arXiv subjects

Vanja Dunjko

Publications and source records attributed to Vanja Dunjko.

At least 19 recordsLinked to original sources

arXiv2025

A canonical approach to quantum fluctuations

We present a canonical formalism for computing quantum fluctuations of certain discrete degrees of freedom in systems governed by integrable partial differential equations with known Hamiltonian structure, provided these models are classical-field approximations of underlying many-body quantum systems. We then apply the formalism to both the 2-soliton and 3-soliton breather solutions of the nonlinear Schr\"odinger equation, assuming the breathers are created from an initial elementary soliton by quenching the coupling constant. In particular, we compute the immediate post-quench quantum fluctuations in the positions, velocities, norms, and phases of the constituent solitons. For each case, we consider both the white-noise and correlated-noise models for the fluctuation vacuum state. Unlike previous treatments of the problem, our method allows for analytic solutions. Additionally, in the correlated-noise case, we consider the particle-number-conserving (also called $U(1)$-symmetry-conserving) Bogoliubov modes, i.e., modes with the proper correction to preserve the total particle number. We find that in most (but not all) cases, these corrections do not change the final result.

cond-mat.quant-gas↗

arXiv2025

Finding ground states of a square Newman-Moore lattice with sides equal to a Mersenne number using the Rule 60 cellular automaton

We offer detailed proofs of some properties of the Rule 60 cellular automaton on a ring with a Mersenne number circumference. We then use these properties to define a propagator, and demonstrate its use to construct all the ground state configurations of the classical Newman-Moore model on a square lattice of the same size. In this particular case, the number of ground states is equal to half of the available spin configurations in any given row of the lattice.

nlin.CG↗

arXiv2022

Massive particle interferometry with lattice solitons

We discuss an interferometric scheme employing interference of bright solitons formed as specific bound states of attracting bosons on a lattice. We revisit the proposal of Castin and Weiss [Phys. Rev. Lett. vol. 102, 010403 (2009)] for using the scattering of a quantum matter-wave soliton on a barrier in order to create a coherent superposition state of the soliton being entirely to the left of the barrier and being entirely to the right of the barrier. In that proposal, it was assumed that the scattering is perfectly elastic, i.e.\ that the center-of-mass kinetic energy of the soliton is lower than the chemical potential of the soliton. Here we relax this assumption: By employing a combination of Bethe ansatz and DMRG based analysis of the dynamics of the appropriate many-body system, we find that the interferometric fringes persist even when the center-of-mass kinetic energy of the soliton is above the energy needed for its complete dissociation into constituent atoms.

cond-mat.quant-gas↗

arXiv2022

Quantum Chirikov criterion: Two particles in a box as a toy model for a quantum gas

We consider a toy model for emergence of chaos in a quantum many-body short-range-interacting system: two one-dimensional hard-core particles in a box, with a small mass defect as a perturbation over an integrable system, the latter represented by two equal mass particles. To that system, we apply a quantum generalization of Chirikov's criterion for the onset of chaos, i.e. the criterion of overlapping resonances. There, classical nonlinear resonances translate almost verbatim to the quantum language. Quantum mechanics intervenes at a later stage: the resonances occupying less than one Hamiltonian eigenstate are excluded from the chaos criterion. Resonances appear as contiguous patches of low purity unperturbed eigenstates, separated by the groups of undestroyed states -- the quantum analogues of the classical KAM tori.

quant-ph↗

arXiv2022

Massive particle interferometry with lattice solitons: robustness against ionization

We revisit the proposal of Castin and Weiss [Phys. Rev. Lett. vol. 102, 010403 (2009)] for using the scattering of a quantum matter-wave soliton on a barrier in order to create a coherent superposition state of the soliton being entirely to the left of the barrier and being entirely to the right of the barrier. In that proposal, is was assumed that the scattering is perfectly elastic, i.e. that the center-of-mass kinetic energy of the soliton is lower than the chemical potential of the soliton. Here we relax this assumption. Also, we introduce an interferometric scheme, which uses interference of soltions, that can be used to detect the degree of coherence between the reflected and transmitted part of the soliton. Using exact diagonalization, we numerically simulate a complete interferometric cycle for a soliton consisting of six atoms. We find that the interferometric fringes persist even when the center-of-mass kinetic energy of the soliton is above the energy needed for complete dissociation of the soliton into constituent atoms.

cond-mat.quant-gas↗

arXiv2022

Path Integral Estimates of the Quantum Fluctuations of the Relative Soliton-Soliton Velocity in a Gross-Pitevskii Breather

In this paper, the quantum fluctuations of the relative velocity of constituent solitons in a Gross-Pitaevskii breather are studied. The breather is confined in a weak harmonic trap. These fluctuations are monitored,indirectly, using a two-body correlation function measured at a quarter of the harmonic period after the breather creation. The results of an ab initio quantum Monte Carlo calculations, based on the Feynman-Kac path integration method, are compared with the analytical predictions using the recently suggested approach within the Bogoliubov approximation, and a good agreement is obtained.

quant-ph↗

arXiv2020

Quantum fluctuations of the center-of-mass and relative parameters of NLS breathers

We study quantum fluctuations of macroscopic parameters of an NLS breathers, i.e., the second-order soliton solution of the nonlinear Schrödinger equation. Uncertainty relations for the parameters are derived and compared to similar relations for fundamental solitons. We compare two models for the state of the quantum field of fluctuations surrounding the classical field of the Bose-Einstein condensate: a conventionally used, computationally convenient "white noise", and a correlated noise which assumes that the breather has been created from a fundamental soliton, by means of the application of the factor-of-four quench of the nonlinearity strength. Theoretical methods used in the work are well suited for a large number of particles, $N$. We thus confirm the possibility of experimental observation of macroscopic quantum fluctuations, which is suggested by an extrapolation to large $N$ of recently reported low-$N$ Bethe-ansatz results [Phys. Rev. Lett. 119 220401 (2017)].

cond-mat.quant-gas↗

arXiv2020

Enhancing sensitivity to rotations with quantum solitonic currents

Quantum mechanics is characterized by quantum coherence and entanglement. After having discovered how these fundamental concepts govern physical reality, scientists have been devoting intense efforts to harness them to shape future science and technology. This is a highly nontrivial task because most often quantum coherence and entanglement are difficult to access. Here, we demonstrate the enhancement of the sensitivity of a quantum many-body system with specific coherence and entanglement properties. Our physical system is made of strongly correlated attracting neutral bosons flowing in a ring-shaped potential of mesoscopic size. Because of attractive interactions, quantum analogs of bright solitons are formed. As a genuine quantum-many-body feature, we demonstrate that angular momentum fractionalization occurs. As a consequence, the matter-wave current in our system can react to very small changes of rotation or other artificial gauge fields. We work out a protocol to entangle such quantum solitonic currents, allowing them to operate rotation sensors and gyroscopes to Heisenberg-limited sensitivity.

cond-mat.quant-gas↗

arXiv2020

Creation and Characterization of Matter-Wave Breathers

We report the creation of quasi-1D excited matter-wave solitons, "breathers", by quenching the strength of the interactions in a Bose-Einstein condensate with attractive interactions. We characterize the resulting breathing dynamics and quantify the effects of the aspect ratio of the confining potential, the strength of the quench, and the proximity of the 1D-3D crossover for the 2-soliton breather. We furthermore demonstrate the complex dynamics of a 3-soliton breather created by a stronger interaction quench. Our experimental results, which compare well with numerical simulations, provide a pathway for utilizing matter-wave breathers to explore quantum effects in large many-body systems.

cond-mat.quant-gas↗

arXiv2020

Resilience of constituent solitons in multisoliton scattering off barriers

We introduce "superheated integrability," which produces characteristic staircase transmission plots for barrier collisions of breathers of the nonlinear Schrödinger equation. The effect makes tangible the inverse scattering transform, which treats the velocities and norms of the constituent solitons as the real and imaginary parts of the eigenvalues of the Lax operator. If all the norms are much greater than the velocities, an integrability-breaking potential may nonperturbatively change the velocities while having no measurable effect on the norms. This could be used to improve atomic interferometers.

cond-mat.quant-gas↗

arXiv2020

Four-dimensional reflection groups and electrostatics

We present a new class of electrostatics problems that are exactly solvable by adding finitely many image charges. Given a charge at some location inside a cavity bounded by up to four conducting grounded segments of spheres: if the spheres have a symmetry derived via a stereographic projection from a 4D finite reflection group, then this is a solvable generalization of the familiar problem of a charge inside a spherical cavity. There are 19 three-parametric families of finite groups formed by inversions relative to at most four spheres, each member of each family giving a solvable problem. We solve a sample problem which derives from the reflection group $\mathbf{D}_{4}$ and requires 191 image charges.

physics.class-ph↗

arXiv2019

Splitting of nonlinear-Schrödinger breathers by linear and nonlinear localized potentials

We consider evolution of one-dimensional nonlinear-Schrödinger (NLS) two-soliton complexes (breathers) with narrow repulsive or attractive potentials (barrier or well, respectively). By means of systematic simulations, we demonstrate that the breather may either split into constituent fundamental solitons (fragments) moving in opposite directions, or bounce as a whole from the barrier. A critical initial position of the breather, which separates these scenarios, is predicted by an analytical approximation. The narrow potential well tends to trap the fragment with the larger amplitude, while the other one escapes. The interaction of the breather with a nonlinear potential barrier is also considered. The ratio of amplitudes of the emerging free solitons may be different from the 3:1 value suggested by the exact NLS solution, especially in the case of the nonlinear potential barrier. Post-splitting velocities of escaping solitons may be predicted by an approximation based on the energy balance.

cond-mat.quant-gas↗

arXiv2018

Metastability versus collapse following a quench in attractive Bose-Einstein condensates

We consider a Bose-Einstein condensate (BEC) with attractive two-body interactions in a cigar-shaped trap, initially prepared in its ground state for a given negative scattering length, which is quenched to a larger absolute value of the scattering length. Using the mean-field approximation, we compute numerically, for an experimentally relevant range of aspect ratios and initial strengths of the coupling, two critical values of quench: one corresponds to the weakest attraction strength the quench to which causes the system to collapse before completing even a single return from the narrow configuration ("perihelion") in its breathing cycle. The other is a similar critical point for the occurrence of collapse before completing two returns. In the latter case, we also compute the limiting value, as we keep increasing the strength of the post-quench attraction towards its critical value, of the time interval between the first two perihelia. We also use a Gaussian variational model to estimate the critical quenched attraction strength below which the system is stable against the collapse for long times. These time intervals and critical attraction strengths---apart from being fundamental properties of nonlinear dynamics of self-attractive BECs---may provide clues to the design of upcoming experiments that are trying to create robust BEC breathers.

cond-mat.quant-gas↗

arXiv2017

A connection between non-local one-body and local three-body correlations of the Lieb-Liniger model

We derive a connection between the fourth coefficient of the short-distance Taylor expansion of the one-body correlation function, and the local three-body correlation function of the Lieb-Liniger model of $δ$-interacting spinless bosons in one dimension. This connection, valid at arbitrary interaction strength, involves the fourth moment of the density of quasi-momenta. Generalizing recent conjectures, we propose approximate analytical expressions for the fourth coefficient covering the whole range of repulsive interactions, validated by comparison with accurate numerics. In particular, we find that the fourth coefficient changes sign at interaction strength $γ_c\simeq 3.816$, while the first three coefficients of the Taylor expansion of the one-body correlation function retain the same sign throughout the whole range of interaction strengths.

cond-mat.quant-gas↗

arXiv2017

Creating Entanglement Using Integrals of Motion

A quantum Galilean cannon is a 1D sequence of $N$ hard-core particles with special mass ratios, and a hard wall; conservation laws due to the reflection group $A_{N}$ prevent both classical stochastization and quantum diffraction. It is realizable through specie-alternating mutually repulsive bosonic soliton trains. We show that an initial disentangled state can evolve into one where the heavy and light particles are entangled, and propose a sensor, containing $N_{\text{total}}$ atoms, with a $\sqrt{N_{\text{total}}}$ times higher sensitivity than in a one-atom sensor with $N_{\text{total}}$ repetitions.

cond-mat.quant-gas↗

arXiv2015

Atom transistor from the point of view of quantum nonequilibrium dynamics

We analyze the atom field-effect transistor scheme [J. A. Stickney, D. Z. Anderson and A. A. Zozulya, Phys. Rev. A 75, 013608 (2007)] using the standard tools of nonequlilibrium dynamics. In particular, we study the deviations from the Eigenstate Thermalization Hypothesis, quantum fluctuations, and the density of states, both ab initio and using their mean-field analogues. Having fully established the quantum vs. mean-field correspondence for this system, we attempt, using a mean-field model, to interpret the off-on threshold in our transistor as the onset of ergodicity---a point where the system becomes able to visit the thermal values of the former integrals of motion in principle, albeit not being fully thermalized yet.

cond-mat.quant-gas↗

arXiv2014

Typical, finite baths as a means of exact simulation of open quantum systems

There is presently considerable interest in accurately simulating the evolution of open systems for which Markovian master equations fail. Examples are systems that are time-dependent and/or strongly damped. A number of elegant methods have now been devised to do this, but all use a bath consisting of a continuum of harmonic oscillators. While this bath is clearly appropriate for, e.g., systems coupled to the EM field, it is not so clear that it is a good model for generic many-body systems. Here we explore a different approach to exactly simulating open-systems: using a finite bath chosen to have certain key properties of thermalizing many-body systems. To explore the numerical resources required by this method to approximate an open system coupled to an infinite bath, we simulate a weakly damped system and compare to the evolution given by the relevant Markovian master equation. We obtain the Markovian evolution with reasonable accuracy by using an additional averaging procedure, and elucidate how the typicality of the bath generates the correct thermal steady-state via the process of "eigenstate thermalization".

quant-ph↗

arXiv2012

An Exactly Solvable Model for the Integrability-Chaos Transition in Rough Quantum Billiards

A central question of dynamics, largely open in the quantum case, is to what extent it erases a system's memory of its initial properties. Here we present a simple statistically solvable quantum model describing this memory loss across an integrability-chaos transition under a perturbation obeying no selection rules. From the perspective of quantum localization-delocalization on the lattice of quantum numbers, we are dealing with a situation where every lattice site is coupled to every other site with the same strength, on average. The model also rigorously justifies a similar set of relationships recently proposed in the context of two short-range-interacting ultracold atoms in a harmonic waveguide. Application of our model to an ensemble of uncorrelated impurities on a rectangular lattice gives good agreement with ab initio numerics.

cond-mat.quant-gas↗