arXiv subjects

Oleksandr V. Marchukov

Publications and source records attributed to Oleksandr V. Marchukov.

12 recordsLinked to original sources

arXiv2026

Scissors modes in generalized Gross-Pitaevskii equations

We investigate scissors modes in nonlinear systems with arbitrary power-law dependence of the nonlinear term. Through analytical derivation, we establish a general expression demonstrating that, in the Thomas-Fermi regime, the frequency of the scissors mode is independent of the specific form of the nonlinearity. We conclude that the scissors mode is a shear mode that does not probe the compressibility of the system, which depends on nonlinearity. To validate our findings, we perform numerical simulations of experimentally relevant Lee-Huang-Yang (LHY) systems. Our results illustrate the transition of the scissors mode frequency from the non-interacting to the strongly interacting (Thomas-Fermi) regime. Finally, we demonstrate that the scissors mode frequency remains clearly identifiable even under strong quenches, which should facilitate the experimental observation of our findings.

cond-mat.quant-gas↗

arXiv2025

Achieving quantum advantage in a search for a violations of the Goldbach conjecture, with driven atoms in tailored potentials

The famous Goldbach conjecture states that any even natural number $N$ greater than $2$ can be written as the sum of two prime numbers $p^{\text{(I)}}$ and $p^{\text{(II)}}$. In this article we propose a quantum analogue device that solves the following problem: given a small prime $p^{\text{(I)}}$, identify a member $N$ of a $\mathcal{N}$-strong set even numbers for which $N-p^{\text{(I)}}$ is also a prime. A table of suitable large primes $p^{\text{(II)}}$ is assumed to be known a priori. The device realizes the Grover quantum search protocol and as such ensures a $\sqrt{\mathcal{N}}$ quantum advantage. Our numerical example involves a set of 51 even numbers just above the highest even classical-numerically explored so far [T. O. e Silva, S. Herzog, and S. Pardi, Mathematics of Computation {\bf 83}, 2033 (2013)]. For a given small prime number $p^{\text{(I)}}=223$, it took our quantum algorithm 5 steps to identify the number $N=4\times 10^{18}+14$ as featuring a Goldbach partition involving $223$ and another prime, namely $p^{\text{(II)}}=4\times 10^{18}-239$. Currently, our algorithm limits the number of evens to be tested simultaneously to $\mathcal{N} \sim \ln(N)$: larger samples will typically contain more than one even that can be partitioned with the help of a given $p^{\text{(I)}}$, thus leading to a departure from the Grover paradigm.

quant-ph↗

arXiv2025

Fiber transmission of cluster states via multi-level time-bin encoding

The next generation of telecommunication networks will rely on the transmission of complex quantum states to enable secure and transformative information processing, utilizing entanglement and superposition. Cluster states - multipartite entangled states that retain entanglement under local measurements - are a vital resource for quantum networking applications such as blind photonic quantum computing, quantum state teleportation and all-photonic quantum repeaters. However, the transmission of cluster states over optical fiber has remained elusive with previous approaches. Here, we demonstrate the first transmission of a four-qubit cluster state over 25 km of single-mode fiber by using a two-photon multi-level time-bin encoding. We directly generate the state by exploiting coherent control of a parametric generation process, rendering a resource-intensive controlled-phase gate obsolete. To enable efficient and reconfigurable projective measurements on the multi-level time-bin encoded state, we introduce chirped-pulse modulation and implement the first time-bin beam splitter, allowing us to certify genuine multipartite entanglement and to demonstrate one-way computing operations. Our approach enables the transmission of complex quantum states over long-distance fibers, permitting the implementation of multipartite protocols and laying the foundation for large-scale quantum resource networks.

quant-ph↗

arXiv2025

Resonance Cascades and Number Theory

In this article, we are interested in situations where the existence of a contiguous cascade of quantum resonant transitions is predicated on the validity of a particular statement in number theory. The setting is a tailored one-atom one-dimensional potential with a prescribed spectrum, under a weak periodic perturbation. The former is, by now, an experimental reality [D. Cassettari, G. Mussardo and A. Trombettoni, PNAS Nexus {\bf 2}, pgac279 (2022)]. As a case study, we look at the following trivial statement: "Any power of $3$ is an integer." Consequently, we "test" this statement in a numerical experiment where we demonstrate an unimpeded upward mobility along an equidistant, $\ln(3)$-spaced subsequence of the energy levels of a potential with a log-natural spectrum, under a frequency $\ln(3)$ time-periodic perturbation. We further show that when we "remove" $9$ from the set of integers -- by excluding the corresponding energy level from the spectrum -- the cascade halts abruptly.

cond-mat.quant-gas↗

arXiv2021

Benchmarking the multiconfigurational Hartree method by the exact wavefunction of two harmonically trapped bosons with contact interaction

We consider two bosons in a one-dimensional harmonic trap, interacting by a contact potential, and compare the exact solution of this problem to a self-consistent numerical solution by using the multiconfigurational time-dependent Hartree (MCTDH) method. We thereby benchmark the predictions of the MCTDH method with a few-body problem that has an analytical solution for the most commonly experimentally realized interaction potential in ultracold quantum gases. It is found that exact ground state energy and first order correlations are accurately reproduced by MCTDH up to the intermediate dimensionless coupling strengths corresponding to typical background scattering lengths of magnetically trapped ultracold dilute Bose gases. For larger couplings, established for example by (a combination of) Feshbach resonances and optical trapping, the MCTDH approach overestimates the depth of the trap-induced correlation dip of first order correlations in position space, as well as overestimates the fragmentation, defined as the average relative occupation of orbitals other than the energetically lowest one. We anticipate that qualitatively similar features in the correlation function may arise for larger particle numbers, paving the way for a quantitative assessment of the accuracy of MCTDH by experiments with ultracold atoms.

cond-mat.quant-gas↗

arXiv2021

Morphology of three-body quantum states from machine learning

The relative motion of three impenetrable particles on a ring, in our case two identical fermions and one impurity, is isomorphic to a triangular quantum billiard. Depending on the ratio $κ$ of the impurity and fermion masses, the billiards can be integrable or non-integrable (also referred to in the main text as chaotic). To set the stage, we first investigate the energy level distributions of the billiards as a function of $1/κ\in [0,1]$ and find no evidence of integrable cases beyond the limiting values $1/κ=1$ and $1/κ=0$. Then, we use machine learning tools to analyze properties of probability distributions of individual quantum states. We find that convolutional neural networks can correctly classify integrable and non-integrable states.The decisive features of the wave functions are the normalization and a large number of zero elements, corresponding to the existence of a nodal line. The network achieves typical accuracies of 97%, suggesting that machine learning tools can be used to analyze and classify the morphology of probability densities obtained in theory or experiment.

quant-ph↗

arXiv2021

Shape of a sound wave in a weakly-perturbed Bose gas

We employ the Gross-Pitaevskii equation to study acoustic emission generated in a uniform Bose gas by a static impurity. The impurity excites a sound-wave packet, which propagates through the gas. We calculate the shape of this wave packet in the limit of long wave lengths, and argue that it is possible to extract properties of the impurity by observing this shape. We illustrate here this possibility for a Bose gas with a trapped impurity atom -- an example of a relevant experimental setup. Presented results are general for all one-dimensional systems described by the nonlinear Schrödinger equation and can also be used in nonatomic systems, e.g., to analyze light propagation in nonlinear optical media. Finally, we calculate the shape of the sound-wave packet for a three-dimensional Bose gas assuming a spherically symmetric perturbation.

cond-mat.quant-gas↗

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↗

arXiv2019

Self-consistent determination of the many-body state of ultracold bosonic atoms in a one-dimensional harmonic trap

We study zero-temperature quantum fluctuations in harmonically trapped one-dimensional interacting Bose gases, using the self-consistent multiconfigurational time-dependent Hartree method. We define $phase$ $fluctuations$ from the full single-particle density matrix by the spatial decay exponent of off-diagonal long-range order. In a regime of mesoscopic particle numbers and moderate contact couplings, we derive the spatial dependence of the amplitude of phase fluctuations, determined from the {\em self-consistently} derived shape of the field operator orbitals and Fock space orbital occupation amplitudes. It is shown that the phase fluctuations display a peak, which in turn corresponds to a dip of the first-order correlations in position space, akin to what has previously been obtained in the Tonks-Girardeau limit of very large interactions and low densities.

cond-mat.quant-gas↗

arXiv2014

Spin-Orbit Coupling in Deformed Harmonic Traps

We consider a two-dimensional system of harmonically trapped particles with pseudo-spin-$\frac{1}{2}$ degree of freedom. This degree of freedom is coupled to the particle's momentum via the so-called Rashba spin-orbit interaction. We present our numerical results for a single-particle and few-particle systems, assuming the repulsive interparticle interaction to be of zero range.

cond-mat.quant-gas↗