arXiv subjects

A. G. Volosniev

Publications and source records attributed to A. G. Volosniev.

At least 37 records · Page 2Linked to original sources

arXiv2016

CONAN -- the cruncher of local exchange coefficients for strongly interacting confined systems in one dimension

We consider a one-dimensional system of particles with strong zero-range interactions. This system can be mapped onto a spin chain of the Heisenberg type with exchange coefficients that depend on the external trap. In this paper, we present an algorithm that can be used to compute these exchange coefficients. We introduce an open source code CONAN (Coefficients of One-dimensional N-Atom Networks) which is based on this algorithm. CONAN works with arbitrary external potentials and we have tested its reliability for system sizes up to around 35 particles. As illustrative examples, we consider a harmonic trap and a box trap with a superimposed asymmetric tilted potential. For these examples, the computation time typically scales with the number of particles as $O(N^{3.5 \pm 0.4})$. Computation times are around 10 seconds for $N=10$ particles and less than 10 minutes for $N=20$ particles.

cond-mat.quant-gas↗

arXiv2016

Simulation of Time-dependent Heisenberg Models in 1D

In this paper, we provide a theoretical analysis of strongly interacting quantum systems confined by a time-dependent external potential in one spatial dimension. We show that such systems can be used to simulate spin chains described by Heisenberg Hamiltonians in which the exchange coupling constants can be manipulated by time-dependent driving of the shape of the external confinement. As illustrative examples, we consider a harmonic trapping potential with a variable frequency and an infinite square well potential with a time-dependent barrier in the middle.

cond-mat.quant-gas↗

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

Real-Time Dynamics of an Impurity in an Ideal Bose Gas in a Trap

We investigate the behavior of a harmonically trapped system consisting of an impurity in a dilute ideal Bose gas after the boson-impurity interaction is suddenly switched on. As theoretical framework, we use a field theory approach in the space-time domain within the T-matrix approximation. We establish the form of the corresponding T-matrix and address the dynamical properties of the system. As a numerical application, we consider a simple system of a weakly interacting impurity in one dimension where the interaction leads to oscillations of the impurity density. Moreover, we show that the amplitude of the oscillations can be driven by periodically switching the interaction on and off.

cond-mat.quant-gas↗

arXiv2015

Strongly interacting confined quantum systems in one dimension

In one dimension, the study of magnetism dates back to the dawn of quantum mechanics when Bethe solved the famous Heisenberg model that describes quantum behaviour in magnetic systems. In the last decade, one-dimensional systems have become a forefront area of research driven by the realization of the Tonks-Girardeau gas using cold atomic gases. Here we prove that one-dimensional fermionic and bosonic systems with strong short-range interactions are solvable in arbitrary confining geometries by introducing a new energy-functional technique and obtaining the full spectrum of energies and eigenstates. As a first application, we calculate spatial correlations and show how both ferro- and anti-ferromagnetic states are present already for small system sizes that are prepared and studied in current experiments. Our work demonstrates the enormous potential for quantum manipulation of magnetic correlations at the microscopic scale.

cond-mat.quant-gas↗

arXiv2015

Repulsively interacting fermions in a two-dimensional deformed trap with spin-orbit coupling

We investigate a two-dimensional system of with two values of the internal (spin) degree of freedom. It is confined by a deformed harmonic trap and subject to a Zeeman field, Rashba or Dresselhaus one-body spin-orbit couplings and two-body short range repulsion. We obtain self-consistent mean-field $N$-body solutions as functions of the interaction parameters. Single-particle Spectra and total energies are computed and compared to the results without interaction. We perform a statistical analysis for the distributions of nearest neighbor energy level spacings and show that quantum signatures of chaos are seen in certain parameters regimes. Furthermore, the effects of two-body repulsion on the nearest neighbor distributions are investigated. This repulsion can either promote or destroy the signatures of potential chaotic behavior depending on relative strengths of parameters. Our findings support the suggestion that cold atoms may be used to study quantum chaos both in the presence and absence of interactions.

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↗

arXiv2015

Engineering the Dynamics of Effective Spin-Chain Models for Strongly Interacting Atomic Gases

We consider a one-dimensional gas of cold atoms with strong contact interactions and construct an effective spin-chain Hamiltonian for a two-component system. The resulting Heisenberg spin model can be engineered by manipulating the shape of the external confining potential of the atomic gas. We find that bosonic atoms offer more flexibility for tuning independently the parameters of the spin Hamiltonian through interatomic (intra-species) interaction which is absent for fermions due to the Pauli exclusion principle. Our formalism can have important implications for control and manipulation of the dynamics of few- and many-body quantum systems; as an illustrative example relevant to quantum computation and communication, we consider state transfer in the simplest non-trivial system of four particles representing exchange-coupled qubits.

cond-mat.quant-gas↗

arXiv2015

Analytic solutions of topologically disjoint systems

We describe a procedure to solve an up to $2N$ problem where the particles are separated topologically in $N$ groups with at most two particles in each. Arbitrary interactions are allowed between the (two) particles within one group. All other interactions are approximated by harmonic oscillator potentials. The problem is first reduced to an analytically solvable $N$-body problem and $N$ independent two-body problems. We calculate analytically spectra, wave functions, and normal modes for both the inverse square and delta-function two-body interactions. In particular, we calculate separation energies between two strings of particles. We find that the string separation energy increases with $N$ and interaction strength.

quant-ph↗

arXiv2014

Statistical properties of spectra in harmonically trapped spin-orbit coupled systems

We compute single-particle energy spectra for a one-body hamiltonian consisting of a two-dimensional deformed harmonic oscillator potential, the Rashba spin-orbit coupling and the Zeeman term. To investigate the statistical properties of the obtained spectra as functions of deformation, spin-orbit and Zeeman strengths we examine the distributions of the nearest neighbor spacings. We find that the shapes of these distributions depend strongly on the three potential parameters. We show that the obtained shapes in some cases can be well approximated with the standard Poisson, Brody and Wigner distributions. The Brody and Wigner distributions characterize irregular motion and help identify quantum chaotic systems. We present a special choices of deformation and spin-orbit strengths without the Zeeman term which provide a fair reproduction of the fourth-power repelling Wigner distribution. By adding the Zeeman field we can reproduce a Brody distribution, which is known to describe a transition between the Poisson and linear Wigner distributions.

cond-mat.quant-gas↗

arXiv2014

Fractional energy states of strongly-interacting bosons in one dimension

We study two-component bosonic systems with strong inter-species and vanishing intra-species interactions. A new class of exact eigenstates is found with energies that are {\it not} sums of the single-particle energies with wave functions that have the characteristic feature that they vanish over extended regions of coordinate space. This is demonstrated in an analytically solvable model for three equal mass particles, two of which are identical bosons, which is exact in the strongly-interacting limit. We numerically verify our results by presenting the first application of the stochastic variational method to this kind of system. We also demonstrate that the limit where both inter- and intra-component interactions become strong must be treated with extreme care as these limits do not commute. Moreover, we argue that such states are generic also for general multi-component systems with more than three particles. The states can be probed using the same techniques that have recently been used for fermionic few-body systems in quasi-1D.

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↗

arXiv2014

Borromean ground state of fermions in two dimensions

The study of quantum mechanical bound states is as old as quantum theory itself. Yet, it took many years to realize that three-body borromean systems that are bound when any two-body subsystem is unbound are abundant in nature. Here we demonstrate the existence of borromean systems of spin-polarized (spinless) identical fermions in two spatial dimensions. The ground state with zero orbital (planar) angular momentum exists in a borromean window between critical two- and three-body strengths. The doubly degenerate first excited states of angular momentum one appears only very close to the two-body threshold. They are the lowest in a possible sequence of so-called super-Efimov states. While the observation of the super-Efimov scaling could be very difficult, the borromean ground state should be observable in cold atomic gases and could be the basis for producing a quantum gas of three-body states in two dimensions.

cond-mat.quant-gas↗

arXiv2014

Hyperspherical Treatment of Strongly-Interacting Few-Fermion Systems in One Dimension

We examine a one-dimensional two-component fermionic system in a trap, assuming that all particles have the same mass and interact through a strong repulsive zero-range force. First we show how a simple system of three strongly interacting particles in a harmonic trap can be treated using the hyperspherical formalism. Next we discuss the behavior of the energy for the N-body system.

cond-mat.quant-gas↗

arXiv2014

Fermionization of two-component few-fermion systems in a one-dimensional harmonic trap

The nature of strongly interacting Fermi gases and magnetism is one of the most important and studied topics in condensed-matter physics. Still, there are many open questions. A central issue is under what circumstances strong short-range repulsive interactions are enough to drive magnetic correlations. Recent progress in the field of cold atomic gases allows to address this question in very clean systems where both particle numbers, interactions and dimensionality can be tuned. Here we study fermionic few-body systems in a one dimensional harmonic trap using a new rapidly converging effective-interaction technique, plus a novel analytical approach. This allows us to calculate the properties of a single spin-down atom interacting with a number of spin-up particles, a case of much recent experimental interest. Our findings indicate that, in the strongly interacting limit, spin-up and spin-down particles want to separate in the trap, which we interpret as a microscopic precursor of one-dimensional ferromagnetism in imbalanced systems. Our predictions are directly addressable in current experiments on ultracold atomic few-body systems.

cond-mat.quant-gas↗

arXiv2014

Higher-order Brunnian structures and possible physical realizations

We consider few-body bound state systems and provide precise definitions of Borromean and Brunnian systems. The initial concepts are more than a hundred years old and originated in mathematical knot-theory as purely geometric considerations. About thirty years ago they were generalized and applied to the binding of systems in nature. It now appears that recent generalization to higher order Brunnian structures may potentially be realized as laboratory made or naturally occurring systems. With the binding energy as measure, we discuss possibilities of physical realization in nuclei, cold atoms, and condensed matter systems. Appearance is not excluded. However, both the form and the strengths of the interactions must be rather special. The most promising subfields for present searches would be in cold atoms because of external control of effective interactions, or perhaps in condensed-matter systems with non-local interactions. In nuclei, it would only be by sheer luck due to a lack of tunability.

quant-ph↗

arXiv2013

Spectral Gaps of Spin-orbit Coupled Particles in Deformed Traps

We consider a spin-orbit coupled system of particles in an external trap that is represented by a deformed harmonic oscillator potential. The spin-orbit interaction is a Rashba interaction that does not commute with the trapping potential and requires a full numerical treatment in order to obtain the spectrum. The effect of a Zeeman term is also considered. Our results demonstrate that variable spectral gaps occur as a function of strength of the Rashba interaction and deformation of the harmonic trapping potential. The single-particle density of states and the critical strength for superfluidity vary tremendously with the interaction parameter. The strong variations with Rashba coupling and deformation implies that the few- and many-body physics of spin-orbit coupled systems can be manipulated by variation of these parameters.

cond-mat.quant-gas↗

arXiv2013

Occurrence conditions for two-dimensional Borromean systems

We search for Borromean three-body systems of identical bosons in two dimensional geometry, i.e. we search for bound three-boson system without bound two-body subsystems. Unlike three spatial dimensions, in two-dimensional geometry the two- and three-body thresholds often coincide ruling out Borromean systems. We show that Borromean states can only appear for potentials with substantial attractive and repulsive parts. Borromean states are most easily found when a barrier is present outside an attractive pocket. Extensive numerical search did not reveal Borromean states for potentials without an outside barrier. We outline possible experimental setups to observe Borromean systems in two spatial dimensions.

quant-ph↗