Bose Gas Research Articles

Upper Bound for the Grand Canonical Free Energy of the Bose Gas in the Gross–Pitaevskii Limit for General Interaction Potentials

AbstractWe consider a homogeneous Bose gas in the Gross–Pitaevskii limit at temperatures that are comparable to the critical temperature for Bose–Einstein condensation. Recently, an upper bound for the grand canonical free energy was proved in Boccato et al. (SIAM J Math Anal 56(2):2611–2660, 2024) capturing two novel contributions. First, the free energy of the interacting condensate is given in terms of an effective theory describing the probability distribution of the number of condensed particles. Second, the free energy of the thermally excited particles equals that of a temperature-dependent Bogoliubov Hamiltonian. We extend this result to a more general class of interaction potentials, including interactions with a hard core. Our proof follows a different approach than the one in Boccato et al. (SIAM J Math Anal 56(2):2611–2660, 2024): We model microscopic correlations between the particles by a Jastrow factor and exploit a cancellation in the computation of the energy that emerges due to the different length scales in the system.

Dynamics of cosmological phase crossover during Bose–Einstein condensation of dark matter in Tsallis cosmology

During the cosmic evolution process, as the temperature of a cosmological boson gas falls below a certain threshold, a Bose–Einstein condensation process can occur at various points throughout the cosmic history of the Universe. In this model, dark matter, conceptualized as a non-relativistic, Newtonian gravitational condensate is governed by the Gross–Pitaevskii–Poisson system. In our present study, we investigate the Bose–Einstein condensation process of bosonic DM by treating it as an approximate first-order phase transition within a modified cosmological framework, known as Tsallis cosmology. We examine the evolution of relevant physical quantities characterizing the evolution dynamics of the Universe, including energy density, temperature, redshift, scale factor, Hubble parameter, and dimensionless deceleration parameter before, during, and following the Bose–Einstein condensation phase transition takes place. Additionally, we especially investigate the specific era of the evolution of the Universe characterized by a mixture of normal and condensate phases of dark matter. We analyze the behavior of temporal evolution of an important time-dependent parameter, called the condensate dark matter fraction throughout the condensation process and find the time duration of condensation of dark matter in the Tsallis cosmological model. We see that the presence of Bose–Einstein condensate dark matter in the framework of Tsallis-modified cosmology significantly alters the cosmological evolution of the Universe as compared to the standard model of cosmology. We also find for a typical value of Tsallis non-extensive parameter β=0.35\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta =0.35$$\\end{document}, the model could explain an accelerated Universe without invoking any additional energy component and solve the age problem of our Universe.

Spin-orbit-coupled mean-field Bose gas at finite temperature

Spin-orbit-coupled mean-field Bose gas at finite temperature

Mott-glass phase induced by long-range correlated disorder in a one-dimensional Bose gas

Mott-glass phase induced by long-range correlated disorder in a one-dimensional Bose gas

Cornwall-Jackiw-Tomboulis effective field theory and the nonuniversal equation of state of an ultracold Bose gas

Cornwall-Jackiw-Tomboulis effective field theory and the nonuniversal equation of state of an ultracold Bose gas

Upper Bound for the Ground State Energy of a Dilute Bose Gas of Hard Spheres

We consider a gas of bosons interacting through a hard-sphere potential with radius a\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathfrak {a}$$\\end{document} in the thermodynamic limit. We derive an upper bound for the ground state energy per particle at low density. Our bound captures the leading term 4πρa\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4\\pi \\rho \\mathfrak {a}$$\\end{document} and shows that corrections are smaller than Cρa(ρa3)1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C \\rho \\mathfrak {a} (\\rho {{\\mathfrak {a}}}^3)^{1/2}$$\\end{document}, for a sufficiently large constant C>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C > 0$$\\end{document}. In combination with a known lower bound, our result implies that the first sub-leading term to the ground state energy of a dilute gas of hard spheres is, in fact, of the order ρa(ρa3)1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho \\mathfrak {a}(\\rho {{\\mathfrak {a}}}^3)^{1/2}$$\\end{document}, in agreement with the Lee–Huang–Yang prediction.

Optical manipulation of spin states in ultracold magnetic atoms via an inner-shell hz transition

Lanthanides, like erbium and dysprosium, have emerged as powerful platforms for quantum-gas research due to their diverse properties, including a significant large spin manifold in their absolute ground state. However, effectively exploiting the spin richness necessitates precise manipulation of spin populations, a challenge yet to be fully addressed in this class of atomic species. In this work, we present an all-optical method for deterministically controlling the spin composition of a dipolar bosonic erbium gas, based on a clocklike transition in the telecom window at 1299nm. The atoms can be prepared in just a few tens of microseconds in any spin-state composition using a sequence of Rabi-pulse pairs, selectively coupling Zeeman sublevels of the ground state with those of the long-lived clocklike state. Finally, we demonstrate that this transition can also be used to create spin-selective light shifts, thus fully suppressing spin-exchange collisions. These experimental results unlock exciting possibilities for implementing advanced spin models in isolated, clean, and fully controllable lattice systems. Published by the American Physical Society 2024

Loss-induced collective mode in one-dimensional Bose gases

Loss-induced collective mode in one-dimensional Bose gases

Excitonic Bose Polarons in Electron-Hole Bilayers.

Bose polarons are mobile particles of one kind dressed by excitations of the surrounding degenerate Bose gas of particles of another kind. These many-body objects have been realized in ultracold atomic gases and become a subject of intensive studies. In this work, we show that excitons in electron-hole bilayers offer new opportunities for exploring polarons in strongly interacting, highly tunable bosonic systems. We found that Bose polarons are formed by spatially direct excitons immersed in degenerate Bose gases of spatially indirect excitons (IXs). We detected both attractive and repulsive Bose polarons by measuring photoluminescence excitation spectra. We controlled the density of IX Bose gas by optical excitation and observed an enhancement of the energy splitting between attractive and repulsive Bose polarons with increasing IX density, in agreement with our theoretical calculations.

Infinite cycles of interacting bosons

Abstract In the first-quantized description of bosonic systems permutation cycles formed by the particles play a fundamental role. In the ideal Bose gas Bose-Enstein condensation (BEC) is signaled by the appearance of infinite cycles. When the particles interact, the two phenomena may not be simultaneous, the existence of infinite cycles is necessary but not sufficient for BEC. We demonstrate that their appearance is always accompanied by a singularity
in the thermodynamic quantities
which in three and four dimensions can be as strong as a one-sided divergence of the isothermal compressibility. Arguments are presented that long-range interactions can give rise to unexpected results, such as the absence of infinite cycles in three dimensions for long-range repulsion or their presence in one and two dimensions if the pair potential has a long attractive tail.

Density-Density Correlation Spectra of Ultracold Bosonic Gas Released from a Deep 1D Optical Lattice.

Density-density correlation analysis is a convenient diagnostic tool to reveal the hidden order in the strongly correlated phases of ultracold atoms. We report on a study of the density-density correlations of ultracold bosonic atoms which were initially prepared in a Mott insulator (MI) state in one-dimensional optical lattices. For the atomic gases released from the deep optical lattice, we extracted the normalized density-density correlation function from the atomic density distributions of freely expanded atomic clouds. Periodic bunching peaks were observed in the density-density correlation spectra, as in the case of higher-dimensional lattices. Treating the bosonic gas within each lattice well as a subcondensate without quantum tunneling, we simulated the post-expansion density distribution along the direction of the 1D lattice, and the calculated density-density correlation spectra agreed with our experimental observations.

Thouless pumping and trapping of two-component gap solitons

We study Thouless pumping and arresting of gap solitons in a two-component Bose gas loaded into an optical superlattice. We show that, depending on the atomic interactions and chemical potentials, the two solitons can be simultaneously pumped or trapped, but we also identify regimes where one soliton is pumped and the other arrested. These behaviors can be understood by considering an effective model of the system based on a variational approach, which reveals that the soliton width is a suitable qualifier for the observed behaviors: solitons with a larger width get transported, while solitons with a smaller width get trapped. Since these widths can be controlled by tuning interactions, it should be possible to observe all behaviors experimentally. Published by the American Physical Society 2024

Effect of trap imperfections on the density of a quasi-two-dimensional uniform dipolar quantum Bose gas

Effect of trap imperfections on the density of a quasi-two-dimensional uniform dipolar quantum Bose gas

Probing early phase coarsening in a rapidly quenched Bose gas using off-resonant matter-wave interferometry

We experimentally investigate the evolution of spatial phase correlations in a rapidly quenched inhomogeneous Bose gas of rubidium using off-resonant matter-wave interferometry. We measure the phase coherence length ℓ of the sample and directly probe its increase during the early stage of condensate growth before vortices are formed. Once the vortices are formed stably in the quenched condensate, the measured value of ℓ is shown to be linearly proportional to the mean distance between the vortex. These results confirm the presence of phase coarsening prior to vortex formation, which is crucial for a quantitative understanding of the resultant defect density in samples undergoing critical phase transitions. Published by the American Physical Society 2024

One-dimensional magnetic excitonic insulators

Abstract Dimensionality significantly affects exciton production and condensation. Despite the report of excitonic instability in one-dimensional materials, it remains unclear whether these spontaneously produced excitons can form Bose–Einstein condensates. In this work, we first prove statistically that one-dimensional condensation exists when the spontaneously generated excitons are thought of as an ideal neutral Bose gas, which is quite different from the inability of free bosons to condense. We then derive a general expression for the critical temperature in different dimensions and find that the critical temperature increases with decreasing dimension. We finally predict by first-principles GW-Bethe–Salpeter equation calculations that experimentally accessible single-chain staircase Scandocene and Chromocene wires are an antiferromagnetic spin-triplet excitonic insulator and a ferromagnetic half-excitonic insulator, respectively.

Unbounded entropy production and violent fragmentation for repulsive-to-attractive interaction quench in long-range interacting systems

Abstract We study the non-equilibrium dynamics of a one-dimensional Bose gas with long-range interactions that decay as ( 1 r α ) ( 0.5 < α < 4.0 ). We investigate exotic dynamics when the interactions are suddenly switched from strongly repulsive to strongly attractive, a procedure known to generate super-Tonks-Girardeau gases in systems with contact interactions. We find that relaxation is achieved through a complex intermediate dynamics demonstrated by violent fragmentation and chaotic delocalization. We establish that the relaxed state exhibits classical gaseous characteristics and an asymptotic state associated with unbounded entropy production. The phase diagram shows an exponential boundary between the coherent (quantum) gas and the chaotic (classical) gas. We show the universality of the dynamics by also presenting analogous results for spinless fermions. Weaker quench protocols give a certain degree of control over the relaxation process and induce a slower initial entropy growth. Our study showcases the complex relaxation behavior of tunable long-range interacting systems that could be engineered in state-of-the-art experiments, e.g. in trapped ions or Rydberg atoms.

Thermal Melting of a Vortex Lattice in a Quasi-Two-Dimensional Bose Gas.

We report the observation of the melting of a vortex lattice in a fast rotating quasi-two dimensional Bose gas, under the influence of thermal fluctuations. We image the vortex lattice after a time-of-flight expansion, for increasing rotation frequency at constant atom number and temperature. We detect the vortex positions and study the order of the lattice using the pair correlation function and the orientational correlation function. We evidence the melting transition by a change in the decay of orientational correlations, associated with a proliferation of dislocations. Our findings are consistent with the hexatic to liquid transition in the Kosterlitz, Thouless, Halperin, Nelson, and Young scenario for two-dimensional melting.

Effective spin models and magnetic phases of an insulating bosonic ladder with unconventional synthetic flux

We investigate the Mott insulating phases of a two-component bosonic lattice gas in the presence of gauge field. Such a system is described by a two-leg ladder model with an unconventional flux. The synthetic flux is generated by the spin-dependent tunneling and the site-dependent spin-flip. In the Mott regime, these two effects lead to Dzyaloshinskii-Moriya (DM) interaction and an external field that is rotating in the xy-plane. We obtain a very general XYZ model with the DM interaction, the spiral field, and the transverse field. Various interesting magnetic Hamiltonians can be covered by adjusting lattice parameters. The DM interaction or the spiral field can lead to spiral order when they appear alone. The interplay of DM coupling and spiral field leads to the emergence of a new multi-frequency spiral order between the paramagnetic phase and the spiral ferromagnetic phase. Ground state phases are investigated by focusing on order parameters, spin-spin correlation functions, and structure factors. Calculations are performed by using time evolution block decimation (TEBD) based on matrix product state (MPS).

Probing the Local Rapidity Distribution of a One-Dimensional Bose Gas.

One-dimensional Bose gases with contact repulsive interactions are characterized by the presence of infinite-lifetime quasiparticles whose momenta are called the "rapidities." Here, we develop a probe of the local rapidity distribution, based on the fact that rapidities are the asymptotic momenta of the particles after a long one-dimensional expansion. This is done by performing an expansion of a selected slice of the gas. We first apply this idea to a cloud in the quasicondensate regime at equilibrium in a trap. We obtain an experimental picture of the position-dependent rapidity distribution which is in fair agreement with the theory prediction. The asymptotic regime is barely reached, but we show that finite expansion time can be taken into account using the generalized hydrodynamics theory. We then apply this local probe to an out-of-equilibrium situation where the local rapidity distribution is expected to be doubly peaked-a hallmark of a nonthermal state-even though the global rapidity distribution would possess no such distinctive feature. We observe the doubly peaked local rapidity distribution.

Atom number fluctuations in Bose gases—statistical analysis of parameter estimation

Abstract The investigation of atom number fluctuations in quantum gases at finite temperatures showcases the ongoing challenges in understanding complex quantum systems. Recently, the microcanonical nature of atom number fluctuations in weakly interacting Bose-Einstein condensates was observed. This motivates an investigation of the thermal component of partially condensed Bose gases, due to the conservation of the total atom number.

Here, we present a combined analysis of both components, including a comprehensive analysis of the uncertainties in the preparation and parameter extraction of partially condensed quantum gases. This enables a complementary observation of the thermal atom number fluctuations and yields and improved value of the peak BEC atom number fluctuations $\Delta N_\mathrm{p,0}^2 =(3.7\pm7)\times10^5$ close to the critical temperature. This corresponds to a reduction by \SI{41}{\percent} with respect to previous analysis and corroborates the microcanonical nature of the fluctuations.

The analysis of noise contributions due to the preparation and evaluation of partially condensed Bose gases is based on Monte Carlo simulations of optical density profiles. Importantly, this allows for an estimation of the technical noise contributions to the atom number and temperature, which is generally applicable in the field of ultracold atoms.