arXiv subjects

Bogdan M. Mihalcea

Publications and source records attributed to Bogdan M. Mihalcea.

9 recordsLinked to original sources

arXiv2024

Contributions to the study of time dependent oscillators in Paul traps. Semiclassical approach

We investigate quantum dynamics for an ion confined within an oscillating quadrupole field, starting from two well known and elegant approaches. It is established that the Hamilton equations of motion, in both Schrödinger and Heisenberg representations, are equivalent to the Hill equation. One searches for a linear independent solution associated to a harmonic oscillator (HO). An adiabatic invariant, which is also a constant of motion, is introduced based on the Heisenberg representation. Thus, the state of the non-autonomous system can be determined at any subsequent moment of time. The quantum states for trapped ions are demonstrated to be Fock (number) states, while the exact solutions of the Schrödinger equation for a trapped ion are exactly the quasienergy states. Semiclassical dynamics is also investigated for many-body systems of trapped ions, where the wavefunction associated to the Schrödinger equation is prepared as a Gauss package multiplied by a Hermite polynomial. We also discuss time evolution for the system under investigation and supply the propagator.

quant-ph↗

arXiv2022

Coherent states for trapped ions. Applications in quantum optics and precision measurements

The evolution of squeezed coherent states (CSs) of motion for trapped ions is investigated by applying the time dependent variational principle (TDVP) for the Schrödinger equation. The method is applied in case of Paul and combined traps, for which the classical Hamiltonian and equations of motion are derived. Hence, CS provide a natural framework to: (a) engineer quantum correlated states for trapped ions intended for ultraprecise measurements, (b) explore the mechanisms responsible for decoherence, and (c) investigate the quantum-classical transition.

quant-ph↗

arXiv2022

The physics and applications of strongly coupled plasmas levitated in electrodynamic traps

Charged (nano)particles confined in electrodynamic traps can evolve into strongly correlated Coulomb systems which are the subject of current investigation. Exciting physical phenomena associated to Coulomb systems are reported such as autowave generation, phase transitions, defect formation, system self-locking at the edges of a linear Paul trap, self-organization in layers, or pattern formation and scaling. We investigate the dynamics of ordered structures consisting of highly nonideal similarly charged nanoparticles with coupling parameter of the order $Γ= 10^8$. This approach enables us to study the interaction of nanoparticle structures in presence and in absence of the neutralizing plasma background, as well as to investigate various types of phenomena and physical forces experienced by these structures. We review applications of electrodynamic levitation for mass spectrometry including containment and study of single aerosols and nanoparticles, with an emphasis on state of the art experiments and techniques, while also focusing on future trends and directions of investigation. Late experimental data suggest that inelastic scattering can be successfully applied to the detection of biological particles such as pollen, bacteria, aerosols, traces of explosives or synthetic polymers. Brownian dynamics is used to characterize charged particle evolution in time and thus identify regions of stable trapping. An analytical model is used to explain the experimental results. Numerical simulations take into account the stochastic forces of random collisions with neutral particles, the viscosity of the gas medium, regular forces produced by the a.c. trapping voltage and the gravitational force. Laser plasma acceleration of charged particles is also discussed, with an emphasize on dielectric capillaries and Paul traps employed for target micropositioning.

physics.plasm-ph↗

arXiv2022

Quasienergy operators and generalized squeezed states for systems of trapped ions

Collective many-body dynamics for time-dependent quantum Hamiltonian functions is investigated for a dynamical system that exhibits multiple degrees of freedom, in this case a combined (Paul and Penning) trap. Quantum stability is characterized by a discrete quasienergy spectrum, while the quasienergy states are symplectic coherent states. We introduce the generators of the Lie algebra of the symplectic group ${\cal {SL}}(2, \mathbb R)$, which we use to build the coherent states (CS) associated to the system under investigation. The trapped ion is treated as a harmonic oscillator (HO) to which we associate the quantum Hamilton function. We obtain the kinetic and potential energy operators as functions of the Lie algebra generators and supply the expressions for the classical coordinate, momentum, kinetic and potential energy, as well as the total energy. In addition, we also infer the dispersions for the coordinate and momentum, together with the asymmetry and the flatness parameter for the distribution. The system interaction with laser radiation is also examined for a system of identical two-level atoms. The Hamilton function for the Dicke model is derived. The optical system is modelled as a HO (trapped ion) that undergoes interaction with an external laser field and we use it to engineer a squeezed state of the electromagnetic (EM) field. We consider coherent and squeezed states associated to both ion dynamics and to the EM field. Such an approach enables one to build CS in a compact and smart manner by use of the group theory.

quant-ph↗

arXiv2022

Investigations on Dynamical Stability in 3D Quadrupole Ion Traps

We firstly discuss classical stability for a dynamical system of two ions levitated in a 3D Radio-Frequency (RF) trap, assimilated with two coupled oscillators. We obtain the solutions of the coupled system of equations that characterizes the associated dynamics. In addition, we supply the modes of oscillation and demonstrate the weak coupling condition is inappropriate in practice, while for collective modes of motion (and strong coupling) only a peak of the mass can be detected. Phase portraits and power spectra are employed to illustrate how the trajectory executes quasiperiodic motion on the surface of torus, namely a Kolmogorov-Arnold-Moser (KAM) torus. In an attempt to better describe dynamical stability of the system, we introduce a model that characterizes dynamical stability and the critical points based on the Hessian matrix approach. The model is then applied to investigate quantum dynamics for many-body systems consisting of identical ions, levitated in 2D and 3D ion traps. Finally, the same model is applied to the case of a combined 3D Quadrupole Ion Trap (QIT) with axial symmetry, for which we obtain the associated Hamilton function. The ion distribution can be described by means of numerical modeling, based on the Hamilton function we assign to the system. The approach we introduce is effective to infer the parameters of distinct types of traps by applying a unitary and coherent method, and especially for identifying equilibrium configurations, of large interest for ion crystals or quantum logic.

physics.atom-ph↗

arXiv2017

Squeezed Coherent States of Motion for Ions Confined in Quadrupole and Octupole Ion Traps

Quasiclassical dynamics of trapped ions is characterized by applying the time dependent variational principle (TDVP) on coherent state orbits, in case of quadrupole and octupole combined (Paul and Penning) and radiofrequency (RF) traps. A dequantization algorithm is proposed, by which the classical Hamilton (energy) function associated to the system results as the expectation value of the quantum Hamiltonian on squeezed coherent states. We develop such method and particularize the quantum Hamiltonian for a combined and for a RF trap, with axial symmetry and a RF anharmonic electric potential. We also build the classical Hamiltonian functions for the particular traps we considered, and find the classical equations of motion.

quant-ph↗

arXiv2016

Multipole Electrodynamic Ion Trap Geometries for Microparticle Confinement under Standard Ambient Temperature and Pressure Conditions

Trapping of microparticles and aerosols is of great interest for physics and chemistry. We report microparticle trapping in multipole linear Paul trap geometries, operating under Standard Ambient Temperature and Pressure (SATP) conditions. An 8-electrode and a 12-electrode linear trap geometries have been designed and tested with an aim to achieve trapping for larger number of particles and to study microparticle dynamical stability in electrodynamic fields. We report emergence of planar and volume ordered structures of the microparticles, depending on the a.c. trapping frequency and particle specific charge ratio. The electric potential within the trap was mapped using the electrolytic tank method. Particle dynamics was simulated using a stochastic Langevin equation. We emphasize extended regions of stable trapping with respect to quadrupole traps, as well as good agreement between experiment and numerical simulations.

physics.plasm-ph↗

arXiv2015

Multipole Traps as Tools in Environmental Studies

Trapping of microparticles, nanoparticles and aerosols is an issue of major interest for physics and chemistry. We present a setup intended for microparticle trapping in multipole linear Paul trap geometries, operating under Standard Ambient Temperature and Pressure (SATP) conditions. A 16-electrode linear trap geometry has been designed and tested, with an aim to confine a larger number of particles with respect to quadrupole traps and thus enhance the signal to noise ratio, as well as to study microparticle dynamical stability in electrodynamic fields. Experimental tests and numerical simulations suggest that multipole traps are very suited for high precision mass spectrometry measurements in case of different microparticle species or to identify the presence of certain aerosols and polluting agents in the atmosphere. Particle traps represent versatile tools for environment monitoring or for the study of many-body Coulomb systems and dusty plasmas.

physics.plasm-ph↗

arXiv2014

Time Dependent Variational Principle and Coherent State Orbits for a Trapped Ion

Spectral properties of the Hamiltonian function which characterizes a trapped ion are investigated. In order to study semiclassical dynamics of trapped ions, coherent state orbits are introduced as sub-manifolds of the quantum state space, with the Kähler structure induced by the transition probability. The time dependent variational principle (TDVP) is applied on coherent states' orbits. The Hamilton equations of motion on Kähler manifolds of the type of classical phase spaces naturally arise. The associated classical Hamiltonian is obtained from the expected values on symplectic coherent states of the quantum Hamiltonian. Spectral information is thus coded within the phase portrait. We deal with the bosonic realization of the Lie algebra of the SU(1,1) group, which we particularize for the case of an ion confined in a combined, Paul and Penning trap. This formalism can be applied to Hamiltonians which are nonlinear in the infinitesimal generators of a dynamical symmetry group, such as the case of ions confined in electrodynamic traps. Discrete quasienergy spectra are obtained and the corresponding quasienergy states are explicitly realized as coherent states parameterized by the stable solutions of the corresponding classical equations of motion. A correspondence between quantum and classical stability domains is thus established, using the Husimi representation.

quant-ph↗