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arXiv:1501.05544 · Physical Review A

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

Dietrich Roscher, Jens Braun, Joaquín E. Drut

Published May 13, 2015• 48 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.91.053611

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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↓/m\ensuremath↑\ensuremath≳3{m}_{\ensuremath{\downarrow}}/{m}_{\ensuremath{\uparrow}}\ensuremath{\gtrsim}3m\ensuremath↓​/m\ensuremath↑​\ensuremath≳3. The extent of the inhomogeneous phase in parameter space increases with increasing mass imbalance.
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.
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 investigate the phase structure of spin-imbalanced unitary Fermi gases beyond mean-field theory by means of the functional renormalization group. In this approach, quantum and thermal fluctuations are resolved in a systematic manner. The discretization of the effective potential on a grid allows us to accurately account for both first- and second-order phase transitions that are present on the mean-field level. We compute the full phase diagram in the plane of temperature and spin imbalance and discuss the existence of other conjectured phases such as the Sarma phase and a precondensation region. In addition, we explain on a qualitative level how we expect that in situ density images are affected by our findings and which experimental signatures may potentially be used to probe the phase structure.
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.
Fermi gases in strongly coupled regimes, such as the unitary limit, are inherently challenging for many-body methods. Although much progress has been made with purely analytic methods, quantitative results require ab initio numerical approaches, such as Monte Carlo (MC) calculations. However, mass-imbalanced and spin-imbalanced gases are not accessible to MC calculations due to the infamous sign problem. It was recently pointed out that the sign problem, for fi nite spin imbalance, can be circumvented by resorting to imaginary polarizations and analytic continuation. Large parts of the phase diagram spanned by temperature and polarization then become accessible to MC calculations. We propose to apply a similar strategy to the mass-imbalanced case, which opens up the possibility to study the associated phase diagram with MC calculations. In particular, our analysis suggests that a detection of a (tri-)critical point in this phase diagram is possible. We also discuss calculations in the zero-temperature limit with our approach.
Fermi gases in strongly coupled regimes are inherently challenging for many-body methods. Although progress has been made analytically, quantitative results require ab initio numerical approaches, such as Monte-Carlo (MC) calculations. However, mass-imbalanced and spin-imbalanced gases are not accessible to MC calculations due to the infamous sign problem. For finite spin imbalance, the problem can be circumvented using imaginary polarizations and analytic continuation, and large parts of the phase diagram then become accessible. We propose to apply this strategy to the mass-imbalanced case, which opens up the possibility to study the associated phase diagram with MC calculations. We perform a first mean-field analysis which suggests that zero-temperature studies, as well as detecting a potential (tri)critical point, are feasible.