solving a cubic equation via Cardano’s method. The efficiency of the algorithm is demonstrated through numerical simulations for the state-to-state transition problem and its complexity is estimated. Robustness of the optimal controls is also studied.

Nested-sphere description of the N -level Chern number and the generalized Bloch hypersphere

The geometric interpretation of (pseudo)spin 1/2 systems on the Bloch sphere has been appreciated across different areas ranging from condensed matter to quantum information and high energy physics. Although similar notions for larger Hilbert spaces are established in mathematics, they have been so far less explored beyond the two-level case for practical usage in condensed matter settings, or have involved restrictions to sub manifolds within the full Hilbert space. We here employ a coherence vector description to theoretically characterize a general N-level system on the higher dimensional generalized Bloch (hyper)sphere by respecting the structure of the underlying SU(N) algebra and construct physically intuitive geometric pictures for topological concepts. Focusing on two spatial dimensions, we reveal a geometric interpretation for the Chern number in larger Hilbert spaces in terms of a nested structure comprising N-1 two-spheres. We demonstrate that for the N-level case, there is an exterior two-sphere that provides a useful characterization of the system, notably by playing a primary role in determining the Chern number. The external sphere can be directly measured in ultracold atoms via well-established band mapping techniques, thereby imparting knowledge of the topological nature of state. We also investigate how the time evolution of the coherence vector defined on the generalized Bloch hypersphere can be utilized to extract the full state vector in experiments, allowing us to develop a tomography scheme involving quenches for three-level systems. Our geometric description opens up a new avenue for the interpretation of the topological classification and the dynamical illustration of multi-level systems, which in turn is anticipated to help in the design of new experimental probes.

Theoretical Analysis and Experimental Validation of Flying-Capacitor Multilevel Converters Under Short-Circuit Fault Conditions

Addressing the increasing demand for high-efficiency and high-power-density converters, the flying-capacitor multilevel converter has shown itself as a promising topology. A key advantage of this topology is the reduced voltage rating of the switches, though also makes it vulnerable to device failure during short-circuit conditions. Despite large interest in fault-tolerant operation of these converters, alongside detailed descriptions of flying-capacitor balancing, little research has focused on the converter short-circuit fault analysis, which may cause a switch failure if not properly designed for. Therefore, this article presents a comprehensive model describing the large-signal short-circuit switching behavior of a general N-level flying-capacitor multilevel converter. Highly simplified models used to predict the evolution of the switch current and voltage stress during the fault are proposed, targeted at practicing engineers for conservative design guidelines. These models are used to determine the critical time for remedial action of the converter before reaching some predefined maximum conditions. A 2-to-10-level fully configurable flying-capacitor multilevel converter and a fault circuit hardware prototype are used to experimentally perform different short-circuit tests that show a good match to the measured behavior.

The structure of phase diagrams in matter-radiation systems**This work is dedicated to the memory of Professor Roy Glauber, for his numerous contributions to the development and promotion of quantum optics and mathematical physics.

We present a study of the structure of phase diagrams for matter-radiation systems, based on the use of coherent states and the catastrophe formalism, that compares very well with the exact quantum solutions as well as providing analytical expressions. Emphasis is made on 2- and 3-level systems, but in general n-level systems in the presence of ℓ electromagnetic modes are described. Due to the infinite-dimensional nature of the Hilbert space, and using the results of the analyses and the behaviour of the solutions, we construct a sequence of ever-approximating reduced bases, which make possible the study of larger systems both, in the number of atoms and in the number of excitations. These studies are of importance in fundamental quantum optics, quantum information, and quantum cryptography scenarios.

Timing Calculations for a General N-Level Dodecagonal Space Vector Structure Using Only Reference Phase Voltages

Multilevel inverters with dodecagonal (12-sided polygon) voltage space vector (SV) structures have advantages like extension of linear modulation range, elimination of fifth and seventh harmonics in phase voltages and currents for the full modulation range including extreme 12-step operation, reduced device voltage ratings, lesser dv/dt stresses on devices and motor phase windings resulting in lower EMI/EMC problems, and lower switching frequency-making it more suitable for high-power drive applications. This paper proposes a simple method to obtain pulsewidth modulation (PWM) timings for a dodecagonal voltage SV structure using only sampled reference voltages. In addition to this, a carrier-based method for obtaining the PWM timings for a general N-level dodecagonal structure is proposed in this paper for the first time. The algorithm outputs the triangle information and the PWM timing values which can be set as the compare values for any carrier-based hardware PWM module to obtain SV PWM like switching sequences. The proposed method eliminates the need for angle estimation, computation of modulation indices, and iterative search algorithms that are typical in multilevel dodecagonal SV systems. The proposed PWM scheme was implemented on a five-level dodecagonal SV structure. Exhaustive simulation and experimental results for steady-state and transient conditions are presented to validate the proposed method.

A New Space Vector Modulation Scheme for Multilevel Inverters Which Directly Vector Quantize the Reference Space Vector

A new space-vector-based sigma delta modulation scheme for any general N-level voltage source inverter is proposed in this paper, which directly quantizes the reference space vector. The proposed scheme uses the sigma delta modulation with the quantizer implemented by the proposed space vector quantizer. A new scheme is proposed for directly quantizing the reference space vector to the multilevel inverter switching vectors without mapping it into two-level inverter vector space. Voronoi regions of the multilevel inverter vector space in the proposed space vector quantizer are defined as a parallelogram with the inverter switching vectors as its vertices. The property of the integer values of the inverter switching vectors in 60° coordinates is utilized for the direct vector quantization of the instantaneous reference voltage space vector. The proposed scheme is implemented for five-level inverters realized by an open-end-winding induction motor fed with two three-level inverters from either side having symmetrical dc-link voltages, and results are presented.

Symmetric logarithmic derivative for general n-level systems and the quantum Fisher information tensor for three-level systems

Within a geometrical context, we derive an explicit formula for the computation of the symmetric logarithmic derivative for arbitrarily mixed quantum systems, provided that the structure constants of the associated unitary Lie algebra are known. To give examples of this procedure, we first recover the known formulae for two-level mixed and three-level pure state systems and then apply it to the novel case of U(3), that is for arbitrarily mixed three-level systems (q-trits). Exploiting the latter result, we finally calculate an expression for the Fisher tensor for a q-trit considering also all possible degenerate subcases.

The n-level, n − 1-mode Jaynes–Cummings model: spectrum and eigenvectors

We explicitly find eigenvectors and eigenvalues of the general n-level, n − 1-mode Jaynes–Cummings model in Λ-configuration possessing arbitrary detuning parameters Δi, and arbitrary interaction strengths gi, . In the case of equal interaction strengths gi = gj, , we compare the obtained answers with those obtained by the algebraic Bethe ansatz method (Skrypnyk 2008 J. Phys. A: Math. Theor. 41 475202; 2009 J. Math. Phys. 50 103523).

Simple multilevel inverter-based induction motor drive scheme using sigma–delta converter with space-vector quantiser

In this study, sigma–delta (ΣΔ) modulation-based random pulse width modulations (PWM) scheme with vector quantisation for three-level inverter is proposed. In the proposed scheme, the instantaneous reference space vector is mapped to an equivalent two-level inverter and the proposed space-vector-based ΣΔ modulation is applied on this mapped reference space vector. The scheme uses the principle of vector quantisation for quantising the mapped reference space vector in the ΣΔ modulator. The switching signals are generated directly from the amplitude of the three-phase reference signal without using lookup table and complex arithmetic calculations. The resultant vectors of the two-level inverter can be easily translated to the actual switching vectors, and this proposed method of working on the mapped reference space vector makes the proposed scheme suitable for any general n-level inverter. The switching vectors of the inverter are naturally selected ensuring optimum switching sequence under all conditions including the over-modulation region. The proposed scheme is implemented for three-level inverter driving a two-horse power (HP) three-phase induction motor. The performance of the proposed scheme is compared with space-vector PWM scheme and random PWM schemes with different modulation indices and experimental results are presented.

Analysis of an asymmetric modulation method for cascaded multilevel inverters

Traditional means for implementing the switching of the power switches in multilevel converters is subharmonic pulse width modulation (SHPWM) or triangulation approach involving a comparison between a target reference waveform and several high-frequency carrier waveforms where all the power switches usually work at high switching frequency. The asymmetric modulation method (AMM) which is derived from hybrid modulation method is illustrated. The contribution of asymmetric modulation is to provide a general method of finding the locus of the output stepped-wave for the hybrid modulation method. This study also provides an illustration of the ‘Mathematic expression of modulation process’ of SHPWM and AMM where it is easy to see how the two techniques are related, and the output expression of the AMM method can be easily obtained from the general N-level double-Fourier output expressions of SHPWM where cumbersome mathematical work has been avoided. Through the analysis of modulation process for SHPWM and AMM, results show that the AMM is an improved version of SHPWM method with optimised switching combination. Theoretical analysis, simulation and experimental results are provided to validate the feasibility of the proposed analysis method.

Optimal laser control of double quantum dots

Coherent single-electron control in a realistic semiconductor double quantum dot is studied theoretically. Using optimal-control theory we show that the energy spectrum of a two-dimensional double quantum dot has a fully controllable transition line. We find that optimized picosecond laser pulses generate population transfer at significantly higher fidelities (> 0.99) than conventional sinusoidal pulses. Finally we design a robust and fast charge switch driven by optimal pulses that are within reach of terahertz laser technology. Double quantum dots (DQDs), i.e., coupled twodimensional (2D) electron traps, have been under recent and extensive studies both experimentally 1,2,3 and theoretically. 4,7,8 The main interest in DQDs arises from their potential for solid-state quantum computation that could be achieved in principle by rapidly switching voltages of electrostatic gates. The gates permit to tune at will the system geometry and hence the electronic properties of DQDs. Coherent manipulation of a single charge 2 and coupled spins 1 has already been achieved, and recently a coherence time of ∼ 200 ns was obtained for a well isolated silicon DQD. 3 Theoretical studies on single-electron transport inside the DQD driven by linear switches and linearly polarized continuous waves (CWs) were reported very recently. 4 In the latter case the transport is rather sensitive to possible anharmonicity of the potential and limited to uncoupled dots far apart from each other. Electron control in DQDs has been studied also using genetic algorithms 5 as well as rotating-wave and resonant approximations leading to a reduction to a threelevel system. 6 To the best of our knowledge, however, a general N-level control scheme by using direct external electric fields has not been introduced for 2D-DQDs until now. In this paper we discuss the controllability criteria for single-electron states of DQDs by means of external laser pulses. We show that at certain interdot distances some of the single-electron states allow full population transfer from the ground state to those states. We apply quantum optimal-control theory (OCT) 9 which yields the optimal laser pulses for predefined transitions. We obtain high occupations (& 99%) of the target states in a realistic DQD in a few picoseconds, which is well in the coherent regime. If the initial and final states are chosen to have full localization of the electron in one or the other dot, this scheme enables rapid and controlled transport which is not sensitive to the interdot distance or to the inevitable anharmonicities in the confining potential.

Linearization of the Multi-Level SVPWM Signal Generation in the Over-Modulation Region Extending up to Six-Step Mode Using Only the Sampled Amplitudes of Reference Phase Voltages

A multi-level PWM signal generation with linear transfer characteristics between fundamental component of output voltage and modulation index is proposed in this paper for a n-level SVPWM signal generation. The reference signal to the PWM modulator is pre-scaled in over-modulation region, keeping the fundamental component of the modified signals same as the original signal. The modified reference signal is always confined within the carrier region. Thus linear transfer characteristics can be extended throughout the over-modulation region up to six-step mode to get the maximum utilization of DC link, for multi-level inverter drive control of any general n-level. In this paper, the principle of pre-scaling the reference signal, based on a look up table, for two-level PWM generation is extended to a general n-level SVPWM. The whole PWM signal generation is implemented using only the sampled amplitudes of reference phase voltages and the algorithm is very suitable for real time implementation on DSP processors. A five-level inverter configuration, using an open-end winding induction motor drive, is used for verifying the SVPWM generation scheme, experimentally.

Resonance theory of decoherence and thermalization

We present a rigorous analysis of the phenomenon of decoherence for general N-level systems coupled to reservoirs. The latter are described by free massless bosonic fields. We apply our general results to the specific cases of the qubit and the quantum register. We compare our results with the explicitly solvable case of systems whose interaction with the environment does not allow for energy exchange (non-demolition, or energy conserving interactions). We suggest a new approach which applies to a wide variety of systems which are not explicitly solvable.

Asymptotically noise decoupling for Markovian open quantum systems

The noise decoupling problem is investigated for general N-level Markovian open quantum systems. Firstly, the concept of Cartan decomposition of the Lie algebra $su(N)$ is introduced as a tool of designing control Hamiltonians. Next, under certain assumptions, it is shown that a part of variables of the coherence vector of the system density matrix can be asymptotically decoupled from the environmental noises. The resulting noise decoupling scheme is applied to one-qubit, qutrit and two-qubit quantum systems, by which the coherence evolution of the one-qubit and qutrit systems can always be asymptotically preserved, while, for two-qubit systems, our findings indicate that evolution of some variables can be preserved only for some initial states.

A Space Vector PWM Scheme for Multilevel Inverters Based on Two-Level Space Vector PWM

Multilevel inverters are increasingly being used in high-power medium voltage applications due to their superior performance compared to two-level inverters. Among various modulation techniques for a multilevel inverter, the space vector pulsewidth modulation (SVPWM) is widely used. However, the implementation of the SVPWM for a multilevel inverter is complicated. The complexity is due to the difficulty in determining the location of the reference vector, the calculation of on-times, and the determination and selection of switching states. This paper proposes a general SVPWM algorithm for multilevel inverters based on standard two-level SVPWM. Since the proposed multilevel SVPWM method uses two-level modulation to calculate the on-times, the computation of on-times for an n-level inverter becomes easier. The proposed method uses a simple mapping to achieve the SVPWM for a multilevel inverter. A general n-level implementation is explained, and experimental results are given for three-level and five-level inverters

Comment on ‘Exact results for survival probability in the multistate Landau–Zener model’

We correct the proof of the Brundobler–Elser formula (BEF) provided in Volkov and Ostrovsky (2004 J. Phys. B: At. Mol. Opt. Phys. 37 4069) and continued in the appendix of Volkov and Ostrovsky (2005 J. Phys. B: At. Mol. Opt. Phys. 38 907). After showing that some changes of variables employed in these articles are used erroneously, we propose an alternative change of variables which solves the problem. In our proof, we reveal the connection between the BEF for a general N-level Landau–Zener system and the exactly solvable bow-tie model. The special importance of the diabatic levels with maximum/minimum slope is emphasized throughout.

Mapping approach to the semiclassical description of nonadiabatic quantum dynamics

A theoretical formulation is outlined that allows us to extend the semiclassical Van Vleck--Gutzwiller formulation to the description of nonadiabatic quantum dynamics on coupled potential-energy surfaces. In this formulation the problem of a classical treatment of discrete quantum degrees of freedom (DoF) such as electronic states is bypassed by transforming the discrete quantum variables to continuous variables. The mapping approach thus consists of two steps: an exact quantum-mechanical transformation of discrete onto continuous DoF (the ``mapping'') and a standard semiclassical treatment of the resulting dynamical problem. Extending previous work [G. Stock and M. Thoss, Phys. Rev. Lett. 78, 578 (1997)], various possibilities for obtaining a mapping from discrete to continuous DoF are investigated, in particular the Holstein-Primakoff transformation, Schwinger's theory of angular momentum [in Quantum Theory of Angular Momentum, edited by L. C. Biedenharn and H. V. Dam (Academic, New York, 1965)], and the spin-coherent-state representation. Although all these representations are exact on the quantum-mechanical level, the accuracy of their semiclassical evaluation is shown to differ considerably. In particular, it is shown that a generalization of Schwinger's theory appears to be the only transformation that provides an exact description of a general N-level system within a standard semiclassical evaluation. Exploiting the connection between spin-coherent states and Schwinger's representation for a two-level system, furthermore, a semiclassical initial-value representation of the corresponding spin-coherent-state propagator is derived. Although this propagator represents an approximation, its appealing numerical features make it a promising candidate for the semiclassical description of large molecular systems with many DoF. Adopting various spin-boson-type models (i.e., a two-level system coupled to a single or many DoF), computational studies are presented for Schwinger's and the spin-coherent-state representation, respectively. The performance of the semiclassical approximation in the case of regular and chaotic classical dynamics as well as for multimode electronic relaxation dynamics is discussed in some detail.

Conditional Hamiltonian and reset operator in the quantum jump approach

For the time development of a single system in the quantum jump approach or for quantum trajectories one requires the conditional (reduced) Hamiltonian between jumps and the reset operator after a jump. Explicit expressions for them are derived for a general N-level system by employing the same assumptions as in the usual derivation of the Bloch equations. We discuss a possible minor problem with positivity for these expressions as well as for the corresponding Bloch equations.

How to reset an atom after a photon detection: Applications to photon-counting processes.

The question is studied as to which state a radiating atom has to be reset to if a photon is detected and absorbed. This is important for applications of a recently proposed approach to photon counts from a radiating atom which is based upon repeated gedanken measurements and associated reductions as a technical tool. The general reset density matrix is determined. It may depend on the atomic state shortly before the photon detection, and may thus be time dependent. It may also have off-diagonal terms which may lead to interesting coherence effects. It is shown that the repeated measurements together with the reset matrix lead to the optical Bloch equations for a general N-level atom. The general photon-counting distribution for an N-level radiating atom is derived and the axiomatic continuous-measurement theory of Srinivas and Davies [Opt. Acta 28, 981 (1981); 29, 235 (1982)] for quantum-counting processes is shown to follow in the present framework from ordinary quantum mechanics.