arXiv subjects

F. F. Bellotti

Publications and source records attributed to F. F. Bellotti.

At least 19 recordsLinked to original sources

arXiv2017

Squeezing the Efimov effect

The quantum mechanical three-body problem is a source of continuing interest due to its complexity and not least due to the presence of fascinating solvable cases. The prime example is the Efimov effect where infinitely many bound states of identical bosons can arise at the threshold where the two-body problem has zero binding energy. An important aspect of the Efimov effect is the effect of spatial dimensionality; it has been observed in three dimensional systems, yet it is believed to be impossible in two dimensions. Using modern experimental techniques, it is possible to engineer trap geometry and thus address the intricate nature of quantum few-body physics as function of dimensionality. Here we present a framework for studying the three-body problem as one (continuously) changes the dimensionality of the system all the way from three, through two, and down to a single dimension. This is done by considering the Efimov favorable case of a mass-imbalanced system and with an external confinement provided by a typical experimental case with a (deformed) harmonic trap.

cond-mat.quant-gas↗

arXiv2017

Mobile Spin Impurity in an Optical Lattice

We investigate the Fermi polaron problem in a spin-1/2 Fermi gas in an optical lattice for the limit of both strong repulsive contact interactions and one dimension. In this limit, a polaronic-like behaviour is not expected, and the physics is that of a magnon or impurity. While the charge degrees of freedom of the system are frozen, the resulting tight-binding Hamiltonian for the impurity's spin exhibits an intriguing structure that strongly depends on the filling factor of the lattice potential. This filling dependency also transfers to the nature of the interactions for the case of two magnons and the important spin balanced case. At low filling, and up until near unit filling, the single impurity Hamiltonian faithfully reproduces a single-band, quasi-homogeneous tight-binding problem. As the filling is increased and the second band of the single particle spectrum of the periodic potential is progressively filled, the impurity Hamiltonian, at low energies, describes a single particle trapped in a multi-well potential. Interestingly, once the first two bands are fully filled, the impurity Hamiltonian is a near-perfect realisation of the Su-Schrieffer-Heeger model. Our studies, which go well beyond the single-band approximation, that is, the Hubbard model, pave the way for the realisation of interacting one-dimensional models of condensed matter physics.

cond-mat.quant-gas↗

arXiv2017

Analytical and numerical studies of Bose-Fermi mixtures in a one-dimensional harmonic trap

In this paper we study a mixed system of bosons and fermions with up to six particles in total. All particles are assumed to have the same mass. The two-body interactions are repulsive and are assumed to have equal strength in both the Bose-Bose and the Fermi-Boson channels. The particles are confined externally by a harmonic oscillator one-body potential. For the case of four particles, two identical fermions and two identical bosons, we focus on the strongly interacting regime and analyze the system using both an analytical approach and DMRG calculations using a discrete version of the underlying continuum Hamiltonian. This provides us with insight into both the ground state and the manifold of excited states that are almost degenerate for large interaction strength. Our results show great variation in the density profiles for bosons and fermions in different states for strongly interacting mixtures. By moving to slightly larger systems, we find that the ground state of balanced mixtures of four to six particles tends to separate bosons and fermions for strong (repulsive) interactions. On the other hand, in imbalanced Bose-Fermi mixtures we find pronounced odd-even effects in systems of five particles. These few-body results suggest that question of phase separation in one-dimensional confined mixtures are very sensitive to system composition, both for the ground state and the excited states.

cond-mat.quant-gas↗

arXiv2017

Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps

We investigate one-dimensional harmonically trapped two-component systems for repulsive interaction strengths ranging from the non-interacting to the strongly interacting regime for Fermi-Fermi mixtures. A new and powerful mapping between the interaction strength parameters from a continuous Hamiltonian and a discrete lattice Hamiltonian is derived. As an example, we show that this mapping does not depend neither on the state of the system nor on the number of particles. Energies, density profiles and correlation functions are obtained both numerically (DMRG and Exact diagonalization) and analytically. Since DMRG results do not converge as the interaction strength is increased, analytical solutions are used as a benchmark to identify the point where these calculations become unstable. We use the proposed mapping to set a quantitative limit on the interaction parameter of a discrete lattice Hamiltonian above which DMRG gives unrealistic results.

cond-mat.quant-gas↗

arXiv2017

Bound states of a light atom and two heavy dipoles in two dimensions

We study a three-body system, formed by a light particle and two identical heavy dipoles, in two dimensions in the Born-Oppenheimer approximation. We present the analytic light-particle wave function resulting from an attractive zero-range potential between the light and each of the heavy particles. It expresses the large-distance universal properties which must be reproduced by all realistic short-range interactions. We calculate the three-body spectrum for zero heavy-heavy interaction as a function of light to heavy mass ratio. We discuss the relatively small deviations from Coulomb estimates and the degeneracies related to radial nodes and angular momentum quantum numbers. We include a repulsive dipole-dipole interaction and investigate the three-body solutions as functions of strength and dipole direction. Avoided crossings occur between levels localized in the emerging small and large-distance minima, respectively. The characteristic exchange of properties such as mean square radii are calculated. Simulation of quantum information transfer is suggested. For large heavy-heavy particle repulsion all bound states have disappeared into the continuum. The corresponding critical strength is inversely proportional to the square of the mass ratio, far from the linear dependence from the Landau criterion.

physics.atom-ph↗

arXiv2016

Mean-square radii in mixed-species systems in two dimensions

We calculate root-mean-square radii for a three-body system confined to two spatial dimensions and consisting of two identical bosons ($A$) and one distinguishable particle ($B$). We use zero-range two-body interactions between each of the pairs, and focus thereby directly on universal properties. We solve the Faddeev equations in momentum space and express the mean-square radii in terms of first-order derivatives of the Fourier transforms of densities. The strengths of the interactions are adjusted for each set of masses to produce equal two-body bound-state energies between different pairs. The mass ratio, ${\cal A}=m_B/m_A$, between particles $B$ and $A$ are varied from $0.01$ to $100$ providing a number of bound states decreasing from $8$ to $2$. Energies and mean-square radii of these states are analyzed for small ${\cal A}$ by use of the Born-Oppenheimer potential between the two heavy $A$-particles. For large ${\cal A}$ the radii of the two bound states are consistent with a slightly asymmetric three-body structure. When ${\cal A}$ approaches thresholds for binding of the three-body excited states, the corresponding mean-square radii diverge inversely proportional to the deviation of the three-body energy from the two-body thresholds. The structures at these three-body thresholds correspond to bound $AB$-dimers and one loosely bound $A$-particle.

physics.atom-ph↗

arXiv2016

Three-body bound states of two bosonic impurities immersed in a Fermi sea in 2D

We consider two identical impurities immersed in a Fermi sea for a broad range of masses and for both interacting and non-interacting impurities. The interaction between the particles is described through attractive zero-range potentials and the problem is solved in momentum space. The two impurities can attach to a fermion from the sea and form three-body bound states. The energy of these states increase as function of the Fermi momentum $k_F$, leading to three-body bound states below the Fermi energy. The fate of the states depends highly on two- and three-body thresholds and we find evidence of medium-induced Borromean-like states in 2D. The corrections due to particle-hole fluctuations in the Fermi sea are considered in the three-body calculations and we show that in spite of the fact that they strongly affect both the two- and three-body systems, the correction to the point at which the three-body states cease to exist is small.

cond-mat.quant-gas↗

arXiv2016

Scaling limit analysis of Borromean halos

The analysis of the core recoil momentum distribution of neutron-rich isotopes of light exotic nuclei is performed within a model of the halo nuclei described by a core and two neutrons dominated by the $s-$wave channel. We adopt the renormalized three-body model with a zero-range force, that accounts for the universal Efimov physics. This model is applicable to nuclei with large two-neutron halos compared to the core size, and a neutron-core scattering length larger than the interaction range. The halo wave function in momentum space is obtained by using as inputs the two-neutron separation energy and the energies of the singlet neutron-neutron and neutron-core virtual states. Within our model, we obtain the momentum probability densities for the Borromean exotic nuclei Lithium-11 ($^{11}$Li), Berylium-14 ($^{14}$Be) and Carbon-22 ($^{22}$C). A fair reproduction of the experimental data was obtained in the case of the core recoil momentum distribution of $^{11}$Li and $^{14}$Be, without free parameters. By extending the model to $^{22}$C, the combined analysis of the core momentum distribution and matter radius suggest (i) a $^{21}$C virtual state well below 1 MeV; (ii) an overestimation of the extracted matter $^{22}$C radius; and (iii) a two-neutron separation energy between 100 and 400 keV.

nucl-th↗

arXiv2016

Single particle momentum distributions for three-bosons in two and three dimensions and dimensional crossover

In this paper, we revise our main results involving the single particle momentum distribution of bosonic trimer states in two and three dimensions. A summary table makes easier the comparison between the matrix elements and the different terms of the momentum distributions. We also show a practical method to continuously interpolate between different dimensions.

cond-mat.quant-gas↗

arXiv2015

Weakly bound states of two- and three-boson systems in the crossover from two to three dimension

The spectrum and properties of quantum bound states is strongly dependent on the dimensionality of space. How this comes about and how one may theoretically and experimentally study the interpolation between different dimensions is a topic of great interest in different fields of physics. In this paper we study weakly bound states of non-relativistic two and three boson systems when passing continuously from a three (3D) to a two-dimensional (2D) regime within a 'squeezed dimension' model. We use periodic boundary conditions to derive a surprisingly simple form of the three-boson Schr{ö}dinger equation in momentum space that we solve numerically. Our results show a distinct dimensional crossover as three-boson states will either disappear into the continuum or merge with a 2D counterpart, and also a series of sharp transitions in the ratios of three-body and two-body energies from being purely 2D to purely 3D.

cond-mat.quant-gas↗

arXiv2014

Two- and three- dimensional few-body systems in the universal regime

Macro properties of cold atomic gases are driven by few-body correlations, even if the gas has thousands of particles. Quantum systems composed of two and three particles with attractive zero\=/range pairwise interactions are considered for general masses and interaction strengths in two and three dimensions (2D and 3D). The Faddeev decomposition is used to derive the equations for the bound state, which is the starting point for the investigation of universal properties of few\=/body systems, i.e. those that all potentials with the same physics at low energy are able to describe in a model\=/independent form. In 2D, the number of bound states in a three\=/body system increases without bound as the mass of one particle becomes much lighter than the other two. The analytic form of an effective potential between the heavy particles explains the mass\=/dependence on the number of bound energy levels. An exact analytic expression for the large\=/momentum asymptotic behaviour of the spectator function in the Faddeev equation is presented. The spectator function and its asymptotic form define the two- and three\=/body contact parameters. The two\=/body parameter is found to be independent of the quantum state in some specific 2D systems. The 2D and 3D momentum distributions have a distinct sub\=/leading form whereas the 3D term depends on the mass of the particles. A model that interpolates between 2D and 3D is proposed and a sharp transition in the energy spectrum of three-body systems is found.

cond-mat.quant-gas↗

arXiv2014

Mass-imbalanced Three-body Systems in 2D: bound states and the analytical approach to the adiabatic potential

Three-body systems in two dimensions with zero-range interactions are considered for general masses and interaction strengths. The problem is formulated in momentum space and the numerical solution of the Schrödinger equation is used to study universal properties of such systems with respect to the bound-state energies. The number of universal bound states is represented in a form of boundaries in a mass-mass diagram. The number of bound states is strongly mass dependent and increases as one particle becomes much lighter than the other ones. This behavior is understood through an accurate analytical approximation to the adiabatic potential for one light particle and two heavy ones.

cond-mat.quant-gas↗

arXiv2014

Universality of three-body systems in 2D: parametrization of the bound states energies

Universal properties of mass-imbalanced three-body systems in 2D are studied using zero-range interactions in momentum space. The dependence of the three-particle binding energy on the parameters (masses and two-body energies) is highly non-trivial even in the simplest case of two identical particles and a distinct one. This dependence is parametrized for ground and excited states in terms of {\itshape supercircles} functions in the most general case of three distinguishable particles.

cond-mat.quant-gas↗

arXiv2014

Contact parameters in two dimensions for general three-body systems

We study the two dimensional three-body problem in the general case of three distinguishable particles interacting through zero-range potentials. The Faddeev decomposition is used to write the momentum-space wave function. We show that the large-momentum asymptotic spectator function has the same functional form as derived previously for three identical particles. We derive analytic relations between the three different Faddeev components for three distinguishable particles. We investigate the one-body momentum distributions both analytically and numerically and analyze the tail of the distributions to obtain two- and three-body contact parameters. We specialize from the general cases to examples of two identical, interacting or non-interacting, particles. We find that the two-body contact parameter is not a universal constant in the general case and show that the universality is recovered when a subsystem is composed of two identical non-interacting particles. We also show that the three-body contact parameter is negligible in the case of one non-interacting subsystem compared to the situation where all subsystem are bound. As example, we present results for mixtures of Lithium with two Cesium or two Potassium atoms, which are systems of current experimental interest.

cond-mat.quant-gas↗

arXiv2013

Single-Particle Momentum Distributions of Efimov States in Mixed-Species Systems

We solve the three-body bound state problem in three dimensions for mass imbalanced systems of two identical bosons and a third particle in the universal limit where the interactions are assumed to be of zero-range. The system displays the Efimov effect and we use the momentum-space wave equation to derive formulas for the scaling factor of the Efimov spectrum for any mass ratio assuming either that two or three of the two-body subsystems have a bound state at zero energy. We consider the single-particle momentum distribution analytically and numerically and analyse the tail of the momentum distribution to obtain the three-body contact parameter. Our finding demonstrate that the functional form of the three-body contact term depends on the mass ratio and we obtain an analytic expression for this behavior. To exemplify our results, we consider mixtures of Lithium with either two Caesium or Rubium atoms which are systems of current experimental interest.

cond-mat.quant-gas↗

arXiv2013

Mass-imbalanced Three-Body Systems in Two Dimensions

We consider three-body systems in two dimensions with zero-range interactions for general masses and interaction strengths. The momentum-space Schrödinger equation is solved numerically and in the Born-Oppenheimer (BO) approximation. The BO expression is derived using separable potentials and yields a concise adiabatic potential between the two heavy particles. The BO potential is Coulomb-like and exponentially decreasing at small and large distances, respectively. While we find similar qualitative features to previous studies, we find important quantitative differences. Our results demonstrate that mass-imbalanced systems that are accessible in the field of ultracold atomic gases can have a rich three-body bound state spectrum in two dimensional geometries. Small light-heavy mass ratios increase the number of bound states. For 87Rb-87Rb-6Li and 133Cs-133Cs-6Li we find respectively 3 and 4 bound states.

cond-mat.quant-gas↗

arXiv2013

Dimensional Effects on the Momentum distribution of Bosonic Trimer States

The momentum distribution is a powerful probe of strongly-interacting systems that are expected to display universal behavior. This is contained in the contact parameters which relate few- and many-body properties. Here we consider a Bose gas in two dimensions and explicitly show that the two-body contact parameter is universal and then demonstrate that the momentum distribution at next-to-leading order has a logarithmic dependence on momentum which is vastly different from the three-dimensional case. Based on this, we propose a scheme for measuring the effective dimensionality of a quantum many-body system by exploiting the functional form of the momentum distribution.

cond-mat.quant-gas↗

arXiv2012

A supercircle description of universal three-body states in two dimensions

We consider bound states of asymmetric three-body systems confined to two dimensions. In the universal regime, two energy ratios and two mass ratios provide complete knowledge of the three-body energy measured in units of one two-body energy. The lowest number of stable bound states is produced when one mass is larger than two similar masses. We focus on selected asymmetric systems of interest in cold atom physics. The scaled three-body energy and the two scaled two-body energies are related through an equation for a supercircle whose radius increases almost linearly with three-body energy. The exponents exhibit an increasing behavior with three-body energy. The mass dependence is highly non-trivial. We give a simple relation that predicts the universal three-body energy.

cond-mat.quant-gas↗