Goldstino spectrum in an ultracold Bose-Fermi mixture with explicitly broken supersymmetry

Abstract

We theoretically investigate a supersymmetric collective mode called 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 the zero momentum and the explicit breaking term. We also numerically evaluate the gap of 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 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 the fermionic single-particle excitation as well as the relationship between the GOR relation and Tan's contact.

26 pages, 9 figures

References in corpus (24)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Quantum degenerate dipolar Fermi gas
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Two-color photoassociation spectroscopy of ytterbium atoms and the precise determinations of s-wave scattering lengths
• Feshbach resonances in ultracold K(39)
• Counting rule for Nambu-Goldstone modes in nonrelativistic systems
• Variational study of polarons in Bose-Einstein condensates
• All-Optical Formation of Quantum Degenerate Mixtures
• Double-degenerate Bose-Fermi mixture of strontium
• Exact Relations for a Strongly-interacting Fermi Gas near a Feshbach Resonance
• Potassium ground state scattering parameters and Born-Oppenheimer potentials from molecular spectroscopy
• Simulating Wess-Zumino Supersymmetry Model in Optical Lattices
• Supersymmetry and Goldstino-like Mode in Bose-Fermi Mixtures
• Counting rule of Nambu-Goldstone modes for internal and spacetime symmetries: Bogoliubov theory approach
• Connecting few-body inelastic decay to many-body correlations: a weakly coupled impurity in a resonant Fermi gas
• Dispersion relations of Nambu-Goldstone modes at finite temperature and density
• Correlated quantum dynamics of two quenched fermionic impurities immersed in a Bose-Einstein Condensate
• Direct evaporative cooling of 41K into a Bose-Einstein condensate
• Cold Atom Quantum Simulator for Dilute Neutron Matter
• Expansion of harmonically trapped interacting particles and time dependence of the contact
• Bose polaron in spherical trap potentials: Spatial structure and quantum depletion
• Relaxation of a Goldstino-like mode due to supersymmetry breaking in Bose-Fermi mixtures
• Equation of state and contact of a strongly interacting Bose gas in the normal state

Cited by in corpus (4)

• 1D Majorana Goldstinos and partial supersymmetry breaking in quantum wires
• Dispersive 1D Majorana modes with emergent supersymmetry in 1D proximitized superconductors via spatially-modulated potentials and magnetic fields
• Probing Goldstino excitation through the tunneling transport in a Bose-Fermi mixture with explicitly broken supersymmetry
• Fingerprints of supersymmetric spin and charge dynamics observed by inelastic neutron scattering