Most recently, path integral molecular dynamics (PIMD) has been successfully applied to perform simulations of identical bosons and fermions by B. Hirshberg et al.. In this work, we demonstrate that PIMD can be developed to calculate Green's function and extract momentum distribution for spin-polarized fermions. In particular, we show that the momentum distribution calculated by PIMD has potential application to numerous quantum systems, such as cold atom simulation of Mott insulator in Fermi-Hubbard model.
We analyze the collision of three identical spin-polarized fermions at zero collision energy, assuming arbitrary finite-range potentials, and define the corresponding three-body scattering hypervolume $D_F$. The scattering hypervolume $D$ was first defined for identical bosons in 2008 by one of us. It is the three-body analog of the two-body scattering length. We solve the three-body Schrödinger equation asymptotically when the three fermions are far apart or one pair and the third fermion are far apart, deriving two asymptotic expansions of the wave function. Unlike the case of bosons for whi…
The spectrum of collective excitations of degenerate partially polarized spin-1/2 fermions is considered. The spin-up fermions and the spin-down fermions are considered as different fluids. Corresponding two-fluid hydrodynamics consistent with a non-linear Pauli equation is suggested. An equation of state for the spin current caused by the distribution of particles on different energy levels is suggested for the degenerate regime, where the spin current is caused by the Pauli blocking. Spectrum of three waves is found as a solution of the hydrodynamic equations: two sound waves and one spin wa…
We study ultracold fermionic atoms trapped in a three dimensional optical lattice by combining the real-space dynamical mean-field approach with continuous-time quantum Monte Carlo simulations. For a spin-unpolarized system we show results the density and pair potential profile in the trap for a range of temperatures. We discuss how a polarized superfluid state is spatially realized in the spin-polarized system with harmonic confinement at low temperatures and present the local particle density, local magnetization, and pair potential.
In the present paper we investigate the Tonks-Girardeau gas confined in a harmonic trap at finite temperature with thermal Bose-Fermi mapping method. The pair distribution, density distribution, reduced one-body density matrix, the occupations number of natural orbitals, and momentum distribution are evaluated. In the whole temperature regime the pair distribution and density distribution exhibit the same properties as those of polarized free Fermions because both of them depend on the modulus of wavefunction rather than wavefunction. While the reduced one-body density matrix, the natural orbi…
Motivated by a recent experiment at MIT, we consider the collision of two clouds of spin-polarized atomic Fermi gases close to a Feshbach resonance. We explain why two dilute gas clouds, with underlying attractive interactions between their constituents, bounce off each other in the strongly interacting regime. Our hydrodynamic analysis, in excellent agreement with experiment, gives strong evidence for a metastable many-body state with effective repulsive interactions.
We study by Monte Carlo methods the thermodynamics of a spin polarized gas of non-relativistic fermions in 1+1 dimensions. The main result of this work is that our action suffers no significant sign problem for any spin polarization in the region relevant for dilute degenerate fermi gases. This lack of sign problem allows us to study attractive spin polarized fermions non-perturbatively at spin polarizations not previously explored. For some parameters values we verify results previously obtained by methods which include an uncontrolled step like complex Langevin and/or analytical continuation…
We study inelastic two-body relaxation in a spin-polarized ultracold Fermi gas in the presence of a p-wave Feshbach resonance. It is shown that in reduced dimensionalities, especially in the quasi-one-dimensional case, the enhancement of the inelastic rate constant on approach to the resonance is strongly suppressed compared to three dimensions. This may open promising paths for obtaining novel many-body states.
We study the exact dynamics of a one-dimensional spin-polarized gas of fermions in a double-well potential at zero and finite temperature. Despite the system is made of non-interacting fermions, its dynamics can be quite complex, showing strongly aperiodic spatio-temporal patterns during the tunneling. The extension of these results to the case of mixtures of spin-polarized fermions in interaction with self-trapped Bose-Einstein condensates (BECs) at zero temperature is considered as well. In this case we show that the fermionic dynamics remains qualitatively similar to the one observed in abs…
I discuss the advantages and disadvantages of several procedures, some known and some new, for constructing stationary states within the mean field approximation for a system with pairing correlations and unequal numbers spin-up and spin-down fermions, using the two chemical potentials framework. One procedure in particular appears to have significant physics advantages over previously suggested in the literature computational frameworks. Moreover, this framework is applicable to study strongly polarized superfluid fermion systems with arbitrarily large polarizations and with arbitrary total p…
We study quantum degenerate Fermi gases of ${^6}$Li atoms at high densities ($10^{15}$ cm$^{-3}$) and observe elastic and inelastic $p$-wave collisions far away from any Feshbach resonance. $P$-wave evaporation reaches temperatures of $T/T_F=0.42$ partially limited by the slow transfer of energy from high to low velocities through $p$-wave collisions. Via cross-dimensional thermalization, the $p$-wave background scattering volume is determined to be $\lvert V_p \rvert =(39^{+1.3}_{-1.6}a_0)^3$. $P$-wave dipolar relaxation creates a metastable mixture of the lowest and highest hyperfine states.
The effective field theory approach simplifies the perturbative computation of the ground state energy of the diluted gas of fermions allowing in the case of the unpolarized system to easily re-derive the classic results up to the $(k_{\rm F}a_0)^2$ order (where $k_{\rm F}$ is the system's Fermi momentum and $a_0$ the $s$-wave scattering length) and (with more labour) to extend it up to the order $(k_{\rm F}a_0)^4$. The corresponding expansion of the ground state energy of the polarized gas of spin $1/2$ fermions is known analytically (to our best knowledge) only up to the $k_{\rm F}a_0$ (wher…
Usually, hydrodynamic equations are restricted by the continuity and Euler equations. However, the account of the higher moments of the distribution function gives better description of the kinetic properties. Therefore, the pressure tensor evolution equation (PTEE) is derived for spin polarized degenerate fermions. Moreover, it is found that the pressure tensor enters the interaction term generalizing the p-wave interaction in the Euler equation. Hence, the PTEE allows to give a more accurate description of the interaction in Euler equation. Next, the interaction is calculated for the PTEE. T…
Repulsive Bose-Einstein condensate, where the short-range interaction is included up to the third order by the interaction radius, demonstrates existence of a bright soliton in a narrow interval of parameters. This soliton is studied here for the boson-fermion mixture, where spin-1/2 fermions are consider in the regime of full spin polarization. Influence of fermions via the boson-fermion interaction is considered up to the third order by the interaction radius. Fermions themselves are considered by hydrodynamic model including the pressure evolution equation. Interaction between fermions is c…
We report the results of the computation of the order $(k_{\rm F}a_0)^2$ correction, where $k_{\rm F}=3π^2ρ$ is the Fermi wave vector and $a_0$ the $s$-wave scattering length of the repulsive interaction, to the ground-state energy of a mixture of oppositely polarized $N_a$ spin $1/2$ fermions $a$ of masses $m_a$ and $N_b$ spin $1/2$ fermions $b$ of masses $m_b$ ($ρ=N/V$, $N=N_a+N_b$). It is shown that the results of the paper \cite{FraPil} in which the same correction has been computed entirely numerically, using a more traditional approach, can be easily and semianalytically reproduced using…
We study the tunneling of a spin polarized Fermi gas in a three-dimensional double well potential, focusing on the time dynamics starting from an initial state in which there is an imbalance in the number of particles in the two wells. Although fermions in different doublets of the double well tunnel with different frequencies, we point out that (incoherent) oscillations of a large number of particles can arise, as a consequence of the presence of transverse degrees of freedom. Estimates of the doublet structure and of the occupation of transverse eigenstates for a realistic experimental setup…
In this paper we analytically investigate the ground-state properties of a two-dimensional polarized degenerate Fermi gas in a high-finesse optical cavity, which is governed by a generalized Fermi-Dicke model with tunable parameters. By solving the photon-number dependent Bogoliubov-de-Gennes equation, we find rich quantum phases and phase diagrams, which depend crucially on the fermion-photon coupling strength, the fermion-fermion interaction strength, and the atomic resonant frequency (effective Zeeman field). In particular, without the fermion-fermion interaction and with a weak atomic reso…
Using the asymptotic Bethe Ansatz, we obtain an exact solution of the many-body problem for 1D spin-polarized fermions with resonant p-wave interactions, taking into account the effects of both scattering volume and effective range. Under typical experimental conditions, accounting for the effective range, the properties of the system are significantly modified due to the existence of "shape" resonances. The excitation spectrum of the considered model has unexpected features, such as the inverted position of the particle- and hole-like branches at small momenta, and roton-like minima. We find …
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 diffu…
We consider a one-dimensional gas of spin-1/2 fermions interacting through $δ$-function repulsive potential of an arbitrary strength. For the case of all fermions but one having spin up, we calculate time-dependent two-point correlation function of the spin-down fermion. This impurity Green's function is represented in the thermodynamic limit as an integral of Fredholm determinants of integrable linear integral operators.
We present a nonperturbative computation of the equation of state of polarized, attractively interacting, nonrelativistic fermions in one spatial dimension at finite temperature. We show results for the density, spin magnetization, magnetic susceptibility, and Tan's contact. We compare with the second-order virial expansion, a next-to-leading-order lattice perturbation theory calculation, and interpret our results in terms of pairing correlations. Our lattice Monte Carlo calculations implement an imaginary chemical potential difference to avoid the sign problem. The thermodynamic results on th…
A possibility of the hydrodynamic description of ultracold fermions via the microscopic derivation of the model is described. Differently truncated hydrodynamic models are derived and compared. All models are based on the microscopic many-particle Schrödinger equation. Minimal coupling model based on the continuity and Euler equations are considered. The extended hydrodynamic model including the independent dynamics of the momentum flux (the pressure evolution) is derived. Influence of the spin polarization is described. The short-range interaction is considered in the isotropic limit. The int…
We define the three-body scattering hypervolume $D_F$ for identical spin-polarized fermions in two dimensions, by considering the wave function of three such fermions colliding at zero energy and zero orbital angular momentum. We derive the asymptotic expansions of such a wave function when three fermions are far apart or one pair and the third fermion are far apart, and $D_F$ appears in the coefficients of such expansions. For weak interaction potentials, we derive an approximate formula of $D_F$ by using the Born expansion. We then study the shift of energy of three such fermions in a large …
We investigate a two-component atomic Fermi gas with population imbalance in the presence of Rashba-type spin-orbit coupling (SOC). As a competition between SOC and population imbalance, the finite-temperature phase diagram reveals a large varieties of new features, including the expanding of the superfluid state regime and the shrinking of both the phase separation and the normal regimes. For sufficiently strong SOC, the phase separation region disappears, giving way to the superfluid state. We find that the tricritical point moves toward regime of low temperature, high magnetic field, and hi…
We study the BCS gap equation for a Fermi gas with unequal population of spin-up and spin-down states. For $\cosh(δ_μ/T) \leq 2$, with $T$ the temperature and $δ_μ$ the chemical potential difference, the question of existence of non-trivial solutions can be reduced to spectral properties of a linear operator, similar to the unpolarized case studied previously in \cite{FHNS,HHSS,HS}. For $\cosh(δ_μ/T) > 2$ the phase diagram is more complicated, however. We derive upper and lower bounds for the critical temperature, and study their behavior in the small coupling limit.
Recent groundbreaking experiments studying the effects of spin polarization on pairing in unitary Fermi gases encountered mutual qualitative and quantitative discrepancies which seem to be a function of the confining geometry. Using novel numerical algorithms we study the solution space for a 3-dimensional fully self-consistent formulation of realistic systems with up to $10^{5}$ atoms. A study of the three types of solutions obtained demonstrates a tendency towards metastability as the confining geometry is elongated. One of these solutions, which is consistent with Rice experiments at high t…
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 …
We calculate the finite-temperature density and polarization equations of state of one-dimensional fermions with a zero-range interaction, considering both attractive and repulsive regimes. In the path-integral formulation of the grand-canonical ensemble, a finite chemical potential asymmetry makes these systems intractable for standard Monte Carlo approaches due to the sign problem. Although the latter can be removed in one spatial dimension, we consider the one-dimensional situation in the present work to provide an efficient test for studies of the higher-dimensional counterparts. To overco…
We study in a nonperturbative fashion the thermodynamics of a unitary Fermi gas over a wide range of temperatures and spin polarizations. To this end, we use the complex Langevin method, a first principles approach for strongly coupled systems. Specifically, we show results for the density equation of state, the magnetization, and the magnetic susceptibility. At zero polarization, our results agree well with state-of-the art results for the density equation of state and with experimental data. At finite polarization and low fugacity, our results are in excellent agreement with the third-order …
We investigate a two-component Fermi gas with unequal spin populations along the BCS-BEC crossover. By using the extended BCS equations and the concept of off-diagonal-long-range-order we derive a formula for the condensate number of Cooper pairs as a function of energy gap, average chemical potential, imbalance chemical potential and temperature. Then we study the zero-temperature condensate fraction of Cooper pairs by varying interaction strength and polarization, finding a depletion of the condensate fraction by increasing the population imbalance. We also consider explicitly the presence o…
We address the phase of a highly polarized Fermi gas across a narrow Feshbach resonance starting from the problem of a single down spin fermion immersed in a Fermi sea of up spins. Both polaron and pairing states are considered using the variational wave function approach, and we find that the polaron to pairing transition will take place at the BCS side of the resonance, strongly in contrast to a wide resonance where the transition is located at the BEC side. For pairing phase, we find out the critical strength of repulsive interaction between pairs above which the mixture of pairs and fermio…
We show that the strongly spin-orbit coupled materials Bi2Te3 and Sb2Te3 (first non-Bi topological insulator) and their derivatives belong to the Z2 (Time-Reversal-Protected, elastic backscattering suppressed) topological-insulator class. Using a combination of first-principles theoretical calculations and photoemission spectroscopy, we directly show that Bi2Te3 is a large spin-orbit-induced indirect bulk band gap (about 150 meV) semiconductor whose surface is characterized by a single topological spin-Dirac cone. The electronic structure of self-doped Sb2Te3 exhibits similar Z2 topological pr…
