Polarized Fermi Gas Research Articles

Universal many-body properties of one-dimensional mass-imbalanced highly polarized Fermi gases

We investigate the universal properties of mass-imbalanced highly polarized Fermi gases in one-dimensional scenarios. By treating the mass ratio as a parameter, we delve into the binding energy, quasiparticle residue, and correlation functions of the systems. We provide a thorough momentum distribution for impurities and spin-up atoms within the Fermi sea. When the impurity mass is infinite, we discover that the quasiparticle residue approaches to zero and the systems exhibit the signature of the Anderson orthogonality catastrophe in strong coupling regime. We observe an increase in Tan contact under large mass ratios and study density correlations by applying Fourier transform. Crucially, we demonstrate the existence of the molecular state in one-dimensional polaron system with strong attractive interactions, unlike previous conclusions.

Dimensional crossover on multileg attractive- U Hubbard ladders

We study the ground state properties of a polarized two-component Fermi gas on multileg attractive-$U$ Hubbard ladders. Using exact diagonalization and density matrix renormalization group method simulations, we construct grand canonical phase diagrams for ladder widths of up to $W=5$ and varying perpendicular geometries, characterizing the quasi-one-dimensional regime of the dimensional crossover. We unveil a multicritical point marking the onset of partial polarization in those phase diagrams, a candidate regime of finite-momentum pairing. We compare our findings with recent experimental and theoretical studies of quasi-one-dimensional polarized Fermi gases.

Viscous flow in a one-dimensional spin-polarized Fermi gas: The role of integrability on viscosity

The transport properties of one-dimensional Fermi gases at low temperatures are often described by the Luttinger liquid (LL) model. However, to study dissipative effects, one needs to examine interactions beyond the LL model. In this work, we provide a simple model that allows for a direct microscopic calculation of the bulk viscosity, namely, the one-dimensional spin polarized $p$-wave Fermi gas. To leading order in the finite interaction strength, we find that the bulk viscosity is finite and consistent with the requirement of scale symmetry. We further show that the bulk viscosity satisfies the Bose-Fermi duality relating the weakly interacting limit of the spin polarized Fermi gas to the strongly interacting limit of the Lieb-Liniger model and vice versa. This work establishes the bulk viscosity to leading order in scale-breaking interactions in both the strongly and weakly interacting limits for both high and low temperatures.

Application of the renormalized random-phase approximation to polarized Fermi gases

We consider a spin imbalanced Fermi gas at zero temperature in the normal phase on the BCS side of the BCS-BEC crossover and around unitarity. We compute the critical polarization for pairing, the correlated occupation numbers and the contact in an extension of particle-particle RPA (also called non self-consistent \textit{T}-matrix approach or ladder approximation). The so-called renormalized RPA consists in computing the \textit{T} matrix with self-consistently determined occupation numbers. The occupation numbers are determined either by keeping the self-energy only to first order or by resumming the Dyson equation. In this way, the result for the critical polarization, strongly overestimated in standard RPA, is clearly improved. We also discuss some problems of this approach.

Probing nonlocal spatial correlations in quantum gases with ultra-long-range Rydberg molecules

We present photo-excitation of ultra-long-range Rydberg molecules as a probe of spatial correlations in quantum gases. Rydberg molecules can be created with well-defined internuclear spacing, set by the radius of the outer lobe of the Rydberg electron wavefunction $R_n$. By varying the principal quantum number $n$ of the target Rydberg state, the molecular excitation rate can be used to map the pair-correlation function of the trapped gas $g^{(2)}(R_n)$. We demonstrate this with ultracold Sr gases and probe pair-separation length scales ranging from $R_n = 1400 - 3200$ $a_0$, which are on the order of the thermal de Broglie wavelength for temperatures around 1 $\mu$K. We observe bunching for a single-component Bose gas of $^{84}$Sr and anti-bunching due to Pauli exclusion at short distances for a polarized Fermi gas of $^{87}$Sr, revealing the effects of quantum statistics.

Andreev trajectory and low-temperature transport in ultracold atoms in the presence of a vortex line: Population imbalance effect

By taking into account Andreev scattering of thermal excitations and using the excitation energy obtained from Bogoliubov-de Gennes equations, the dynamics of quasiparticle excitation of a mass-asymmetric cold polarized Fermi gas near a vortex line is determined. Also, the fraction of heat transmitted by the quasiparticle across the velocity field of the vortex is obtained. Then, the relation between the relevant physical parameters (such as, the scattering length, a, the average chemical potential, μs, the imbalance chemical potential, hs, and the mass ratio, mr) and the Andreev trajectory is obtained and discussed. Also, the heat transmitted by the quasiparticle in terms of the imbalance chemical potential and temperature is calculated. As an important result, in ultracold atomic system, the Andreev trajectory and heat transmitted can be controlled by the relevant physical parameters via the species population imbalance.

Coherent oscillations in small Fermi-polaron systems

We study the ground state and excitations of a one-dimensional trapped polarized Fermi gas interacting with a single impurity. First, we study the tunnelling dynamics of the impurity through a potential barrier, such as one effectively created by a double-well trap. To this end, we perform an exact diagonalization of the full few-body Hamiltonian and analyze the results in a Local Density Approximation. Off-diagonal and one-particle correlation matrices are studied and are shown to be useful for discerning between different symmetries of the states. Second, we consider a radio-frequency (RF) spectroscopy of our system and the resulting spectral function. These calculations can motivate future experiments, which can provide a further insight into the physics of a Fermi polaron.

Topological superfluid in a two-dimensional polarized Fermi gas with spin–orbit coupling and adiabatic rotation

We study the properties of superfluid in a two-dimensional (2D) polarized Fermi gas with spin–orbit coupling and adiabatic rotation which are trapped in a harmonic potential. Due to the competition between polarization, spin–orbit coupling, and adiabatic rotation, the Fermi gas exhibits many intriguing phenomena. By using the Bardeen–Cooper– Schrieffer (BCS) mean-field method with local density approximation, we investigate the dependence of order parameter solution on the spin–orbit coupling strength and the rotation velocity. The energy spectra with different rotation velocities are studied in detail. Besides, the conditions for the zero-energy Majorana fermions in topological superfluid phase to be observed are obtained. By investigating distributions of number density, we find that the rotation has opposite effect on the distribution of number density with different spins, which leads to the enhancement of the polarization of Fermi gas. Here, we focus on the region of BCS pairing and ignore the Fulde–Ferrell–Larkin–Ovchinnikov state.

Homogeneous Atomic Fermi Gases.

We report on the creation of homogeneous Fermi gases of ultracold atoms in a uniform potential. In the momentum distribution of a spin-polarized gas, we observe the emergence of the Fermi surface and the saturated occupation of one particle per momentum state: the striking consequence of Pauli blocking in momentum space for a degenerate gas. Cooling a spin-balanced Fermi gas at unitarity, we create homogeneous superfluids and observe spatially uniform pair condensates. For thermodynamic measurements, we introduce a hybrid potential that is harmonic in one dimension and uniform in the other two. The spatially resolved compressibility reveals the superfluid transition in a spin-balanced Fermi gas, saturation in a fully polarized Fermi gas, and strong attraction in the polaronic regime of a partially polarized Fermi gas.

Crossover from collisionless to collisional spin dynamics of polarized fermions

We study the transverse spin dynamics of trapped polarized Fermi gases in the high-temperature limit. In the non-interacting collisionless regime, a magnetic-field gradient induces collective spin wave oscillations. In the strongly interacting collisional regime, the dynamics are governed by spin diffusion. These two limits have been extensively studied both experimentally and theoretically, but the crossover between them has received less attention. In this paper, we use a quantum Boltzmann equation to study transverse spin dynamics and show how the excitations evolve from dispersive to diffusive in the high-temperature limit. We provide analytical solutions in the two limiting regimes, which agree well with our numerical results.

Large-momentum distribution of a polarized Fermi gas and p -wave contacts

We present a derivation of the adiabatic energy relations as well as the large momentum distribution of a polarized Fermi gas near p-wave Feshbach resonances. The leading asymptotic behavior ($k^{-2}$) and subleading behavior ($k^{-4}$) of the large momentum distribution have recently been predicted by Yu et al. [Phys. Rev. Lett. 115, 135304 (2015)] and by He et al. [Phys. Rev. Lett. 116, 045301 (2016)] using two different approaches. Here, we show that the subleading asymptotic behavior ($\sim k^{-4}$) can not fully be captured by the contact defined from the adiabatic energy relation related to the p-wave effective range, and there should be an extra term resulted from the center-of-mass motion of the pairs. The omission of this extra term is perhaps a reasonable approximation at zero temperature. However, it should be taken into account at finite temperature and should be of significant importance to understand the recently measured momentum distribution in a resonant p-wave Fermi gas of ultracold $^{40}$K atoms [Luciuk et al., Nature Phys. 12, 599 (2016)].

Erratum: Polarized Fermi gases at finite temperature in the BCS-BEC crossover [Phys. Rev. A 90, 053629 (2014)

Erratum: Polarized Fermi gases at finite temperature in the BCS-BEC crossover [Phys. Rev. A 90, 053629 (2014)

Ferromagnetism in a repulsive atomic Fermi gas with correlated disorder

We investigate the zero-temperature ferromagnetic behavior of a two-component repulsive Fermi gas in the presence of a correlated random field that represents an optical speckle pattern. The density is tuned so that the (noninteracting) Fermi energy is close to the mobility edge of the Anderson localization transition. We employ quantum Monte Carlo simulations to determine various ground-state properties, including the equation of state, the magnetic susceptibility, and the energy of an impurity immersed in a polarized Fermi gas (repulsive polaron). In the weakly interacting limit, the magnetic susceptibility is found to be suppressed by disorder. However, it rapidly increases with the interaction strength, and it diverges at a much weaker interaction strength compared to the clean gas. Both the transition from the paramagnetic phase to the partially ferromagnetic phase, and the one from the partially to the fully ferromagnetic phase are strongly favored by disorder, indicating a case of order induced by disorder.

BCS–BEC crossover of spin imbalanced Fermi gases with Rashba spin–orbit coupling

We study the BCS–Bose Einstein Condensation (BEC) crossover of a three-dimensional spin polarized Fermi gas with Rashba spin–orbital coupling (SOC). At finite temperature, the effects of non-condensed pairs due to the thermal excitation are considered based on the G0G pair fluctuation theory. These fluctuations generate a pseudogap even persistent above Tc. Within this framework, the Sarma state or the spin polarized superfluid state and polarized pseudogap state are explored in detail. The resulting Tc curves show that the enhancement of pairing due to the SOC roughly cancels out the suppression of pairing due to the population imbalance. Thus we observed that in a large portion of the parameter space, the polarized superfluid state are stabilized by the SOC.

Dissociation of Feshbach molecules via spin-orbit coupling in ultracold Fermi gases

We study the dissociation of Feshbach molecules in ultracold Fermi gases with spin-orbit (SO) coupling. Since SO coupling can induce quantum transition between the Feshbach molecules and the fully polarized Fermi gas, the Feshbach molecules can be dissociated by the SO coupling. We experimentally realized this new type of dissociation in ultracold gases of 40K atoms with SO coupling created by Raman beams, and observed that the dissociation rate is highly non-monotonic on both the positive and negative Raman-detuning sides. Our results show that the dissociation of Feshbach molecules can be controlled by new degrees of freedoms, i.e., the SO-coupling intensity or the momenta of the Raman beams, as well as the detuning of the Raman beams.

Condensed phase of Bose-Fermi mixtures with a pairing interaction

We study the condensed phase of a Bose-Fermi mixture with a tunable pairing interaction between bosons and fermions with many-body diagrammatic methods and fixed-node diffusion Quantum Monte Carlo simulations. A universal behavior of the condensate fraction and bosonic momentum distribution with respect to the boson concentration is found to hold in an extended range of boson-fermion couplings and concentrations. For vanishing boson density, we prove that the bosonic condensate fraction reduces to the quasiparticle weight Z of the Fermi polaron studied in the context of polarized Fermi gases, unifying in this way two apparently unrelated quantities.

Polarized Fermi gases at finite temperature in the BCS-BEC crossover

We consider a polarized Fermi gas in the BCS-BEC crossover region above the critical temperature within a T matrix formalism. By treating the mean-field like shift of the quasiparticle energies in a self-consistent manner, we avoid the known pathological behavior of the standard Nozieres-Schmitt-Rink approach in the polarized case, i.e., the polarization has the right sign and the spin polarizability is positive. The momentum distributions of the correlated system are computed and it is shown that, in the zero-temperature limit, they satisfy the Luttinger theorem. Results for the phase diagram, the spin susceptibility, and the compressibility are discussed.

Occupation numbers in strongly polarized Fermi gases and the Luttinger theorem

We study a two-component Fermi gas that is so strongly polarized that it remains normal fluid at zero temperature. We calculate the occupation numbers within the particle-particle random-phase approximation, which is similar to the Nozieres-Schmitt-Rink approach. We show that the Luttinger theorem is fulfilled in this approach. We also study the change of the chemical potentials which allows us to extract, in the limit of extreme polarization, the polaron energy.

Production of Feshbach molecules induced by spin–orbit coupling in Fermi gases

The creation of Feshbach molecules by exploiting engineered spin–orbit coupling in a spin-polarized Fermi gas advances the experimental study of topological superfluidity in ultracold gases. The search for topological superconductors is a challenging task1,2. One of the most promising directions is to use spin–orbit coupling through which an s-wave superconductor can induce unconventional p-wave pairing in a spin-polarized metal3,4. Recently, synthetic spin–orbit couplings have been realized in cold-atom systems5,6,7,8,9,10,11,12,13,14,15,16 where instead of a proximity effect, s-wave pairing originates from a resonant coupling between s-wave molecules and itinerant atoms17. Here we demonstrate a dynamic process in which spin–orbit coupling coherently produces s-wave Feshbach molecules from a fully polarized Fermi gas, and induces a coherent oscillation between these two. This demonstrates experimentally that spin–orbit coupling does coherently couple singlet and triplet states, and implies that the bound pairs of this system have a triplet p-wave component, which can become a topological superfluid by further cooling to condensation and confinement to one dimension.

Energy, decay rate, and effective masses for a moving polaron in a Fermi sea: Explicit results in the weakly attractive limit

We study the properties of an impurity of mass M moving through a spatially homogeneous three-dimensional fully polarized Fermi gas of particles of mass m. In the weakly attractive limit, where the effective coupling constant and perturbation theory can be used, both for a broad and a narrow Feshbach resonance, we obtain an explicit analytical expression for the complex energy of the moving impurity up to order two included in g. This also gives access to its longitudinal and transverse effective masses , , as functions of the impurity wave vector K. Depending on the modulus of K and on the impurity-to-fermion mass ratio M/m we identify four regions separated by singularities in derivatives with respect to K of the second-order term of , and we discuss the physical origin of these regions. Remarkably, the second-order term of presents points of non-differentiability, replaced by a logarithmic divergence for M = m, when K is on the Fermi surface of the fermions. We also discuss the third-order contribution and relevance for cold-atom experiments.