Simple Two-level System Research Articles

Path-filtering in path-integral simulations of open quantum systems using GFlowNets.

An important class of methods for modeling dynamics in open quantum systems is based on the well-known influence functional (IF) approach to solving path-integral equations of motion. Within this paradigm, path-filtering schemes based on the removal of IF elements that fall below a certain threshold aim to reduce the effort needed to calculate and store the influence functional, making very challenging simulations possible. A filtering protocol of this type is considered acceptable as long as the simulation remains mathematically stable. This, however, does not guarantee that the approximated dynamics preserve the physics of the simulated process. In this paper, we explore the possibility of training Generative Flow Networks (GFlowNets) to produce filtering protocols while optimizing for mathematical stability and for physical accuracy. Trained using the trajectory balance objective, the model produces sets of paths to be added to a truncated initial set; it is rewarded if the combined set of paths gives rise to solutions in which the trace of the density matrix is conserved, the populations remain real, and the dynamics approach the exact reference. Using a simple two-level system coupled to a dissipative reservoir, we perform proof-of-concept simulations and demonstrate the elegant and surprising filtering solutions proposed by the GFlowNet.

Quantum Otto cycle under strong coupling.

Quantum heat engines are often discussed under the weak-coupling assumption that the interaction between the system and the reservoirs is negligible. Although this setup is easier to analyze, this assumption cannot be justified on the quantum scale. In this study, a quantum Otto cycle model that can be generally applied without the weak-coupling assumption is proposed. We replace the thermalization process in the weak-coupling model with a process comprising thermalization and decoupling. The efficiency of the proposed model is analytically calculated and indicates that, when the contribution of the interaction terms is neglected in the weak-interaction limit, it reduces to that of the earlier model. The sufficient condition for the efficiency of the proposed model not to surpass that of the weak-coupling model is that the decoupling processes of our model have a positive cost. Moreover, the relation between the interaction strength and the efficiency of the proposed model is numerically examined by using a simple two-level system. Furthermore, we show that our model's efficiency can surpass that of the weak-coupling model under particular cases. From analyzing the majorization relation, we also find a design method of the optimal interaction Hamiltonians, which are expected to provide the maximum efficiency of the proposed model. Under these interaction Hamiltonians, the numerical experiment shows that the proposed model achieves higher efficiency than that of its weak-coupling counterpart.

Quasi-parity-time symmetric dynamics in periodically driven two-level non-Hermitian system

<sec>In recent years, there have been intensive studies of non-Hermitian physics and parity–time (PT) symmetry due to their fundamental importance in theory and outstanding applications. A distinctive character in PT-symmetric system is phase transition (spontaneous PT-symmetry breaking), i.e. an all-real energy spectrum changes into an all-complex one when the non-Hermitian parameter exceeds a certain threshold. However, the conditions for PT-symmetric system with real energy spectrum to occur are rather restrictive. The generalization of PT-symmetric potentials to wider classes of non-PT-symmetric complex potentials with all-real energy spectra is a currently important endeavor. A simple PT-symmetric two-level Floquet quantum system is now being actively explored, because it holds potential for the realization of non-unitary single-qubit quantum gate. However, studies of the evolution dynamics of non-PT-symmetric two-level non-Hermitian Floquet quantum system are still relatively rare.</sec><sec></sec><sec>In this paper, we investigate the non-Hermitian physics of a periodically driven non-PT-symmetric two-level quantum system. By phase-space analysis, we find that there exist so-called pseudo fixed points in phase space representing the Floquet solutions with fixed population difference and a time-dependent relative phase between the two levels. According to these pseudo fixed points, we analytically construct a non-unitary evolution operator and then explore the dynamic behaviors of the non-PT-symmetric two-level quantum system in different parameter regions. We confirm both analytically and numerically that the two-level non-Hermitian Floquet quantum system, although it is non-parity-time-symmetric, still features a phase transition with the quasienergy spectrum changing from all-real to all-complex energy spectrum, just like the PT symmetric system. Furthermore, we reveal that a novel phenomenon called quasi-PT symmetric dynamics occurs in the time evolution process. The quasi-PT symmetric dynamics is so named in our paper, in the sense that the time-evolution of population probabilities in the non-PT-symmetric two-level system satisfies fully the time-space symmetry (PT symmetry), while time-evolution of the quantum state (containing the phase) does not meet such a PT symmetry, due to the fact that time-evolution of the phases of the probability amplitudes on the two levels violates the requirement for the PT symmetry.</sec>

Quasi-Parity-Time symmetric dynamics in a periodcially driven two-level non-Hermitian system

In recent years, there have been intensive studies on non-Hermitian physics and parity-time (PT) symmetry, due to their fundamental importance in theory and outstanding applications. A distinctive character in PT-symmetric systems is phase transition (spontaneous PT-symmetry breaking), where the energy spectrum changes from all real to complex when the non-Hermitian parameter exceeds a certain threshold. However, the conditions for PT-symmetric system with real energy spectrum to occur are rather restrictive. Generalization of PT-symmetric potentials to wider classes of non-PT-symmetric complex potentials with all-real spectra is a currently important endeavor. The simple PT-symmetric two-level Floquet quantum system is now being actively explored, because it holds potential for realization of non-unitary single-qubit quantum gate. However, studies on the evolution dynamics of non-PT-symmetric two-level non-Hermitian Floquet quantum system still remain relatively rare.<br>In this paper, we investigate the non-Hermitian physics of a periodically driven non-PT-symmetric two-level quantum system. By phase-space analysis, we find that there exist so-called pseudo fixed points in phase space representing the Floquet solutions with fixed population difference and a time-dependent relative phase between the two levels. Based on these pseudo fixed points, we analytically construct the non-unitary evolution operator and then explore the dynamics of the non-PT-symmetric two-level quantum system in different parameter regions. We confirm both analytically and numerically that the two-level non-Hermitian Floquet quantum system, although being non-parity-time-symmetric, still features a phase transition with the quasienergy spectrum changing from all real to complex, just as for PT symmetric systems. Furthermore, we reveal that a novel phenomenon called quasi-PT symmetric dynamics occurs in the time evolution process. The quasi-PT symmetric dynamics is so named in our paper, in the sense that the time-evolution of population probabilities in the non-PT-symmetric two-level system respects fully the time-space symmetry (PT symmetry), while time-evolution of the quantum state (containing the phase) does not, due to the fact that time-evolution of the phases of the probability amplitudes on the two levels violates the PT symmetry requirement.

Weak-value amplification and the lifetime of a decaying particle

We study the possibility of varying the measured lifetime of a decaying particle based on the technique of weak value amplification in which an additional filtering process called postselection is performed. Our analysis made in a direct measurement scheme presented here shows that, for simple two-level systems, the lifetime may be prolonged more than three times compared to the original one, while it can also be shortened arbitrarily by a proper choice of postselection. This result is consistent with our previous analysis on the possible prolongation of the lifetime of $B$ mesons that may be observed in laboratories, and suggests room for novel applications of weak-value amplification beyond precision measurement conventionally considered.

Relaxation of a dense ensemble of spins in diamond under a continuous microwave driving field

Decoherence of Rabi oscillation in a two-level quantum system consists of two components, a simple exponential decay and a damped oscillation. In dense-ensemble spin systems like negatively charged nitrogen-vacancy (NV−) centers in diamond, fast quantum state decoherence often obscures clear observation of the Rabi nutation. On the other hand, the simple exponential decay (or baseline decay) of the oscillation in such spin systems can be readily detected but has not been thoroughly explored in the past. This study investigates in depth the baseline decay of dense spin ensembles in diamond under continuously driving microwave (MW). It is found that the baseline decay times of NV− spins decrease with the increasing MW field strength and the MW detuning dependence of the decay times shows a Lorentzian-like spectrum. The experimental findings are in good agreement with simulations based on the Bloch formalism for a simple two-level system in the low MW power region after taking into account the effect of inhomogeneous broadening. This combined investigation provides new insight into fundamental spin relaxation processes under continuous driving electromagnetic fields and paves ways to better understanding of this underexplored phenomena using single NV− centers, which have shown promising applications in quantum computing and quantum metrology.

Derivation of the stationary fluorescence spectrum formula for molecular systems from the perspective of quantum electrodynamics

Numerical simulations of stationary fluorescence spectra of molecular systems usually rely on the relation between the photon emission rate and the system’s dipole–dipole correlation function. However, research papers usually take this relation for granted, and standard textbook expositions of the theory of fluorescence spectra also tend to leave out this important relation. In order to help researchers with less theoretical training gain a deeper understanding of the emission process, we perform a step-by-step derivation of the expression for the fluorescence spectrum, focusing on rigorous mathematical treatment and the underlying physical content. Right from the start, we employ quantum description of the electromagnetic field, which provides a clear picture of emission that goes beyond the phenomenological treatment in terms of the Einstein A coefficient. Having obtained the final expression, we discuss the relation of the latter to the present level of theory by studying a simple two-level system. From the technical perspective, the present work also aims at familiarizing the reader with the density matrix formalism and with the application of the double-sided Feynman diagrams.

A Gen-3 10-kV SiC MOSFET-Based Medium-Voltage Three-Phase Dual Active Bridge Converter Enabling a Mobile Utility Support Equipment Solid State Transformer

The emergence of medium-voltage silicon carbide (SiC) power semiconductor devices, in ranges of 10&#x2013;15 kV, has led to the development of simple two-level converter systems for medium-voltage applications. A medium-voltage mobile utility support equipment-based three-phase solid state transformer (MUSE-SST) system, based on Gen3 10 kV SiC MOSFETs, is developed to interconnect a three-phase 4160 V/60 Hz grid to a three-phase 480 V/60 Hz grid to provide a shore-to-ship power interface for naval vessels. The MUSE-SST system consists of three power conversion stages, namely, MVac/MVdc stage (MV: active front-end converter), MVdc/LVdc stage (dual active bridge converter), and LVdc/LVac stage (LV: active front-end converter). The galvanic isolation is introduced in the MVdc/LVdc stage using MV/LV high-frequency transformers (HFTs). This article demonstrates the operation of the three-phase Y&#x2013;<inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula> connected dual active bridge converter used in the MVdc/LVdc stage of the MUSE-SST system. Equations for phase currents, power flow, and zero-voltage switching (ZVS) boundaries are derived for all possible modes for the three-phase Y&#x2013;<inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula> configuration. A detailed parasitic simulation model is derived by measuring and experimentally verifying the parasitic elements of the HFT. A brief discussion regarding the design considerations required for the hardware development of the medium- and low-voltage sides of the three-phase dual active bridge converter is also provided. Successful tests demonstrating the operation and feasibility of the medium-voltage dual active bridge converter, at medium-voltage levels (7.2 kV dc-link voltage), are shown. The results indicate that these devices can accelerate the growth and deployment of the medium-voltage SiC-based converter for isolated and bidirectional medium- to low-voltage dc systems.

Optimal Quantum Control Theory

This article explains some fundamental ideas concerning the optimal control of quantum systems through the study of a relatively simple two-level system coupled to optical fields. The model for this system includes both continuous and impulsive dynamics. Topics covered include open- and closed-loop control, impulsive control, open-loop optimal control, quantum filtering, and measurement feedback optimal control.

Reconfigurable nonreciprocity with low insertion loss using a simple two-level system.

Nonreciprocal light propagation is essential to control the direction of the light flow. Here, we report the realization of magnetic-free optical nonreciprocity using a simple two-level system driven by a pump field in warm atoms. In our experiment, we not only demonstrate less than 0.5 dB of insertion loss and up to 20 dB of isolation but also provide flexible and reconfigurable operations of the isolation bandwidth, frequency, and direction. Nonreciprocal scheme with these characteristics may find important applications in photonic devices.

NESSi: The Non-Equilibrium Systems Simulation package

The nonequilibrium dynamics of correlated many-particle systems is of interest in connection with pump–probe experiments on molecular systems and solids, as well as theoretical investigations of transport properties and relaxation processes. Nonequilibrium Green’s functions are a powerful tool to study interaction effects in quantum many-particle systems out of equilibrium, and to extract physically relevant information for the interpretation of experiments. We present the open-source software package NESSi (The Non-Equilibrium Systems Simulation package) which allows to perform many-body dynamics simulations based on Green’s functions on the L-shaped Kadanoff–Baym contour. NESSi contains the library libcntr which implements tools for basic operations on these nonequilibrium Green’s functions, for constructing Feynman diagrams, and for the solution of integral and integro-differential equations involving contour Green’s functions. The library employs a discretization of the Kadanoff–Baym contour into time N points and a high-order implementation of integration routines. The total integrated error scales up to O(N−7), which is important since the numerical effort increases at least cubically with the simulation time. A distributed-memory parallelization over reciprocal space allows large-scale simulations of lattice systems. We provide a collection of example programs ranging from dynamics in simple two-level systems to problems relevant in contemporary condensed matter physics, including Hubbard clusters and Hubbard or Holstein lattice models. The libcntr library is the basis of a follow-up software package for nonequilibrium dynamical mean-field theory calculations based on strong-coupling perturbative impurity solvers. Program summaryProgram Title: NESSiCPC Library link to program files:http://dx.doi.org/10.17632/973crf9hgd.1Licensing provisions: MPL v2.0Programming language: C++, pythonExternal routines/libraries: cmake, eigen3, hdf5 (optional), mpi (optional), omp (optional)Nature of problem: Solves equations of motion of time-dependent Green’s functions on the Kadanoff–Baym contour.Solution method: Higher-order solution methods of integral and integro-differential equations on the Kadanoff–Baym contour.

EM Field Frequency Down-Conversion in a Quantum Two-Level System Damped by Squeezed Vacuum Reservoir

Down-conversion of high-frequency EM field in a simple quantum two-level system (also known as two-level atom) with broken inversion symmetry driven by a coherent laser field and damped by a squeezed vacuum reservoir is analyzed. It is shown that the squeezing leads to broadening of the low-frequency radiative peak in the fluorescence spectrum of the system. At the same time, changing the reference phase of the squeezed field and the degree of squeezing allows to manipulate the shape of this peak.

Tunable and switchable triple-wavelength ytterbium-doped fiber ring laser based on Sagnac interferometer with a polarization-maintaining photonic crystal fiber

A tunable and switchable triple-wavelength ytterbium-doped fiber laser (YDFL) based on a polarization-maintaining photonic crystal fiber (PMPCF) Sagnac interferometer is proposed and experimentally demonstrated. Owing to the large inhomogeneity of gain profile and simple two-level system of ytterbium-doped fiber, a tunable triple-wavelength lasing output is achieved with a tuning range of 1.6 nm. At room temperature, the maximum wavelength shift and peak power fluctuation are less than 0.018 nm and 0.64 dB, respectively. Moreover, the output lasing can be switched to single-wavelength lasing or dual-wavelength lasing through adjusting polarization controller. A tunable single-wavelength lasing with the side-mode suppression ratio above 50 dB is achieved from the wavelength of 1034.276 nm to 1038.314 nm. Two kinds of tunable dual-wavelength lasing with the tuning range of 3.2 nm are obtained in our experiment. In addition, the temperature stability is discussed by constructing the YDFL with PMPCF and conventional polarization-maintaining fiber (PMF), respectively. Experimental results demonstrate that the measured temperature sensitivity for PMPCF-based YDFL is 0.014 nm/℃, which is five times lower than that for PMF-based YDFL.

Vibration-assisted exciton transfer in molecular aggregates strongly coupled to confined light fields.

We investigate exciton transport through one-dimensional molecular aggregates interacting strongly with a cavity mode. Unlike several prior theoretical studies treating the monomers as simple two-level systems, exciton-vibration coupling is explicitly included in the description of open quantum dynamics of the system. In the framework of the Holstein-Tavis-Cummings model with truncated vibrational space, we investigate the steady-state exciton transfer through both a molecular dimer and longer molecular chains. For a molecular dimer, we find that vibration-assisted exciton transfer occurs at strong exciton-cavity coupling regime where the vacuum Rabi splitting matches the frequency of a single vibrational quantum, whereas for longer molecular chains, vibration-assisted transfer is found to occur at the ultrastrong exciton-cavity coupling limit. In addition, finite relaxation of vibrational modes induced by the continuous phonon bath is found to further facilitate the exciton transport in vibrational enhancement regimes.

Dual frequency comb photon echo spectroscopy

Dual frequency comb (DFC) nonlinear spectroscopy is an emerging technique that can be used to study a variety of molecular nonlinear responses by exploiting the automatic pulse-to-pulse time delay scanning and fast data acquisition characteristics of the DFC techniques. Here, we propose a DFC-based photon echo spectroscopy (DFC-PES), where two optical frequency comb lasers have slightly different repetition rates and are also allowed to have different carrier frequencies. We first demonstrate our theoretical approach for DFC linear spectroscopy. Then, the signals expected from the proposed DFC-PES are theoretically calculated. The slight offset in the pulse repetition rates enables asynchronous optical sampling and automatic scanning of the time intervals between different field–matter interaction events, making frequency tuning unnecessary. Analytic expression of the third-order photon echo signal is demonstrated in two frequency dimensions for a simple two-level model system. The signal has a well-defined and simple connection to the underlying third-order response function and exhibits the expected down-conversion features from the optical frequency into the radio frequency region with a down-conversion factor that is experimentally controllable.

Reconsideration of the generalized second law based on information geometry

The maximum work formulation of the second law of thermodynamics has been generalized to transitions between nonequilibrium states. The generalization involves the relative entropy between nonequilibrium states and canonical states. The relative entropy scaled by the temperature of the canonical state quantifies the work available for extraction from the nonequilibrium state. This scaled relative entropy can be interpreted as an energy-dimensional divergence in information geometry. The generalized Pythagorean theorem relating three energy-scaled divergences, which we interpret as thermodynamic distances, gives a geometrical interpretation of the generalized maximum work formulation. Under this interpretation the optimal cyclic operation to extract work from a nonequilibrium state is discussed in a simple two-level quantum system.

Intermolecular mechanism for multiple maxima in molecular dynamic susceptibility

A simple two-level system is introduced to demonstrate the existence of the intermolecular mechanism of the appearance/disappearance of multiple maxima in molecular dynamic susceptibility at low temperature. With minimum two relaxation processes, quantum tunneling induced by the nuclear spin bath and the direct process due to the spin-phonon interaction, we prove that the existence of a sufficiently wide dipolar field distribution in the experimental sample is the main cause of this phenomenon in zero or weak applied dc field. The correlations between the phenomenon and the applied dc field, temperature, or magnetic dilution of the sample are also investigated. Application to several experimental systems has shown a good agreement between the proposed theory and experiments. Cases with more complex multiplet spectrum, more relaxation processes,and possibility of more maxima in the molecular dynamic susceptibility are discussed.

Universal, high-fidelity quantum gates based on superadiabatic, geometric phases on a solid-state spin-qubit at room temperature

Geometric phases and holonomies are a promising resource for the realization of high-fidelity quantum operations in noisy devices, due to their intrinsic fault-tolerance against parametric noise. However, for a long time their practical use in quantum computing was limited to proof of principle demonstrations. This was partly due to the need for adiabatic time evolution or the requirement of complex, high-dimensional state spaces and a large number of driving field parameters to achieve universal quantum gates employing holonomies. In 2016 Liang et al. proposed universal, superadiabatic, geometric quantum gates exploiting transitionless quantum driving, thereby offering fast and universal quantum gate performance on a simple two-level system. Here, we report on the experimental implementation of a set of non-commuting single-qubit superadiabatic, geometric quantum gates on the electron spin of the nitrogen-vacancy center in diamond under ambient conditions. This provides a promising and powerful tool for large-scale quantum computing under realistic, noisy experimental conditions.

Optimal operating protocol to achieve efficiency at maximum power of heat engines.

Efficiency at maximum power has been investigated extensively, yet the practical control scheme to achieve it remains elusive. We fill this gap with a stepwise Carnot-like cycle, which consists of the discrete isothermal process (DIP) and adiabatic process. With DIP, we validate the widely adopted assumption of the C/t relation of the irreversible entropy generation S^{(ir)} and show the explicit dependence of the coefficient C on the fluctuation of the speed of tuning energy levels as well as the microscopic coupling constants to the heat baths. Such a dependence allows us to control the irreversible entropy generation by choosing specific control schemes. We further demonstrate the achievable efficiency at maximum power and the corresponding control scheme with the simple two-level system. Our current work opens new avenues for an experimental test, which was not feasible due to the lack the of the practical control scheme in the previous low-dissipation model or its equivalents.

Quantum Jarzynski equality of measurement-based work extraction.

Many studies of quantum-size heat engines assume that the dynamics of an internal system is unitary and that the extracted work is equal to the energy loss of the internal system. Both assumptions, however, should be under scrutiny. In the present paper, we analyze quantum-scale heat engines, employing the measurement-based formulation of the work extraction recently introduced by Hayashi and Tajima [M. Hayashi and H. Tajima, arXiv:1504.06150]. We first demonstrate the inappropriateness of the unitary time evolution of the internal system (namely, the first assumption above) using a simple two-level system; we show that the variance of the energy transferred to an external system diverges when the dynamics of the internal system is approximated to a unitary time evolution. Second, we derive the quantum Jarzynski equality based on the formulation of Hayashi and Tajima as a relation for the work measured by an external macroscopic apparatus. The right-hand side of the equality reduces to unity for "natural" cyclic processes but fluctuates wildly for noncyclic ones, exceeding unity often. This fluctuation should be detectable in experiments and provide evidence for the present formulation.