arXiv subjects

Nimrod Moiseyev

Publications and source records attributed to Nimrod Moiseyev.

53 records · Page 3Linked to original sources

arXiv2012

Time-dependent Hamiltonians with 100% evolution speed efficiency

The evolution speed in projective Hilbert space is considered for Hermitian Hamiltonians and for non-Hermitian (NH) ones. Based on the Hilbert-Schmidt norm and the spectral norm of a Hamiltonian, resource-related upper bounds on the evolution speed are constructed. These bounds are valid also for NH Hamiltonians and they are illustrated for an optical NH Hamiltonian and for a non-Hermitian $\mathcal{PT}-$symmetric matrix Hamiltonian. Furthermore, the concept of quantum speed efficiency is introduced as measure of the system resources directly spent on the motion in the projective Hilbert space. A recipe for the construction of time-dependent Hamiltonians which ensure 100% speed efficiency is given. Generally these efficient Hamiltonians are NH but there is a Hermitian efficient Hamiltonian as well. Finally, the extremal case of a non-Hermitian non-diagonalizable Hamiltonian with vanishing energy difference is shown to produce a 100% efficient evolution with minimal resources consumption.

quant-ph↗

arXiv2011

Fingerprints of exceptional points in the survival probability of resonances in atomic spectra

The unique time signature of the survival probability exactly at the exceptional point parameters is studied here for the hydrogen atom in strong static magnetic and electric fields. We show that indeed the survival probability S(t)=| |^2 decays exactly as |1-a*t|^2 e^(-Gamma_EP*t/hbar) where Gamma_EP is associated with the decay rate at the exceptional point and a is a complex constant depending solely on the initial wave packet that populates exclusively the two almost degenerate states of the non-Hermitian Hamiltonian. This may open the possibility for a first experimental detection of exceptional points in a quantum system.

nlin.CD↗

arXiv2010

Strong impact of light induced conical intersections on the spectrum of diatomic molecules

We show that dressing of diatomic molecules by running laser waves gives rise to conical intersections (CIs). Due to presence of such CIs, the rovibronic molecular motions are strongly coupled. A pronounced impact of the CI on the spectrum of $Na_2$ molecule is demonstrated via numerical calculation for weak and moderate laser intensity, and an experiment is suggested on this basis. The position of the light induced CI and the strength of its non-adiabatic couplings can be chosen by changing the frequency and intensity of the used running laser wave. This offers new possibilities to control the photo-induced rovibronic molecular dynamics.

physics.atom-ph↗

arXiv2010

The absolute position of a resonance peak

It is common practice in scattering theory to correlate between the position of a resonance peak in the cross section and the real part of a complex energy of a pole of the scattering amplitude. In this work we show that the resonance peak position appears at the absolute value of the pole's complex energy rather than its real part. We further demonstrate that a local theory of resonances can still be used even in cases previously thought impossible.

quant-ph↗

arXiv2008

Visualization of Branch Points in PT-Symmetric Waveguides

The visualization of an exceptional point in a PT symmetric directional coupler(DC) is demonstrated. In such a system the exceptional point can be probed by varying only a single parameter. Using the Rayleigh-Schroedinger perturbation theory we prove that the spectrum of a PT symmetric Hamiltonian is real as long as the radius of convergence has not been reached. We also show how one can use a PT symmetric DC to measure the radius of convergence for non PT symmetric structures. For such systems the physical meaning of the rather mathematical term: radius of convergence, is exemplified.

quant-ph↗

arXiv2008

Generation of Higher-Order Harmonics By Addition of a High Frequency XUV Radiation to the IR One

The irradiation of atoms by a strong IR laser field of frequency $ω$ results in the emission of odd-harmonics of $ω$ ("IR harmonics") up to some maximal cut-off frequency. The addition of an XUV field of frequency $\tilde{q}ω$ larger than the IR cut-off frequency to the IR driver field leads to the appearance of new higher-order harmonics ("XUV harmonics") $\tilde{q} \pm 2K, 2\tilde{q} \pm (2K-1), 3\tilde{q} \pm 2K,...$ ($K$ integer) which were absent in the spectra in the presence of the IR field alone. The mechanism responsible for the appearance of the XUV harmonics is analyzed analytically using a generalization of the semiclassical re-collision (three-step) model of high harmonic generation. It is shown that the emitted HHG radiation field can be written as a serie of terms, with the HHG field obtained from the three-step model in its most familiar context [P. B. Corkum, \textit{Phys. Rev. Lett.} {\bf 71}, 1994 (1993)] resulting from the zeroth-order term. The origin of the higher-order terms is shown to be the ac-Stark oscillations of the remaining ground electronic state which are induced by the XUV field. These terms are responsible for the appearance of the new XUV harmonics in the HGS. The XUV harmonics are formed by the same electron trajectories which form the IR harmonics and have the same emission times, but a much lower intensity than the IR harmonics, due to the small quiver amplitude of the ac-Stark oscillation. Nevertheless, this mechanism allows the extension of the cut-off in the HGS without the necessity of increasing the IR field intensity, as is verified by numerical time-dependent Schrödinger equation simulation of a Xe atom shined by a combination of IR and XUV field.

physics.atom-ph↗

arXiv2007

Amplification of High Harmonics Using Weak Perturbative High Frequency Radiation

The mechanism underlying the substantial amplification of the high-order harmonics q \pm 2K (K integer) upon the addition of a weak seed XUV field of harmonic frequency qωto a strong IR field of frequency ωis analyzed in the framework of the quantum-mechanical Floquet formalism and the semiclassical re-collision model. According to the Floquet analysis, the high-frequency field induces transitions between several Floquet states and leads to the appearance of new dipole cross terms. The semiclassical re-collision model suggests that the origin of the enhancement lies in the time-dependent modulation of the ground electronic state induced by the XUV field.

physics.atom-ph↗

arXiv2006

Hohenberg-Kohn theorem for the lowest-energy resonance of unbound systems

We show that under well-defined conditions the Hohenberg-Kohn theorem (HKT) can be extended to the lowest-energy resonance of unbound systems. Using the Gel'fand Levitan theorem, the extended version of the HKT can also be applied to systems that support a finite number of bound states. The extended version of the HKT provides an adequate framework to carry out DFT calculations of negative electron affinities.

cond-mat.other↗

arXiv2006

Trapping of cold atoms by the quadrupole force

Cold atoms are traditionally trapped by the dipole force in periodically spaced potential wells induced by the standing laser field. We derive here a theory beyond the conventional dipole approximation which provides field/atom coupling potential terms that so far have not been taken into consideration in theoretical or experimental studies. We show that for some atoms for specific laser parameters despite the absence of dipole transition laser trapping is still possible due to the quadrupole force. Illustrative numerical calculations for Ca and Na trapped by the quadrupole force are given.

cond-mat.mes-hall↗

arXiv2006

Theory of diatomic molecules in an external electromagnetic field from first quantum mechanical principles

We study a general problem of the translational/rotational/vibrational/electronic dynamics of a diatomic molecule exposed to an interaction with an arbitrary external electromagnetic field. The theory developed in this paper is relevant to a variety of specific applications. Such as, alignment or orientation of molecules by lasers, trapping of ultracold molecules in optical traps, molecular optics and interferometry, rovibrational spectroscopy of molecules in the presence of intense laser light, or generation of high order harmonics from molecules. Starting from the first quantum mechanical principles, we derive an appropriate molecular Hamiltonian suitable for description of the center of mass, rotational, vibrational and electronic molecular motions driven by the field within the electric dipole approximation. Consequently, the concept of the Born-Oppenheimer separation between the electronic and the nuclear degrees of freedom in the presence of an electromagnetic field is introduced. Special cases of the dc/ac field limits are then discussed separately. Finally, we consider a perturbative regime of a weak dc/ac field, and obtain simple analytic formulas for the associated Born-Oppenheimer translational/rotational/vibrational molecular Hamiltonian.

quant-ph↗

arXiv2005

Optimal reflection-free complex absorbing potentials for quantum propagation of wave packets

The conditions for optimal reflection-free complex-absorbing potentials (CAPs) are discussed. It is shown that the CAPs as derived from the smooth-exterior-scaling transformation of the Hamiltonian,[J. Phys. B. 31, 1431 (1998)], serve as optimal reflection-free CAPs (RF-CAPs) in wave-packet propagation calculations of open systems. The initial wave packet, can be located in the interaction region (as in half collision experiments) where the CAPs have vanished or in the asymptote where the absorbing potential non zero. As we show the optimal CAPs can be introduced also in the region where the physical potential has not vanished. The un-avoided reflections due to the use of finite number of grid points (or basis functions) are discussed. A simple way to reduce the "edge grid" reflection effect is described.

quant-ph↗

arXiv2005

Calculations of time-dependent observables in non-Hermitian quantum mechanics: The problem and a possible solution

The solutions of the time independent Schrodinger equation for non-Hermitian (NH) Hamiltonians have been extensively studied and calculated in many different fields of physics by using L^2 methods that originally have been developed for the calculations of bound states. The existing non-Hermitian formalism breaks down when dealing with wavepackets(WP). An open question is how time dependent expectation values can be calculated when the Hamiltonian is NH ? Using the F-product formalism, which was recently proposed, [J. Phys. Chem., 107, 7181 (2003)] we calculate the time dependent expectation values of different observable quantities for a simple well known study test case model Hamiltonian. We carry out a comparison between these results with those obtained from conventional(i.e., Hermitian) quantum mechanics (QM) calculations. The remarkable agreement between these results emphasizes the fact that in the NH-QM, unlike standard QM, there is no need to split the entire space into two regions; i.e., the interaction region and its surrounding. Our results open a door for a type of WP propagation calculations within the NH-QM formalism that until now were impossible.

quant-ph↗

arXiv2005

Adiabatic theorem for non-hermitian time-dependent open systems

In the conventional quantum mechanics (i.e., hermitian QM) the adia- batic theorem for systems subjected to time periodic fields holds only for bound systems and not for open ones (where ionization and dissociation take place) [D. W. Hone, R. Ketzmerik, and W. Kohn, Phys. Rev. A 56, 4045 (1997)]. Here with the help of the (t,t') formalism combined with the complex scaling method we derive an adiabatic theorem for open systems and provide an analytical criteria for the validity of the adiabatic limit. The use of the complex scaling transformation plays a key role in our derivation. As a numerical example we apply the adiabatic theorem we derived to a 1D model Hamiltonian of Xe atom which interacts with strong, monochromatic sine-square laser pulses. We show that the gener- ation of odd-order harmonics and the absence of hyper-Raman lines, even when the pulses are extremely short, can be explained with the help of the adiabatic theorem we derived.

physics.atom-ph↗

arXiv2004

Ground state fragmentation of repulsive BEC in double-trap potentials

The fragmentation of the ground state of a repulsive condensate immersed into a double-trap potential is found to be a general and critical phenomenon. It takes place for a given number of bosons if their scattering length is larger than some critical value or for a given value of the scattering length if the number of bosons is above some critical number. We demonstrate that the geometry of the inner trap determines these critical parameters while the number of the fragments and the fraction of bosons in the various fragments can be manipulated by the outer trap. There is also a maximal number of bosons for which the ground state is fragmented. If this number is exceeded, the fragmented state becomes a very low-lying excited state of the condensate. This maximal number of bosons can be substantially manipulated by varying the inner and outer traps. To study three-fold fragmentation we have chosen a potential well with two barriers as the inner trap and embedded by two types of outer ones. A many-fold fragmentation is also addressed.

cond-mat.other↗

arXiv2004

Tunneling lifetime of trapped condensates

Using the complex scaling transformation we calculate the tunneling lifetime of a condensate inside a magnetic/optical trap. We show that by varying the scattering length, the external potential acts like a 'selective membrane' which controls the direction of the flux of the cold atoms through the barriers and thereby controls the size of the stable condensate inside the trap.

cond-mat.other↗

arXiv2004

Transition from Resonances to Bound States in Nonlinear Systems: Application to Bose-Einstein condensates

It is shown using the Gross-Pitaevskii equation that resonance states of Bose-Einstein condensates with attractive interactions can be stabilized into true bound states. A semiclassical variational approximation and an independent quantum variational numerical method are used to calculate the energies (chemical potentials) and linewidths of resonances of the time-independent Gross-Pitaevskii equation; both methods produce similar results. Borders between the regimes of resonances, bound states, and, in two and three dimensions, collapse, are identified.

cond-mat.soft↗

arXiv1998

Infinite matrices may violate the associative law

The momentum operator for a particle in a box is represented by an infinite order Hermitian matrix $P$. Its square $P^2$ is well defined (and diagonal), but its cube $P^3$ is ill defined, because $P P^2\neq P^2 P$. Truncating these matrices to a finite order restores the associative law, but leads to other curious results.

quant-ph↗