Superconducting circuits coupled to acoustic waveguides have extended the range of phenomena that can be experimentally studied using tools from quantum optics. In particular giant artificial atoms permit the investigation of systems in which the electric dipole approximation breaks down and pronounced non-Markovian effects become important. While previous studies of giant atoms focused on the realm of the rotating-wave approximation, we go beyond this and perform a numerically exact analysis of giant atoms strongly coupled to their environment, in regimes where counterrotating terms cannot be neglected. To achieve this, we use a Lanczos transformation to cast the field Hamiltonian into the form of a one-dimensional chain and employ matrix-product state simulations. This approach yields access to a wide range of system-bath observables and to previously unexplored parameter regimes.
An alternative approximation scheme has been used in solving the Schroedinger equation for the exponential-cosine-screened Coulomb potential. The bound state energies for various eigenstates and the corresponding wave functions are obtained analytically up to the second perturbation term.
We examine a generalized script{PT}-Symmetric quartic anharmonic oscillator model to determine the various physical variables perturbatively in powers of a small quantity ε. We make use of the Bender-Dunne operator basis elements and exploit the properties of the totally symmetric operator T_{m,n}.
We develop a hierarchical functional derivative method to investigate the reduced dynamics of a quantum dissipative system within the framework of a stochastic decoupling description. Keeping only the lowest order truncation of the hierarchical functional derivatives, one can recover the second order Nakajima-Zwanzig quantum master equation. Taking into account the higher-order corrections, our method can be implemented as a highly efficient numerical scheme for a general quantum dissipative system beyond the usual Markovian, rotating-wave, and weak-coupling approximations.
A novel perturbative treatment of the time evolution operator of a quantum system is applied to the model describing a Raman-driven trapped ion in order to obtain a suitable 'effective model'. It is shown that the associated effective Hamiltonian describes the system dynamics up to a certain transformation which may be interpreted as a 'dynamical dressing' of the effective model.
We present a perturbative treatment of the subohmic spin-boson model which remedies a crucial flaw in previous treatments. The problem is traced back to the incorrect application of a Markov type approximation to specific terms in the temporal evolution of the reduced density matrix. The modified solution is consistent both with numerical simulations and the exact solution obtained when the bath-coupling spin-space direction is parallel to the qubit energy-basis spin. We therefore demonstrate that %in distinction to previous findings the subohmic spin-boson model is capable of %consistently de…
Energy levels of neutral atoms have been re-examined by applying an alternative perturbative scheme in solving the Schrodinger equation for the Yukawa potential model with a modified screening parameter. The predicted shell binding energies are found to be quite accurate over the entire range of the atomic number $Z$ up to 84 and compare very well with those obtained within the framework of hyper-virial-Pade scheme and the method of shifted large-N expansion. It is observed that the new perturbative method may also be applied to the other areas of atomic physics.
The quantum dynamics of coupled subsystems connected to a thermal bath is studied. In some of the earlier work the effect of intercenter coupling on the dissipative part was neglected. This is equivalent to a zeroth-order perturbative expansion of the damping term with respect to the intercenter coupling. It is shown numerically for two coupled harmonic oscillators that this treatment can lead to artifacts and a completely wrong description, for example, of a charge transfer processes even for very weak intercenter coupling. Here we perform a first-order treatment and show that these artifacts…
The local approach to construct master equation for a composite open system with a weak internal coupling is simple and seems reasonable. However, it is thermodynamic consistent only when the subsystems are resonantly coupled. Efforts are being made to understand the inconsistency and test the validity of the local master equation. We present a perturbative method to solve the steady-state solutions of linear local master equations, which are demonstrated by two simple models. The solving process shows the stationary state as the result of competition between incoherent operations and the unit…
We discuss the applicability, within the Random Matrix Theory, of perturbative treatment of symmetry breaking to the experimental data on the flip symmetry breaking in quartz crystal. We found that the values of the parameter that measures this breaking are different for the spacing distribution as compared to those for the spectral rigidity. We consider both twofold and threefold symmetries. The latter was found to account better for the spectral rigidity than the former. Both cases, however, underestimate the experimental spectral rigidity at large L. This discrepancy can be resolved if an a…
A new approximation formalism is applied to study the bound states of the Hellmann potential, which represents the superposition of the attractive Coulomb potential $-a/r$ and the Yukawa potential $b\exp (-δr)/r$ of arbitrary strength $b$ and screening parameter $δ$. Although the analytic expressions for the energy eigenvalues $E_{n,l\text{}}$ yield quite accurate results for a wide range of $n,\ell $ in the limit of very weak screening, the results become gradually worse as the strength $b$ and the screening coefficient $δ$ increase. This is because that the expansion parameter is not suffici…
We identify the conditions that guarantee equivalence of the reduced dynamics of an open quantum system (OQS) for two different types of environments - one a continuous bosonic environment leading to a unitary system-environment evolution and the other a discrete-mode bosonic environment resulting in a system-mode (non-unitary) Lindbladian evolution. Assuming initial Gaussian states for the environments, we prove that the two OQS dynamics are equivalent if both the expectation values and two-time correlation functions of the environmental interaction operators are the same at all times for the…
We develop a fully quantum treatment of electromagnetically induced transparency (EIT) in a vapor of three-level $Λ$-type atoms. Both the probe and coupling lasers with arbitrary intensities are quantized, and treated on the same footing. In addition to reproducing known results on ultraslow pulse propagation at the lowest order in the ratio of their Rabi frequencies, our treatment uncovers that the atomic medium with EIT exhibits giant Kerr as well as higher order non-linearities. Enhancement of many orders of magnitude is predicted for higher-order refractive-index coefficients.
The problem of construction of a quantum master equation for a system of sites weakly coupled to each other and to one or more reservoirs (open quantum network) is considered. Microscopic derivation of a quantum master equation requires a diagonalization of the Hamiltonian of the network, which can be a difficult task. When the inter-site couplings are weak, the local approach, which neglects the influence of the inter-site couplings on the system-reservoir couplings, is often used. Recently, some doubts were cast to the consistency of the local approach. We develop a systematic perturbation e…
The theory of full counting statistics allows complete characterization of charge transport processes through nanoscale systems. The majority of existing theoretical treatments used to obtain the current cumulants rely on perturbative approximations with respect to either the system-bath coupling or the electronic tunnelling coupling within the system. This is not generally well suited to electron transfer through organic molecules where these couplings can be on the same order of magnitude. Here we present a non-perturbative approach that uses the formalism of the hierarchical equations of mo…
We examine the dynamics of chiral states of chiral molecules with high tunneling rates in dilute and condensed phases in the context of time-dependent perturbation theory. The chiral molecule is effectively described by an asymmetric double-well potential, whose asymmetry is a measure of chiral interactions. The dilute and condensed phases are conjointly described by a collection of harmonic oscillators but respectively with temperature-dependent sub-ohmic and temperature-independent ohmic spectral densities. We examine our method quantitatively by applying the dynamics to isotopic ammonia mol…
In some instances of study of quantum evolution of classical backgrounds it is considered inevitable to resort to non-perturbative methods at the price of treating the system semiclassically. We show that a fully quantum perturbative treatment, in which the background is resolved as a multi-particle state, recovers the semiclassical non-perturbative results and allows going beyond. We reproduce particle-creation by a classical field in a theory of two scalars as well as in scalar QED in terms of scattering processes of high multiplicity. The multi-particle treatment also gives a transparent pi…
Quantum optics with giant emitters has shown a new route for the observation and manipulation of non-Markovian properties in waveguide-QED. In this paper we extend the theory of giant atoms, hitherto restricted to the perturbative light-matter regime, to deal with the ultrastrong coupling regime. Using static and dynamical polaron methods we address the low energy subspace of a giant atom coupled to an Ohmic waveguide beyond the standard rotating wave approximation. We analyze the equilibrium properties of the system by computing the atomic frequency renormalization as a function of the coupli…
Interesting nonlinear generalization of both Schrödinger's and Klein-Gordon's equations have been recently advanced by Tsallis, Rego-Monteiro, and Tsallis (NRT) in [Phys. Rev. Lett. {\bf 106}, 140601 (2011)]. There is much current activity going on in this area. The non-linearity is governed by a real parameter $q$. It is a fact that the ensuing non linear q-Schrödinger and q-Klein-Gordon equations are natural manifestations of very high energy phenomena, as verified by LHC-experiments. This happens for $q-$values close to unity [Nucl. Phys. A {\bf 955}, 16 (2016), Nucl. Phys. A {\bf 948}, 19 …
