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|As Contributors:||Miroslaw Brewczyk · Mariusz Gajda · Tomasz Karpiuk · Debraj Rakshit|
|Submitted by:||Brewczyk, Miroslaw|
|Submitted to:||SciPost Physics|
|Subject area:||Quantum Physics|
We study stability of a zero temperature mixture of attractively interacting degenerate bosons and spin-polarized fermions in the absence of confinement. We demonstrate that higher order corrections to the standard mean field energy of the system can lead to a formation of Bose-Fermi liquid droplets -- self-bound incompressible systems in a three-dimensional space. The stability analysis of the homogeneous system is supported by numerical simulations of finite systems by explicit inclusion of surface effects. Our results indicate that Bose-Fermi droplets can be realized experimentally.
1. The current manuscript certainly touches on a highly topical and interesting area. A feasible approach to dilute quantum droplets in free space was presented in just 2015 (for Bose-Bose mixtures ). Dilute dipolar gas droplets were observed in 2016 , and droplets of Bose-Bose mixtures very recently [3-4].
2. This submission appears to be the first work considering self-bound Bose-Fermi mixtures stabilized by Lee-Huang-Yang effects with only contact interactions.
3. The submission is clearly laid out.
1. The use of a single complex function to represent all of the fermions in this system is not physically reasonable. There are significant issues both for the ground state and for dynamics.
1. Ground state
In a dilute self-bound system there do not tend to be many bound states. For example Fig. 3(a) of  identifies in the order of 10 modes for fermionic impurities in a dipolar Bose droplet, and  identifies only a few modes for a Bose-Bose mixture. At most one fermion can occupy each bound state. Any additional fermions in addition to those in bound modes will occupy the continuum and escape from the mixture. Since the number of bound modes is small, each of them should be treated discretely, as  did for fermions trapped in a dipolar Bose droplet.
There will be a balance. The system needs to be deeply self-bound to have enough discrete modes below the energy cutoff at the continuum, but not so deeply bound that the density is too high. The loss from three-body interactions would then make the time-scales unfeasible in experiment.
The phase of a single Fermi wavefunction cannot generally be used to represent the dynamics of the fermions, as shown by Ref.  (with mapping from bosons).
The submission cites three papers related to the single Fermi wavefunction, two on very different systems (metal clusters and a single helium atom) and Ref. . The only comparison to experiment or other methods in Ref.  seems to be Fig. 1. The difference of the spin dipole mode from one (the non-interacting limit) is either small or the difference from one is comparable to the difference from experiment.
 D. S. Petrov, Phys. Rev. Lett. 115, 155302 (2015)
 M. Schmitt et al, Nature 539, 259 (2016)
 C. R. Cabrera et al, Science 359, 301 (2018)
 G. Semeghini et al, Phys. Rev. Lett. 120, 235301 (2018)
 M. Wenzel et al, Phys. Scr. 93 104004 (2018)
 K. K. Das, G. J. Lapeyre, and E. M. Wright, Phys. Rev. A 65, 063603 (2002)
 P. T. Grochowski et al, Phys. Rev. Lett. 119, 215303 (2017)
1. Use a methodology that allows for the small number of discrete modes available to the fermions.
2. With that methodology show the bounds on the number of bosons and fermions for a droplet to exist and how that varies with interaction strength.
3. For reasonable interaction strengths, then give corresponding peak densities in SI units to allow comment on three-body loss.
1- The topic is interesting and timely.
1-The methods used are not valid to describe fermion dynamics.
2-The methods used are not valid to describe fermions in self-bound droplets.
This manuscript theoretically investigates the possibility of self-bound Bose-Fermi droplets. It begins with an infinite uniform system analysis then moves to the finite self-bound droplet. Later, dynamic simulations are considered to test droplet stability, and droplet preparation. I do not recommend this manuscript for publication because the methods employed are inappropriate to describe the system studied.
Self-bound droplets typically support only a small number of bound states, usually a tiny percentage of the total atom number, see Petrov, PRL 115, 155302 (2015), Wenzel et al., Physica Scripta 93, 104004 (2018), and Baillie et al., PRL 119, 255302 (2017). While this is not a problem for the bosons, only one fermion can occupy each bound state. If the number of fermions exceeds the number of bound states then the excess fermions must be unbound, which will affect the stability of the entire droplet. The model in the present manuscript doesn’t account for this crucial physics, nor do they consider how the ratio of fermion number to bound state number behaves in the thermodynamic limit. Therefore, the authors cannot claim that their results are physically relevant for either the finite or uniform systems. Such considerations must be a central focus for any paper considering the self-bound nature of Bose-Fermi droplets, as was demonstrated in the paper on Bose-Fermi droplets with dipolar interactions by the Pfau group: Physica Scripta 93, 104004 (2018).
Furthermore, for the section on finite systems, the small numbers of fermions expected (typically 10s of bound states) should instead be treated as discrete modes, as was done in the paper by the Pfau group: Physica Scripta 93, 104004 (2018). Even if the fermion number was large, any continuous treatment (e.g. local density approximation) of the fermions would require a high energy cutoff (at zero energy) so that only the bound fermion states are included within the droplet.
Another significant problem is that Eq. (10) is inappropriate to describe the dynamics of fermions. Equation (10) attempts to describe all fermions within a single pseudo wavefunction. However, it is well-known that this is unphysical for describing dynamics. What would be the physical interpretation of the ‘phase’ of the fermion wavefunction? The unphysical effects on the dynamics from assigning a ‘phase’ to a single wavefunction to describe many fermions has already been clearly addressed in the literature. For example, the paper by Girardeau et al. PRL 84, 5239 (2000), which considers fermionized bosons, focusses quite a lot on this point. For another example see Kunal et al. PRA 65, 063603 (2002).