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arXiv:1510.06525 · Physical Review A

Spectral properties of the Goldstino in supersymmetric Bose-Fermi mixtures

Jean-Paul Blaizot, Yoshimasa Hidaka, Daisuke Satow

Published Dec 22, 2015• 15 citations
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Abstract

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.

DOI
10.1103/physreva.92.063629

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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 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 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 investigate nearly degenerate Bose-Fermi mixtures and show that the breaking of generalized supersymmetry (gSUSY) between bosons and fermions, with up to two internal states, manifests itself through the emergence of fermionic Goldstino modes with up to four flavors. In particular, we draw a distinction between typical supersymmetry (SUSY), where bosons have pseudospin 0 and fermions have pseudospin 1/2, and inverse supersymmetry (iSUSY), where bosons have pseudospin 1/2 and fermions have pseudospin 0. In such systems, we highlight that the Goldstino pseudospin is carried by either its constituent fermion (SUSY) or boson (iSUSY). We then distinguish between these two cases by depicting their differing effects on the spectral functions of the bosonic and fermionic atomic species. Lastly, we propose radio-frequency- or microwave-spectroscopy experiments, analogous to momentum (angular) resolved photoemission in condensed matter physics, to measure the pseudospin-dependent spectral functions and detect the emergence of Goldstino modes in mixtures of 39^{39}39K and 40^{40}40K.
In the presence of nonrelativistic supersymmetry, a sharp fermionic collective mode similar to the Goldstino mode in high-energy physics was proposed to be realized in Bose-Fermi mixtures. The Goldstino mode is relaxed (a.k.a. decays) if supersymmetry is explicitly broken, which can be revealed as the broadening of the corresponding spectral function. We find that the situation shares many similarities with the electron spin resonance in magnetic systems and adopt the well-known Kubo-Tomita theory to perform a general analysis of the spectral function lineshape broadening of the Goldstino mode.
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.
In the presence of nonrelativistic supersymmetry, a sharp fermionic collective mode similar to the Goldstino mode in high-energy physics was proposed to be realized in Bose-Fermi mixtures. The Goldstino mode is relaxed (i.e., decays) if supersymmetry is explicitly broken, which can be revealed as the broadening of the corresponding spectral function. We find that the situation shares many similarities with the electron-spin resonance in magnetic systems and adopt the well-known Kubo-Tomita theory to perform a general analysis of the spectral-function line-shape broadening of the Goldstino mode.