Polarized Fermi Gas Research Articles

Phase diagram of a polarized Fermi gas across a Feshbach resonance in a potential trap

We map out the detailed phase diagram of a trapped ultracold Fermi gas with population imbalance across a wide Feshbach resonance. We show that under the local density approximation, the properties of the atoms in any (anisotropic) harmonic traps are universally characterized by three dimensionless parameters: the normalized temperature, the dimensionless interaction strength, and the population imbalance. We then discuss the possible quantum phases in the trap, and quantitatively characterize their phase boundaries in various typical parameter regions.

Ultracold polarized Fermi gas at intermediate temperatures

We consider non-zero temperature properties of the polarized two-component Fermi gas. We point out that stable polarized paired states which are more stable than their phase separated counterparts with unpolarized superfluid region can exist below the critical temperature. We also solve the system behavior in a trap using the local density approximation and find gradually increasing polarization in the center of the system as the temperature is increased. However, in the strongly interacting region the central polarization increases most rapidly close to the mean-field critical temperature, which is known to be substantially higher than the critical temperature for superfluidity. This indicates that most of the phase separation occurs in the fluctuation region prior to superfluidity and that the polarization in the actual superfluid is modest.

Pairs and loners in a polarized fermi gas

Pairs and loners in a polarized fermi gas

Pairing and Phase Separation in a Polarized Fermi Gas

We report the observation of pairing in a gas of atomic fermions with unequal numbers of two components. Beyond a critical polarization, the gas separates into a phase that is consistent with a superfluid paired core surrounded by a shell of normal unpaired fermions. The critical polarization diminishes with decreasing attractive interaction. For near-zero polarization, we measured the parameter beta = -0.54 +/- 0.05, describing the universal energy of a strongly interacting paired Fermi gas, and found good agreement with recent theory. These results are relevant to predictions of exotic new phases of quark matter and of strongly magnetized superconductors.

Itinerant Ferromagnetism in an Ultracold Atom Fermi Gas

We address the possible occurrence of ultracold atom ferromagnetism by evaluating the free energy of a spin polarized Fermi gas to second order in its interaction parameter. We find that Hartree-Fock theory underestimates the tendency toward ferromagnetism, predict that the ferromagnetic transition is first order at low temperatures, and point out that the spin coherence time of gases prepared in a ferromagnetic state is strongly enhanced as the transition is approached. We relate our results to recent experiments.

Quantum Phase Transitions across a p-Wave Feshbach Resonance

We study a single-species polarized Fermi gas tuned across a narrow p-wave Feshbach resonance. We show that in the course of a Bose-Einstein condensation (BEC)-BCS crossover, the system can undergo a magnetic-field-tuned quantum phase transition from a px-wave to a px+ipy-wave superfluid. The latter state, that spontaneously breaks time-reversal symmetry, furthermore undergoes a topological px+ipy to px+ipy transition at zero chemical potential mu. In two dimensions, for mu > 0 it is characterized by a Pfaffian ground state exhibiting topological order and non-Abelian excitations familiar from fractional quantum Hall systems.

Atom interferometry in a vertical optical lattice

AbstractWe have studied the interference of degenerate quantum gases in a vertical optical lattice. The coherence of the atoms leads to an interference pattern when the atoms are released from the lattice. This has been shown for a Bose‐Einstein condensate in early experiments. Here we demonstrate that also for fermions an interference pattern can be observed provided that the momentum distribution is smaller than the recoil momentum of the lattice. Special attention is given to the role of interactions which wash out the interference pattern for a condensate trapped in the lattice but do not affect a spin polarized Fermi gas, where collisions at ultra cold temperatures are forbidden. Comparing the interference of the two quantum gases we find a clear superiority of fermions for trapped atom interferometry.

Superfluid pairing in a polarized dipolar Fermi gas

We calculate the critical temperature of a superfluid phase transition in a polarized Fermi gas of dipolar particles. In this case the order parameter is anisotropic and has a nontrivial energy dependence. Cooper pairs do not have a definite value of the angular momentum and are coherent superpositions of all odd angular momenta. Our results describe prospects for achieving the superfluid transition in single-component gases of fermionic polar molecules.

Fermi Gas in Harmonic Oscillator Potentials

Assuming the validity of grand canonical statistics, we study the properties of a spin polarized Fermi gas in harmonic traps. Universal forms of Fermi temperature TF, internal energy U and the specific heat per particle of the trapped Fermi gas are calculated as a function of particle number, and the results are compared with those of infinite number particles.

Longitudinal spin relaxation in a dilute, degenerate Fermi gas at arbitrary polarization

We calculate the longitudinal magnetic relaxation timeT1−1 for a dilute, polarized Fermi gas with short range interactions at low temperatures. In the limit of small polarizationsT1−1 is proportional toT−2 in agreement with earlier predictions, while in the opposite caseT1−1 is strongly affected by polarization, and in the limit of large polarizations becomes proportional to the square of the energy separation between the Fermi surfaces for up and down spins. The possibility of measuringT1 in dilute solutions of3He in superfluid4He is investigated.

Zero-temperature attenuation and transverse spin dynamics in fermi liquids. II. Dilute fermi systems

This is the second in a series of papers on a consistent microscopic theory of transverse dynamics in spin-polarized or binary Fermi liquids. We demonstrate when and how the exact theory of Ref. 1 reduces to the conventional theory of highly polarized degenerate low-density Fermi liquids and gases. In the lowest approximations, i.e. for an ideal polarized Fermi gas and in the first (Born) order, our theory assumes the standard form. In the next order in density and/or interaction, the main equations still have a fairly conventional form, though they already contain the peculiar zero-temperature attenuation which is missing in the standard theory. This attenuation can be incorporated into the standard Fermi liquid formalism by adding an imaginary part to a mixed spin component of the Landau interaction function. The source of this imaginary contribution atT = 0 is a pole in the integral expression for the Landau interaction function (the situation is very similar to the case of collisionless Landau damping). In the next order, the standard theory fails completely, and even the form of the equations of transverse dynamics becomes very unconventional. We calculated explicitly the parameters of transverse spin dynamics and the spectrum of spin waves, including the zero-temperature attenuation, and, as a by-product, the polarization dependencies of thermodynamic parameters. The calculation includes a possible non-locality of the interaction. An application of the results to3He↑-4He mixtures covers the non-locality in the direct interaction channel as well as the non-locality and retardation associated with a phonon-mediated part of particles' interaction.

NMR relaxation times for a dilute polarized Fermi gas

We calculate the longitudinal relaxation time T1 for a polarized Boltzmann spin−12 Fermi gas. We show that T1 is independent of polarization of the gas. At high T, where the thermal wavelength a is small compared to the scattering length a, T1 is proportional T12, while at low T, such that λ is greater than a, T1 is proportional to T−12. T1 thus has a minimum at some intermediate temperature confirming the numerical results of Shizgal. The existence of the minimum does not depend on the presence of an attractive part of the potential. As an example of the expected temperature dependence we calculate T1 numerically for a hard core gas.

NMR relaxation times for a dilute polarized fermi gas

Abstract We calculate the longitudinal relaxation time T1 for a polarized Boltzmann spin − 1 2 Fermi gas. We show that T1 is independent of polarization of the gas. At high T, where the thermal wavelength a is small compared to the scattering length a, T1 is proportional T 1 2 , while at low T, such that λ is greater than a, T1 is proportional to T − 1 2 . T1 thus has a minimum at some intermediate temperature confirming the numerical results of Shizgal. The existence of the minimum does not depend on the presence of an attractive part of the potential. As an example of the expected temperature dependence we calculate T1 numerically for a hard core gas.

Flow of polarized Fermi gases through narrow channels.

The flow of a polarized Fermi gas through channels from one cell to another can be used to study its transport properties. If the mean free path $\ensuremath{\lambda}$ in the gas is smaller than the radius $r$ of a channel, the time constant for the filling of an empty chamber can yield the viscosity of the gas in both the Boltzmann and degenerate cases. If $\ensuremath{\lambda}>r$ and the gas is degenerate, a novel effect is predicted: Because the Fermi velocities of the two spin species are different, the polarization in the second cell will initially have a value greater than the equilibrium value in the first cell.

Heat capacity of an ideal, polarized Fermi gas in two dimensions

The chemical potential, energy, and heat capacity of a spin-1/2, ideal Fermi gas are calculated for two-dimensional constraint of the translational motion. Numerical calculations are made of the heat capacity for values of the basic physical parameters corresponding to solutions of3He in monolayers of4He in the fields of superconducting magnets. The results are displayed graphically and the main features of the heat capacity curves are discussed.