arXiv subjects

Axel Pelster

Publications and source records attributed to Axel Pelster.

At least 19 recordsLinked to original sources

arXiv2026

Regularization of Vortex Core Size in Photon BECs due to Harmonic Trap: An Analytical Approach

Quantized vortices are a hallmark of superfluidity. However, in a photon Bose--Einstein condensate, the photon-photon interaction is so weak that in a homogeneous system the healing length exceeds the experimentally achievable size of the condensate itself. Here we show that a harmonic confinement regularizes the vortex size to experimentally achievable scales. Moreover, such an external confinement closely resembles the standard experimental setup of a pumped dye-filled microcavity. We model the condensate via a complex Gross--Pitaevskii equation and obtain an approximate dynamical single-vortex solution by applying the recently proposed projection optimization method. The latter generalizes the variational approach of closed systems to open-dissipative systems without assuming a specific form for the condensate phase. The radial photon flow, which is characteristic for driven-dissipative systems, yields a definition of the vortex core size based on the competition of gain and loss. However, this condition reproduces the heuristic closed system definition now based on physical grounds. A subsequent linear stability analysis shows that interaction, as well as pumping and loss can drive the system to an unstable regime. In this way one can fundamentally distinguish between closed and open-dissipative systems.

cond-mat.quant-gas↗

arXiv2026

Weakly interacting Bose gases in the canonical ensemble

Based on the canonical description of a non-interacting Bose gas, we work out how both thermodynamic and statistical properties change perturbatively with respect to weak two-particle interactions. Up to first order, we obtain a recursion formula for the canonical partition function, which consists of the same Feynman diagrams as the grand-canonical description but with different Feynman rules. Resumming this recursion formula for the canonical partition function allows one to characterize the statistics of the ground-state occupancy by its respective cumulants. We demonstrate the applicability of this approach by analyzing a dilute Bose gas with contact interaction in a box trap. To this end, we used Dirichlet boundary conditions in view of their relevance for current experiments with atomic gases, where the box trap is implemented, for instance, with digital mirror devices.

cond-mat.quant-gas↗

arXiv2026

The quantum harmonic oscillator in a dissipative bath of anyon pairs

We generalize the formalism of open quantum systems to introduce anyon baths. In particular, we work out a dissipative anyon bath composed of independent pairs of one-dimensional Grundberg-Hansson harmonically bound anyons, which are characterized by one statistical parameter. Using a mapping of these anyons to a bosonic bath with rescaled oscillator frequencies, we show that the original bilinear system-bath coupling assumes a particular non-polynomial form. To determine the relaxation properties, we use the imaginary-time path integral formalism together with a generalization of Wick's theorem in the form of a smearing formula. The latter allows to approximately calculate the anyon bath spectral density, which acquires a nontrivial temperature dependence. The corresponding relaxation dynamics of the dissipative harmonic oscillator in an anyon bath is found. Well defined limits are revealed for both low and high temperatures. Anyonic features turn out to be most pronounced in the regime of intermediate temperatures.

cond-mat.stat-mech↗

arXiv2026

Equal-spin and opposite-spin density-density correlations in the BCS-BEC crossover: Gauge Symmetry, Pauli Exclusion Principle, Wick's Theorem and Experiments

We develop a general theory of spin-dependent density-density correlations, that is valid for any temperature, interactions, dimensions and mass or population status of Fermi gases with two internal states. We use gauge invariance and the Pauli principle to establish constraints on the spin-dependent density-density correlations that are consistent with the fluctuation-dissipation and Wick's theorem. As an example, we study the spin-dependent density-density correlations from the BCS to the Bose regime in two dimensions at zero temperature, inspired by experiments in 6Li. We show that two-particle irreducible contributions involving collective excitations, many-particle scattering and vertex corrections, are essential to describe experiments. In particular they turn out to be responsible for the emergence of an experimentally observed minimum in the opposite-spin density-density correlations.

cond-mat.quant-gas↗

arXiv2025

Dynamical signatures of superfluidity and shear rigidity in different phases of a dipolar Bose-Einstein condensate

We show that a sudden change in the polarization direction of the magnetic dipole moments of the atoms in a dipolar Bose-Einstein condensate (BEC) can serve as a useful dynamical probe to sense its superfluid and solid-like properties. We find that for small angular deviation of the polarization direction, actuated for instance by modifying an external magnetic field, the superfluid state undergoes an undamped scissors mode oscillation, a characteristic signature of superfluidity. In contrast, both the droplet and supersolid states exhibit a scissors-mode oscillation, which is effectively damped due to multiple closely spaced frequency components. Notably, we find that this damping rate provides a qualitative measure for the rigidity of different phases of a dipolar BEC. Furthermore, there exists a maximum angular deviation of the polarization direction, beyond which the droplet and the supersolid states undergo a permanent deformation i.e., we find an analog of the usual elastic to plastic phase transition of solids. We characterize this transition numerically using the fidelity of the condensate wavefunction with the ground state as well as the droplet width and periodicity of the supersolid density of the condensate which are experimentally accessible. Thus, the dynamical protocol introduced here can be an important experimental benchmark to identify and characterize the superfluid and solid properties of different phases of dipolar BECs.

cond-mat.quant-gas↗

arXiv2025

From Lasers to Photon Bose--Einstein Condensates: A Unified Description via an Open-Dissipative Bose--Einstein Distribution

Photon condensation was first experimentally realized in 2010 within a dye-filled microcavity at room temperature. Since then, interest in the field has increased significantly, as a photon Bose-Einstein condensate (BEC) represents a prototypical driven-dissipative system. Here, we investigate how its inherent open nature influences the condensation process both quantitatively and qualitatively. To this end, we consider a mean-field model, which can be derived microscopically from a Lindblad master equation. The underlying rate equations depend on various external parameters such as emission and absorption rates of the dye molecules as well as the cavity photon loss rate. In steady state, we obtain an open-dissipative Bose-Einstein distribution for the mode occupations. The chemical potential of this distribution depends on the occupations of the dye molecules in both their ground and excited state and must therefore be determined self-consistently. We find that the resulting photon distribution is strongly influenced by the driven-dissipative parameters. Based on this result, we identify the main differences between a photonic BEC, an atomic BEC, and a laser.

cond-mat.quant-gas↗

arXiv2025

Weighted Hartree-Fock-Bogoliubov method for interacting fermions: An application to ultracold Fermi superfluids

For several decades it has been known that divergences arise in the ground-state energy and chemical potential of unitary superfluids, where the scattering length diverges, due to particle-hole scattering. Leading textbooks and research articles recognize that there are serious issues but ignore them due to the lack of an approach that can regularize these divergences. We find a solution to this difficulty by proposing a general method, called the weighted Hartree-Fock-Bogoliubov theory, to handle multiple decomposition channels originating from the same interaction. We distribute the interaction in weighted channels determined by minimization of the action, and we apply this idea to unpolarized Fermi superfluids. Using our method, we solve a long-standing difficulty in the partitioning of the interaction into Hartree, Fock, and Bogoliubov channels for Fermi superfluids, and we obtain a phase diagram at the saddle-point level, which contains multichannel nonperturbative corrections. In particular, we find a previously overlooked superfluid phase for weak interactions, which is dominated by particle-hole processes, in addition to the usual superfluid phase only containing particle-particle physics.

cond-mat.quant-gas↗

arXiv2025

Understanding Floquet Resonances in Ultracold Gas Scattering

Scattering by a short-range potential with time-periodic interaction strength is investigated with a Floquet-scattering theory. Sharp resonances occur, at which the s-wave scattering length can be tuned to large positive and negative values. We show that the shape of these resonances is described by a simple formula, and find that both resonance position and prefactor can be altered by the driving strength. Our approach allows to identify the physical origin of the scattering resonances as Floquet bound states with positive energies, which are dynamically created by the drive. This insight is valuable for a detailed analysis and uncovers a general resource for enhanced or reduced scattering in Floquet systems.

cond-mat.quant-gas↗

arXiv2025

Out-of-equilibrium dynamical properties of Bose-Einstein condensates in a ramped up weak disorder

We theoretically study how the superfluid and condensate deformation of a weakly interacting ultracold Bose gas evolve during the ramp-up of an external weak disorder potential. Both resulting deformations turn out to consist of two distinct contributions, namely a reversible equilibrium one, already predicted by Huang and Meng in 1992, and a nonequilibrium dynamical one, whose magnitude depends on the details of the ramping protocol. For the specific case of the exponential ramp-up protocol, we are able to derive analytical time-dependent expressions for the above quantities. After a sufficiently long time, a steady state emerges that is generically out of equilibrium. We take the first step in investigating its properties by studying its relaxation dynamics. In addition, we analyze the two-time correlation function and elucidate its relation to the equilibrium and the dynamical part of the condensate deformation.

cond-mat.quant-gas↗

arXiv2024

Cavity-induced quantum droplets

Quantum droplets are formed in quantum many-body systems when the competition of quantum corrections with the mean-field interaction yields a stable self-bound quantum liquid. We predict the emergence of a quantum droplet when a Bose-Einstein condensate is placed in an optical resonator with transverse pumping. The strong coupling between the atoms and the cavity mode induces long-range interactions in the atoms and a roton mode for negative cavity detuning emerges. Using a Bogoliubov theory, we show that the roton mode competes with the repulsive atomic $s$-wave scattering. Due to the favorable scaling of the quantum fluctuations with respect to the volume, a self-bound stable quantum liquid emerges.

cond-mat.quant-gas↗

arXiv2024

Anyonic phase transitions in the 1D extended Hubbard model with fractional statistics

We study one-dimensional (1D) lattice anyons with extended Hubbard interactions at unit filling using bosonization and numerical simulations. The behavior can be continuously tuned from Bosonic to Fermionic behavior by adjusting the topological exchange angle $\theta$, which leads to a competition of different instabilities. We present the bosonization theory in presence of dynamic gauge fields, which predicts a phase diagrams of four different gapped phases with distinct dominant correlations. Advanced numerical simulations determine and analyze the exact phase transitions between Mott insulator, charge density wave, dimerized state, and Haldane insulator, all of which meet at a multi-critical line in the parameter space of anyonic angle $\theta$, onsite interaction $U$, and nearest neighbor repulsion $V$. Superfluid and pair-superfluid phases are stable in a region of small $V$.

cond-mat.str-el↗

arXiv2024

Engineering quantum droplet formation by cavity-induced long-range interactions

We investigate a dilute Bose gas with both a short-range contact and an effective long-range interaction between the atoms. The latter is induced by the strong coupling to a cavity light mode and is spatially characterized by a periodic signature and a tunable envelope rooted in the pumping of the cavity. We formulate a Bogoliubov theory based on a homogeneous mean-field description and quantum fluctuations around it. The competition between the repulsive contact interaction and the long-range interaction allows the formation of self-bound quantum droplets. This generic approach is applied to two cavity setups, one without and one with a momentum-conserving effective long-range interaction between the atoms in the form of a driven dispersive cavity mode and a multimode cavity, respectively. For both cases we show analytically how the size and the central density of the cavity-induced quantum droplets depend on the contact interaction strength and on the shape of the spatial envelope of the long-range interaction.

cond-mat.quant-gas↗

arXiv2024

Nanomechanically-induced nonequilibrium quantum phase transition to a self-organized density wave of a Bose-Einstein condensate

We report on a nonequilibrium quantum phase transition (NQPT) in a hybrid quantum many-body system consisting of a vibrational mode of a damped nanomembrane interacting optomechanically with a cavity, whose output light couples to two internal states of an ultracold Bose gas held in an external quasi-one-dimensional box potential. For small effective membrane-atom couplings, the system is in a homogeneous Bose-Einstein condensate (BEC) steady state, with no membrane displacement. Depending on the transition frequency between the two internal atomic states, either one or both internal states are occupied. By increasing the atom-membrane couplings, the system transitions to a symmetry-broken self-organized BEC phase, which is characterized by a considerably displaced membrane steady-state and density-wave-like BEC profiles. This NQPT can be both discontinuous and continuous for a certain interval of transition frequencies and is purely discontinuous outside of it.

cond-mat.quant-gas↗

arXiv2023

Projection Optimization Method for Open-Dissipative Quantum Fluids and its Application to a Single Vortex in a Photon Bose-Einstein Condensate

Open dissipative systems of quantum fluids have been well studied numerically. In view of a complementary analytical description we extend here the variational optimization method for Bose-Einstein condensates of closed systems to open-dissipative condensates. The resulting projection optimization method is applied to a complex Gross-Pitaevski equation, which models phenomenologically a photon Bose-Einstein condensate. Together with known methods from hydrodynamics we obtain an approximate vortex solution, which depends on the respective open system parameters and has the same properties as obtained numerically in the literature.

cond-mat.quant-gas↗

arXiv2023

Unravelling Interaction and Temperature Contributions in Unpolarized Trapped Fermionic Atoms in the BCS Regime

In the BCS limit density profiles for unpolarized trapped fermionic clouds of atoms are largely featureless. Therefore, it is a delicate task to analyze them in order to quantify their respective interaction and temperature contributions. Temperature measurements have so far been mostly considered in an indirect way, where one sweeps isentropically from the BCS to the BEC limit. Instead we suggest here a direct thermometry, which relies on measuring the column density and comparing the obtained data with a Hartree-Bogoliubov mean-field theory combined with a local density approximation. In case of an attractive interaction between two-components of $^{6}$Li atoms trapped in a tri-axial harmonic confinement we show that minimizing the error within such an experiment-theory collaboration turns out to be a reasonable criterion for analyzing in detail measured densities and, thus, for ultimately determining the sample temperatures. The findings are discussed in view of various possible sources of errors.

cond-mat.quant-gas↗

arXiv2023

Bose-Einstein condensation of photons in a vertical-cavity surface-emitting laser

Many bosons can occupy a single quantum state without a limit. This state is described by quantum-mechanical Bose-Einstein statistics, which allows the formation of a Bose-Einstein condensate at low temperatures and high particle densities. Photons, historically the first considered bosonic gas, were late to show this phenomenon, which was observed in rhodamine-filled microlaser cavities and doped fiber cavities. These more recent findings have raised the natural question as to whether condensation is common in laser systems, with potential technological applications. Here, we show the Bose-Einstein condensation of photons in a broad-area vertical-cavity surface-emitting laser with positive cavity mode-gain peak energy detuning. We observed a Bose-Einstein condensate in the fundamental transversal optical mode at the critical phase-space density. The experimental results follow the equation of state for a two-dimensional gas of bosons in thermal equilibrium, although the extracted spectral temperatures were lower than those of the device. This is interpreted as originating from the driven-dissipative nature of the device and the stimulated cooling effect. In contrast, non-equilibrium lasing action is observed in the higher-order modes in a negatively detuned device. Our work opens the way for the potential exploration of superfluid physics of interacting photons mediated by semiconductor optical non-linearities. It also shows great promise for enabling single-mode high-power emission from a large aperture device.

physics.optics↗

arXiv2023

Coherence Properties of the Repulsive Anyon-Hubbard Dimer

One-dimensional anyonic models of the Hubbard type show intriguing ground-state properties, effectively transmuting between Bose-Einstein and Fermi-Dirac statistics. The simplest model that one can investigate is an anyonic version of the bosonic Josephson junction, the repulsive anyon-Hubbard dimer. In the following we find an exact duality relation to the Bethe-solvable Bose-Hubbard dimer, which is well known from quantum optics and information theory and has interesting connections to spin squeezing and entangled coherent states. Conversely, we show that the anyonic Hubbard dimer has nontrivial coherence properties that emerge from the anyonic statistics. In particular, we find that coherences can be suppressed and amplified and show that these features are remarkably robust against additional repulsive on-site interactions highlighting the distinct nature of anyons.

cond-mat.quant-gas↗

arXiv2022

Bose-Einstein condensates and the thin-shell limit in anisotropic bubble traps

Within the many different models that appeared with the use of cold atoms to design BECs the bubble trap shaped potential has been of great interest. For the anisotropic bubble trap physics in the thin-shell limit the relationship between the physical parameters and the resulting manifold geometry is yet to be fully understood. In this paper, we work towards this goal showing how the parameters of the system must be manipulated in order to allow for a non-collapsing thin-shell limit. In such a limit, a dimensional compactification takes place thus leading to an effective 2D Hamiltonian which relates to up-to-date bubble trap experiments. At last, our Hamiltonian is pertubatively solved for some particular cases as applications of our theory.

cond-mat.quant-gas↗