Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2210.08946 · Physical Review A

Polarized Rabi-coupled and spinor boson droplets

Taha Alper Yogurt, Ahmet Keleş, Mehmet Özgür Oktel

Published Feb 27, 2023• 5 citations
arXivHTMLPDF

Abstract

Self-bound quantum droplets form when the mean-field tendency of the gas to collapse is stabilized by the effectively repulsive beyond-mean-field fluctuations. The beyond-mean-field effects depend on Rabi frequency ${\ensuremath{\omega}}_{R}$ and quadratic Zeeman effect $q$ for the Rabi-coupled Bose mixtures and the spinor gases, respectively. For a quantum droplet, the effects of varying ${\ensuremath{\omega}}_{R}$ and $q$ have recently been examined only for unpolarized Rabi-coupled Bose mixtures and unpolarized spinor gases. In this paper, we theoretically explore the stability of the droplet phase for polarized Rabi-coupled Bose mixtures and polarized spinor gases. We calculate the beyond-mean-field corrections for both gases with polarized order parameters and obtain the phase diagram of the droplets on the parameter space of Rabi frequency ${\ensuremath{\omega}}_{R}$ and detuning $\ensuremath{\delta}$ for Rabi-coupled mixtures and quadratic Zeeman energy $q$ and linear Zeeman energy $p$ for spinor gases. Finally, we highlight the similarities and differences between the two systems and discuss their experimental feasibility.

DOI
10.1103/physreva.107.023322

Related papers

Spinor boson droplets stabilized by spin fluctuations

Taha Alper Yogurt, Ahmet Keleş, Mehmet Özgür Oktel

Self-trapped droplets stabilized by quantum fluctuations have been experimentally realized in dipolar gases and binary boson mixtures. In this paper, we propose spinor Bose gases as another candidate for droplet formation. For spin-1 gas, we find that spin fluctuations give a dilute but self-trapped state for two different order parameters where the mean-field picture predicts collapse. A polar droplet phase can be stabilized by spin fluctuations for both antiferromagnetic and ferromagnetic spin-dependent coupling. An antiferromagnetic droplet phase can be stabilized similarly with a negative quadratic Zeeman shift. Furthermore, the beyond mean-field energy of the system depends on the quadratic Zeeman coupling, which provides a mechanism to tune the droplet formation and its density. We discuss the parameters necessary for the experimental realization of such spinor droplets.

arXiv:2201.09628•Physical Review A•Apr 13, 2022•8 citations

SPIN ÇALKANTILARIYLA KARARLI HALE GELEN SPIN-1 DAMLACIKLARI

YOĞURT, TAHA ALPER

The interacting Bose-Einstein condensates are mechanically stabilized by an external confinement such as magnetic, or optical traps. When the confinement is removed, they exhibit an expansion or collapse behavior depending on the interaction being repulsive, or attractive, respectively. The Gross-Pitaevskii mean-field theories are generally sufficient to provide a qualitative understanding of the condensate equilibrium properties and dynamics, therefore, beyond mean-field fluctuations are considered as minor quantitative corrections. The quantum droplet phases are self-stabilized phases of the condensate, in which the attractive mean-field interaction is stabilized by the repulsive Lee-Huang-Yang fluctuations without any external trap. The droplets are studied theoretically for binary Bose mixture and dipolar condensates, and both are recently realized in the ultracold atomic gas experiments. Here we propose the spin-1 condensate as another candidate to exhibit a quantum droplet phase. We argue that the spin-1 condensates in the polar and anti-ferromagnetic order parameters can exhibit a similar self-stabilizing mechanism. We also realize an analogy between the polarized spin-1 and Rabi-coupled binary mixture condensates. The Rabi frequency $\omega_R$ and quadratic Zeeman energy $q$ can tune the Lee-Huang-Yang energy for the Rabi-coupled mixture and spin-1 gas, respectively. Furthermore, the detuning $\delta$ and linear Zeeman energy $p$ are external parameters to tune the polarization in Rabi-coupled mixture, and spin-1 gas, respectively, which can significantly change the mean-field energy. We create the phase diagram for the mechanical stability of the Rabi-coupled mixture and spin-1 gas on the parameter planes of $\omega_R-\delta$ and $q-p$, respectively. We finally address how the Bose mixture quantum droplets respond to the rotation. We find that the strongly confined quantum droplets exhibit triangular vortex lattices under rapid rotation. The properties of the vortex lattices differ from the repulsive condensates in three points. First, the change in the droplet size is only fractional at the rapid rotation limit, unlike the diverging radius of the repulsive condensate. This property can lead the way to realizing the lowest Landau level states and strongly correlated phases in the rotating ultracold gases. Secondly, the change in the core size throughout the vortex lattice is more tractable due to the finite density at the edge of the condensate. Finally, the vortex lattices are slightly distorted, which agrees with the expected vortex density profile due to the nonuniform superfluid density. In the rapid rotation limit, the droplet approaches the flat-top density profile, in which the vortex lattice is closest to a perfect periodicity.

•Sep 13, 2023•0 citations

Equation of state and self-bound droplet in Rabi-coupled Bose mixtures

Alberto Cappellaro, Tommaso Macrì, Giovanni F. Bertacco +1 more

Abstract Laser induced transitions between internal states of atoms have been playing a fundamental role to manipulate atomic clouds for many decades. In absence of interactions each atom behaves independently and their coherent quantum dynamics is described by the Rabi model. Since the experimental observation of Bose condensation in dilute gases, static and dynamical properties of multicomponent quantum gases have been extensively investigated. Moreover, at very low temperatures quantum fluctuations crucially affect the equation of state of many-body systems. Here we study the effects of quantum fluctuations on a Rabi-coupled two-component Bose gas of interacting alkali atoms. The divergent zero-point energy of gapless and gapped elementary excitations of the uniform system is properly regularized obtaining a meaningful analytical expression for the beyond-mean-field equation of state. In the case of attractive inter-particle interaction we show that the quantum pressure arising from Gaussian fluctuations can prevent the collapse of the mixture with the creation of a self-bound droplet. We characterize the droplet phase and discover an energetic instability above a critical Rabi frequency provoking the evaporation of the droplet. Finally, we suggest an experiment to observe such quantum droplets using Rabi-coupled internal states of K39 atoms.

arXiv:1705.01814•Scientific Reports•Oct 11, 2017•75 citations

Liquid Quantum Bose-Fermi droplets

Tomasz Karpiuk, Debraj Rakshit, Mirosław Brewczyk +1 more

We study stability of a zero temperature mixture of attractively interacting degenerate bosons and spin-polarized fermions in the absence of confinement. We demonstrate that higher order corrections to the standard mean field energy of the system can lead to a formation of liquid droplets -- self-bound incompressible systems in a three-dimensional space. In addition to the quantum Lee-Huang-Yang correction to the boson-boson interaction energy, a higher order term in the Bose-Fermi coupling constant is crucial for stabilization of the system. We study a stability region of droplets for three different mixtures of species with different mass ratios, namely: $^{41}$K$\,$-$^{40}$K, $^{87}$Rb$\,$-$^{40}$K, and $^{133}$Cs$\,$-$^{6}$Li as a function of the ratio of Bose-Fermi to Bose-Bose scattering length. The stability analysis is supported by a numerical simulations of droplet formation dynamics starting with a trapped system which is subsequently released from the trap. Our results indicate that Bose-Fermi droplets can be realized experimentally.

•Dec 31, 2017•0 citations

Bosonic quantum mixtures with competing interactions: quantum liquid droplets and supersolids

Sarah Hirthe, Leticia Tarruell

These lecture notes contain an introduction to quantum simulation of bosonic systems in the continuum, focusing on weakly interacting Bose-Bose mixtures with competing mean-field interactions. When the values of such interactions are fine-tuned to almost completely cancel the mean-field energy, quantum fluctuations become apparent and dominate the behavior of the system, stabilizing an ultradilute quantum liquid phase. An analogous situation appears in single-component dipolar quantum gases. We review the mechanism that gives rise to this exotic quantum liquid, which can form droplets that are self-bound in the absence of any external confinement, and discuss their properties and dynamics in both the mixture and the dipolar cases. In dipolar gases, arrays of dipolar droplets stabilized by quantum fluctuations can establish global phase coherence and form supersolids. In bosonic mixtures, supersolidity can emerge already at the mean-field level through spin-orbit coupling. We discuss the properties of such spin-orbit-coupled supersolids, comparing them to their dipolar counterparts. Specifically, we focus on their periodic density modulation, phase coherence, and peculiar excitation spectrum, which hosts both superfluid and crystal excitations. Finally, we conclude by discussing open research directions in the areas of quantum liquid droplets and spin-orbit-coupled supersolids, in particular at the interface of the two research topics.

cond-mat.quant-gasCross-listedarXiv:2603.17745•Mar 19, 2026•0 citations

Low-dimensional self-bound quantum Rabi-coupled bosonic droplets

Emerson Chiquillo

We analytically calculate the leading quantum corrections of the ground-state energy of two- and one-dimensional weakly interacting Rabi-coupled Bose-Bose mixtures in the frame of the Bogoliubov approximation. We show that to repulsive intraspecies and attractive interspecies interactions, the effect of quantum fluctuations favors the formation of self-bound droplets. These liquidlike states are crucially affected by the Rabi coupling, leading thus to the appearance of a quantum instability. We derive meaningful formulas to describe the droplet phase in the one-dimensional case.

arXiv:1905.07775•Physical Review A•May 22, 2019•31 citations
Self-bound quantum droplets form when the mean-field tendency of the gas to collapse is stabilized by the effectively repulsive beyond-mean-field fluctuations. The beyond-mean-field effects depend on Rabi frequency \ensuremathωR{\ensuremath{\omega}}_{R}\ensuremathωR​ and quadratic Zeeman effect qqq for the Rabi-coupled Bose mixtures and the spinor gases, respectively. For a quantum droplet, the effects of varying \ensuremathωR{\ensuremath{\omega}}_{R}\ensuremathωR​ and qqq have recently been examined only for unpolarized Rabi-coupled Bose mixtures and unpolarized spinor gases. In this paper, we theoretically explore the stability of the droplet phase for polarized Rabi-coupled Bose mixtures and polarized spinor gases. We calculate the beyond-mean-field corrections for both gases with polarized order parameters and obtain the phase diagram of the droplets on the parameter space of Rabi frequency \ensuremathωR{\ensuremath{\omega}}_{R}\ensuremathωR​ and detuning \ensuremathδ\ensuremath{\delta}\ensuremathδ for Rabi-coupled mixtures and quadratic Zeeman energy qqq and linear Zeeman energy ppp for spinor gases. Finally, we highlight the similarities and differences between the two systems and discuss their experimental feasibility.
Self-trapped droplets stabilized by quantum fluctuations have been experimentally realized in dipolar gases and binary boson mixtures. In this paper, we propose spinor Bose gases as another candidate for droplet formation. For spin-1 gas, we find that spin fluctuations give a dilute but self-trapped state for two different order parameters where the mean-field picture predicts collapse. A polar droplet phase can be stabilized by spin fluctuations for both antiferromagnetic and ferromagnetic spin-dependent coupling. An antiferromagnetic droplet phase can be stabilized similarly with a negative quadratic Zeeman shift. Furthermore, the beyond mean-field energy of the system depends on the quadratic Zeeman coupling, which provides a mechanism to tune the droplet formation and its density. We discuss the parameters necessary for the experimental realization of such spinor droplets.
The interacting Bose-Einstein condensates are mechanically stabilized by an external confinement such as magnetic, or optical traps. When the confinement is removed, they exhibit an expansion or collapse behavior depending on the interaction being repulsive, or attractive, respectively. The Gross-Pitaevskii mean-field theories are generally sufficient to provide a qualitative understanding of the condensate equilibrium properties and dynamics, therefore, beyond mean-field fluctuations are considered as minor quantitative corrections. The quantum droplet phases are self-stabilized phases of the condensate, in which the attractive mean-field interaction is stabilized by the repulsive Lee-Huang-Yang fluctuations without any external trap. The droplets are studied theoretically for binary Bose mixture and dipolar condensates, and both are recently realized in the ultracold atomic gas experiments. Here we propose the spin-1 condensate as another candidate to exhibit a quantum droplet phase. We argue that the spin-1 condensates in the polar and anti-ferromagnetic order parameters can exhibit a similar self-stabilizing mechanism. We also realize an analogy between the polarized spin-1 and Rabi-coupled binary mixture condensates. The Rabi frequency ωR\omega_RωR​ and quadratic Zeeman energy qqq can tune the Lee-Huang-Yang energy for the Rabi-coupled mixture and spin-1 gas, respectively. Furthermore, the detuning δ\deltaδ and linear Zeeman energy ppp are external parameters to tune the polarization in Rabi-coupled mixture, and spin-1 gas, respectively, which can significantly change the mean-field energy. We create the phase diagram for the mechanical stability of the Rabi-coupled mixture and spin-1 gas on the parameter planes of ωR−δ\omega_R-\deltaωR​−δ and q−pq-pq−p, respectively. We finally address how the Bose mixture quantum droplets respond to the rotation. We find that the strongly confined quantum droplets exhibit triangular vortex lattices under rapid rotation. The properties of the vortex lattices differ from the repulsive condensates in three points. First, the change in the droplet size is only fractional at the rapid rotation limit, unlike the diverging radius of the repulsive condensate. This property can lead the way to realizing the lowest Landau level states and strongly correlated phases in the rotating ultracold gases. Secondly, the change in the core size throughout the vortex lattice is more tractable due to the finite density at the edge of the condensate. Finally, the vortex lattices are slightly distorted, which agrees with the expected vortex density profile due to the nonuniform superfluid density. In the rapid rotation limit, the droplet approaches the flat-top density profile, in which the vortex lattice is closest to a perfect periodicity.
Abstract Laser induced transitions between internal states of atoms have been playing a fundamental role to manipulate atomic clouds for many decades. In absence of interactions each atom behaves independently and their coherent quantum dynamics is described by the Rabi model. Since the experimental observation of Bose condensation in dilute gases, static and dynamical properties of multicomponent quantum gases have been extensively investigated. Moreover, at very low temperatures quantum fluctuations crucially affect the equation of state of many-body systems. Here we study the effects of quantum fluctuations on a Rabi-coupled two-component Bose gas of interacting alkali atoms. The divergent zero-point energy of gapless and gapped elementary excitations of the uniform system is properly regularized obtaining a meaningful analytical expression for the beyond-mean-field equation of state. In the case of attractive inter-particle interaction we show that the quantum pressure arising from Gaussian fluctuations can prevent the collapse of the mixture with the creation of a self-bound droplet. We characterize the droplet phase and discover an energetic instability above a critical Rabi frequency provoking the evaporation of the droplet. Finally, we suggest an experiment to observe such quantum droplets using Rabi-coupled internal states of K39 atoms.
We study stability of a zero temperature mixture of attractively interacting degenerate bosons and spin-polarized fermions in the absence of confinement. We demonstrate that higher order corrections to the standard mean field energy of the system can lead to a formation of liquid droplets -- self-bound incompressible systems in a three-dimensional space. In addition to the quantum Lee-Huang-Yang correction to the boson-boson interaction energy, a higher order term in the Bose-Fermi coupling constant is crucial for stabilization of the system. We study a stability region of droplets for three different mixtures of species with different mass ratios, namely: 41^{41}41K \,-40^{40}40K, 87^{87}87Rb \,-40^{40}40K, and 133^{133}133Cs \,-6^{6}6Li as a function of the ratio of Bose-Fermi to Bose-Bose scattering length. The stability analysis is supported by a numerical simulations of droplet formation dynamics starting with a trapped system which is subsequently released from the trap. Our results indicate that Bose-Fermi droplets can be realized experimentally.
These lecture notes contain an introduction to quantum simulation of bosonic systems in the continuum, focusing on weakly interacting Bose-Bose mixtures with competing mean-field interactions. When the values of such interactions are fine-tuned to almost completely cancel the mean-field energy, quantum fluctuations become apparent and dominate the behavior of the system, stabilizing an ultradilute quantum liquid phase. An analogous situation appears in single-component dipolar quantum gases. We review the mechanism that gives rise to this exotic quantum liquid, which can form droplets that are self-bound in the absence of any external confinement, and discuss their properties and dynamics in both the mixture and the dipolar cases. In dipolar gases, arrays of dipolar droplets stabilized by quantum fluctuations can establish global phase coherence and form supersolids. In bosonic mixtures, supersolidity can emerge already at the mean-field level through spin-orbit coupling. We discuss the properties of such spin-orbit-coupled supersolids, comparing them to their dipolar counterparts. Specifically, we focus on their periodic density modulation, phase coherence, and peculiar excitation spectrum, which hosts both superfluid and crystal excitations. Finally, we conclude by discussing open research directions in the areas of quantum liquid droplets and spin-orbit-coupled supersolids, in particular at the interface of the two research topics.
We analytically calculate the leading quantum corrections of the ground-state energy of two- and one-dimensional weakly interacting Rabi-coupled Bose-Bose mixtures in the frame of the Bogoliubov approximation. We show that to repulsive intraspecies and attractive interspecies interactions, the effect of quantum fluctuations favors the formation of self-bound droplets. These liquidlike states are crucially affected by the Rabi coupling, leading thus to the appearance of a quantum instability. We derive meaningful formulas to describe the droplet phase in the one-dimensional case.