The strongly interacting bosonic and non-interacting fermionic mixtures of diluted gases are studied.An articial magnetic eld is introduced in theory by imposing a Peierls phase shift on the wave functions of the constituents.A highly nontrivial limit of the quantum-Hall limit is achieved which provides oscillations eects of the fermion mediated interaction between bosons.In consequence the eective interaction between bosons can change the magnitude and sign.This provides possible explanations of the bosonic coherence loss observed experimentally in the time of ight and peak width experiments.
The strongly interacting bosonic and non-interacting fermionic mixtures of diluted gases are studied.An articial magnetic eld is introduced in theory by imposing a Peierls phase shift on the wave functions of the constituents.A highly nontrivial limit of the quantum-Hall limit is achieved which provides oscillations eects of the fermion mediated interaction between bosons.In consequence the eective interaction between bosons can change the magnitude and sign.This provides possible explanations of the bosonic coherence loss observed experimentally in the time of ight and peak width experiments.
We study the mutually coupled, strongly interacting bosonic and noninteracting fermionic, species of unequal masses in the regime were the retardation effects are an important part of the physics. A cloud of neutral atoms experiences a synthetic magnetic field because of a vector potential that imposes a phase shift on the constituents. The magnetic field causes the oscillations of the magnitude and sign of the effective interaction between bosons from repulsive to attractive in contrast to the static case. We show that the dynamics for the gaseous Bose-Fermi mixtures when reaching the quantum-Hall regime becomes highly nontrivial.
We have studied eects of inter-species interaction of the bosons in a BoseFermi mixture over a large regime of particle numbers under the synthetic magnetic eld.Analytically derived formulas for the density of states for several values of the magnetic elds f = 1/2, 1/3, 1/4, 1/6, 1/8 and 3/8 allows us to calculate, with a very good accuracy, the eective interaction between bosons.The presence of the Hofstadter buttery spectrum and fermionic species induces alternating sign potential between neutral bosonic atoms.Consequently bosons can attract or repulse each other whether sign of it strongly depends on the strength of the magnetic eld applied to the sample.
The theory of composite fermion provides a simple and unified picture to understand a vast amount of phenomenology in the quantum Hall regime. However it has remained challenging to formulate this concept properly within a single Landau level, which provides the relevant degrees of freedom in the limit of strong magnetic field. Recently a low-energy noncommutative field theory for bosons at Landau-level filling factor $\ensuremath{\nu}=1$ has been formulated by Dong and Senthil [Z. Dong and T. Senthil, Phys. Rev. B 102, 205126 (2020)]. In the limit of long-wavelength and small-amplitude gauge fluctuation, they found it reduces to the celebrated Halperin-Lee-Read theory of a composite fermion liquid. In this work we consider a Bose-Fermi mixture at total filling factor $\ensuremath{\nu}=1$. Different from previous work, the number density of composite fermions in the mixture and corresponding Fermi momentum can be tuned by changing the filling factor of bosons, ${\ensuremath{\nu}}_{b}=1\ensuremath{-}{\ensuremath{\nu}}_{f}$. This tunability enables us to study the dilute limit ${\ensuremath{\nu}}_{b}\ensuremath{\ll}1$, which allows for a controlled and asymptotically exact calculation of the energy dispersion and effective mass of composite fermions. Furthermore, the approximation of the low-energy description by a commutative field theory is manifestly justified. Most importantly, we demonstrate that gauge fluctuations acquire a Higgs mass due to the presence of a composite boson condensate, as a result of which the system behaves like a genuine Landau- Fermi liquid. Combined with the irrelevance of four-fermion interaction in the dilute limit, we are able to obtain asymptotically exact properties of this composite fermion Fermi liquid. In the opposite limit of ${\ensuremath{\nu}}_{f}\ensuremath{\ll}1$, the Higgs mass goes to zero and we find crossover between Fermi liquid and non-Fermi liquid as temperature increases. Observing these properties either experimentally or numerically provides unambiguous evidence of not only the composite fermions and the Fermi surface they form, but also the presence of emergent gauge fields and their fluctuations due to strong correlation.
Interactions in an ultracold boson-fermion mixture are often manifested by elastic collisions. In a mixture of a condensed Bose gas (BEC) and spin polarized degenerate Fermi gas (DFG), fermions can mediate spin-spin interactions between bosons, leading to an effective long-range magnetic interaction analogous to Ruderman-Kittel-Kasuya-Yosida [Phys. Rev. 96, 99 (1954); Prog. Theor. Phys. 16, 45 (1956); Phys. Rev. 106, 893 (1957)] interaction in solids. We used Ramsey spectroscopy of the hyperfine clock transition in a ^{87}Rb BEC to measure the interaction mediated by a ^{40}K DFG. By controlling the boson density we isolated the effect of mediated interactions from mean-field frequency shifts due to direct collision with fermions. We measured an increase of boson spin-spin interaction by a factor of η=1.45±0.05^{stat}±0.13^{syst} in the presence of the DFG, providing clear evidence of spin-spin fermion mediated interaction. Decoherence in our system was dominated by inhomogeneous boson density shift, which increased significantly in the presence of the DFG, again indicating mediated interactions. We also measured a frequency shift due to boson-fermion interactions in accordance with a scattering length difference of a_{bf_{2}}-a_{bf_{1}}=-5.36±0.44^{stat}±1.43^{syst}a_{0} between the clock-transition states, a first measurement beyond the low-energy elastic approximation [R. Côté, A. Dalgarno, H. Wang, and W. C. Stwalley, Phys. Rev. A 57, R4118 (1998); A. Dalgarno and M. Rudge, Proc. R. Soc. A 286, 519 (1965)] in this mixture. This interaction can be tuned with a future use of a boson-fermion Feshbach resonance. Fermion-mediated interactions can potentially give rise to interesting new magnetic phases and extend the Bose-Hubbard model when the atoms are placed in an optical lattice.
The ground-state phase diagram of mixtures of spin polarized fermions and bosons in a 1D periodic lattice is discussed in the limit of large fermion hopping and half filling of the fermions. Numerical simulations performed with the density matrix renormalization group (DMRG) show in addition to bosonic Mott insulating (MI), superfluid (SF), and charge density-wave phases (CDW) a yet unreported phase with spatial separation of MI and CDW regions. We derive an effective bosonic theory which allows for a complete understanding and quantitative prediction of the bosonic phase diagram. In particular the origin of CDW phase and the MI-CDW phase separation is revealed as an effective fermion-mediated long-range interaction between bosons with alternating sign.
Quantitative theory of composite fermions in Bose-Fermi mixtures at ν=1.
Composite fermion provides a simple and unified picture to understand a vast amount of phenomenology in the quantum Hall regime. However it has remained challenging to formulate this concept properly within a single Landau level. Recently a low-energy noncommutative field theory for bosons at Landau-level filling factor ν=1 has been formulated by Dong and Senthil. In the limit of long-wavelength and small-amplitude gauge fluctuation, they found it reduces to the celebrated Halperin-Lee-Read theory of composite fermion liquid. In this work we consider a Bose-Fermi mixture at total filling factor ν=1. Different from previous work, the number density of composite fermions in the mixture and corresponding Fermi momentum can be tuned by changing the filling factor of bosons, νb=1−νf. This tunability enables us to study the dilute limit νb≪1, which allows for a controlled and asymptotically exact calculation of the energy dispersion and effective mass of composite fermions. Furthermore, the approximation of the low-energy description by a commutative field theory is manifestly justified. Most importantly, we demonstrate gauge fluctuations acquire a Higgs mass due to the presence of a composite boson condensate, as a result of which the system behaves like a genuine Landau Fermi liquid. Combined with the irrelevance of four-fermion interaction in the dilute limit, we are able to obtain asymptotically exact properties of this composite fermion Fermi liquid. In the opposite limit of νf≪1, the Higgs mass goes to zero and we find crossover between Fermi liquid and non-Fermi liquid as temperature increases. Observing these properties either experimentally or numerically provides unambiguous evidence of not only the composite fermions and the Fermi surface they form, but also the presence of emergent gauge fields and their fluctuations due to strong correlation.