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:1311.0179 · Physical Review A

Inhomogeneous phases in one-dimensional mass- and spin-imbalanced Fermi gases

Dietrich Roscher, Jens Braun, Joaquín E. Drut

Published Jun 11, 2014• 32 citations
arXivHTMLPDF

Abstract

We study the phase diagram of strongly interacting fermions in one dimension at finite temperature, with mass and spin imbalance. By including the possibility of the existence of a spatially inhomogeneous ground state, we find regions where spatially varying superfluid phases are favored over homogeneous phases. We obtain estimates for critical values of the temperature, mass, and spin imbalance, above which these phases disappear. Finally, we show that an intriguing relation exists between the general structure of the phase diagram and the binding energies of the underlying two-body bound-state problem. Although our present study of the many-body aspects is based on a mean-field approximation, it may still yield phenomenologically important insights into the dynamics of strongly interacting fermions in one dimension. Most importantly, however, we expect that our present mean-field study can be considered worthwhile from a field-theoretical point of view as it may help to better understand the mechanisms underlying the emergence of inhomogeneous phases in higher dimensions as well as the general structure of the associated phase diagrams.

DOI
10.1103/physreva.89.063609

Related papers

Phase structure of mass- and spin-imbalanced unitary Fermi gases

Dietrich Roscher, Jens Braun, Joaquín E. Drut

We study the phase diagram of mass- and spin-imbalanced unitary Fermi gases, in search for the emergence of spatially inhomogeneous phases. To account for fluctuation effects beyond the mean-field approximation, we employ renormalization group techniques. We thus obtain estimates for critical values of the temperature, mass and spin imbalance, above which the system is in the normal phase. In the unpolarized, equal-mass limit, our result for the critical temperature is in accordance with state-of-the-art Monte Carlo calculations. In addition, we estimate the location of regions in the phase diagram where inhomogeneous phases are likely to exist. We show that an intriguing relation exists between the general structure of the many-body phase diagram and the binding energies of the underlying two-body bound-state problem, which further supports our findings. Our results suggest that inhomogeneous condensates form for mass imbalances ${m}_{\ensuremath{\downarrow}}/{m}_{\ensuremath{\uparrow}}\ensuremath{\gtrsim}3$. The extent of the inhomogeneous phase in parameter space increases with increasing mass imbalance.

arXiv:1501.05544•Physical Review A•May 13, 2015•48 citations

Phase Structure of Strongly Correlated Fermi Gases

Dietrich Roscher

Strongly correlated fermionic many-body systems are ubiquitous in nature. Their theoretical description poses challenging problems which are further complicated when imbalances in, e.g., the particle numbers of the involved species or their masses are introduced. In this thesis, a number of different approaches is developed and applied in order to obtain predictions for physical observables of such systems that mutually support and confirm each other. In a first step, analytically well-founded mean-field analyses are carried through. One- and three-dimensional ultracold Fermi gases with spin and mass imbalance as well as Gross-Neveu and NJL-type relativistic models at finite baryon chemical potential are investigated with respect to their analytic properties in general and the occurrence of spontaneous breaking of translational invariance in particular. Based on these studies, further methods are devised or adapted allowing for investigations also beyond the mean-field approximation. Lattice Monte Carlo simulations with imaginary imbalance parameters are employed to surmount the infamous sign problem and compute the equation of state of the respective unitary Fermi gases. Moreover, in-medium two-body analyses are used to confirm and explain the characteristics of inhomogeneously ordered phases. Finally, functional RG methods are applied to the unitary Fermi gas with spin and mass imbalance. Besides quantitatively competitive predictions for critical temperatures for the superfluid state, strong hints on the stability of inhomogeneous phases with respect to order parameter fluctuations in the regime of large mass imbalance are obtained. Combining the findings from these different theoretical studies suggests the possibility to find such phases in experiments presently in preparation.

•Jan 1, 2015•0 citations

Phases of spin- and mass-imbalanced ultracold Fermi gases in harmonic traps

Jens Braun, Joaquín E. Drut, P. Thomas Jahn +2 more

We analyze the phase structure of mass- and spin-imbalanced unitary Fermi gases in harmonic traps. To this end, we employ density functional theory in the local density approximation. Depending on the values of the control parameters measuring mass and spin imbalance, we observe that three regions exist in the trap, namely, a superfluid region at the center, surrounded by a mixed region of resonantly interacting spin-up and spin-down fermions, and, finally, a fully polarized phase surrounding the previous two regions. We also find regimes in the phase diagram where the existence of a superfluid region at the center of the trap is not energetically favored. We point out the limitations of our approach at the present stage and call for more detailed (ab initio) studies of the equation of state of uniform, mass-imbalanced unitary Fermi gases.

arXiv:1402.7042•Physical Review A•May 12, 2014•13 citations

In-medium bound-state formation and inhomogeneous condensation in Fermi gases in a hard-wall box

Dietrich Roscher, Jens Braun

The formation of bosonic bound states underlies the formation of a superfluid ground state in the many-body phase diagram of ultracold Fermi gases. We study bound-state formation in a spin- and mass-imbalanced ultracold Fermi gas confined in a box with hard-wall boundary conditions. Because of the presence of finite Fermi spheres, the center-of-mass momentum of the potentially formed bound states can be finite, depending on the parameters controlling mass and spin imbalance as well as the coupling strength. We exploit this observation to estimate the potential location of inhomogeneous phases in the many-body phase diagram as a function of spin-and mass imbalance as well as the box size. Our results suggest that a hard-wall box does not alter substantially the many-body phase diagram calculated in the thermodynamic limit. Therefore, such a box may serve as an ideal trap potential to bring experiment and theory closely together and facilitate the search for exotic inhomogeneous ground states.

•Jan 1, 2017•2 citations

Imbalanced Fermi Gases at Unitarity

K. B. Gubbels, Henk T. C. Stoof, Theoretical Physics +3 more

We consider imbalanced Fermi gases with strong attractive interactions, for which Cooper-pair formation plays an important role. The two-component mix-tures consist either of identical fermionic atoms in two different hyperfine states, or of two different atomic species both occupying only a single hyperfine state. In both cases, the number of atoms for each component is allowed to be differ-ent, which leads to a spin imbalance, or spin polarization. Two different atomic species also lead to a mass imbalance. Imbalanced Fermi gases are relevant to condensed-matter physics, nuclear physics and astroparticle physics. They have been studied intensively in recent years, following their experimental realization in ultracold atomic Fermi gases. The experimental control in such a system allows for a systematic study of the equation of state and the phase diagram as a function of temperature, spin polarization and interaction strength. In this re-view, we discuss the progress in understanding strongly-interacting imbalanced Fermi gases, where a main goal is to describe the results of the highly controlled experiments. We start by discussing Feshbach resonances, after which we treat the imbalanced Fermi gas in mean-field theory to give an introduction to the relevant physics. We encounter several unusual superfluid phases, including phase-separation, gapless Sarma superfluidity, and supersolidity. To obtain a more quantitative description of the experiments, we review also more sophisti-cated techniques, such as diagrammatic methods and the renormalization-group theory. We end the review by discussing two theoretical approaches to treat the inhomogeneous imbalanced Fermi gas, namely the Landau-Ginzburg theory and the Bogoliubov-de Gennes approach. Key words:

•Jan 1, 2013•38 citations

In-medium bound-state formation and inhomogeneous condensation in Fermi gases in a hard-wall box

Dietrich Roscher, Jens Braun

Abstract The formation of bosonic bound states underlies the formation of a superfluid ground state in the many-body phase diagram of ultracold Fermi gases. We study bound-state formation in a spin- and mass-imbalanced ultracold Fermi gas confined in a box with hard-wall boundary conditions. Because of the presence of finite Fermi spheres, the center-of-mass momentum of the potentially formed bound states can be finite, depending on the parameters controlling mass and spin imbalance as well as the coupling strength. We exploit this observation to estimate the potential location of inhomogeneous phases in the many-body phase diagram as a function of spin- and mass imbalance as well as the box size. Our results suggest that a hard-wall box does not alter substantially the many-body phase diagram calculated in the thermodynamic limit. Therefore, such a box may serve as an ideal trap potential to bring experiment and theory closely together and facilitate the search for exotic inhomogeneous ground states.

arXiv:1611.02081•Journal of Physics B Atomic Molecular and Optical Physics•Sep 8, 2017•2 citations
We study the phase diagram of strongly interacting fermions in one dimension at finite temperature, with mass and spin imbalance. By including the possibility of the existence of a spatially inhomogeneous ground state, we find regions where spatially varying superfluid phases are favored over homogeneous phases. We obtain estimates for critical values of the temperature, mass, and spin imbalance, above which these phases disappear. Finally, we show that an intriguing relation exists between the general structure of the phase diagram and the binding energies of the underlying two-body bound-state problem. Although our present study of the many-body aspects is based on a mean-field approximation, it may still yield phenomenologically important insights into the dynamics of strongly interacting fermions in one dimension. Most importantly, however, we expect that our present mean-field study can be considered worthwhile from a field-theoretical point of view as it may help to better understand the mechanisms underlying the emergence of inhomogeneous phases in higher dimensions as well as the general structure of the associated phase diagrams.
We study the phase diagram of mass- and spin-imbalanced unitary Fermi gases, in search for the emergence of spatially inhomogeneous phases. To account for fluctuation effects beyond the mean-field approximation, we employ renormalization group techniques. We thus obtain estimates for critical values of the temperature, mass and spin imbalance, above which the system is in the normal phase. In the unpolarized, equal-mass limit, our result for the critical temperature is in accordance with state-of-the-art Monte Carlo calculations. In addition, we estimate the location of regions in the phase diagram where inhomogeneous phases are likely to exist. We show that an intriguing relation exists between the general structure of the many-body phase diagram and the binding energies of the underlying two-body bound-state problem, which further supports our findings. Our results suggest that inhomogeneous condensates form for mass imbalances ${m}_{\ensuremath{\downarrow}}/{m}_{\ensuremath{\uparrow}}\ensuremath{\gtrsim}3$. The extent of the inhomogeneous phase in parameter space increases with increasing mass imbalance.
Strongly correlated fermionic many-body systems are ubiquitous in nature. Their theoretical description poses challenging problems which are further complicated when imbalances in, e.g., the particle numbers of the involved species or their masses are introduced. In this thesis, a number of different approaches is developed and applied in order to obtain predictions for physical observables of such systems that mutually support and confirm each other. In a first step, analytically well-founded mean-field analyses are carried through. One- and three-dimensional ultracold Fermi gases with spin and mass imbalance as well as Gross-Neveu and NJL-type relativistic models at finite baryon chemical potential are investigated with respect to their analytic properties in general and the occurrence of spontaneous breaking of translational invariance in particular. Based on these studies, further methods are devised or adapted allowing for investigations also beyond the mean-field approximation. Lattice Monte Carlo simulations with imaginary imbalance parameters are employed to surmount the infamous sign problem and compute the equation of state of the respective unitary Fermi gases. Moreover, in-medium two-body analyses are used to confirm and explain the characteristics of inhomogeneously ordered phases. Finally, functional RG methods are applied to the unitary Fermi gas with spin and mass imbalance. Besides quantitatively competitive predictions for critical temperatures for the superfluid state, strong hints on the stability of inhomogeneous phases with respect to order parameter fluctuations in the regime of large mass imbalance are obtained. Combining the findings from these different theoretical studies suggests the possibility to find such phases in experiments presently in preparation.
We analyze the phase structure of mass- and spin-imbalanced unitary Fermi gases in harmonic traps. To this end, we employ density functional theory in the local density approximation. Depending on the values of the control parameters measuring mass and spin imbalance, we observe that three regions exist in the trap, namely, a superfluid region at the center, surrounded by a mixed region of resonantly interacting spin-up and spin-down fermions, and, finally, a fully polarized phase surrounding the previous two regions. We also find regimes in the phase diagram where the existence of a superfluid region at the center of the trap is not energetically favored. We point out the limitations of our approach at the present stage and call for more detailed (ab initio) studies of the equation of state of uniform, mass-imbalanced unitary Fermi gases.
The formation of bosonic bound states underlies the formation of a superfluid ground state in the many-body phase diagram of ultracold Fermi gases. We study bound-state formation in a spin- and mass-imbalanced ultracold Fermi gas confined in a box with hard-wall boundary conditions. Because of the presence of finite Fermi spheres, the center-of-mass momentum of the potentially formed bound states can be finite, depending on the parameters controlling mass and spin imbalance as well as the coupling strength. We exploit this observation to estimate the potential location of inhomogeneous phases in the many-body phase diagram as a function of spin-and mass imbalance as well as the box size. Our results suggest that a hard-wall box does not alter substantially the many-body phase diagram calculated in the thermodynamic limit. Therefore, such a box may serve as an ideal trap potential to bring experiment and theory closely together and facilitate the search for exotic inhomogeneous ground states.
We consider imbalanced Fermi gases with strong attractive interactions, for which Cooper-pair formation plays an important role. The two-component mix-tures consist either of identical fermionic atoms in two different hyperfine states, or of two different atomic species both occupying only a single hyperfine state. In both cases, the number of atoms for each component is allowed to be differ-ent, which leads to a spin imbalance, or spin polarization. Two different atomic species also lead to a mass imbalance. Imbalanced Fermi gases are relevant to condensed-matter physics, nuclear physics and astroparticle physics. They have been studied intensively in recent years, following their experimental realization in ultracold atomic Fermi gases. The experimental control in such a system allows for a systematic study of the equation of state and the phase diagram as a function of temperature, spin polarization and interaction strength. In this re-view, we discuss the progress in understanding strongly-interacting imbalanced Fermi gases, where a main goal is to describe the results of the highly controlled experiments. We start by discussing Feshbach resonances, after which we treat the imbalanced Fermi gas in mean-field theory to give an introduction to the relevant physics. We encounter several unusual superfluid phases, including phase-separation, gapless Sarma superfluidity, and supersolidity. To obtain a more quantitative description of the experiments, we review also more sophisti-cated techniques, such as diagrammatic methods and the renormalization-group theory. We end the review by discussing two theoretical approaches to treat the inhomogeneous imbalanced Fermi gas, namely the Landau-Ginzburg theory and the Bogoliubov-de Gennes approach. Key words:
Abstract The formation of bosonic bound states underlies the formation of a superfluid ground state in the many-body phase diagram of ultracold Fermi gases. We study bound-state formation in a spin- and mass-imbalanced ultracold Fermi gas confined in a box with hard-wall boundary conditions. Because of the presence of finite Fermi spheres, the center-of-mass momentum of the potentially formed bound states can be finite, depending on the parameters controlling mass and spin imbalance as well as the coupling strength. We exploit this observation to estimate the potential location of inhomogeneous phases in the many-body phase diagram as a function of spin- and mass imbalance as well as the box size. Our results suggest that a hard-wall box does not alter substantially the many-body phase diagram calculated in the thermodynamic limit. Therefore, such a box may serve as an ideal trap potential to bring experiment and theory closely together and facilitate the search for exotic inhomogeneous ground states.