Hamiltonians of a wide-spread class of strongly coupled quantum system models are expressed as nonlinear functions of $sl(2)$ generators. It enables us to use the $sl(2)$ formalism, in particular, $sl(2)$ generalized coherent states (GCS) for solving both spectral and evolution tasks. In such a manner, using standard variational schemes with $sl(2)$ GCS as trial functions we find new analytical expressions for energy spectra and non-linear evolution equations for cluster dynamics variables in mean-field approximations which are beyond quasi-harmonic ones obtained earlier. General results are illustrated on certain concrete models of quantum optics and laser physics.
We study the quasiclassical dynamics of the cross-Kerr effect. In this approximation, the typical periodical revivals of the decorrelation between the two polarization modes disappear and they remain entangled. By mapping the dynamics onto the Poincare space, we find simple conditions for polarization squeezing. When dissipation is taken into account, the shape of the states in such a space is not considerably modified, but their size is reduced.
This work sets the exact equations for the quasiclassical response function and susceptibility of a Brownian particle immersed in a bath of quantum harmonic oscillators driving by nonlinear harmonic potentials. A delta force perturbation gives rise to a response whose susceptibility is the combination of a linear term, own of the harmonic oscillator, plus a nonlinear one involving an integral \textcolor{black}{equation. It is provided a recursion method to find its solutions based on functional equations in the Banach space.} The ODE for the response function is a highly nonlinear damped non-a…
The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to understand the classical chaos in terms of quantum mechanics. The first question has been partially solved by the Gutzwiller semiclassical trace formula for the eigenvalues of chaotic systems, while the classical chaos may be derived from quantum equations only introducing the decoherence process due to interaction with system's environment or intermediate frequent m…
We present the application of variational-wavelet analysis to numerical/analytical calculations of Wigner functions in (nonlinear) quasiclassical beam dynamics problems. (Naive) deformation quantization and multiresolution representations are the key points. We construct the representation via multiscale expansions in generalized coherent states or high-localized nonlinear eigenmodes in the base of compactly supported wavelets and wavelet packets.
We present the application of variational-wavelet analysis to numerical/analytical calculations of Wigner functions in (nonlinear) quasiclassical beam dynamics problems. (Naive) deformation quantization and multiresolution representations are the key points.
We propose and experimentally demonstrate a new method to generate arbitrary Fock-state superpositions in a superconducting quantum circuit, where a qubit is dispersively coupled to a microwave cavity mode without the need of fine-frequency tuning. Here the qubit is used to conditionally modulate the probability amplitudes of the Fock state components of a coherent state to those of the desired superposition state, instead of pumping photons one by one into the cavity as in previous schemes. Our method does not require the adjustment of the qubit frequency during the cavity state preparation, …
Experimentally, certain degrees of freedom may appear classical because their quantum fluctuations are smaller than the experimental error associated with measuring them. An approximation to a fully quantum theory is described in which the self-interference of such ``quasiclassical'' variables is neglected so that they behave classically when not coupled to other quantum variables. Coupling to quantum variables can lead to evolution in which quasiclassical variables do not have definite values, but values which are correlated to the state of the quantum variables. A mathematical description im…
The process of measurement of a phase qubit by a resonant microwave cavity is considered for various interactions between the qubit and the cavity. A novel quasiclassical approach is described based on adiabatic reversals of the qubit state by an effective field. A similar approach was implemented earlier for the detection of electron and nuclear spins using magnetic resonance force microscopy (MRFM), but this approach has not previously been used for the measurement of a quantum state. Quasiclassical and quantum regimes are described. We consider both linear and nonlinear resonators. The effe…
Smite: A quasiclassical trajectory (QCT) program for bimolecular collisions and unimolecular dynamics on ab-initio, and machine-learned potential energy surfaces
Belgian Institute for Space Aeronomy (BIRA-IASB)（比利时空间气旋研究所）；Department of Chemistry, KU Leuven（荷语鲁汶大学化学系）
We study the dynamical generation of entanglement for a two-body interacting system, starting from a separable coherent state. We show analytically that in the quasiclassical regime the entanglement growth rate can be simply computed by means of the underlying classical dynamics. Furthermore, this rate is given by the Kolmogorov-Sinai entropy, which characterizes dynamical complexity of classical motion. Our results, illustrated by numerical simulations on a model of coupled rotators, establish in the quasiclassical regime a link between the generation of entanglement, a purely quantum phenome…
The coherent state representations of the group $G = W_1 \otimes G_0$ (where $G_0 = SU(2), SU(1,1)$) are used in computer simulation of the dynamics of single two-level atom $(G_0 = SU(2))$ interacting with a quantized photon cavity mode - the Jaynes - Cummings model (JCM) without the rotating wave approximation and, in general, nonlinear in photon variables). The second case (hyperbolic Jaynes - Cummings model (HJCM), $G_0 = SU(1,1))$ corresponds to the quantum dynamics of quadratic nonlinear coupled oscillators (the parametric resonance on double field frequency and a three - wave parametric…
Electrical resonators are widely used in quantum information processing, by engineering an electromagnetic interaction with qubits based on real or virtual exchange of microwave photons. This interaction relies on strong coupling between the qubits' transition dipole moments and the vacuum fluctuations of the resonator in the same manner as cavity QED, and has consequently come to be called "circuit QED" (cQED). Great strides in the control of quantum information have already been made experimentally using this idea. However, the central role played by photon exchange induced by quantum fluctu…
The output fields of a pair of coherently coupled nonlinear optical cavities are found to exhibit strong optical entanglement. For sufficiently strong coupling the quantum correlations become asynchronous providing a resource for quantum information protocols such as all-optical quantum memories. A straightforward experimental implementation applicable to whispering gallery mode resonators such as microtoroids is proposed.
In this paper we consider a class of coupled nonlinear Schroedinger equations for the fields $ψ_i$ containing complex nonlinearities, that has been obtained by requiring that the norms $|ψ_i|^2$ are conserved densities. For this class of equations we introduce a Cole-Hopf like transformation, whose effect is to reduce the complex nonlinearities into real ones, this way reducing the continuity equations of the system to the standard bilinear form. Some examples are presented to illustrate the applicability of the method. Pacs numbers: 03.50.-z, 03.65.-w, 11.30.Na, 11.40.Dw Keywords: Coupled non…
Except for the universe, all quantum systems are open, and according to quantum state diffusion theory, many systems localize to wave packets in the neighborhood of phase space points. This is due to decoherence from the interaction with the environment, and makes the quasiclassical limit of such systems both more realistic and simpler in many respects than the more familiar quasiclassical limit for closed systems. A linearized version of this theory leads to the correct classical dynamics in the macroscopic limit, even for nonlinear and chaotic systems. We apply the theory to the forced, damp…
When the nonlinearity of nanomechanical resonator is not negligible, the quantum decoherence of charge qubit is studied analytically. Using nonlinear Jaynes-Cummings model, one explores the possibility of being quantum data bus for nonlinear nanomechanical resonator, the nonlinearity destroys the dynamical quantum information-storage and maintains the revival of quantum coherence of charge qubit. With the calculation of decoherence factor, we demonstrate the influence of the nonlinearity of nanomechanical resonator on engineered decoherence of charge qubit.
We model a collection of $N$ two-level systems (TLSs) coupled to a multimode cavity via Meyer-Miller-Stock-Thoss (MMST) dynamics, sampling both electronic and photonic zero-point energies (ZPEs) and propagating independent trajectories in Wigner phase space. By investigating the ground state stability of a single TLS, we use MMST dynamics to separately study both electronic ZPE effects (which would naively lead to the breakdown of the electronic ground state) as well as photonic ZPE effects (which would naively lead to spontaneous absorption). By contrast, including both effects (i.e., samplin…
Quantized nonlinear lattice models are considered for two different classes, boson and fermionic ones. The quantum discrete nonlinear Schroedinger model (DNLS) is our main objective, but its so called modified discrete nonlinear (MDNLS) version is also included, together with the fermionic polaron (FP) model. Based on the respective dynamical symmetries of the models, a method is put forward which by use of the associated boson and spin coherent state vectors (CSV) and a factorization ansatz for the solution of the Schroedinger equation, leads to quasiclassical Hamiltonian equations of motion …
The quantum dynamics of two weakly coupled nonlinear oscillators is analytically and numerically investigated in the context of nonlinear dissipation. The latter facilitates the creation and preservation of non-classical steady states. Starting from a microscopic description of two oscillators individually interacting with their dissipative environments, it is found that in addition to energy relaxation, dephasing arises due to the mutual coupling. Using the negativity as an entanglement measure, it is shown that the coupling entangles the oscillators in the long-time limit. For finite tempera…
We propose and analyze an on-chip all-optical dynamical tuning scheme for coupled nonlinear resonators employing a single control beam injected in parallel with a signal beam. We show that nonlinear Kerr response can be used to dynamically switch the spectral properties between "dark-state" and electromagnetically-induced transparency configurations. Such scheme can be realized in integrated optical applications for pulse trapping and delaying.
An adiabatic approximation in terms of instantaneous resonances is developed to study the steady-state and time-dependent transport of interacting electrons in biased resonant tunneling heterostructures. The resulting model consists of quantum reservoirs coupled to regions where the system is described by nonlinear ordinary differential equations and has a general conceptual interest.
We present the application of the variational-wavelet analysis to the quasiclassical calculations of the solutions of Wigner/von Neumann/Moyal and related equations corresponding to the nonlinear (polynomial) dynamical problems. (Naive) deformation quantization, the multiresolution representations and the variational approach are the key points. We construct the solutions via the multiscale expansions in the generalized coherent states or high-localized nonlinear eigenmodes in the base of the compactly supported wavelets and the wavelet packets. We demonstrate the appearance of (stable) locali…
