Maxim Olshanii’s research while affiliated with University of Massachusetts Boston and other places

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 [Cassettari et al., PNAS Nexus 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.

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).

The recently proposed exact quantum solution for two \delta δ -function-interacting particles with a mass-ratio 3\!:\!1 3 : 1 in a hard-wall box [Y. Liu, F. Qi, Y. Zhang and S. Chen, iScience 22, 181 (2019)] violates the conventional necessary condition for a Bethe Ansatz integrability, the condition being that the system must be reducible to a superposition of semi-transparent mirrors that is invariant under all the reflections it generates. In this article, we found a way to relax this condition: some of the semi-transparent mirrors of a known self-invariant mirror superposition can be replaced by the perfectly reflecting ones, thus breaking the self-invariance. The proposed name for the method is asymmetric Bethe Ansatz (asymmetric BA). As a worked example, we study in detail the bound states of the nominally non-integrable system comprised of a bosonic dimer in a \delta δ -well. Finally, we show that the exact solution of the Liu-Qi-Zhang-Chen problem is a particular instance of the the asymmetric BA.

The goal of this paper is to review the properties of a Rule 60 cellular automaton on a ring with a Mersenne number circumference and to use this knowledge to explicitly construct all the ground state configurations of the classical Newman-Moore model (a particular two-dimensional spin lattice model with a specific three-spin interaction) 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.

We study the thermal behavior of correlations in a one-dimensional Bose gas with tunable interaction strength, crossing from weakly repulsive to the Tonks-Girardeau regime. A reference temperature in this system is that of the hole anomaly, observed as a peak in the specific heat and a maximum in the chemical potential. We find that at large momenta k and temperature above the anomaly threshold, the tail C/k^4 of the momentum distribution (proportional to the Tan contact C) is screened by the 1/|k|^3 term due to a dramatic thermal increase of the internal energy emerging from the thermal occupation of spectral excitation states. The same fading is consistently revealed in the behavior at short distances x of the one-body density matrix (OBDM) where the |x|^3 dependence disappears for temperatures above the anomaly. We obtain a general analytic tail for the momentum distribution and a minimum k fixing its validity range, both calculated with exact Bethe-Ansatz method and valid in all interaction and thermal regimes, crossing from the quantum to the classical gas limit. Our predictions are confirmed by comparison with ab initio path-integral Monte Carlo calculations for the momentum distribution and the OBDM exploring a wide range of interaction strength and temperature. Our results unveil a connection between excitations and correlations. We expect them to be of interest to any cold atomic, nuclear, solid-state, electronic, and spin system exhibiting an anomaly or a thermal second-order phase transition.

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.

This work is motivated by an article by Wang, Casati, and Prosen [Phys. Rev. E vol. 89, 042918 (2014)] devoted to a study of ergodicity in two-dimensional irrational right-triangular billiards. Numerical results presented there suggest that these billiards are generally not ergodic. However, they become ergodic when the billiard angle is equal to \pi/2 π / 2 times a Liouvillian irrational, morally a class of irrational numbers which are well approximated by rationals. In particular, Wang et al. study a special integer counter that reflects the irrational contribution to the velocity orientation; they conjecture that this counter is localized in the generic case, but grows in the Liouvillian case. We propose a generalization of the Wang-Casati-Prosen counter: this generalization allows to include rational billiards into consideration. We show that in the case of a 45°\!\!:\!45°\!\!:\!90° 45 ° : 45 ° : 90 ° billiard, the counter grows indefinitely, consistent with the Liouvillian scenario suggested by Wang et al.

We provide the first ab-initio Path Integral Monte Carlo calculation of the momentum distribution in a one-dimensional repulsive Bose gas at finite temperatures. We explore all interaction and thermal regimes. An important reference temperature is that of the hole anomaly, observed as a peak in the specific heat and a maximum in the chemical potential. We find that at large momentum k and temperature above the anomaly threshold, the universal tail $\mathcal{C}/k^4$ of the distribution (proportional to the Tan's contact $\mathcal{C}$) is screened by the $1/|k|^3$-term due to a dramatic thermal increase of the internal energy. The same fading is consistently revealed in the short-distance behavior of the one-body density matrix (OBDM) where the $|x|^3$-dependence disappears for temperatures above the anomaly. At very high temperatures, the OBDM and the momentum distribution approach the Gaussian of classical gases. We obtain a new and general analytic tail for the momentum distribution and a minimum k fixing its range of validity, both calculated with Bethe-Ansatz and valid for any interaction strength and temperature.

Progress in understanding quantum systems has been driven by the exploration of the geometry, topology, and dimensionality of ultracold atomic systems. The NASA Cold Atom Laboratory (CAL) aboard the International Space Station has enabled the study of ultracold atomic bubbles, a terrestrially-inaccessible topology. Proof-of-principle bubble experiments have been performed on CAL with an radiofrequency-dressing technique; an alternate technique (dual-species interaction-driven bubbles) has also been proposed. Both techniques can drive discovery in the next decade of fundamental physics research in microgravity.

Progress in understanding quantum systems has been driven by the exploration of the geometry, topology, and dimensionality of ultracold atomic systems. The NASA Cold Atom Laboratory (CAL) aboard the International Space Station has enabled the study of ultracold atomic bubbles, a terrestrially-inaccessible topology. Proof-of-principle bubble experiments have been performed on CAL with an rf-dressing technique; an alternate technique (dual-species interaction-driven bubbles) has also been proposed. Both techniques can drive discovery in the next decade of fundamental physics research in microgravity.