arXiv subjects

Jeongwon Lee

Publications and source records attributed to Jeongwon Lee.

14 recordsLinked to original sources

arXiv2025

Restricted inversion polynomials

For a finite subset $I$ of positive integers, the descent polynomial $\mathcal{D}(I;n)$ counts the number of permutations in $S_n$ that have descent set $I$. We generalize descent polynomials by considering permutations with a specific subset $S$ of common inversions called $\mathbf{h}$-inversions, where $\mathbf{h} = (\mathbf{h}(1), \mathbf{h}(2), \ldots )$ is a weakly increasing sequence of positive integers such that $\mathbf{h}(i)> i$. We prove that this more general count, denoted by $\mathcal{I}_\mathbf{h}(S;n)$, is also a polynomial. We give three explicit expansions for $\mathcal{I}_\mathbf{h}(S;n)$, prove the coefficients for two of these expansions are log-concave, and define a graded generalization.

math.CO↗

arXiv2023

Enhancing Disruption Prediction through Bayesian Neural Network in KSTAR

Disruption in tokamak plasmas, stemming from various instabilities, poses a critical challenge, resulting in detrimental effects on the associated devices. Consequently, the proactive prediction of disruptions to maintain stability emerges as a paramount concern for future fusion reactors. While data-driven methodologies have exhibited notable success in disruption prediction, conventional neural networks within a frequentist approach cannot adequately quantify the uncertainty associated with their predictions, leading to overconfidence. To address this limit, we utilize Bayesian deep probabilistic learning to encompass uncertainty and mitigate false alarms, thereby enhancing the precision of disruption prediction. Leveraging 0D plasma parameters from EFIT and diagnostic data, a Temporal Convolutional Network adept at handling multi-time scale data was utilized. The proposed framework demonstrates proficiency in predicting disruptions, substantiating its effectiveness through successful applications to KSTAR experimental data.

physics.plasm-ph↗

arXiv2020

Heuristic machinery for thermodynamic studies of SU(N) fermions with neural networks

The power of machine learning (ML) provides the possibility of analyzing experimental measurements with an unprecedented sensitivity. However, it still remains challenging to probe the subtle effects directly related to physical observables and to understand physics behind from ordinary experimental data using ML. Here, we introduce a heuristic machinery by using machine learning analysis. We use our machinery to guide the thermodynamic studies in the density profile of ultracold fermions interacting within SU($N$) spin symmetry prepared in a quantum simulator. Although such spin symmetry should manifest itself in a many-body wavefuction, it is elusive how the momentum distribution of fermions, the most ordinary measurement, reveals the effect of spin symmetry. Using a fully trained convolutional neural network (NN) with a remarkably high accuracy of $\sim$94$\%$ for detection of the spin multiplicity, we investigate how the accuracy depends on various less-pronounced effects with filtered experimental images. Guided by our machinery, we directly measure a thermodynamic compressibility from density fluctuations within the single image. Our machine learning framework shows a potential to validate theoretical descriptions of SU($N$) Fermi liquids, and to identify less-pronounced effects even for highly complex quantum matter with minimal prior understanding.

cond-mat.quant-gas↗

arXiv2020

Minimal universality criterion sets on the representations of quadratic forms

For a set $S$ of (positive definite and integral) quadratic forms with bounded rank, a quadratic form $f$ is called $S$-universal if it represents all quadratic forms in $S$. A subset $S_0$ of $S$ is called an $S$-universality criterion set if any $S_0$-universal quadratic form is $S$-universal. We say $S_0$ is minimal if there does not exist a proper subset of $S_0$ that is an $S$-universality criterion set. In this article, we study various properties of minimal universality criterion sets. In particular, we show that for `most' binary quadratic forms $f$, minimal $S$-universality criterion sets are unique in the case when $S$ is the set of all subforms of the binary form $f$.

math.NT↗

arXiv2020

Effective statistical fringe removal algorithm for high-sensitivity imaging of ultracold atoms

High-sensitivity imaging of ultracold atoms is often challenging when interference patterns are imprinted on the imaging light. Such image noises result in low signal-to-noise ratio and limit the capability to extract subtle physical quantities. Here we demonstrate an advanced fringe removal algorithm for absorption imaging of ultracold atoms, which efficiently suppresses unwanted fringe patterns using a small number of sample images without taking additional reference images. The protocol is based on an image decomposition and projection method with an extended image basis. We apply this scheme to raw absorption images of degenerate Fermi gases for the measurement of atomic density fluctuations and temperatures. The quantitative analysis shows that image noises can be efficiently removed with only tens of reference images, which manifests the efficiency of our protocol. Our algorithm would be of particular interest for the quantum emulation experiments in which several physical parameters need to be scanned within a limited time duration.

cond-mat.quant-gas↗

arXiv2019

Collective excitations in two-dimensional SU($N$) Fermi gases with tunable spin

We measure collective excitations of a harmonically trapped two-dimensional (2D) SU($N$) Fermi gas of $^{173}$Yb confined to a stack of layers formed by a one-dimensional optical lattice. Quadrupole and breathing modes are excited and monitored in the collisionless regime $\lvert\ln(k_F a_{2D})\rvert\gg 1$ with tunable spin. We observe that the quadrupole mode frequency decreases with increasing number of spin components due to the amplification of the interaction effect by $N$ in agreement with a theoretical prediction based on 2D kinetic equations. The breathing mode frequency, however, is measured to be twice the dipole oscillation frequency regardless of $N$. We also follow the evolution of collective excitations in the dimensional crossover from two to three dimensions and characterize the damping rate of quadrupole and breathing modes for tunable SU($N$) fermions, both of which reveal the enhanced inter-particle collisions for larger spin. Our result paves the way to investigate the collective property of 2D SU($N$) Fermi liquid with enlarged spin.

cond-mat.quant-gas↗

arXiv2019

A sum of three nonunit squares of integers

We say a positive integer is a sum of three nonunit squares if it is a sum of three squares of integers other than one. In this article, we find all integers which are sums of three nonunit squares assuming that the Generalized Riemann Hypothesis(GRH) holds. As applications, we find all integers, under the GRH only when $k=3$, which are sums of $k$ nonzero triangular numbers, sums of $k$ nonzero generalized pentagonal numbers, and sums of $k$ nonzero generalized octagonal numbers, respectively for any integer $k\ge 3$.

math.NT↗

arXiv2018

How to dress radio-frequency photons with tunable momentum

We demonstrate how the combination of oscillating magnetic forces and radio-frequency (RF) pulses endows RF photons with tunable momentum. We observe velocity-selective spinflip transitions and the associated Doppler shift. This realizes the key component of purely magnetic spin-orbit coupling schemes for ultracold atoms, which does not involve optical transitions and therefore avoids the problem of heating due to spontaneous emission.

physics.atom-ph↗

arXiv2017

Observation of the supersolid stripe phase in spin-orbit coupled Bose-Einstein condensates

Supersolidity is an intriguing concept. It combines the property of superfluid flow with the long-range spatial periodicity of solids, two properties which are often mutually exclusive. The original discussion of quantum crystals and supersolidity focuses on solid Helium-4 where it was predicted that vacancies could form dilute weakly interacting Bose-Einstein condensates. In this system, direct observation of supersolidity has been elusive. The concept of supersolidity was then generalized to include other superfluid systems which break the translational symmetry of space. One of such systems is a Bose-Einstein condensate with spin-orbit coupling which has a supersolid stripe phase. Despite several recent studies of this system, the stripe phase has not been observed. Here we report the direct observation of the predicted density modulation of the stripe phase using Bragg reflection. Our work establishes a system with unique symmetry breaking properties. Of future interest is further spatial symmetry breaking through the introduction of vortices, solitons, impurities or disorder.

cond-mat.quant-gas↗

arXiv2016

Spin-Orbit Coupling and Spin Textures in Optical Superlattices

We proposed and demonstrated a new approach for realizing spin orbit coupling with ultracold atoms. We use orbital levels in a double well potential as pseudospin states. Two-photon Raman transitions between left and right wells induce spin-orbit coupling. This scheme does not require near resonant light, features adjustable interactions by shaping the double well potential, and does not depend on special properties of the atoms. A pseudospinor Bose-Einstein condensate spontaneously acquires an antiferromagnetic pseudospin texture which breaks the lattice symmetry similar to a supersolid.

cond-mat.quant-gas↗

arXiv2016

Precise measurements of optical Feshbach resonances of $^{174}$Yb atoms

We present precise measurements of the optical Feshbach resonances (OFRs) of $^{174}$Yb atoms for the intercombination transition. We measure the photoassociation (PA) spectra of a pure $^{174}$Yb Bose-Einstein condensate, and determine the dependence of OFRs to PA laser intensities and frequencies for four least bound vibrational levels near the intercombination transition. We confirm that our measurements are consistent with the temporal decay of a BEC subjected to a PA beam in the vicinity of the fourth vibrational level from the dissociation limit.

physics.atom-ph↗

arXiv2014

Core-Shell Magneto-Optical Trap for Alkaline-Earth-Metal-Like Atoms

We propose and demonstrate a new magneto-optical trap (MOT) for alkaline-earth-metal-like (AEML) atoms where the narrow $^{1}S_{0}\rightarrow$$^{3}P_{1}$ transition and the broad $^{1}S_{0}\rightarrow$$^{1}P_{1}$ transition are spatially arranged into a core-shell configuration. Our scheme resolves the main limitations of previously adopted MOT schemes, leading to a significant increase in both the loading rate and the steady state atom number. We apply this scheme to $^{174}$Yb MOT, where we show about a hundred-fold improvement in the loading rate and ten-fold improvement in the steady state atom number compared to reported cases that we know of to date. This technique could be readily extended to other AEML atoms to increase the statistical sensitivity of many different types of precision experiments.

physics.atom-ph↗

arXiv2013

Observation of the universal jump across the Berezinskii-Kosterlitz-Thouless transition in two-dimensional Bose gases

The physics in two-dimensional (2D) systems is very different from what we observe in three-dimensional (3D) systems. Thermal fluctuations in 2D systems are enhanced, and they prevent the conventional Bose-Einstein condensation (BEC) at non-zero temperatures by destroying the long-range order. However, a phase transition to a superfluid phase is still expected to occur in a 2D system along with an emergence of a quasi-long-range order, explained by the Berezinskii-Kosterlitz-Thouless (BKT) mechanism. Within the BKT mechanism, a universal jump of the superfluid density in a 2D Bosonic system was theoretically predicted by Nelson and Kosterlitz, and was first observed in 2D \textsuperscript{4}He films by Bishop and Reppy. Recent experiments in trapped ultracold 2D Bose gas systems have shown signatures of the BKT transition, and its superfluidity. However, the universal jump in the superfluid density was not observed in these systems. Here we report the first observation of the universal jump in the superfluid density using an optically trapped ultracold 2D Bose gas. The measured superfluid phase space density at the BKT transition agrees well with the predicted value within our measurement uncertainty. Additionally, we measure the phase fluctuations in our density profiles to show that the BKT transition occurs first, followed by the BEC transition.

cond-mat.quant-gas↗

arXiv2012

High resolution isotope shifts and hyperfine structure measurements of tungsten by laser induced fluorescence spectroscopy

Isotope shifts and hyperfine structure of tungsten were studied in the near UV range. We have used laser induced fluorescence spectroscopy on a pulsed supersonic beam to probe the 5D0 -> 5F1 transition at 384.9 nm, 7S3 -> 7P4 transition at 400.9 nm, and 7S3 -> 7P3 transition at 407.4 nm. Three new magnetic hyperfine constants are reported for 7P3,7P4, and 5F1 states. The isotope shifts of the 384.9 nm transition are presented for the first time, and the isotope shifts of 400.9 nm and 407.4 nm transition are measured with an order of magnitude higher precision compared to the previous measurements. As a result, the nuclear parameters lambda and lambda_{rel} are extracted from the isotope shifts with an improved precision.

physics.atom-ph↗