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arXiv:1707.05634 · Physical Review A

Goldstino in supersymmetric Bose-Fermi mixtures in the presence of a Bose-Einstein condensate

Jean-Paul Blaizot, Yoshimasa Hidaka, Daisuke Satow

Published Dec 19, 2017• 15 citations
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Abstract

We analyze the spectral properties of the Goldstino excitation in a Bose-Fermi mixture of cold atoms, whose masses and interaction strengths are tuned so that the Hamiltonian is supersymmetric. We consider systems at zero temperature and assume that, in the weak-coupling regime, the fermions form a Fermi sea, while the bosons form a Bose-Einstein condensate. We study the excitation spectrum within a simple extension of the random phase approximation, taking into account the mixing between the supercharge and the fermion caused by the condensate. This mixing affects the fermion spectrum strongly. We argue that the corresponding modification of the fermion spectrum, and the associated fermion distribution in momentum space, could be accessible experimentally and potentially allow for a determination of the Goldstino properties.

DOI
10.1103/physreva.96.063617

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We analyze the spectral properties of the Goldstino excitation in a Bose-Fermi mixture of cold atoms, whose masses and interaction strengths are tuned so that the Hamiltonian is supersymmetric. We consider systems at zero temperature and assume that, in the weak-coupling regime, the fermions form a Fermi sea, while the bosons form a Bose-Einstein condensate. We study the excitation spectrum within a simple extension of the random phase approximation, taking into account the mixing between the supercharge and the fermion caused by the condensate. This mixing affects the fermion spectrum strongly. We argue that the corresponding modification of the fermion spectrum, and the associated fermion distribution in momentum space, could be accessible experimentally and potentially allow for a determination of the Goldstino properties.
We evaluate the spectral properties of the Goldstino in a Bose-Fermi mixture of cold atoms and molecules whose dynamics is governed by a supersymmetric Hamiltonian. Model-independent results are obtained from sum rules obeyed by the spectral function. We carry out specific calculations, at zero and finite temperature, using the random-phase approximation, and obtain in particular analytic expressions for the dispersion relation at low momentum. These explicit calculations allow us to pin down more precisely the features of the Goldstino that can be attributed to the supersymmetry alone, together with its spontaneous breaking. The anomalous large effect of the Fermi sea at moderate and large momenta is emphasized.
We theoretically investigate a supersymmetric collective mode called the Goldstino in a Bose-Fermi mixture.The explicit supersymmetry breaking, which is unavoidable in cold-atom experiments, is considered.We derive the Gell-Mann-Oakes-Renner (GOR) relation for the Goldstino, which gives the relation between the energy gap at zero momentum and the explicit breaking term.We also numerically evaluate the gap of the Goldstino above the Bose-Einstein condensation temperature within the random phase approximation (RPA).While the gap obtained from the GOR relation coincides with that in the RPA for the mass-balanced system, there is a deviation from the GOR relation in the mass-imbalanced system.We point out that the deviation becomes large when the Goldstino pole is close to the branch point, although it is parametrically a higher order with respect to the mass-imbalanced parameter.To examine the existence of the Goldstino pole in realistic cold atomic systems, we show how the mass-imbalance effect appears in 6 Li -7 Li, 40 K -41 K, and 173 Yb -174 Yb mixtures.Furthermore, we analyze the Goldstino spectral weight in a 173 Yb -174 Yb mixture with realistic interactions and show a clear peak due to the Goldstino pole.As a possibility to observe the Goldstino spectrum in cold-atom experiments, we discuss the effects of the Goldstino pole on fermionic single-particle excitation as well as the relationship between the GOR relation and Tan's contact.
We theoretically investigate the tunneling transport in a repulsively interacting ultracold Bose-Fermi mixture. A two-terminal model is applied to such a mixture, and the supersymmetry-like tunneling current through the junction can be induced by the bias of the fermion chemical potential between two reservoirs. The goldstino, which is the Nambu-Goldstone fermionic mode associated with the spontaneous sypersymmetry breaking and appears as a gapped mode in the presence of the explicit supersymmetry breaking in existing Bose-Fermi mixtures, is found to contribute to the tunneling transport as a supercharge exchanging process. Our study provides a potential way to detect the goldstino transport in cold atom experiments.
We investigate the fermion spectrum within the Bose–Fermi–Hubbard model used for the description of boson-fermion mixtures of ultra-cold atoms in optical lattices. We used the method based on the Hubbard operator approach for an on-site basis. The equation for fermion Green’s function in the Bose–Fermi–Hubbard model is built; Green’s functions of higher orders are decoupled in the Hubbard-I approximation (the case of the strong on-site interaction). The corresponding spectral densities are calculated. In the case of hard-core bosons, the condition of appearance of additional bands in the fermion spectrum is investigated. It is shown that these bands exist only in the state with a Bose–Einstein condensate and appear because of the mixing of states with different numbers of bosons. These additional bands can be interpreted as a manifestation of composite excitations (when the appearance of a fermion on the site is accompanied by the simultaneous creation (or annihilation) of a boson).
Supersymmetry is assumed to be a basic symmetry of the world in many high-energy theories, but none of the superpartners of any known elementary particle have been observed yet. We argue that supersymmetry can also be realized and studied in ultracold atomic systems with a mixture of bosons and fermions, with properly tuned interactions and single particle dispersion. We further show that in such nonrelativistic systems supersymmetry is either spontaneously broken or explicitly broken by a chemical potential difference between the bosons and fermions. In both cases the system supports a sharp fermionic collective mode similar to the Goldstino mode in high-energy physics, due to supersymmetry. We also discuss possible ways to detect this mode experimentally.
The mixture of the scalar bosonic and the spinless or polarized fermionic cold atoms in the one-dimensional optical lattice is studied. The system is modeled by the Bose-Fermi-Hubbard Hamiltonian, which shows different behavior from that of the Bose-Hubbard or the Fermi-Hubbard models. Because the $\text{SU}(1\ensuremath{\mid}1)$-supersymmetric Bethe ansatz solution gives an excellent approximation to this kind of mixed cold atomic systems, the ground-state properties of the system such as the densities of state in the momentum space are obtained based on the Bethe ansatz. If the number of bosons is equal to that of fermions and the filling factor is 1, it is found that there exists a critical on-site interaction Uc{U}_{c}Uc​. If U<UcU<{U}_{c}U<Uc​, the ground state of the system is in the superfluid phase, while if U>UcU>{U}_{c}U>Uc​, the ground state is in the insulating phase. The superfluid-insulator transition occurs at Uc{U}_{c}Uc​. From the analysis of the superfluid density, the value of the critical point is determined as Uc=2.79256{U}_{c}=2.79256Uc​=2.79256, which is larger than the Uc=0{U}_{c}=0Uc​=0 for the Fermi-Hubbard model and smaller than the Uc=3.28{U}_{c}=3.28Uc​=3.28 for the Bose-Hubbard model. The elementary excitations and effective Hamiltonian in the strong-coupling limit are also discussed.