arXiv subjects

Vladimir A. Yurovsky

Publications and source records attributed to Vladimir A. Yurovsky.

16 recordsLinked to original sources

arXiv2025

Eigenstate thermalization to non-monotonic distributions in strongly-interacting chaotic lattice gases

We find non-monotonic equilibrium energy distributions, qualitatively different from the Fermi-Dirac and Bose-Einstein forms, in strongly-interacting many-body chaotic systems. The effect emerges in systems with finite energy spectra, supporting both positive and negative temperatures, in the regime of quantum ergodicity. The results are supported by exact diagonalization calculations for chaotic Fermi-Hubbard and Bose-Hubbard models, when they have Wigner-Dyson statistics of energy spectra and demonstrate eigenstate thermalization. The proposed effects may be observed in experiments with cold atoms in optical lattices.

cond-mat.quant-gas↗

arXiv2023

Quantum chaos in a harmonic waveguide with scatterers

A set of zero-range scatterers along its axis lifts the integrability of a harmonic waveguide. Effective solution of the Schrödinger equation for this model is possible due to the separable nature of the scatterers and millions of eigenstates can be calculated using modest computational resources. Integrability-chaos transition can be explored as the model chaoticity increases with the number of scatterers and their strengths. The regime of complete quantum chaos and eigenstate thermalization can be approached with 32 scatterers. This is confirmed by properties of energy spectra, the inverse participation ratio, and fluctuations of observable expectation values.

quant-ph↗

arXiv2023

Exploring integrability-chaos transition with a sequence of independent perturbations

A gas of interacting particles is a paradigmatic example of chaotic systems. It is shown here that even if all but one particle are fixed in generic positions, the excited states of the moving particle are chaotic. They are characterized by the number of principal components (NPC) -- the number of integrable system eigenstates involved into the non-integrable one, which increases linearly with the number of strong scatterers. This rule is a particular case of the general effect of an additional perturbation on the system chaotic properties. The perturbation independence criteria supposing the system chaoticity increase are derived here as well. The effect can be observed in experiments with photons or cold atoms as the decay of observable fluctuation variance, which is inversely proportional to NPC, and, therefore, to the number of scatterers. This decay indicates that the eigenstate thermalization is approached. The results are confirmed by numerical calculations for a harmonic waveguide with zero-range scatterers along its axis.

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

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↗

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↗

arXiv2017

Dissociation of one-dimensional matter-wave breathers due to quantum many-body effects

We use the ab initio Bethe Ansatz dynamics to predict the dissociation of one-dimensional cold-atom breathers that are created by a quench from a fundamental soliton. We find that the dissociation is a robust quantum many-body effect, while in the mean-field (MF) limit the dissociation is forbidden by the integrability of the underlying nonlinear Schrödinger equation. The analysis demonstrates the possibility to observe quantum many-body effects without leaving the MF range of experimental parameters. We find that the dissociation time is of the order of a few seconds for a typical atomic-soliton setting.

cond-mat.quant-gas↗

arXiv2017

Phase transitions in definite total spin states of two-component Fermi gases

Second-order phase transitions have no latent heat and are characterized by a change in symmetry. In addition to the conventional symmetric and anti-symmetric states under permutations of bosons and fermions, mathematical group-representation theory allows for non-Abelian permutation symmetry. Such symmetry can be hidden in states with defined total spins of spinor gases, which can be formed in optical cavities. The present work shows that the symmetry reveals itself in spin-independent or coordinate-independent properties of these gases, namely as non-Abelian entropy in thermodynamic properties. In weakly interacting Fermi gases, two phases appear associated with fermionic and non-Abelian symmetry under permutations of particle states, respectively. The second-order transitions between the phases are characterized by discontinuities in specific heat. Unlike other phase transitions, the present ones are not caused by interactions and can appear even in ideal gases. Similar effects in Bose gases and strong interactions are discussed.

cond-mat.quant-gas↗

arXiv2016

Molecular spectra in collective Dicke states

We study a model describing competition of interactions between $N$ two-level systems (TLSs) against decoherence. We apply it to analyze dye molecules in an optical microcavity, where molecular vibrations provide a local source for decoherence. Most interesting is the case when decoherence strongly affects each individual TLS, e.g. via broadening of emission lines as well as vibrational satellites, however its influence is strongly suppressed for large $N$ due to the interactions between TLSs. In this interaction dominated regime we find unique signatures in the emission spectrum, including strong $\mathcal{O}(\sqrt{N})$ level shifts, as well as $1/N$ suppression of both the decoherence width and of the vibrational satellites.

cond-mat.quant-gas↗

arXiv2016

Long-lived states with well-defined spins in spin-$1/2$ homogeneous Bose gases

Many-body eigenfunctions of the total spin operator can be constructed from the spin and spatial wavefunctions with non-trivial permutation symmetries. Spin-dependent interactions can lead to relaxation of the spin eigenstates to the thermal equilibrium. A mechanism that stabilizes the many-body entangled states is proposed here. Surprisingly, in spite coupling with the chaotic motion of the spatial degrees of freedom, the spin relaxation can be suppressed by destructive quantum interference due to spherical vector and tensor terms of the spin-dependent interactions. Tuning the scattering lengths by the method of Feshbach resonances, readily available in cold atomic labs, can enhance the relaxation timescales by several orders of magnitude.

cond-mat.quant-gas↗

arXiv2015

Sum rules for spin-$1/2$ quantum gases in states with well-defined spins: II. Spin-dependent two-body interactions

Sums of matrix elements of spin-dependent two-body momentum-independent interactions and sums of their products are calculated analytically in the basis of many-body states with given total spin --- the states built from spin and spatial wavefunctions belonging to multidimensional irreducible representations of the symmetric group, unless the total spin has the maximal allowed value. As in the first part of the series [V. A. Yurovsky, Phys. Rev. A 91, 053601 (2015)], the sum dependence on the many-body states is given by universal factors, which are independent of the Hamiltonians of non-interacting particles. The sum rules are applied to perturbative analysis of energy spectra and to calculation of two-body spin-dependent local correlations.

cond-mat.quant-gas↗

arXiv2015

Sum rules for spin-$1/2$ quantum gases in states with well-defined spins: spin-independent interactions and spin-dependent external fields

Analytical expressions are derived for sums of matrix elements and their squared moduli over many-body states with given total spin --- the states built from spin and spatial wavefunctions belonging to multidimensional irreducible representations of the symmetric group, unless the total spin has the maximal allowed value. For spin-dependent one-body interactions with external fields and spin-independent two-body ones between the particles, the sum dependence on the many-body states is given by universal factors, which are independent of the interaction details and Hamiltonians of non-interacting particles. The sum rules are applied to perturbative analysis of energy spectra.

cond-mat.quant-gas↗

arXiv2014

Permutation symmetry in spinor quantum gases: selection rules, conservation laws, and correlations

Many-body systems of identical arbitrary-spin particles, with separable spin and spatial degrees of freedom, are considered. Their eigenstates can be classified by Young diagrams, corresponding to non-trivial permutation symmetries (beyond the conventional paradigm of symmetric--antisymmetric states). The present work obtains (a) selection rules for additional non-separable (dependent on spins and coordinates) $k$-body interactions: the Young diagrams, associated with the initial and the final states of a transition, can differ by relocation of no more than $k$ boxes between their rows; and (b) correlation rules: eigenstate-averaged local correlations of $k$ particles vanish if $k$ exceeds the number of columns (for bosons) or rows (for fermions) in the associated Young diagram. It also elucidates the physical meaning of the quantities conserved due to permutation symmetry --- in 1929, Dirac identified those with characters of the symmetric group --- relating them to experimentally observable correlations of several particles. The results provide a way to control the formation of entangled states belonging to multidimensional non-Abelian representations of the symmetric group. These states can find applications in quantum computation and metrology.

cond-mat.quant-gas↗

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↗

arXiv2009

Faddeev equations in one-dimensional problems with resonant interactions

A problem of three one-dimensional bosons with resonant multichannel interactions is considered. The problem is reduced to a single-channel Faddeev-Lovelace equation by elimination of the closed and output channels. The equation is regularized using algebraic properties of their singularities.

physics.atom-ph↗

arXiv2006

Formation of molecules and entangled atomic pairs from atomic BEC due to Feshbach resonance

Bose-Einstein condensate (BEC) is considered under conditions of Feshbach resonance in two-atom collisions due to a coupling of atomic pair and resonant molecular states. The association of condensate atoms can form a molecular BEC, and the molecules can dissociate to pairs of entangled atoms in two-mode squeezed states. Both entanglement and squeezing can be applied to quantum measurements and information processing. The processes in the atom-molecule quantum gas are analyzed using two theoretical approaches. The mean-field one takes into account deactivating collisions of resonant molecules with other atoms and molecules, neglecting quantum fluctuations. This method allows analysis of inhomogeneous systems, such as expanding BEC. The non-mean-field approach -- the parametric approximation -- takes into account both deactivation and quantum fluctuations. This method allows determination of optimal conditions for formation of molecular BEC and describes Bose-enhanced dissociation of molecular BEC, as well as entanglement and squeezing of the non-condensate atoms.

cond-mat.soft↗