arXiv subjects

M. Olshanii

Publications and source records attributed to M. Olshanii.

At least 19 recordsLinked to original sources

arXiv2026

Diffraction induced quantum chaos in a one-dimensional Bose gas

We investigate the Lieb--Liniger model of interacting one-dimensional bosons coupled to a localized impurity, modeled by a delta barrier. While the Lieb--Liniger gas is integrable, the impurity breaks integrability and induces a transition towards quantum chaos. We show that the low-energy spectrum exhibits random-matrix statistics, in striking contrast to the Bohigas--Giannoni--Schmit conjecture, where chaotic behavior typically emerges at high energy. For two bosons, the odd-parity sector remains integrable, whereas the even-parity sector displays clear signatures of chaos at low energy and a crossover back to quasi-integrable behavior at higher energies. For three bosons, both parity sectors exhibit spectral statistics close to chaos at low energy. We argue that this unconventional form of few-body quantum chaos originates from diffractive processes induced by the impurity.

cond-mat.quant-gas↗

arXiv2025

Quantum dynamics of atoms in number-theory-inspired potentials

In this paper we study transitions of atoms between energy levels of several number-theory-inspired atom potentials, under the effect of time-dependent perturbations. First, we simulate in detail the case of a trap whose one-particle spectrum is given by prime numbers. We investigate one-body Rabi oscillations and the excitation lineshape for two resonantly coupled energy levels. We also show that techniques from quantum control are effective in reducing the transition time, compared to the case of a periodic perturbation. Next, we investigate cascades of such transitions. To this end, we pose the following question: can one construct a quantum system where the existence of a continuous resonant cascade is predicted on the validity of a particular statement in number theory? We find that a one-body trap with a log-natural spectrum, parametrically driven with a perturbation of a log-natural frequency, provides such a quantum system. Here, powers of a given natural number will form a ladder of equidistant energy levels; absence of gaps in this ladder is an indication of the validity of the number theory statement in question. Ideas for two more resonance cascade experiments are presented as well: they are designed to illustrate the validity of the Diophantus-Brahmagupta-Fibonacci identity (the set of sums of two squares of integers is closed under multiplication) and the validity of the Goldbach conjecture (every even number is a sum of two primes).

quant-ph↗

arXiv2021

The origin of the period-$2T/7$ quasi-breathing in disk-shaped Gross-Pitaevskii breathers

We address the origins of the quasi-periodic breathing observed in [Phys. Rev.\ X vol. 9, 021035 (2019)] in disk-shaped harmonically trapped two-dimensional Bose condensates, where the quasi-period $T_{\text{quasi-breathing}}\sim$~$2T/7$ and $T$ is the period of the harmonic trap. We show that, due to an unexplained coincidence, the first instance of the collapse of the hydrodynamic description, at $t^{*} = \arctan(\sqrt{2})/(2π) T \approx T/7$, emerges as a `skillful impostor' of the quasi-breathing half-period $T_{\text{quasi-breathing}}/2$. At the time $t^{*}$, the velocity field almost vanishes, supporting the requisite time-reversal invariance. We find that this phenomenon persists for scale-invariant gases in all spatial dimensions, being exact in one dimension and, likely, approximate in all others. In $d$ dimensions, the quasi-breathing half-period assumes the form $T_{\text{quasi-breathing}}/2 \equiv t^{*} = \arctan(\sqrt{d})/(2π) T$. Remaining unresolved is the origin of the period-$2T$ breathing, reported in the same experiment.

cond-mat.quant-gas↗

arXiv2021

Roadmap on Atomtronics: State of the art and perspective

Atomtronics deals with matter-wave circuits of ultra-cold atoms manipulated through magnetic or laser-generated guides with different shapes and intensities. In this way, new types of quantum networks can be constructed, in which coherent fluids are controlled with the know-how developed in the atomic and molecular physics community. In particular, quantum devices with enhanced precision, control and flexibility of their operating conditions can be accessed. Concomitantly, new quantum simulators and emulators harnessing on the coherent current flows can also be developed. Here, we survey the landscape of atomtronics-enabled quantum technology and draw a roadmap for the field in the near future. We review some of the latest progresses achieved in matter-wave circuits design and atom-chips. Atomtronic networks are deployed as promising platforms for probing many-body physics with a new angle and a new twist. The latter can be done both at the level of equilibrium and non-equilibrium situations. Numerous relevant problems in mesoscopic physics, like persistent currents and quantum transport in circuits of fermionic or bosonic atoms, are studied through a new lens. We summarize some of the atomtronics quantum devices and sensors. Finally, we discuss alkali-earth and Rydberg atoms as potential platforms for the realization of atomtronic circuits with special features.

cond-mat.quant-gas↗

arXiv2021

Triangular Gross-Pitaevskii breathers and Damski-Chandrasekhar shock waves

The recently proposed map [arXiv:2011.01415] between the hydrodynamic equations governing the two-dimensional triangular cold-bosonic breathers [Phys. Rev. X 9, 021035 (2019)] and the high-density zero-temperature triangular free-fermionic clouds, both trapped harmonically, perfectly explains the former phenomenon but leaves uninterpreted the nature of the initial ($t=0$) singularity. This singularity is a density discontinuity that leads, in the bosonic case, to an infinite force at the cloud edge. The map itself becomes invalid at times $t<0$. A similar singularity appears at $t = T/4$, where $T$ is the period of the harmonic trap, with the Fermi-Bose map becoming invalid at $t > T/4$. Here, we first map -- using the scale invariance of the problem -- the trapped motion to an untrapped one. Then we show that in the new representation, the solution [arXiv:2011.01415] becomes, along a ray in the direction normal to one of the three edges of the initial cloud, a freely propagating one-dimensional shock wave of a class proposed by Damski in [Phys.~Rev.~A 69, 043610 (2004)]. There, for a broad class of initial conditions, the one-dimensional hydrodynamic equations can be mapped to the inviscid Burgers' equation, which is equivalent to a nonlinear transport equation. More specifically, under the Damski map, the $t=0$ singularity of the original problem becomes, verbatim, the initial condition for the wave catastrophe solution found by Chandrasekhar in 1943 [Ballistic Research Laboratory Report No. 423 (1943)]. At $t=T/8$, our interpretation ceases to exist: at this instance, all three effectively one-dimensional shock waves emanating from each of the three sides of the initial triangle collide at the origin, and the 2D-1D correspondence between the solution of [arXiv:2011.01415] and the Damski-Chandrasekhar shock wave becomes invalid.

cond-mat.quant-gas↗

arXiv2020

The dynamics of digits: Calculating pi with Galperin's billiards

In Galperin billiards, two balls colliding with a hard wall form an analog calculator for the digits of the number $π$. This classical, one-dimensional three-body system (counting the hard wall) calculates the digits of $π$ in a base determined by the ratio of the masses of the two particles. This base can be any integer, but it can also be an irrational number, or even the base can be $π$ itself. This article reviews previous results for Galperin billiards and then pushes these results farther. We provide a complete explicit solution for the balls' positions and velocities as a function of the collision number and time. We demonstrate that Galperin billiard can be mapped onto a two-particle Calogero-type model. We identify a second dynamical invariant for any mass ratio that provides integrability for the system, and for a sequence of specific mass ratios we identify a third dynamical invariant that establishes superintegrability. Integrability allows us to derive some new exact results for trajectories, and we apply these solutions to analyze the systematic errors that occur in calculating the digits of $π$ with Galperin billiards, including curious cases with irrational number bases.

math.DS↗

arXiv2017

Truncated Calogero-Sutherland models

A one-dimensional quantum many-body system consisting of particles confined in a harmonic potential and subject to finite-range two-body and three-body inverse-square interactions is introduced. The range of the interactions is set by truncation beyond a number of neighbors and can be tuned to interpolate between the Calogero-Sutherland model and a system with nearest and next-nearest neighbors interactions discussed by Jain and Khare. The model also includes the Tonks-Girardeau gas describing impenetrable bosons as well as a novel extension with truncated interactions. While the ground state wavefunction takes a truncated Bijl-Jastrow form, collective modes of the system are found in terms of multivariable symmetric polynomials. We numerically compute the density profile, one-body reduced density matrix, and momentum distribution of the ground state as a function of the range $r$ and the interaction strength.

quant-ph↗

arXiv2016

Exactly solvable quantum few-body systems associated with the symmetries of the three-dimensional and four-dimensional icosahedra

The purpose of this article is to demonstrate that non-crystallographic reflection groups can be used to build new solvable quantum particle systems. We explicitly construct a one-parametric family of solvable four-body systems on a line, related to the symmetry of a regular icosahedron: in two distinct limiting cases the system is constrained to a half-line. We repeat the program for a 600-cell, a four-dimensional generalization of the regular three-dimensional icosahedron.

math-ph↗

arXiv2015

Three-dimensional Gross-Pitaevskii solitary waves in optical lattices: stabilization using the artificial quartic kinetic energy induced by lattice shaking

In this Letter, we show that a three-dimensional Bose-Einstein solitary wave can become stable if the dispersion law is changed from quadratic to quartic. We suggest a way to realize the quartic dispersion, using shaken optical lattices. Estimates show that the resulting solitary waves can occupy as little as $\sim 1/20$-th of the Brillouin zone in each of the three directions and contain as many as $N = 10^{3}$ atoms, thus representing a \textit{fully mobile} macroscopic three-dimensional object.

cond-mat.quant-gas↗

arXiv2015

Monopole excitations of a harmonically trapped one-dimensional Bose gas from the ideal gas to the Tonks-Girardeau regime

Using a time-dependent modified nonlinear Schrödinger equation (m-NLSE) -- where the conventional chemical potential proportional to the density is replaced by the one inferred from Lieb-Liniger's exact solution -- we study frequencies of the collective monopole excitations of a one-dimensional (1D) Bose gas. We find that our method accurately reproduces the results of a recent experimental study [E. Haller et al., Science Vol. 325, 1224 (2009)] in the full spectrum of interaction regimes from the ideal gas, through the mean-field regime, through the mean-field Thomas-Fermi regime, all the way to the Tonks-Giradeau gas. While the former two are accessible by the standard time-dependent NLSE and inaccessible by the time-dependent local density approximation (LDA), the situation reverses in the latter case. However, the m-NLSE treats all these regimes within a single numerical method.

cond-mat.quant-gas↗

arXiv2014

Breakdown of the scale invariance in the vicinity of Tonks-Girardeau gas

In this article, we consider the monopole excitations of the harmonically trapped Bose gas in the vicinity of the Tonks-Girardeau limit. Using Girardeau's Fermi-Bose duality and subsequently an effective fermion-fermion odd-wave interaction, we obtain the dominant correction to the scale-invariance-protected value of the excitation frequency, for microscopically small excitation amplitudes. We produce a series of diffusion Monte Carlo results that confirm our analytic prediction for three particles. And less expectedly, our result stands in excellent agreement with the result of a hydrodynamic simulation of the microscopically large but macroscopically small excitations.

cond-mat.quant-gas↗

arXiv2010

Restricted Thermalization for Two Interacting Atoms in a Multimode Harmonic Waveguide

In this article, we study the thermalizability of a system consisting of two atoms in a circular, transversely harmonic waveguide in the multimode regime. While showing some signatures of the quantum-chaotic behavior, the system fails to reach a thermal equilibrium in a relaxation from an initial state, even when the interaction between the atoms is infinitely strong. We relate this phenomenon to the previously addressed unattainability of a complete quantum chaos in the Seba billiard [P. Seba, Phys. Rev. Lett., 64, 1855 (1990)], and we conjecture the absence of a complete thermalization to be a generic property of integrable quantum systems perturbed by a non-integrable but well localized perturbation.

physics.atom-ph↗

arXiv2005

One-dimensional Bose chemistry: effects of non-integrability

Three-body collisions of ultracold identical Bose atoms under tight cylindrical confinement are analyzed. A Feshbach resonance in two-body collisions is described by a two-channel zero-range interaction. Elimination of the closed channel in the three-body problem reduces the interaction to a one-channel zero-range one with an energy dependent strength. The related problem with an energy independent strength (the Lieb-Liniger-McGuire model) has an exact solution and forbids all chemical processes, such as three-atom association and diatom dissociation, as well as reflection in atom-diatom collisions. The resonant case is analyzed by a numerical solution of the Faddeev-Lovelace equations. The results demonstrate that as the internal symmetry of the Lieb-Liniger-McGuire model is lifted, the reflection and chemical reactions become allowed and may be observed in experiments.

physics.atom-ph↗

arXiv2004

Theory of spinor Fermi and Bose gases in tight atom waveguides

Divergence-free pseudopotentials for spatially even and odd-wave interactions in spinor Fermi gases in tight atom waveguides are derived. The Fermi-Bose mapping method is used to relate the effectively one-dimensional fermionic many-body problem to that of a spinor Bose gas. Depending on the relative magnitudes of the even and odd-wave interactions, the N-atom ground state may have total spin S=0, S=N/2, and possibly also intermediate values, the case S=N/2 applying near a p-wave Feshbach resonance, where the N-fermion ground state is space-antisymmetric and spin-symmetric. In this case the fermionic ground state maps to the spinless bosonic Lieb-Liniger gas. An external magnetic field with a longitudinal gradient causes a Stern-Gerlach spatial separation of the corresponding trapped Fermi gas with respect to various values of $S_z$.

cond-mat.soft↗

arXiv2004

Effective interactions, Fermi-Bose duality, and ground states of ultracold atomic vapors in tight de Broglie waveguides

Derivation of effective zero-range one-dimensional (1D) interactions between atoms in tight waveguides is reviewed, as is the Fermi-Bose mapping method for determination of exact and strongly-correlated states of ultracold bosonic and fermionic atomic vapors in such waveguides, including spin degrees of freedom. Odd-wave 1D interactions derived from 3D p-wave scattering are included as well as the usual even-wave interactions derived from 3D s-wave scattering, with emphasis on the role of 3D Feshbach resonances for selectively enhancing s-wave or p-wave interactions. A duality between 1D fermions and bosons with zero-range interactions suggested by Cheon and Shigehara is shown to hold for the effective 1D dynamics of a spinor Fermi gas with both even and odd-wave interactions and that of a spinor Bose gas with even and odd-wave interactions, with even(odd)-wave Bose coupling constants inversely related to odd(even)-wave Fermi coupling constants. Some recent applications of Fermi-Bose mapping to determination of many-body ground states of Bose gases and of both magnetically trapped, spin-aligned and optically trapped, spin-free Fermi gases are described, and a new generalized Fermi-Bose mapping is used to determine the phase diagram of ground-state total spin of the spinor Fermi gas as a function of the even and odd-wave coupling constants.

cond-mat.soft↗

arXiv2004

Scattering in tight atom waveguides

Using the Theory of Scattering in Restricted Geometries developed by A. Lupu-Sax as a starting point, we present a comprehensive multi-channel theory of atom-atom scattering in tight atom waveguides.

cond-mat.other↗

arXiv2003

Fermi-Bose mapping and N-particle ground state of spin-polarized fermions in tight atom waveguides

A K-matrix for waveguide confined spin-polarized fermionic atoms recently computed by Granger and Blume is identified, in the low-energy domain, with a contact condition for one-dimensional (1D) spinless fermions. Difficulties in consistently formulating the contact conditions in terms of interaction potentials are discussed and a rigorous alternative variational reformulation is constructed. A duality between 1D fermions and bosons with zero-range interactions suggested by Cheon and Shigehara is shown to hold for the effective 1D dynamics of a spin-polarized Fermi gas with 3D p-wave interactions and that of a Bose gas with 3D s-wave interactions in a tight waveguide. This generalizes the mapping from impenetrable bosons (TG gas) to free fermions and is used to derive the equation of state of an ultracold spin-polarized fermionic vapor in a tight waveguide. Near a 1D confinement-induced resonance one has a "fermionic TG gas" which maps to an ideal Bose gas.

cond-mat.soft↗

arXiv2003

Atom-Atom Scattering Under Cylindrical Harmonic Confinement: Numerical and Analytical Studies of the Confinement Induced Resonance

In a recent article [M. Olshanii, Phys. Rev. Lett. {\bf 81}, 938 (1998)], an analytic solution of atom-atom scattering with a delta-function pseudopotential interaction in the presence of transverse harmonic confinement yielded an effective coupling constant that diverged at a `confinement induced resonance.' In the present work, we report numerical results that corroborate this resonance for more realistic model potentials. In addition, we extend the previous theoretical discussion to include two-atom bound states in the presence of transverse confinement, for which we also report numerical results here

cond-mat↗