Quantum Dynamical Theory Research Articles

A Quantum Algorithm from Response Theory: Digital Quantum Simulation of Two-Dimensional Electronic Spectroscopy.

Multidimensional optical spectroscopies are powerful techniques to investigate energy transfer pathways in natural and artificial systems. Because of the high information content of the spectra, numerical simulations of the optical response are of primary importance to assist the interpretation of spectral features. However, the increasing complexity of the investigated systems and their quantum dynamics call for the development of novel simulation strategies. In this work, we consider using digital quantum computers. By combining quantum dynamical simulation and nonlinear response theory, we present a quantum algorithm for computing the optical response of molecular systems. The quantum advantage stems from the efficient quantum simulation of the dynamics governed by the molecular Hamiltonian, and it is demonstrated by explicitly considering exciton-vibrational coupling. The protocol is tested on a near-term quantum device, providing the digital quantum simulation of the linear and nonlinear response of simple molecular models.

The electron–phonon coupling coefficient for high-temperature superconductors

The expression for the electron–phonon coupling coefficient (gk) is obtained by solving a six order polynomial equation obtained via the quantum dynamical many-body theory of the electron and phonon Green’s function for high-temperature superconductors (HTSs). The developed equation depends on the temperature; electron, phonon, and pairon frequencies; and distribution functions. The YBa2Cu3O7−δ cuprate superconductor has been used for the purpose of analysis and is found to be in agreement with the fact that gk decreases with the increase in temperature above 0 K. The distinct behavior obtained via dispersion for gk in different directions, [100] and [010], marked the anisotropy of electron–phonon coupling in HTSs. The derived expression for gk is further used for the evaluation of the superconducting gap via the Bardeen–Cooper–Schrieffer and the McMillan gap equation and both superconducting gap equations approach the Tc value for YBa2Cu3O7−δ, and the obtained reduced gap ratio [2Δ(0)/kBTc] is found to be in the limit of the reduced gap ratio of HTSs.

Study of Electron Density of States and Electronic Heat Capacity of High-temperature Cuprate Superconductor: La2−xSrxCuO4

The renormalized electron density of states (REDOS) has been studied using quantum dynamical many-body theory of electron Green’s functions via model Hamiltonian and Born-Mayer-Huggins (BMH) potential. Different leading contributions due to harmonic phonons and electrons, their interactions, anharmonicities, and defects are included in the Hamiltonian. The cuprate superconductor La2−xSrxCuO4 has been taken up for numerical investigation purposes. The modified scenario of REDOS displays strong dependence on temperature. The results of REDOS have been utilized to investigate the electronic heat capacity (EHC). The REDOS and EHC are resolved into the isolated contributions coming from point impurities, electron-phonon interactions, and anharmonic modes. The obtained results of EHC concluding that EHC strongly affected by the contribution of defects, anharmonicities, and electron-phonon interactions and their amplitude are very small as per establish results. Thus, the considered effects show a substantial role in the study of REDOS and EHC and reveal some fascinating features.

Quantum process identification: a method for characterizing non-markovian quantum dynamics

Established methods for characterizing quantum information processes do not capture non-Markovian (history-dependent) behaviors that occur in real systems. These methods model a quantum process as a fixed map on the state space of a predefined system of interest. Such a map averages over the system’s environment, which may retain some effect of its past interactions with the system and thus have a history-dependent influence on the system. Although the theory of non-Markovian quantum dynamics is currently an active area of research, a systematic characterization method based on a general representation of non-Markovian dynamics has been lacking. In this article we present a systematic method for experimentally characterizing the dynamics of open quantum systems. Our method, which we call quantum process identification (QPI), is based on a general theoretical framework which relates the (non-Markovian) evolution of a system over an extended period of time to a time-local (Markovian) process involving the system and an effective environment. In practical terms, QPI uses time-resolved tomographic measurements of a quantum system to construct a dynamical model with as many dynamical variables as are necessary to reproduce the evolution of the system. Through numerical simulations, we demonstrate that QPI can be used to characterize qubit operations with non-Markovian errors arising from realistic dynamics including control drift, coherent leakage, and coherent interaction with material impurities.

The high-temperature superconductor gap equation

The expressions for superconducting gap (SG) have been derived using the quantum dynamical many-body theory of electron density of states for high-temperature superconductors (HTSs). The developed two-gap equations depend on the temperature, Fermi energy and renormalized electron and phonon energies that emerge as signatures of anharmonic effects. The computation of the SG compared with the Bardeen–Cooper–Schrieffer gap is found to be in good agreement in the low-temperature region with slight deviation near the critical temperature (Tc). The gap equation reveals anisotropic nature and the reduced gap ratio ( for ) is found in the upper limit of the reduced gap ratio for HTSs. Both the SG equations approach the same critical temperature. The pairing potential is derived using the SG equation and numerically analyzed for , which shows that Tc depends on the strength of the pairing potential and we explore the possibilities to elevate the transition temperature Tc.

Theory of open quantum dynamics with hybrid noise

We develop a theory to describe dynamics of a non-stationary open quantum system interacting with a hybrid environment, which includes high-frequency and low-frequency noise components. One part of the system–bath interaction is treated in a perturbative manner, whereas the other part is considered exactly. This approach allows us to derive a set of master equations where the relaxation rates are expressed as convolutions of the Bloch–Redfield and Marcus formulas. Our theory enables analysis of systems that have extremely small energy gaps in the presence of a realistic environment. As an illustration, we apply the theory to the 16 qubit quantum annealing problem with dangling qubits (Dickson et al 2013 Nat. Commun. 4 1903) and show qualitative agreement with experimental results.

Modern Approach to Optical Absorption in Cuprate Superconductors

Adopting the many body quantum dynamical theory of phonon Green’s functions via a general Hamiltonian which includes the effects of electron-phonon interactions, anharmonicities and impurities (but not those of BCS terms) the theory of infrared (i.r.) absorption has been investigated which separates out into (i) diagonal and (ii) non-diagonal contributions. The non-diagonal contribution emerges only in the impure crystals and becomes extinct in pure crystals. The critical investigations divulges that the infrared (i.r.) absorption coefficients not only depends upon electron-phonon coupling coefficient but also on temperature, which appears as the unique feature of the present theory and provide us a plat form to study a system in superconducting and normal regions. The Y B a 2 C u 3 O 7−δ superconductor has been taken for the purpose of analysis and comparison with the well-established experimental results.

Completely positive dynamical semigroups and quantum resonance theory

Starting form a microscopic system-environment model, we construct a quantum dynamical semigroup for the reduced evolution of the open system. The difference between the true system dynamics and its approximation by the semigroup has the following two properties: It is (linearly) small in the system-environment coupling constant for all times, and it vanishes exponentially quickly in the large time limit. Our approach is based on the quantum dynamical resonance theory.

Quantum dynamical field theory for nonequilibrium phase transitions in driven open systems

We develop a quantum dynamical field theory for studying phase transitions in driven open systems coupled to Markovian noise, where non-linear noise effects and fluctuations beyond semiclassical approximations influence the critical behaviour. We systematically compare the diagrammatics, the properties of the renormalization group flow and the structure of the fixed points, of the novel quantum dynamical field theory and of its semi-classical counterpart, which is employed to characterise dynamical criticality in three dimensional driven-dissipative condensates. As an application, we perform the Keldysh Functional Renormalization of a one dimensional driven open Bose gas, where a tailored diffusion Markov noise realises an analog of quantum criticality for driven-dissipative condensation. We find that the associated non-equilibrium quantum phase transition does not map into the critical behaviour of its three dimensional classical driven counterpart.

Scattering Events and Heat Conductivity of Layered La 2-x Sr x CuO 4 Superconductors

The problem of heat conduction in layered La2-x SrxCuO4 superconductor has been investigated in a new frame work of in-plane and cross-plane concepts with the help of modified Callaway model of thermal conductivity based on relaxation time approximation. Using the many body quantum dynamical theory of the expressions for thermal conductivity in context of in-plane and cross plane have been obtained and results are found in excellent agreement with experimental observations for layered La2-x SrxCuO4 cuprate superconductors. The theory explores the possibility of device fabrication cold in one direction and hot in the other.

First-principles quantum dynamical theory for the dissociative chemisorption of H2O on rigid Cu(111).

Despite significant progress made in the past decades, it remains extremely challenging to investigate the dissociative chemisorption dynamics of molecular species on surfaces at a full-dimensional quantum mechanical level, in particular for polyatomic-surface reactions. Here we report, to the best of our knowledge, the first full-dimensional quantum dynamics study for the dissociative chemisorption of H2O on rigid Cu(111) with all the nine molecular degrees of freedom fully coupled, based on an accurate full-dimensional potential energy surface. The full-dimensional quantum mechanical reactivity provides the dynamics features with the highest accuracy, revealing that the excitations in vibrational modes of H2O are more efficacious than increasing the translational energy in promoting the reaction. The enhancement of the excitation in asymmetric stretch is the largest, but that of symmetric stretch becomes comparable at very low energies. The full-dimensional characterization also allows the investigation of the validity of previous reduced-dimensional and approximate dynamical models.

Computational multiqubit tunnelling in programmable quantum annealers.

Quantum tunnelling is a phenomenon in which a quantum state traverses energy barriers higher than the energy of the state itself. Quantum tunnelling has been hypothesized as an advantageous physical resource for optimization in quantum annealing. However, computational multiqubit tunnelling has not yet been observed, and a theory of co-tunnelling under high- and low-frequency noises is lacking. Here we show that 8-qubit tunnelling plays a computational role in a currently available programmable quantum annealer. We devise a probe for tunnelling, a computational primitive where classical paths are trapped in a false minimum. In support of the design of quantum annealers we develop a nonperturbative theory of open quantum dynamics under realistic noise characteristics. This theory accurately predicts the rate of many-body dissipative quantum tunnelling subject to the polaron effect. Furthermore, we experimentally demonstrate that quantum tunnelling outperforms thermal hopping along classical paths for problems with up to 200 qubits containing the computational primitive.

Density‐matrix theory of quantum dynamics under a strong external field switched on nonadiabatically

Quantum time‐evolution equations for the density matrix are formulated in the unrestricted Hartree–Fock approximation, with an emphasis on the nonperturbative effect due to a sudden or gradual onset of a strong external field. Numerical simulations are performed for ideal Fermi gas around a square‐well potential which is switched on dynamically. When the switching is fast enough, an oscillatory motion of the particle is induced by a nonadiabatic transition at the Landau–Zener crossing point, which is most clearly seen in a small‐size system. When the switching is sufficiently slow, the simulation corroborates the adiabatic theorem. It is shown that the Anderson's infrared catastrophe in a metal is strongly enhanced by the nonperturbative effect. The Keldysh formula of atomic multiphoton ionization can also be derived from the nonperturbative term in the density‐matrix equation, indicating a wide applicability of the present theory. © 2014 Wiley Periodicals, Inc.

Anharmonicity and Disorder Effect on the Free Energy of Crystalline Solids

Dealing with the anharmonic phonon-electron problem with the help of double time temperature dependent Green’s Function theory of quantum dynamics the general and explicit expressions for the lattice energy, partition function, free energy have been derived for an impurity induced anharmonic crystalline solid. The effects of mass and force constant change terms between the impurity and host lattice atoms are taken into account, and the cubic and quartic anharmonic terms are also retained in an almost complete Hamiltonian to develop the many body theory. The general trend of low and high temperature contributions to Helmholtz free energy is obtained via three dimensional graphics.

Towards many-dimensional real-time quantum theory for heavy-particle dynamics. II. Beyond semiclassics by quantum smoothing of the singularity in quantum-classical correspondence

A theory of many-dimensional real-time quantum dynamics is studied in terms of action decomposed function (ADF), a class of quantum wave function. In the preceding companion paper [S. Takahashi and K. Takatsuka, Phys. Rev. A 89, 012108 (2014)], we showed that semiclassical dynamics for ADF in the Lagrange picture of phase flow can be described in terms of what we call deviation determinant and associated quantum phases without use of the stability matrix. Consequently, the Hessian of the involved potential functions is not required in this formalism. This paper is devoted to an analysis of the mechanism of quantum diffusion (quantum smoothing) that removes the singularity inherent in the semiclassical ADF: We derive a Lorentzian form for the amplitude factor of ADF. The real part of its denominator comes from the deviation determinant, while the imaginary part reflects quantum diffusion and is proportional to the Planck constant. The presence of the nonzero imaginary part smooths out the singularity and removes the divergence. Besides, this imaginary part can be obtained through a Wronskian relation with the deviation vectors, which can be solved rather easily at each space-time point on a classical trajectory. A number of theoretical advantages of the Lorentzian form and the Wronskian relation are illustrated theoretically and numerically. It turns out that there is no essential difficulty in applications to many-dimensional heavy-particle systems such as molecules. The theory is examined with stringent numerical tests.

Truncated configuration interaction expansions as solvers for correlated quantum impurity models and dynamical mean-field theory

The development of polynomial cost solvers for correlated quantum impurity models, with controllable errors, is a central challenge in quantum many-body physics, where these models find applications ranging from nano-science to the dynamical mean-field theory (DMFT). Here we describe how configuration interaction (CI) approximations to exact diagonalization (ED) may be used as solvers in DMFT. CI approximations retain the main advantages of ED, such as the ability to treat general interactions and off-diagonal hybridizations and to obtain real spectral information, but are of polynomial cost. Furthermore, their errors can be controlled by monitoring the convergence of physical quantities as a function of the CI hierarchy. Using benchmark DMFT applications, such as single-site DMFT of the 1D Hubbard model and $2\times 2$ cluster DMFT of the 2D Hubbard model, we show that CI approximations allow us to obtain near-exact ED results for a tiny fraction of the cost. This is true over the entire range of interaction strengths including "difficult" regimes, such as in the pseudogap phase of the 2D Hubbard model. We use the ability of CI approximations to treat large numbers of orbitals to demonstrate convergence of the bath representation in the $2\times 2$ cluster DMFT using a 24 bath orbital representation. CI approximations thus form a promising route to extend ED to problems that are currently difficult to study using other solvers such as continuous-time quantum Monte Carlo, including impurity models with large numbers of orbitals and general interactions.

Static Structure Factor of Two-Dimensional Liquid 3He Adsorbed on Graphite

Liquid 3He is a model system for strongly correlated Fermi liquids. For this reason, many X-ray and neutron scattering experiments have been performed to understand the structure and dynamics of this quantum fluid. We have recently shown that two-dimensional liquid 3He sustains long-lived zero-sound excitations at large wave-vectors (Godfrin et al., Nature, 483:576, 2012). Here we show that its static structure factor can be obtained with reasonable accuracy by integrating the experimental S(Q,ω) over a suitable energy range. A good agreement is found between the static structure factor deduced from the experiment and theoretical models: Quantum Monte Carlo simulations and Dynamical Many Body Theory (DMBT). At high wave-vectors, the experimental values are underestimated because of the limited accessible phase space; nevertheless, even at atomic wave-vectors a semi-quantitative agreement is observed with the theoretical predictions.

Quantum dynamics in ultracold atomic physics

We review recent developments in the theory of quantum dynamics in ultra-cold atomic physics, including exact techniques, but focusing on methods based on phase-space mappings that are appli- cable when the complexity becomes exponentially large. These phase-space representations include the truncated Wigner, positive-P and general Gaussian operator representations which can treat both bosons and fermions. These phase-space methods include both traditional approaches using a phase-space of classical dimension, and more recent methods that use a non-classical phase-space of increased dimensionality. Examples used include quantum EPR entanglement of a four-mode BEC, time-reversal tests of dephasing in single-mode traps, BEC quantum collisions with up to 106 modes and 105 interacting particles, quantum interferometry in a multi-mode trap with nonlinear absorp- tion, and the theory of quantum entropy in phase-space. We also treat the approach of variational optimization of the sampling error, giving an elementary example of a nonlinear oscillator.

Full-band quantum-dynamical theory of saturation and four-wave mixing in graphene

The linear and nonlinear optical response of graphene are studied within a quantum-mechanical, full-band, steady-state density-matrix model. This nonpurtabative method predicts the saturatable absorption and saturable four-wave mixing of graphene. The model includes τ(1) and τ(2) time constants that denote carrier relaxation and quantum decoherence, respectively. Fits to existing experimental data yield τ(2) < 1 fs due to carrier-carrier scattering. τ(1) is found to be on the timescale from 250 fs to 550 fs, showing agreement with experimental data obtained by differential transmission measurements.

Squeezing components in linear quantum feedback networks

The aim of this article is to extend linear quantum dynamical network theory to include static Bogoliubov components (such as squeezers). Within this integrated quantum network theory, we provide general methods for cascade or series connections, as well as feedback interconnections using linear fractional transformations. In addition, we define input-output maps and transfer functions for representing components and describing convergence. We also discuss the underlying group structure in this theory arising from series interconnection. Several examples illustrate the theory.