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Register a new userVirial coefficients for Bose and Fermi trapped gases beyond the unitary limit: an S-Matrix approach
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We study the virial expansion for three-dimensional Bose and Fermi gases at finite temperature using an approximation that only considers two-body processes and is valid for high temperatures and low densities. The first virial coefficients are computed and the second is exact. The results are obtained for the full range of values of the scattering length and the unitary limit is recovered as a particular case. A weak coupling expansion is performed and the free case is also obtained as a proper limit. The influence of an anisotropic harmonic trap is considered using the Local Density Approximation - LDA, analytical results are obtained and the special case of the isotropic trap is discussed in detail.
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Using a coarse temporal lattice approximation, we calculate the first few terms of the virial expansion of a three-species fermion system with a three-body contact interaction in $d$ spatial dimensions, both in homogeneous space as well as in a harmonic trapping potential of frequency $omega$. Using the three-body problem to renormalize, we report analytic results for the change in the fourth- and fifth-order virial coefficients $Delta b_4$ and $Delta b_5$ as functions of $Delta b_3$. Additionally, we argue that in the $omega to 0$ limit the relationship $b_n^text{T} = n^{-d/2} b_n$ holds between the trapped (T) and homogeneous coefficients for arbitrary temperature and coupling strength (not merely in scale-invariant regimes). Finally, we point out an exact, universal (coupling- and frequency-independent) relationship between $Delta b_3^text{T}$ in 1D with three-body forces and $Delta b_2^text{T}$ in 2D with two-body forces.
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 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 ratios of the spin-down and spin-up fermions greater than three. The extent of the inhomogeneous phase in parameter space increases with increasing mass imbalance.
The Hartree energy shift is calculated for a unitary Fermi gas. By including the momentum dependence of the scattering amplitude explicitly, the Hartree energy shift remains finite even at unitarity. Extending the theory also for spin-imbalanced systems allows calculation of polaron properties. The results are in good agreement with more involved theories and experiments.
We work out the effective scaling approach to frictionless quantum quenches in a one-dimensional Bose gas trapped in a harmonic trap. The effective scaling approach produces an auxiliary equation for the scaling parameter interpolating between the noninteracting and the Thomas-Fermi limits. This allows us to implement a frictionless quench by engineering inversely the smooth trap frequency, as compared to the two-jump trajectory. Our result is beneficial to design the shortcut-to-adiabaticity expansion of trapped Bose gases for arbitrary values of interaction, and can be directly extended to the three-dimensional case.
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