Quasiparticle decay in a one-dimensional Bose-Fermi mixture

Abstract

In a one-dimensional weakly interacting Bose-Fermi mixture one branch of elementary excitations is well described by the Bogoliubov spectrum. Here we use the microscopic theory to study the decay of such quasiparticle excitations. The main scattering process which leads to their decay is the backscattering of a Bogoliubov quasiparticle off the Fermi sea, where a particle-hole pair is excited. For a low-momentum quasiparticle (phonon) of momentum $q$, we find that the decay rate scales as $q^3$ provided $q$ is smaller than the Fermi momentum $k_F$, while in the opposite case the decay behaves as $q^2$. If the ratio of the masses of fermions and bosons equals to the ratio of the boson-fermion and the boson-boson interaction strengths, the decay rate changes dramatically. It scales as $q^7$ for $q<k_F$ while we find $q^6$ scaling at $q>k_F$. For a high momentum Bogoliubov quasiparticle, we find a constant decay rate for $q<k_F$, while it scales as $1/q$ for $q>k_F$. We also find an analytic expression for the decay rate in the crossover region between low and high momenta. The decay rate is a continuous, but nonanalytic function of the momentum at $q=k_F$. In the special case when the parameters of our system correspond to the integrable model, we observe that the decay rate vanishes.

14 pages

References in corpus (40)

• Many-Body Physics with Ultracold Gases
• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• A quasi-pure Bose-Einstein condensate immersed in a Fermi sea
• Fermi gases in one dimension: From Bethe Ansatz to experiments
• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Two-species mixture of quantum degenerate Bose and Fermi gases
• A two atomic species superfluid
• A Mixture of Bose and Fermi Superfluids
• Instabilities in binary mixtures of one-dimensional quantum degenerate gases
• Luttinger liquid of polarons in one-dimensional boson-fermion mixtures
• Interaction-driven Dynamics of 40K / 87Rb Fermi-Bose Gas Mixtures in the Large Particle Number Limit
• Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
• Measurement of the interaction strength in a Bose-Fermi mixture with 87Rb and 40K
• Phase diagram of Bose-Fermi mixtures in one-dimensional optical lattices
• Exactly solvable case of a one-dimensional Bose-Fermi mixture
• Bose-Fermi Mixtures in One Dimension
• Applications of exact solution for strongly interacting one dimensional bose-fermi mixture: low-temperature correlation functions, density profiles and collective modes
• Fermionic Quasiparticle Representation of Tomonaga-Luttinger Hamiltonian
• Exact solution for the degenerate ground-state manifold of a strongly interacting one-dimensional Bose-Fermi mixture
• Energy relaxation and thermalization of hot electrons in quantum wires
• Relaxation of a high-energy quasiparticle in a one-dimensional Bose gas
• Exact results for the 1D interacting mixed Bose-Fermi gas
• Quantum decay of dark solitons in one dimensional Bose systems
• Correlation functions of one-dimensional Bose-Fermi mixtures
• Phase diagrams of one-dimensional Bose-Fermi mixtures of ultra-cold atoms
• Pairing of 1D Bose-Fermi mixtures with unequal masses
• One-dimensional superfluid Bose-Fermi mixture: mixing, demixing and bright solitons
• Thermalization of acoustic excitations in a strongly interacting one-dimensional quantum liquid
• Decay of fermionic quasiparticles in one-dimensional quantum liquids
• Magnetic ordering and quantum statistical effects in strongly repulsive Fermi-Fermi and Bose-Fermi mixtures
• Thermalization of nonequilibrium electrons in quantum wires
• Mixing-demixing transition in one-dimensional boson-fermion mixtures
• Relaxation in Luttinger liquids: Bose-Fermi duality
• Strongly interacting Bose-Fermi mixtures in one dimension
• Decay of Bogoliubov excitations in one-dimensional Bose gases
• Competition of superfluidity and density waves in one-dimensional Bose-Fermi mixtures
• Relaxation of weakly interacting electrons in one dimension
• Decay of Bogoliubov quasiparticles in a nonideal one-dimensional Bose gas
• Quantum criticality of a one-dimensional Bose-Fermi mixture
• Equilibration in a chiral Luttinger liquid

Cited by in corpus (6)

• Induced pairing of fermionic impurities in a one-dimensional strongly correlated Bose gas
• Microscopic theory of the friction force exerted on a quantum impurity in one-dimensional quantum liquids
• Exact result for the polaron mass in a one-dimensional Bose gas
• Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture
• Dispersion relation of a polaron in the Yang-Gaudin Bose gas
• Relaxation dynamics of a mobile impurity injected into a one-dimensional Bose gas