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arXiv:1611.01143 · Physical review. B./Physical review. B

Quasiparticle decay in a one-dimensional Bose-Fermi mixture

Benjamin Reichert, Aleksandra Petković, Zoran Ristivojević

Published Jan 27, 2017• 7 citations
arXivHTMLPDF

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 is equal 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.

DOI
10.1103/physrevb.95.045426

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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 qqq, we find that the decay rate scales as q3{q}^{3}q3 provided qqq is smaller than the Fermi momentum kF{k}_{F}kF​, while in the opposite case the decay behaves as q2{q}^{2}q2. If the ratio of the masses of fermions and bosons is equal to the ratio of the boson-fermion and the boson-boson interaction strengths, the decay rate changes dramatically. It scales as q7{q}^{7}q7 for q<kFq<{k}_{F}q<kF​, while we find q6{q}^{6}q6 scaling at q>kFq>{k}_{F}q>kF​. For a high-momentum Bogoliubov quasiparticle, we find a constant decay rate for q<kFq<{k}_{F}q<kF​, while it scales as 1/q1/q1/q for q>kFq>{k}_{F}q>kF​. 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=kFq={k}_{F}q=kF​. In the special case when the parameters of our system correspond to the integrable model, we observe that the decay rate vanishes.
We study the decay of Bogoliubov quasiparticles in one-dimensional Bose gases. Starting from the hydrodynamic Hamiltonian, we develop a microscopic theory that enables one to systematically study both the excitations and their decay. At zero temperature, the leading mechanism of decay of a quasiparticle is disintegration into three others. We find that low-energy quasiparticles (phonons) decay with the rate that scales with the seventh power of momentum, whereas the rate of decay of the high-energy quasiparticles does not depend on momentum. In addition, our approach allows us to study analytically the quasiparticle decay in the whole crossover region between the two limiting cases. When applied to integrable models, including the Lieb-Liniger model of bosons with contact repulsion, our theory confirms the absence of the decay of quasiparticle excitations. We account for two types of integrability-breaking perturbations that enable finite decay: three-body interaction between the bosons and two-body interaction of finite range.
We study the relaxation of excitations in a system of one-dimensional weakly interacting bosons. Due to residual weak interactions, Bogoliubov quasiparticles in this system have finite lifetimes. As a result of the conservation laws in one dimension, at zero temperature the leading mechanism of decay of a quasiparticle is disintegration into three others. We focus on phonon quasiparticles and find that their decay rate is proportional to the seventh power of momentum. In the integrable case of contact interaction between the bosons, the decay rate vanishes.
We study the integrable model of one-dimensional bosons with contact repulsion. In the limit of weak interaction, we use the microscopic hydrodynamic theory to obtain the excitation spectrum. The statistics of quasiparticles changes with the increase of momentum. At lowest momenta good quasiparticles are fermions, while at higher momenta they are Bogoliubov bosons, in accordance with recent studies. In the limit of strong interaction, we analyze the exact solution and find exact results for the spectrum in terms of the asymptotic series. Those results undoubtedly suggest that fermionic quasiparticle excitations actually exist at all momenta for moderate and strong interaction and also at lowest momenta for arbitrary interaction. Moreover, at strong interaction we find highly accurate analytical results for several relevant quantities of the Lieb-Liniger model.
In this Letter, we study the effect of quasiparticle interactions in a Bose-Fermi superfluid mixture. We consider the lifetime of a quasiparticle of the Bose superfluid due to its interaction with quasiparticles in the Fermi superfluid. We find that this damping rate, i.e., the inverse of the lifetime, has quite a different threshold behavior at the BCS and the BEC side of the Fermi superfluid. The damping rate is a constant near the threshold momentum in the BCS side, while it increases rapidly in the BEC side. This is because, in the BCS side, the decay process is restricted by the constraint that the fermion quasiparticle is located near the Fermi surface, while such a restriction does not exist in the BEC side where the damping process is dominated by bosonic quasiparticles of the Fermi superfluid. Our results are related to the collective mode experiment in the recently realized Bose-Fermi superfluid mixture.
In the presence of dipolar interactions, the excitation spectrum of a Bose gas can acquire a local minimum.The corresponding quasiparticles are known as rotons.They are gapped and do not decay at zero temperature.Here we study the decay of rotons in one-dimensional Bose gases at low temperatures.It predominantly occurs due to the backscattering of thermal phonons on rotons.The resulting rate scales with the third power of temperature and is inversely proportional to the sixth power of the roton gap near the solidification phase transition.The hydrodynamic approach used here enables us to find the decay rate for quasiparticles at practically any momenta, with minimal assumptions on the exact form of the interparticle interactions.Our results are an essential prerequisite for the description of all the dissipative phenomena in dipolar gases and have direct experimental relevance.
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