arXiv subjects

A. S. Dehkharghani

Publications and source records attributed to A. S. Dehkharghani.

13 recordsLinked to original sources

arXiv2022

Coalescence of Two Impurities in a Trapped One-dimensional Bose Gas

We study the ground state of a one-dimensional (1D) trapped Bose gas with two mobile impurity particles. To investigate this set-up, we develop a variational procedure in which the coordinates of the impurity particles are slow-like variables. We validate our method using the exact results obtained for small systems. Then, we discuss energies and pair densities for systems that contain of the order of one hundred atoms. We show that bosonic non-interacting impurities cluster. To explain this clustering, we calculate and discuss induced impurity-impurity potentials in a harmonic trap. Further, we compute the force between static impurities in a ring ({\it {à} la} the Casimir force), and contrast the two effective potentials: the one obtained from the mean-field approximation, and the one due to the one-phonon exchange. Our formalism and findings are important for understanding (beyond the polaron model) the physics of modern 1D cold-atom systems with more than one impurity.

cond-mat.quant-gas↗

arXiv2020

Impenetrable Mass-Imbalanced Particles in One-Dimensional Harmonic Traps

Strongly interacting particles in one dimension subject to external confinement have become a topic of considerable interest due to recent experimental advances and the development of new theoretical methods to attack such systems. In the case of equal mass fermions or bosons with two or more internal degrees of freedom, one can map the problem onto the well-known Heisenberg spin models. However, many interesting physical systems contain mixtures of particles with different masses. Therefore, a generalization of the recent strong-coupling techniques would be highly desirable. This is particularly important since such problems are generally considered non-integrable and thus the hugely successful Bethe ansatz approach cannot be applied. Here we discuss some initial steps towards this goal by investigating small ensembles of one-dimensional harmonically trapped particles where pairwise interactions are either vanishing or infinitely strong with focus on the mass-imbalanced case. We discuss a (semi)-analytical approach to describe systems using hyperspherical coordinates where the interaction is effectively decoupled from the trapping potential. As an illustrative example we analyze mass-imbalanced four-particle two-species mixtures with strong interactions between the two species. For such systems we calculate the energies, densities and pair-correlation functions.

quant-ph↗

arXiv2018

One-Dimensional Quantum Systems - From Few to Many Particles

In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical models and numerical methods both for the few- and many-body systems. One-dimensional systems are very interesting in a sense that particles aligned on a line can only change seats by going through each other. This property can be exploited in the strongly interacting regime, where particles are forced to sit in a specific configuration, which can be easily manipulated. The knowledge of how and where the particles are can be exploited in future quantum applications. In short, the thesis is about establishing a solid knowledge about everything that one needs to know about the one-dimensional few- and many-component interacting quantum systems trapped in harmonic oscillator potentials.

cond-mat.quant-gas↗

arXiv2017

Quantum Simulation of Abelian Lattice Gauge Theories via State-Dependent Hopping

We develop a quantum simulator architecture that is suitable for the simulation of $U(1)$ Abelian gauge theories such as quantum electrodynamics. Our approach relies on the ability to control the hopping of a particle through a barrier by means of the internal quantum states of a neutral or charged impurity-particle sitting at the barrier. This scheme is experimentally feasible, as the correlated hopping does not require fine-tuning of the intra- and inter-species interactions. We investigate the applicability of the scheme in a double well potential, which is the basic building block of the simulator, both at the single-particle and the many-body mean-field level. Moreover, we evaluate its performance for different particle interactions and trapping, and, specifically for atom-ion systems, in the presence of micro-motion.

quant-ph↗

arXiv2017

Integrable families of hard-core particles with unequal masses in a one-dimensional harmonic trap

We show that the dynamics of particles in a one-dimensional harmonic trap with hard-core interactions can be solvable for certain arrangements of unequal masses. For any number of particles, there exist two families of unequal mass particles that have integrable dynamics, and there are additional exceptional cases for three, four and five particles. The integrable mass families are classified by Coxeter reflection groups and the corresponding solutions are Bethe ansatz-like superpositions of hyperspherical harmonics in the relative hyperangular coordinates that are then restricted to sectors of fixed particle order. We also provide evidence for superintegrability of these Coxeter mass families and conjecture maximal superintegrability.

quant-ph↗

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↗

arXiv2016

An interpolatory ansatz captures the physics of one-dimensional confined Fermi systems

Interacting one-dimensional quantum systems play a pivotal role in physics. Exact solutions can be obtained for the homogeneous case using the Bethe ansatz and bosonisation techniques. However, these approaches are not applicable when external confinement is present. Recent theoretical advances beyond the Bethe ansatz and bosonisation allow us to predict the behaviour of one-dimensional confined systems with strong short-range interactions, and new experiments with cold atomic Fermi gases have already confirmed these theories. Here we demonstrate that a simple linear combination of the strongly interacting solution with the well-known solution in the limit of vanishing interactions provides a simple and accurate description of the system for all values of the interaction strength. This indicates that one can indeed capture the physics of confined one-dimensional systems by knowledge of the limits using wave functions that are much easier to handle than the output of typical numerical approaches. We demonstrate our scheme for experimentally relevant systems with up to six particles. Moreover, we show that our method works also in the case of mixed systems of particles with different masses. This is an important feature because these systems are known to be non-integrable and thus not solvable by the Bethe ansatz technique.

quant-ph↗

arXiv2016

Correlation properties of a three-body bosonic mixture in a harmonic trap

We make use of a simple pair correlated wave function approach to obtain results for the ground-state densities and momentum distribution of a one-dimensional three-body bosonic system with different interactions in a harmonic trap. For equal interactions this approach is able to reproduce the known analytical cases of zero and infinite repulsion. We show that our results for the correlations agree with the exact diagonalization in all interaction regimes and with analytical results for the strongly repulsive impurity. This method also enables us to access the more complicated cases of mixed interactions, and the probability densities of these systems are analyzed.

cond-mat.quant-gas↗

arXiv2016

Entanglement of an Impurity in a Few-Body One-Dimensional Ideal Bose System

We study the correlation between an impurity and a small ensemble of bosonic particles in one dimension. Our study analyzes the one-body density matrix and calculates the corresponding von Neumann entanglement entropy as a function of the interaction strength between the impurity and the bosons when all particles have the same mass. We show that the entropy grows very fast for small and moderate interaction strength and then increases slowly toward the strongly interacting regime. Then we study the effect over the quantum correlations of a mass imbalance between the impurity and the bosons. In the strongly interacting case, we discover that when the impurity is much heavier than the bosons, then we have the least possible correlation. However, the entropy tops its maximum when the mass ratio is between 3 and 4 in the case where there are four bosonic particles and then falls off to its minimum for higher mass imbalance.

quant-ph↗

arXiv2015

Quantum Impurity in a One-dimensional Trapped Bose Gas

We present a new theoretical framework for describing an impurity in a trapped Bose system in one spatial dimension. The theory handles any external confinement, arbitrary mass ratios, and a weak interaction may be included between the Bose particles. To demonstrate our technique, we calculate the ground state energy and properties of a sample system with eight bosons and find an excellent agreement with numerically exact results. Our theory can thus provide definite predictions for experiments in cold atomic gases.

cond-mat.quant-gas↗

arXiv2015

A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap

We study a three-body system with zero-range interactions in a one-dimensional harmonic trap. The system consists of two spin-polarized fermions and a third particle which is distinct from two others (2+1 system). First we assume that the particles have equal masses. For this case the system in the strongly and weakly interacting limits can be accurately described using wave function factorized in hyperspherical coordinates. Inspired by this result we propose an interpolation ansatz for the wave function for arbitrary repulsive zero-range interactions. By comparison to numerical calculations, we show that this interpolation scheme yields an extremely good approximation to the numerically exact solution both in terms of the energies and also in the spin-resolved densities. As an outlook, we discuss the case of mass imbalanced systems in the strongly interacting limit. Here we find spectra that demonstrate that the triply degenerate spectrum at infinite coupling strength of the equal mass case is in some sense a singular case as this degeneracy will be broken down to a doubly degenerate or non-degenerate ground state by any small mass imbalance.

cond-mat.quant-gas↗

arXiv2014

Quantum magnetism in strongly interacting one-dimensional spinor Bose systems

Strongly interacting one-dimensional quantum systems often behave in a manner that is distinctly different from their higher-dimensional counterparts. When a particle attempts to move in a one-dimensional environment it will unavoidably have to interact and 'push' other particles in order to execute a pattern of motion, irrespective of whether the particles are fermions or bosons. A present frontier in both theory and experiment are mixed systems of different species and/or particles with multiple internal degrees of freedom. Here we consider trapped two-component bosons with short-range inter-species interactions much larger than their intra-species interactions and show that they have novel energetic and magnetic properties. In the strongly interacting regime, these systems have energies that are fractions of the basic harmonic oscillator trap quantum and have spatially separated ground states with manifestly ferromagnetic wave functions. Furthermore, we predict excited states that have perfect antiferromagnetic ordering. This holds for both balanced and imbalanced systems, and we show that it is a generic feature as one crosses from few- to many-body systems.

cond-mat.quant-gas↗