arXiv subjects

Zbigniew Idziaszek

Publications and source records attributed to Zbigniew Idziaszek.

At least 37 records · Page 2Linked to original sources

arXiv2013

Quantum theory of reactive collisions for 1/r^n potentials

We develop a general quantum theory for reactive collisions involving power-law potentials (-1/r^n) valid from the ultracold up to the high-temperature limit. Our quantum defect framework extends the conventional capture models to include the non-universal case when the short-range reaction probability P^{re} < 1. We present explicit analytical formulas as well as numerical studies for the van der Waals (n = 6) and polarization (n = 4) potentials, and relate our work to recent merged beam experiments on Penning ionization for collision energies below 0.1 meV [Henson et al, Science 338, 234(2012)].

physics.atom-ph↗

arXiv2013

Feshbach resonances in a nonseparable trap

We consider a pair of atoms in an arbitrary trapping potential in the presence of magnetically tunable Feshbach resonance. We find the energy levels and occupation of the bound molecular states taking into account possible coupling between center of mass and relative motion induced by the trap. As a specific example we discuss the case of different atomic species in harmonic potential, where each atom feels different trapping frequency.

cond-mat.quant-gas↗

arXiv2012

Light scattering from ultracold gases in disordered optical lattices

We consider a gas of bosons in a bichromatic optical lattice at finite temperatures. As the amplitude of the secondary lattice grows, the single-particles eigenstates become localized. We calculate the canonical partition function using exact methods for the noninteracting and strongly interacting limit and analyze the statistical properties of the superfluid phase, localized phase and the strongly interacting gas. We show that those phases may be distinguished in experiment using off-resonant light scattering.

cond-mat.quant-gas↗

arXiv2011

Sympathetic cooling of the Ba$^+$ ion by collisions with ultracold Rb atoms: theoretical prospects

State-of-the-art {\em ab initio} techniques have been applied to compute the potential energy curves of the (BaRb)$^+$ molecular ion in the Born-Oppenheimer approximation. The long-range coefficients describing the electrostatic, induction, and dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments governing the X$^1Σ\to ^1Σ, ^1Π$ have been obtained as the first residue of the polarization propagator computed with the linear response coupled-cluster method restricted to single and double excitations. Nonadiabatic radial and angular coupling matrix elements, as well as the spin-orbit coupling matrix elements have been evaluated using the multireference configuration interaction method restricted to single and double excitations with a large active space. With these couplings, the spin-orbit coupled (relativistic) potential energy curves for the 0$^+$ and 1 states relevant for the running experiments have been obtained. Finally, relativistic transition moments and nonadiabatic coupling matrix elements were obtained from the nonrelativistic results and spin-orbit eigenvectors. The electronic structure input has been employed in the single channel scattering calculations of the collisional cross sections between the Ba$^+$ ion and Rb atom. Both nonrelativistic and relativistic potentials were used in these calculations. Our results show that the inelastic cross section corresponding to the charge transfer from the Rb atom to the Ba$^+$ ion is much smaller than the elastic one over a wide range of energies up to 1 mK. This suggests that sympathetic cooling of the Ba$^+$ ion by collisions with ultracold Rb atoms should be possible.

physics.atom-ph↗

arXiv2011

Universal ultracold collision rates for polar molecules of two alkali-metal atoms

Universal collision rate constants are calculated for ultracold collisions of two like bosonic or fermionic heteronuclear alkali-metal dimers involving the species Li, Na, K, Rb, or Cs. Universal collisions are those for which the short range probability of a reactive or quenching collision is unity such that a collision removes a pair of molecules from the sample. In this case, the collision rates are determined by universal quantum dynamics at very long range compared to the chemical bond length. We calculate the universal rate constants for reaction of the reactive dimers in their ground vibrational state $v=0$ and for vibrational quenching of non-reactive dimers with $v \ge 1$. Using the known dipole moments and estimated van der Waals coefficients of each species, we calculate electric field dependent loss rate constants for collisions of molecules tightly confined to quasi-two-dimensional geometry by a one-dimensional optical lattice. A simple scaling relation of the quasi-two-dimensional loss rate constants with dipole strength, trap frequency and collision energy is given for like bosons or like fermions. It should be possible to stabilize ultracold dimers of any of these species against destructive collisions by confining them in a lattice and orienting them with electric field of less than 20 kV/cm.

physics.chem-ph↗

arXiv2011

Multichannel quantum-defect theory for ultracold atom-ion collisions

We develop an analytical model for ultracold atom-ion collisions using the multichannel quantum-defect formalism. The model is based on the analytical solutions of the r^-4 long-range potential and on the application of a frame transformation between asymptotic and molecular bases. This approach allows the description of the atom-ion interaction in the ultracold domain in terms of three parameters only: the singlet and triplet scattering lengths, assumed to be independent of the relative motion angular momentum, and the lead dispersion coefficient of the asymptotic potential. We also introduce corrections to the scattering lengths that improve the accuracy of our quantum-defect model for higher order partial waves, a particularly important result for an accurate description of shape and Feshbach resonances at finite temperature. The theory is applied to the system composed of a 40Ca+ ion and a Na atom, and compared to numerical coupled-channel calculations carried out using ab initio potentials. For this particular system, we investigate the spectrum of bound states, the rate of charge-transfer processes, and the collision rates in the presence of magnetic Feshbach resonances at zero and finite temperature.

physics.atom-ph↗

arXiv2010

Ion-assisted ground-state cooling of a trapped polar molecule

We propose and analyze a scheme for sympathetic cooling of the translational motion of polar molecules in an optical lattice, interacting one by one with laser-cooled ions in a radio-frequency trap. The energy gap between the excitation spectra of the particles in their respective trapping potentials is bridged by means of a parametric resonance, provided by the additional modulation of the RF field. We analyze two scenarios: simultaneous laser cooling and energy exchange between the ion and the molecule, and a scheme when these two processes take place separately. We calculate the lowest final energy of the molecule and the cooling rate depending on the amplitude of the parametric modulation. For small parametric modulation, the dynamics can be solved analytically within the rotating wave approximation.

physics.atom-ph↗

arXiv2010

A Simple Quantum Model of Ultracold Polar Molecule Collisions

We present a unified formalism for describing chemical reaction rates of trapped, ultracold molecules. This formalism reduces the scattering to its essential features, namely, a propagation of the reactant molecules through a gauntlet of long-range forces before they ultimately encounter one another, followed by a probability for the reaction to occur once they do. In this way, the electric-field dependence should be readily parametrized in terms of a pair of fitting parameters (along with a $C_6$ coefficient) for each asymptotic value of partial wave quantum numbers $|L,M \rangle$. From this, the electric field dependence of the collision rates follows automatically. We present examples for reactive species such as KRb, and non-reactive species, such as RbCs.

quant-ph↗

arXiv2010

Universal rates for reactive ultracold polar molecules in reduced dimensions

Analytic expressions describe universal elastic and reactive rates of quasi-two-dimensional and quasi-one-dimensional collisions of highly reactive ultracold molecules interacting by a van der Waals potential. Exact and approximate calculations for the example species of KRb show that stability and evaporative cooling can be realized for spin-polarized fermions at moderate dipole and trapping strength, whereas bosons or unlike fermions require significantly higher dipole or trapping strengths.

physics.atom-ph↗

arXiv2010

Universal rate constants for reactive collisions of ultracold molecules

A simple quantum defect model gives analytic expressions for the complex scattering length and threshold collision rates of ultracold molecules. If the probability of reaction in the short-range part of the collision is high, the model gives universal rate constants for s- and p-wave collisions that are independent of short-range dynamics. This model explains the magnitudes of the recently measured rate constants for collisions of two ultracold 40K87Rb molecules, or an ultracold 40K atom with the 40K87Rb molecule [Ospelkaus et al., Science 327, 853 (2010)].

physics.atom-ph↗

arXiv2009

Controlled collisions of two ultracold atoms in separate harmonic traps

We consider controlled collisions between two ultracold atoms guided by external harmonic potentials. We derive analytical solutions of the Schroedinger equation for this system, and investigate the properties of eigenergies and eigenstates for different trap geometries as a function of a trap separation and of the scattering length. When varying the trap separation the energy spectrum exhibits avoided crossings, corresponding to trap-induced shape resonances. Introducing an energy-dependent scattering length we investigate the behavior of the system in the vicinity of a magnetic Feshbach resonance. Finally, we illustrate our analytical results with two examples: the quantum phase gate controlled by the external magnetic field, and a scheme for a coherent transport of atoms in optical lattices into higher Bloch bands.

cond-mat.quant-gas↗

arXiv2009

Thermal effects in light scattering from ultracold bosons in an optical lattice

We study the scattering of a weak and far-detuned light from a system of ultracold bosons in 1D and 3D optical lattices. We show the connection between angular distributions of the scattered light and statistical properties of a Bose gas in a periodic potential. The angular patterns are determined by the Fourier transform of the second-order correlation function, and thus they can be used to retrieve information on particle number fluctuations and correlations. We consider superfluid and Mott insulator phases of the Bose gas in a lattice, and we analyze in detail how the scattering depends on the system dimensionality, temperature and atom-atom interactions.

cond-mat.quant-gas↗

arXiv2009

Atom-ion quantum gate

We study ultracold collisions of ions with neutral atoms in traps. Recently, ultracold atom-ion systems are becoming available in experimental setups, where their quantum states can be coherently controlled. This allows for an implementation of quantum information processing combining the advantages of charged and neutral particles. The state-dependent dynamics that is a necessary ingredient for quantum computation schemes is provided in this case by the short-range interaction forces depending on hyperfine states of both particles. In this work we develop a theoretical description of spin-state-dependent trapped atom-ion collisions in the framework of a Multichannel Quantum Defect Theory (MQDT) and formulate an effective single channel model that reduces the complexity of the problem. Based on this description we simulate a two-qubit phase gate between a Ba135+ ion and a Rb87 atom using a realistic combination of the singlet and triplet scattering lengths. We optimize and accelerate the gate process with the help of optimal control techniques. Our result is a gate fidelity 0.999 within 350 microseconds.

quant-ph↗

arXiv2009

Analytical solutions for two atoms in a harmonic trap: p-wave interactions

We derive analytical solutions for the system of two ultracold spin-polarized fermions interacting in p wave and confined in an axially symmetric harmonic trap. To this end we utilize p-wave pseudopotential with an energy-dependent scattering volume. This allows to describe the scattering in tight trapping potentials in the presence of scattering resonances. We verify predictions of the pseudopotential treatment for some model interaction potential, obtaining an excellent agreement with exact energy levels. Then we turn to the experimentally relevant case of neutral atom interactions in the vicinity of a p-wave Feshbach resonance. In the framework of the multichannel quantum-defect theory we derive relatively simple formula for an energy-dependent scattering volume, and later we apply it to investigate the energy spectrum of trapped atoms close to the p-wave Feshbach resonance.

physics.atom-ph↗

arXiv2008

Quantum theory of ultracold atom-ion collisions

We study atom-ion scattering in the ultracold regime. To this aim, an analytical model based on the multichannel quantum defect formalism is developed and compared to close-coupled numerical calculations. We investigate the occurrence of magnetic Feshbach resonances focusing on the specific 40Ca+ - Na system. The presence of several resonances at experimentally accessible magnetic fields should allow the atom-ion interaction to be precisely tuned. A fully quantum-mechanical study of charge exchange processes shows that charge-exchange rates should remain small even in the presence of resonance effects. Most of our results can be cast in a system-independent form and are important for the realization of the charge-neutral ultracold systems.

physics.atom-ph↗

arXiv2008

Modified effective-range theory for low energy e-N2 scattering

We analyze the low-energy e-N2 collisions within the framework of the Modified-Effective Range Theory (MERT) for the long-range potentials, developed by O'Malley, Spruch and Rosenberg [Journal of Math. Phys. 2, 491 (1961)]. In comparison to the traditional MERT we do not expand the total cross-section in the series of the incident momentum \hbar k, but instead we apply the exact analytical solutions of the Schroedinger equation for the long-range polarization potential, as proposed in the original formulation of O'Malley et al. This extends the applicability of MERT up to few eV regime, as we confirm using some simplified model potential of the electron-molecule interaction. The parameters of the effective-range expansion (i.e. the scattering length and the effective range) are determined from experimental, integral elastic cross sections in the 0.1 - 1.0 eV energy range by fitting procedure. Surprisingly, our treatment predicts a shape resonance that appears slightly higher than experimentally well known resonance in the total cross section. Agreement with the experimentally observed shape-resonance can be improved by assuming the position of the resonance in a given partial wave. Influence of the quadrupole potential on resonances is also discussed: we show that it can be disregarded for N2. In conclusion, the modified-effective range formalism treating the long-range part of the potential in an exact way, reproduces well both the very low-energy behavior of the integral cross section as well as the presence of resonances in the few eV range.

physics.atom-ph↗

arXiv2008

Shape resonances in modified effective range theory for electron-molecule collisions

We develop a simple model of shape resonances in electron-molecule collisions that is based on the modified effective-range expansion and analytical solutions of the Schrodinger equation for the long-range part of the interaction potential. We apply our model to electron scattering on N$_2$ and CO$_2$. The parameters of the effective-range expansion (i.e. the scattering length and the effective range) are determined from experimental, integral elastic cross sections in the 0.1 - 1.0 eV energy range. For both molecular targets our treatment predicts shape resonances that appear slightly higher than experimentally known resonances in total cross sections. Agreement with the experiment can be improved by assuming the position of the resonance in a given partial wave. Influence of quadrupole potential on resonances is also discussed: it can be disregarded for N$_2$ but gets significant for CO$_2$. In conclusion, our model developed within the effective range formalism reproduces well both the very low-energy behavior of the integral cross section as well as the presence of resonances in the few eV range.

physics.atom-ph↗

arXiv2006

Applicability of Modified Effective-Range Theory to positron-atom and positron-molecule scattering

We analyze low-energy scattering of positrons on Ar atoms and N2 molecules using Modified Effective-Range Theory (MERT) developped by O'Malley, Spruch and Rosenberg [Journal of Math. Phys. 2, 491 (1961)]. We use formulation of MERT based on exact solutions of Schroedinger equation with polarization potential rather than low-energy expansions of phase shifts into momentum series. We show that MERT describes well experimental data, provided that effective-range expansion is performed both for s- and p-wave scattering, which dominate in the considered regime of positron energies (0.4 - 2 eV). We estimate the values of the s-wave scattering lenght and the effective range for e+ - Ar and e+ - N2 collisions.

physics.atom-ph↗