arXiv subjects

Zbigniew Idziaszek

Publications and source records attributed to Zbigniew Idziaszek.

At least 19 recordsLinked to original sources

arXiv2022

Self-consistent Description of Bose-Bose Droplets: Modified Gapless Hartree-Fock-Bogoliubov Method

We define a formalism of a self-consistent description of the ground state of a weakly interacting Bose system, accounting for higher order terms in expansion of energy in the diluteness parameter. The approach is designed to be applied to a Bose-Bose mixture in a regime of weak collapse where quantum fluctuations lead to stabilization of the system and formation of quantum liquid droplets. The approach is based on the Generalized Gross -- Pitaevskii equation accounting for quantum depletion and anomalous density terms. The equation is self-consistently coupled to modified Bogoliubov equations. The modification we introduce resolves the longstanding issue of missing phonon-branch excitations when higher order terms are included. Our method ensures a gapless phononic low-energy excitation spectrum, crucial to correctly account for quantum fluctuations. We pay particular attention to the case of droplets harmonically confined in some directions. The method allows to determine the Lee-Huang-Yang-type contribution to the chemical potential of inhomogeneous droplets when the local density approximation fails.

cond-mat.quant-gas↗

arXiv2021

Controlling the dynamics of ultracold polar molecules in optical tweezers

Ultracold molecules trapped in optical tweezers show great promise for the implementation of quantum technologies and precision measurements. We study a prototypical scenario where two interacting polar molecules placed in separate traps are controlled using an external electric field. This, for instance, enables a quantum computing scheme in which the rotational structure is used to encode the qubit states. We estimate the typical operation timescales needed for state engineering to be in the range of few microseconds. We further underline the important role of the spatial structure of the two-body states, with the potential for significant gate speedup employing trap-induced resonances.

quant-ph↗

arXiv2021

Quantum droplets in a dipolar Bose gas at a dimensional crossover

We study the beyond-mean-field corrections to the energy of a dipolar Bose gas confined to two dimensions by a box potential with dipoles oriented in plane. At a critical strength of the dipolar interaction the system becomes unstable on the mean field level. We find that the ground state of the gas is strongly influenced by the corrections, leading to formation of a self-bound droplet, in analogy to the free space case. Properties of the droplet state can be found by minimizing the extended Gross-Pitaevskii energy functional. In the limit of strong confinement we show analytically that the correction can be interpreted as an effective three-body repulsion which stabilizes the gas at finite density.

cond-mat.quant-gas↗

arXiv2021

Quantum reactive scattering in the long-range ion-dipole potential

An ion and a polar molecule interact by an anisotropic ion-dipole potential scaling as $- α\cos (θ)/r^2$ at large distances. Due to its long-range character, it modifies the properties of angular wave functions, which are no longer given by spherical harmonics. In addition, an effective centrifugal potential in the radial equation can become attractive for low angular momenta. In this paper, we develop a general framework for an ion-dipole reactive scattering, focusing on the regime of large $α$. We introduce modified spherical harmonics as solutions of the angular part of the Schrödinger equation and derive several useful approximations in the limit of large $α$. We present a formula for the scattering amplitude expressed in terms of the modified spherical harmonics and we derive expressions for the elastic and reactive collision rates. The solutions of the radial equation are given by Bessel functions, and we analyse their behaviour in two distinct regimes corresponding, basically, to attractive and repulsive long-range centrifugal potentials. Finally, we study reactive collisions in the universal regime, where the short-range probability of loss or reaction is equal to unity.

physics.atom-ph↗

arXiv2020

Bound states of an ultracold atom interacting with a set of stationary impurities

In this manuscript we analyse properties of bound states of an atom interacting with a set of static impurities. We begin with the simplest system of a single atom interacting with two static impurities. We consider two types of atom-impurity interaction: (i) zero-range potential represented by regularized delta, (ii) more realistic polarization potential, representing long-range part of the atom-ion interaction. For the former we obtain analytical results for energies of bound states. For the latter we perform numerical calculations based on the application of finite element method. Then, we move to the case of a single atom interacting with one-dimensional (1D) infinite chain of static ions. Such a setup resembles Kronig-Penney model of a 1D crystalline solid, where energy spectrum exhibits band structure behaviour. For this system, we derive analytical results for the band structure of bound states assuming regularized delta interaction, and perform numerical calculations, considering polarization potential to model atom-impurity interaction. Both approaches agree quite well when separation between impurities is much larger than characteristic range of the interaction potential.

cond-mat.quant-gas↗

arXiv2020

Analytically solvable quasi-one-dimensional Kronig-Penney model

We generalize the textbook Kronig-Penney model to realistic conditions for a quantum-particle moving in the quasi-one-dimensional (quasi-1D) waveguide, where motion in the transverse direction is confined by a harmonic trapping potential. Along the waveguide, the particle scatters on an infinite array of regularized delta potentials. Our starting point is the Lippmann-Schwinger equation, which for quasi-1D geometry can be solved exactly, based on the analytical formula for the quasi-1D Green's function. We study the properties of eigen-energies as a function of particle quasi-momentum, which form band structure, as in standard Kronig-Penney model. We test our model by comparing it to the numerical calculations for an atom scattering on an infinite chain of ions in quasi-1D geometry. The agreement is fairly good and can be further improved by introducing energy-dependent scattering length in the regularized delta potential. The energy spectrum exhibits the presence of multiple overlapping bands resulting from excitations in the transverse direction. At large lattice constants, our model reduces to standard Kronig-Penney result with one-dimensional coupling constant for quasi-1D scattering, exhibiting confinement-induced resonances. In the opposite limit, when lattice constant becomes comparable to harmonic oscillator length of the transverse potential, we calculate the correction to the quasi-1D coupling constant due to the quantum interference between scatterers. Finally, we calculate the effective mass for the lowest band and show that it becomes negative for large and positive scattering lengths.

quant-ph↗

arXiv2019

Impact of ion motion on atom-ion confinement-induced resonances in hybrid traps

We investigate confinement-induced resonances in atom-ion quantum mixtures confined in hybrid traps. Specifically, we consider an ion confined in a time-dependent radio-frequency Paul trap with linear geometry, while the atom is constrained to move into a quasi-one-dimensional optical waveguide within the ion trap. We evaluate the impact of the ion intrinsic micromotion on the resonance position. Thus, we solve the atom-ion dynamics semiclassically, namely the atom dynamics is governed by the three-dimensional time-dependent Schrödinger equation, whereas the ion motion is described by the classical Hamilton equations. We find that the energy of the ion provided by the oscillating radiofrequency fields can affect the resonance position substantially. Notwithstanding, the peculiar phenomenology of those resonances regarding perfect transmission and reflection is still observable. These findings indicate that the intrinsic micromotion of the ion is not detrimental for the occurrence of the resonance and that its position can be controlled by the radiofrequency fields. This provides an additional mean for tuning atom-ion interactions in low spatial dimensions. The study represents an important advancement in the scattering physics of compound atomic quantum systems in time-dependent traps.

physics.atom-ph↗

arXiv2019

Cold hybrid ion-atom systems

Hybrid systems of laser-cooled trapped ions and ultracold atoms combined in a single experimental setup have recently emerged as a new platform for fundamental research in quantum physics. This paper reviews the theoretical and experimental progress in research on cold hybrid ion-atom systems which aim to combine the best features of the two well-established fields. We provide a broad overview of the theoretical description of ion-atom mixtures and their applications, and report on advances in experiments with ions trapped in Paul or dipole traps overlapped with a cloud of cold atoms, and with ions directly produced in a Bose-Einstein condensate. We start with microscopic models describing the electronic structure, interactions, and collisional physics of ion-atom systems at low and ultralow temperatures, including radiative and non-radiative charge transfer processes and their control with magnetically tunable Feshbach resonances. Then we describe the relevant experimental techniques and the intrinsic properties of hybrid systems. In particular, we discuss the impact of the micromotion of ions in Paul traps on ion-atom hybrid systems. Next, we review recent proposals for using ions immersed in ultracold gases for studying cold collisions, chemistry, many-body physics, quantum simulation, and quantum computation and their experimental realizations. In the last part we focus on the formation of molecular ions via spontaneous radiative association, photoassociation, magnetoassociation, and sympathetic cooling. We discuss applications and prospects of cold molecular ions for cold controlled chemistry and precision spectroscopy.

physics.atom-ph↗

arXiv2018

Quantum Bose-Bose droplets at a dimensional crossover

We study a liquid quantum droplets in a mixture of two-component Bose-Einstein condensates under a variable confinement introduced along one or two spatial dimensions. Despite the atom-atom scattering has a three-dimensional character, discreetness of the available modes in the reduced dimension(s) strongly influences the zero-point energy -- the Lee-Huang-Yang term. In a weakly interaction limit, it is the leading correction to the mean-field energy at the crossover from three to two dimensions, or from three to one dimension. We analyze the properties of the droplets at the dimensional crossovers, and provide the demanding conditions for accessing quasi-low dimensions. We predict new kinds of droplets which are formed only due to the quantum fluctuations when the mean-field interaction vanishes. Our results pave the way for exploring new states of quantum matter, and are important for experiments with liquid quantum droplets in reduced dimensions.

cond-mat.quant-gas↗

arXiv2018

Quantum state engineering with a trapped atom and a set of static impurities

Hybrid systems of ultracold atoms and trapped ions or Rydberg atoms can be useful for quantum simulation purposes. By tuning the geometric arrangement of the impurities it is possible to mimic solid state and molecular systems. Here we study a single trapped atom interacting with a set of arbitrarily arranged static impurities and show that the problem admits an analytical solution. We analyze in detail the case of two impurities, finding multiple trap-induced resonances which can be used for entanglement generation. Our results serve as a building block for the studies of quantum dynamics of complex systems.

quant-ph↗

arXiv2018

Single-atom transistor as a precise magnetic field sensor

Feshbach resonances, which allow for tuning the interactions of ultracold atoms with an external magnetic field, have been widely used to control the properties of quantum gases. We propose a~scheme for using scattering resonances as a probe for external fields, showing that by carefully tuning the parameters it is possible to reach a $10^{-5}$G (or nT) level of precision with a single pair of atoms. We show that for our collisional setup it is possible to saturate the quantum precision bound with a simple measurement protocol.

quant-ph↗

arXiv2016

Inelastic collisions of ultracold triplet Rb$_\textbf{2}$ molecules in the rovibrational ground state

Exploring inelastic and reactive collisions on the quantum level is a main goal of the developing field of ultracold chemistry. We present first experimental studies of inelastic collisions of metastable ultracold triplet molecules in the vibrational ground state. The measurements are performed with nonpolar $\textrm{Rb}_2$ dimers which are prepared in precisely-defined quantum states and trapped in an array of quasi-1D potential tubes. In particular, we investigate collisions of molecules in the absolute lowest triplet energy level where any inelastic process requires a change of the electronic state. Nevertheless, we find similar decay rates as for collisions between rotationally or vibrationally excited triplet molecules and they are close to the rates for universal reactions. As anticipated theoretically, the measured decay rate constants vary considerably when confinement and collision energy are changed. This might be exploited to control the collisional properties of molecules.

cond-mat.quant-gas↗

arXiv2015

Reactive collisions of two ultracold particles in a harmonic trap

We consider two ultracold particles confined in spherically symmetric harmonic trap and interacting via isotropic potential with absorbing boundary conditions at short range that models reactive scattering. First, we apply the contact pseudopotential with complex scattering length and investigate the properties of eigenergies and eigenfunctions for different trap states as a function of real and imaginary part of the scattering length. In the analyzed case the eigenenergies take complex values, and their imaginary part can be interpreted in terms of decay rates. Then we introduce the model of a square well with absorbing boundary conditions that is later used to investigate the effects of the finite range of interaction on the properties of a reactive scattering in the trap. Finally, we analyze the decay rates for some reactive alkali dimer molecules assuming short-range probability of reaction equal to unity. In this case the complex scattering length is given by universal value related to the mean scattering length of van der Waals interaction between molecules.

quant-ph↗

arXiv2015

Reactive collisions in confined geometries

We consider low energy threshold reactive collisions of particles interacting via a van der Waals potential at long range in the presence of external confinement and give analytic formulas for the confinement modified scattering in such circumstances. The reaction process is described in terms of the short range reaction probability. Quantum defect theory is used to express elastic and inelastic or reaction collision rates analytically in terms of two dimensionless parameters representing phase and reactivity. We discuss the modifications to Wigner threshold laws for quasi-one-dimensional and quasi-two-dimensional geometries. Confinement-induced resonances are suppressed due to reactions and are completely absent in the universal limit where the short-range loss probability approaches unity.

cond-mat.quant-gas↗

arXiv2014

Description of ion motion in a Paul trap immersed in a cold atomic gas

We investigate the problem of a single ion in a radio-frequency trap and immersed in an ultracold Bose gas either in a condensed or a non-condensed phase. We develop master equation formalism describing the sympathetic cooling and we determine the cooling rates of ions. We show that cold atomic reservoir modifies the stability diagram of the ion in the Paul trap creating the regions where the ion is either cooled or heated due to the energy quanta exchanged with the time-dependent potential.

cond-mat.quant-gas↗

arXiv2014

Quantum defect model of a reactive collision at finite temperature

We consider a general problem of inelastic collision of particles interacting with power-law potentials. Using quantum defect theory we derive an analytical formula for the energy-dependent complex scattering length, valid for arbitrary collision energy, and use it to analyze the elastic and reactive collision rates. Our theory is applicable for both universal and non-universal collisions. The former corresponds to the unit reaction probability at short range, while in the latter case the reaction probability is smaller than one. In the high-energy limit we present a method that allows to incorporate quantum corrections to the classical reaction rate due to the shape resonances and the quantum tunneling.

physics.atom-ph↗

arXiv2014

Polar molecule reactive collisions in quasi-1D systems

We study polar molecule scattering in quasi-one-dimensional geometries. Elastic and reactive collision rates are computed as a function of collision energy and electric dipole moment for different confinement strengths. The numerical results are interpreted in terms of first order scattering and of adiabatic models. Universal dipolar scattering is also discussed. Our results are relevant to experiments where control of the collision dynamics through one dimensional confinement and an applied electric field is envisioned.

cond-mat.quant-gas↗

arXiv2014

Fast quantum gate via Feshbach-Pauli blocking in a nanoplasmonic trap

We propose a simple idea for realizing a quantum gate with two identical fermions in a double well trap via external optical pulses without addressing the atoms individually. The key components of the scheme are Feshbach resonance and Pauli blocking, which decouple unwanted states from the dynamics. As a physical example we study atoms in the presence of a magnetic Feshbach resonance in a nanoplasmonic trap and discuss the constraints on the operation times for realistic parameters, reaching a fidelity above $99.9\%$ within $42μ$s.

quant-ph↗