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arXiv:1504.08019 · Physical Review A

Supersymmetric waves in Bose-Fermi mixtures

Barry Bradlyn, Andrey Gromov

Published Mar 23, 2016• 15 citations
arXivHTMLPDF

Abstract

Interacting Bose-Fermi mixtures possess a fermionic (super)symmetry when bosons and fermions in the mixture have equal masses, and when the interaction strengths are appropriately tuned. This symmetry is spontaneously broken in the ground state of the mixture, leading to a novel Goldstone mode with fermionic statistics and quadratic dispersion. Here we examine the effect of explicit symmetry-breaking perturbations on the Goldstone mode. When the symmetry is not exact and the system is allowed to deviate from the symmetric point, we find that the Goldstone mode acquires an energy gap. We show that the excitations manifest themselves as a nonanalyticity of the thermodynamic pressure.

DOI
10.1103/physreva.93.033642

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Interacting Bose-Fermi mixtures possess a fermionic (super)symmetry when bosons and fermions in the mixture have equal masses, and when the interaction strengths are appropriately tuned. This symmetry is spontaneously broken in the ground state of the mixture, leading to a novel Goldstone mode with fermionic statistics and quadratic dispersion. Here we examine the effect of explicit symmetry-breaking perturbations on the Goldstone mode. When the symmetry is not exact and the system is allowed to deviate from the symmetric point, we find that the Goldstone mode acquires an energy gap. We show that the excitations manifest themselves as a nonanalyticity of the thermodynamic pressure.
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.
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 the superfluidity and the associated Nambu-Goldstone modes in a three-flavor atomic Fermi gas with SU(3)\mathrm{SU}(3)SU(3) global symmetry. The sss-wave pairing occurs in flavor antitriplet channel due to the Pauli principle, and the superfluid state contains both gapped and gapless fermionic excitations. Corresponding to the spontaneous breaking of the SU(3)\mathrm{SU}(3)SU(3) symmetry to a SU(2)\mathrm{SU}(2)SU(2) symmetry with five broken generators, there are only three Nambu-Goldstone modes, one is with linear dispersion law and two are with quadratic dispersion law. The other two expected Nambu-Goldstone modes become massive with a mass gap of the order of the fermion energy gap in a wide coupling range. The abnormal number of Nambu-Goldstone modes, the quadratic dispersion law, and the mass gap have significant effect on the low-temperature thermodynamics of the matter.
Bragg spectroscopy shows the evolution of gapless Goldstone modes and single-particle-like excitations in an atomic Fermi superfluid as it crosses from a Bardeen–Cooper–Schrieffer superfluid to the Bose–Einstein condensate regime. Spontaneous symmetry breaking is a central paradigm of elementary particle physics1, magnetism2, superfluidity3 and superconductivity4. According to Goldstone’s theorem, phase transitions that break continuous symmetries lead to the existence of gapless excitations in the long-wavelength limit5. These Goldstone modes can become the dominant low-energy excitation, showing that symmetry breaking has a profound impact on the physical properties of matter. Here, we present a comprehensive study of the elementary excitations in a homogeneous strongly interacting Fermi gas through the crossover from a Bardeen–Cooper–Schrieffer (BCS) superfluid to a Bose–Einstein condensate (BEC) of molecules using two-photon Bragg spectroscopy. The spectra exhibit a discrete Goldstone mode, associated with the broken-symmetry superfluid phase, as well as pair-breaking single-particle excitations. Our techniques yield a direct determination of the superfluid pairing gap and speed of sound in close agreement with strong-coupling theories.
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 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.