Relevant Density Matrix Research Articles

Gradient-based reconstruction of molecular Hamiltonians and density matrices from time-dependent quantum observables

We consider a quantum system with a time-independent Hamiltonian parametrized by a set of unknown parameters $\alpha$. The system is prepared in a general quantum state by an evolution operator that depends on a set of unknown parameters $P$. After the preparation, the system evolves in time, and it is characterized by a time-dependent observable ${\cal O}(t)$. We show that it is possible to obtain closed-form expressions for the gradients of the distance between ${\cal O}(t)$ and a calculated observable with respect to $\alpha$, $P$ and all elements of the system density matrix, whether for pure or mixed states. These gradients can be used in projected gradient descent to infer $\alpha$, $P$ and the relevant density matrix from dynamical observables. We combine this approach with random phase wave function approximation to obtain closed-form expressions for gradients that can be used to infer population distributions from averaged time-dependent observables in problems with a large number of quantum states participating in dynamics. The approach is illustrated by determining the temperature of molecular gas (initially, in thermal equilibrium at room temperature) from the laser-induced time-dependent molecular alignment.

Controlling the Pump-Probe Optical Response in Asymmetric Tunneling-Controlled Double Quantum Dot Molecule—Metal Nanoparticle Hybrids

In the present work, we investigate the modified nonlinear pump-probe optical properties due to the excitonic–plasmonic interaction of a double semiconductor quantum dot (SQD) molecule coupled to a metal nanoparticle (MNP). More specifically, we study the absorption and the dispersion spectra of a weak electromagnetic field in a hybrid structure with two counterparts, a molecule of two coupled SQDs, and a spherical MNP driven by a field of high intensity. We solve the relevant density matrix equations, calculate the first-order optical susceptibility of the probe field in the strong pumping regime, and investigate the way in which the distance between the two counterparts modifies the optical response, for a variety of values of the physical constants of the system, including the pump-field detuning, the tunnelling rate, and the energy separation gap associated with the excited states of the coupled SQDs.

Optical transparency and nonlinearity for a five-level tripod system involving a Rydberg state

We demonstrate electromagnetically-induced transparency and giant Kerr nonlinearity in a five-level atomic system where the upper level is a Rydberg-state coupled coherently to a four-level tripod subsystem. Since the high Rydberg states exhibit rather long lifetimes, the system evolves into a dark state that is a superposition of all long-lived states resulting in an optical transparency for the probe field. We solve the relevant density matrix equations for the atomic system in steady-state and utilize the perturbation approach to obtain the expressions for the linear and nonlinear susceptibility. It is shown that depending on the system parameters, the system can exhibit triple, double or single, optical transparency. Therefore, there is a resulting change in the sign of linear dispersion for different parametric situations giving, rise to switching in the group velocity of the probe pulse from superluminal to subluminal or vice versa. We also identify the existence of giant third-order Kerr nonlinearities within regions of optical transparency and under the slow light condition.

Rapid Optical Spin Initialization of a Quantum Dot in the Voigt Geometry Coupled to a Two-Dimensional Semiconductor

We study the interaction of a quantum dot in the Voigt configuration with a laser pulse and particularly analyze the potential for rapid spin initialization by putting the quantum dot near a molybdenum disulfide (MoS 2 ) monolayer. The MoS 2 monolayer influences the spontaneous decay rates of the quantum dot, leading to anisotropically enhanced decay rates, for the quantum dot’s electric dipole moments parallel and perpendicular to the layer. By solving the relevant density matrix equations, we find that high spin initialization fidelity is obtained at short times. The fidelity is significantly higher than when the quantum dot is in free-space vacuum. We examine two different cases of the interaction of the quantum dot with the applied optical field. First, we use a continuous wave laser field and determine for various quantum dot—MoS 2 layer distances the field strength that leads to acceptable fidelity levels. The effect of the quality of the MoS 2 material on the fidelity of spin initialization is also examined. We also study the interaction of the quantum dot with a laser pulse and apply numerical optimal control to obtain the time-dependent field strength, which leads to maximum final fidelity for short time intervals. The latter approach gives beneficial results in comparison to the continuous wave field excitation.

Coherent control of Kerr nonlinearity via double dark resonances

A theoretical scheme for enhanced Kerr nonlinearity is proposed in a four-level ladder-type atomic system based on double dark resonances (DDRs). We solve the relevant density matrix equations in steady state and utilize the perturbation theory to obtain the analytical expressions for the third order susceptibility of the atomic system. The influence of system parameters on behavior of the first and third order susceptibilities is then discussed. In particular, it is found that an enhanced Kerr nonlinearity with reduced linear and nonlinear absorption is obtained around zero probe detuning under the slow light condition through proper adjusting the laser field intensity and frequency detuning of driving fields. The dressed state analysis is employed to explain the physical origin of the obtained result. The obtained results may be important for all-optical signal processing and quantum information technology.

Nonlinear optical susceptibilities of semiconductor quantum dot – metal nanoparticle hybrids

We theoretically study nonlinear optical effects of a semiconductor quantum dot and a spherical metal nanoparticle coupled via long-range Coulomb interaction. We solve the relevant density matrix equations in steady state and use proper perturbation theory to obtain closed-form analytical expressions for the nonlinear susceptibilities of the quantum dot, the metal nanoparticle, and the entire coupled system, up to fifth order. We also investigate the influence of the material of the semiconductor and the impact of the interparticle distance on the form of the spectra of the nonlinear susceptibilities.

Control of indirect exciton population in an asymmetric quantum dot molecule

Abstract We analyze the problem of coherent population transfer to the indirect exciton state in an asymmetric double semiconductor quantum dot molecule that interacts with an external electromagnetic field. Using the controlled rotation method, we obtain analytical solutions of the time-dependent Schrodinger equation and determine closed-form conditions for the parameters of the applied field and the quantum system that lead to complete population transfer to the indirect exciton state, in the absence of decay effects. Then, by numerical solution of the relevant density matrix equations we study the influence of decay mechanisms to the efficiency of population transfer.

Effects of probe field intensity in nonlinear optical processes in asymmetric semiconductor quantum dots

We study nonlinear optical absorption and nonlinear optical rectification in an asymmetric semiconductor quantum dot structure under a strong probe field excitation. We apply a form of the rotating wave approximation for asymmetric quantum systems, solve the relevant density matrix equations under steady state conditions, and derive the formulae for nonlinear optical absorption and nonlinear optical rectification under the interaction with a strong probe field. The differences between our formulae and those of a previous study are also presented for the case of an electron confined in an asymmetric double quantum dot nanostructure.

Pressure of the nonequilibriumO(N)Φ4theory in the largeNlimit

We calculate the off-equilibrium hydrostatic pressure for the O(N) Phi^{4} theory to the leading order in 1/N. The present paper, the first of a series, concentrates on the calculation of pressure in the non-equilibrium but translationally invariant medium. The Jaynes-Gibbs principle of maximal entropy is used to introduce the relevant density matrix which is then directly implemented into dynamical equations through generalised Kubo-Martin-Schwinger (KMS) conditions. We show that in the large N limit use of Ward identities enables the pressure to be expressed in terms of two point Green's functions. These satisfy the Kadanoff-Baym equations which are exactly solvable, and we explicitly calculate the pressure for three illustrative choices of \rho.

Coarse-graining approach to quantum cosmology.

We consider a Friedmann-Robertson-Walker model with both classical radiation and a massive (conformally coupled) quantum scalar field in the framework of quantum cosmology. We define a density matrix and introduce a notion of relevance which splits this density matrix into a and an part. A generalized coarse-graining method is used to obtain the evolution (in Robertson-Walker $a$ time) of the relevant density matrix, taking into account the back reaction of the irrelevant variables. We discuss the physical basis for the choice of a concept of relevance, and the features of cosmic evolution brought forward by the effective dynamics. In the limit of small universes, the relevant subdynamics is dissipative.

Quantum-statistical theory of proton-transfer reactions. Dynamics of proton motion in an asymmetric double-well potential interacting with a heat bath

Quantum-statistical theory of open systems, based on the projected form of the Liouville-von Neumann equation, is applied to the study of proton motion in an asymmetric double-well potential interacting with a heat bath. In Born-Markoff approximation a set of coupled equations of motion for matrix elements of the relevant density matrix is derived. It is demonstrated by the corresponding time-dependent analytic form of the product state population that the method can describe the dynamics correctly. An incoherent gain of the product state population is determiend by both, the dephasing and the decay of levels population. The rate constant, derived within the postulated theory, describes in a consistent manner the temperature dependence as well as the non-classical behaviour of the system in the limit of zero temperature.

On nonlinear generalized master equations in nonequilibrium statistical mechanics

It is shown that the Nakajima-Zwanzig method to derive an exact equation of motion for a relevant density matrix can be generalized to cases where the relevant density matrix depends in a nonlinear way on the microscopic state.

On polarization effects in high-energy vector-meson photoproduction

In a recent paper (1) an analysis of vcetor-meson photoproduetion at high energies was presented in terms of a multiehannel impact-parameter formalism which provided a unified description of all diffractive photon-induced reactions. I t was argued there that a helieity-flip component of the asymptotic part of the amplitude, i.e. the pomeron, may well be present in the proposed unitarized multiple-scattering picture of diffraction and it was indeed subsequently found in the analysis of 7 ~ and p~ data. As is well known, ~0 photoproduction is an ideal testing ground for the properties of the Pomeranchuk contribution since no other Regge exchanges are supposed to contr ibute there (2). I t was shown that for the c~~ amplitude (and for the i~ ~ amplitude) there is a substantial amount of helicity flip at the proton vertex (*). Of course, this model-dependent result has to be confirmed by direct measurement of the relevant density matrix elements. Unfortunately, the present data cannot provide information about this point because of lack of appropriate data on polarization experiments. One is therefore forced to use the available differential cross-section data in order to get information on this particular helicity amplitude with flip at the nucleon-~nucleon transition. I t seems therefore worth-while to discuss the possible experiments with polarized beams and/or polarized target which could directly test our rather indirect finding of a violation of SCIIC (s-channel helicity conservation) (a) for the recoiling proton in ~o (po) photoproduction. In view of the recent progress in preparing polarized targets possessing polarizations up to (70--80)~o it is feasible to carry out such experiments in the near future. Let us represent the state of polarization of the incoming nucleon and of the photon by the spin density matrices (4.5)

Dynamic Orientation of Nuclei with Spin >1

The dynamic orientation of nuclei with spin >1 is theoretically investigated in experimental samples where the nucleus is in well resolved hyperfine interaction with a paramagnetic ion of spin (1/2). It is shown that the contribution from off-diagonal elements of the relevant density matrix vanishes in the steady state, and the rate equation approach is justified. The nuclear orientation parameters are computed using the simplified method of partial distributions, both at low and high temperatures, and numerical results are presented for Pa(4+) in Cs(2)ZrCl(6).

Theory of Chemical Exchange Effects in Magnetic Resonance

The Anderson—Weiss formalism is used to develop a general theory for calculating the effects of chemical exchange and spin coupling on echo amplitudes in Carr—Purcell pulse sequences on spin systems in the liquid phase. The theory is shown to involve the matrix integral solution of the Hahn—Maxwell—McConnell equations, generalized to include spin coupling, and of Alexander's equations for the relevant density matrix elements, subject to the boundary conditions imposed by the pulses. Some specific systems are treated in detail, and closed formulas are given for the decay of the echo train in several situations, including the coupled and uncoupled AB systems, and the coupled ABX and ABXq systems. We show that if the natural relaxation rates of nuclei in exchanging sites are identical, then in general effects of both exchange and spin coupling can be removed by pulsing sufficiently rapidly. Modulation of the echo train by spin coupling is removed by rapid exchange between the coupled sites. The Carr—Purcell experiment on an equivalent set of spins affords effective decoupling from another equivalent set unaffected by the pulses, in the absence of exchange between the sets. An analogy is drawn between chemical exchange and quadrupolar relaxation, and a method is outlined which in principle should provide an indirect determination of quadrupolar or other fast relaxation rates. We illustrate the applicability of the theory to the calculation of line shapes in steady-state spectra by treating the exchanging coupled AB system in detail, and show that in the fast exchange limit the theory predicts weak broad resonances not previously described.