Olga Goulko

Thermodynamics of Balanced and Slightly Spin-Imbalanced Fermi Gases at Unitarity

In this article we present a Monte Carlo calculation of the critical temperature and other thermodynamic quantities for the unitary Fermi gas with a population imbalance (unequal number of fermions in the two spin components). We describe an improved worm-type algorithm that is less prone to autocorrelations than the previously available methods and show how this algorithm can be applied to simulate the unitary Fermi gas in presence of a small imbalance. Our data indicate that the critical temperature remains almost constant for small imbalances h={Delta}{mu}/{epsilon}{sub F} -0.5{epsilon}{sub F}h{sup 2}. Using an additional assumption a tighter lower bound can be obtained. We also calculate the energy per particle and the chemical potential in the balanced and imbalanced cases.

Collision of two spin-polarized fermionic clouds

We study the collision of two spin-polarized Fermi clouds in a harmonic trap using a simulation of the Boltzmann equation. As observed in recent experiments, we find three distinct regimes of behavior. For weak interactions the clouds pass through each other. If interactions are increased they approach each other exponentially and for strong interactions they bounce off each other several times. We thereby demonstrate that all these phenomena can be reproduced using a semiclassical collisional approach and that these changes in behavior are associated with an increasing collision rate. We then show that the oscillation of the clouds in the bounce regime is an example of an unusual case in quantum gases: a nonlinear coupling between collective modes, namely, the spin dipole mode and the axial breathing mode, which is enforced by collisions. We also determine the frequency of the bounce as a function of the final temperature of the equilibrated system.

Numerical Analytic Continuation: Answers to Well-Posed Questions

We formulate the problem of numerical analytic continuation in a way that lets us draw meaningful conclusions about the properties of the spectral function based solely on the input data. Apart from ensuring consistency with the input data (within their error bars) and the a priori and a posteriori (conditional) constraints, it is crucial to reliably characterize the accuracy---or even ambiguity---of the output. We explain how these challenges can be met with two approaches: stochastic optimization with consistent constraints and the modified maximum entropy method. We perform illustrative tests for spectra with a double-peak structure, where we critically examine which spectral properties are accessible (second peak position and its spectral weight) and which ones are lost (second peak width/shape). For an important practical example, we apply our protocol to the Fermi polaron problem.

Effect of spin-orbit interactions on the 0.7 anomaly in quantum point contacts.

We study how the conductance of a quantum point contact is affected by spin-orbit interactions, for systems at zero temperature both with and without electron-electron interactions. In the presence of spin-orbit coupling, tuning the strength and direction of an external magnetic field can change the dispersion relation and hence the local density of states in the point contact region. This modifies the effect of electron-electron interactions, implying striking changes in the shape of the 0.7-anomaly and introducing additional distinctive features in the first conductance step.

Boltzmann equation simulation for a trapped Fermi gas of atoms

The dynamics of an interacting Fermi gas of atoms at sufficiently high temperatures can be efficiently studied via a numerical simulation of the Boltzmann equation. In this paper, we describe in detail the setup we used recently to study the oscillations of two spin-polarized fermionic clouds in a trap. We focus here on the evaluation of interparticle interactions. We compare different ways of choosing the phase space coordinates of a pair of atoms after a successful collision and demonstrate that the exact microscopic setup has no influence on the macroscopic outcome.

Numerical study of the unitary Fermi gas across the superfluid transition

We thank Evgeni Burovski, Tilman Enss, Mark Ku, Rabin Paudel, Nikolay Prokof’ev, Yoav Sagi, Boris Svistunov, Kris Van Houcke, Felix Werner and Martin Zwierlein for providing us with their data and for helpful discussions. OG acknowledges support from the NSF under Grant No. PHY-1314735. MW is supported by the Science and Technologies Facilities Council.

The imbalanced Fermi gas at unitarity

Lattice field theory is a useful tool for studying strongly interacting theories in condensed matter physics. A prominent example is the unitary Fermi gas: a two-component system of fermions interacting with divergent scattering length. With Monte Carlo methods this system can be studied from first principles. In the presence of an imbalance (unequal number of particles in the two components) a sign problem arises, which makes conventional algorithms inapplicable. We will show how to apply reweighting techniques to generalise the recently developed worm algorithm to the imbalanced case, and present results for the critical temperature, the energy per particle, the chemical potential and the contact density for equal, as well as unequal number of fermions in the two spin components.

Monte Carlo study of a Fermi gas with infinite scattering length

The Fermi gas at unitarity is a particularly interesting system of cold atoms, being dilute and strongly interacting at the same time. It can be studied non-perturbatively with Monte Carlo methods, like the recently developed worm algorithm. We discuss our implementation and tests of this algorithm and suggest a modification that increases its efficiency by reducing autocorrelations. We then show how the worm algorithm can be applied to calculate the critical temperature of an imbalanced Fermi gas (unequal number of fermions in the two spin components). We finally present some results obtained with the modified algorithm, in the balanced as well as in the imbalanced case.

Spin Drag of a Fermi Gas in a Harmonic Trap

Using a Boltzmann equation approach, we analyze how the spin drag of a trapped interacting fermionic mixture is influenced by the nonhomogeneity of the system in a classical regime where the temperature is much larger than the Fermi temperature. We show that for very elongated geometries, the spin damping rate can be related to the spin conductance of an infinitely long cylinder. We characterize analytically the spin conductance both in the hydrodynamic and collisionless limits and discuss the influence of the velocity profile. Our results are in good agreement with recent experiments and provide a quantitative benchmark for further studies of spin drag in ultracold gases.

Collective modes of an imbalanced unitary Fermi gas

We study theoretically the collective mode spectrum of a strongly imbalanced two-component unitary Fermi gas in a cigar-shaped trap, where the minority species forms a gas of polarons. We describe the collective breathing mode of the gas in terms of the Fermi liquid kinetic equation taking collisions into account using the method of moments. Our results for the frequency and damping of the longitudinal in-phase breathing mode are in good quantitative agreement with an experiment by S. Nascimb`ene et al. [Phys. Rev. Lett. 103, 170402 (2009)] and interpolate between a hydrodynamic and a collisionless regime as the polarization is increased. A separate out-of phase breathing mode, which for a collisionless gas is sensitive to the effective mass of the polaron, however, is strongly damped at finite temperature, whereas the experiment observes a well-defined oscillation.