We explore the interaction between two trapped ions mediated by a surrounding quantum degenerate Bose or Fermi gas. Using perturbation theory valid for weak atom-ion interaction, we show analytically that the interaction mediated by a Bose gas has a power-law behavior for large distances whereas it has a Yukawa form for intermediate distances. For a Fermi gas, the mediated interaction is given by a power law for large density and by a Ruderman-Kittel-Kasuya-Yosida form for low density. For strong atom-ion interaction, we use a diagrammatic theory to demonstrate that the mediated interaction can be a significant addition to the bare Coulomb interaction between the ions, when an atom-ion bound state is close to threshold. Finally, we show that the induced interaction leads to substantial and observable shifts in the ion phonon frequencies.
We explore the interaction between two trapped ions mediated by a surrounding quantum degenerate Bose or Fermi gas. Using perturbation theory valid for weak atom-ion interaction, we show analytically that the interaction mediated by a Bose gas has a power-law behavior for large distances whereas it has a Yukawa form for intermediate distances. For a Fermi gas, the mediated interaction is given by a power law for large density and by a Ruderman-Kittel-Kasuya-Yosida form for low density. For strong atom-ion interaction, we use a diagrammatic theory to demonstrate that the mediated interaction can be a significant addition to the bare Coulomb interaction between the ions, when an atom-ion bound state is close to threshold. Finally, we show that the induced interaction leads to substantial and observable shifts in the ion phonon frequencies.
We describe recent theoretical and experimental developments on mediated interactions in mixtures of bosonic and fermionic atoms. We discuss how particle-hole excitations of a Fermi sea can induce long-range interactions between heavy impurities or atoms in a Bose-Einstein condensate. Conversely, phonon excitations of a Bose-Einstein condensate induce interactions between fermionic atoms. These mediated interactions exhibit different short-range and long-range scaling regimes with distance and, if strong enough, can induce fermion superfluidity. We discuss the prospects for observing new phenomena that could arise from mediated interactions. Experimentally, we outline recent studies of the 133Cs-6Li Bose-Fermi mixture, a platform well-suited for investigating fermion-mediated interactions. A Cs Bose-Einstein condensate immersed in a degenerate Li Fermi gas is prepared with tunable interspecies interactions. In the weak-coupling regime, precision measurements of condensate properties reveal fermion-mediated attractions between bosons, matching theoretical predictions. In the strong-coupling regime, we observe suppression and revival of sound modes and novel many-body resonances. Altogether, we aim to highlight both instances where experiment and theory agree well, and promising prospects to engineer long-range interactions in atomic quantum gases.
Motivated by recent surprising experimental findings, we develop a strong-coupling theory for Bose-Fermi mixtures capable of treating resonant interspecies interactions while satisfying the compressibility sum rule. We show that the mixture can be stable at large interaction strengths close to resonance, in agreement with the experiment, but at odds with the widely used perturbation theory. We also calculate the sound velocity of the Bose gas in the ^{133}Cs-^{6}Li mixture, again finding good agreement with the experimental observations both at weak and strong interactions. A central ingredient of our theory is the generalization of a fermion mediated interaction to strong Bose-Fermi scatterings and to finite frequencies. This further leads to a predicted hybridization of the sound modes of the Bose and Fermi gases, which can be directly observed using Bragg spectroscopy.
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.
We study a weakly interacting one-dimensional Bose gas with two impurities coupled locally to the boson density. We derive analytical results for the induced interaction between the impurities at arbitrary positive coupling and separation r. At $r\ensuremath{\lesssim}\ensuremath{\xi}$, where $\ensuremath{\xi}$ denotes the healing length of the Bose gas, the interaction is well described by the mean-field contribution. Its form changes as the coupling is increased, approaching a linear function of r at short distances in the regime of strong coupling. The mean-field contribution decays exponentially at arbitrary coupling for $r\ensuremath{\gg}\ensuremath{\xi}$. At such long distances, however, the effect of quantum fluctuations becomes important, giving rise to a long-ranged quantum contribution to the induced interaction. At longest distances it behaves as 1/r3, while at strong coupling we find an intermediate distance regime with a slower decay, 1/r. The quantum contribution in the crossover regime is also calculated. The induced interaction between impurities (i.e., polarons) is attractive and leads to the formation of their bound state, known as bipolaron. We discuss its binding energy.
The remarkable single-particle control of individual ions combined with the versatility of ultracold atomic gases makes hybrid ion-atom systems an exciting new platform for quantum simulation of few- and many-body quantum physics. Here, we study theoretically the properties of a mobile ion immersed in a quantum degenerate gas of fermionic atoms. Using an effective low-energy atom-ion interaction together with a well-established approach that includes exactly two-body correlations, we calculate the full spectral response of the ion and demonstrate the existence of several quasiparticle branches, which are charged analogs of the Fermi polaron observed in neutral atomic gases. Due to the long-range nature of the atom-ion interaction, these ionic Fermi polarons have several properties distinct from their neutral counterparts such as the simultaneous presence of several stable states and smooth transitions from repulsive to attractive polarons with increasing interaction strength. Surprisingly, the residue of the ionic polaron is shown to increase with the Fermi density for fixed interaction strength, which is in marked contrast with the neutral polaron. The properties of the ionic polaron approach that of the neutral polaron only in the low-density limit where the average interparticle spacing is larger than the characteristic length of the atom-ion interaction. We finally analyze the effects of the Fermi gas on the molecular ions, which are bound atom-dimer states.
Interactions between particles play an important role in quantum degenerate gases.\nIn fact, the system’s behavior is usually largely determined by the strength, range, and\nsymmetry of the interactions, even if very weak. For more than two decades after the\nfirst experimental realization of a Bose-Einstein condensate (BEC) in 1995, investigations of ultracold atomic gases have mainly considered contact-type interactions, which\nmodel the short-range van der Waals interactions between the atoms in terms of a single\nparameter, the s-wave scattering length. However, some atomic or molecules species\npossess a magnetic or electric dipole moment and additionally interact among each\nother via the dipole-dipole interaction (DDI), which is long-ranged and anisotropic.\nSignatures of the DDI have been first observed in a BEC of chromium atoms in 2005.\nIn the last several years, a new class of atoms from the lanthanide series, e.g., dysprosium and erbium, with stronger dipolar properties, have come into play. This permits\na more full-fledged study of dipolar effects in BECs. Furthermore, ultracold molecules\nand highly excited Rydberg atoms are other promising examples for futures studies of\nsystems where dipolar interaction will be even more dominant, but they still need experimental efforts to achieve the desired quantum regime. Whereas the weak DDI in a\nchromium BEC is well described with the Gross-Pitaevskii equation, stronger dipolar\ninteractions certainly necessitate a beyond-mean-field description within a Bogoliubov\ntheory.\nIn parallel to research on bosons, cold fermions also trigger great interest because\nthey are actually often found in nature, e.g., within the electron gas of metals, as\nneutrons of heavy stars, or as quarks in plasmas as constituent elements of composite particles. Contrary to Bose systems, quantum degeneracy in experiments is much\nmore difficult to achieve in Fermi systems, since s-wave scattering is absent between\nidentical fermions, due to the Pauli exclusion principle. It was first achieved in 1999\nfor alkali atoms using a technique based on the sympathetic cooling with a second spin\nstate, another species, or a different isotope. For highly magnetic atoms, quantum degeneracy was achieved for dysprosium in 2012 using the standard sympathetic cooling\ntechnique, while in 2014 erbium was cooled deep into the degenerate regime using a\ndirect evaporative cooling mediated by dipolar collisions. This direct cooling scheme\nivallows producing very dense Fermi gas down to 10% of the Fermi temperature.\nFurthermore, a novel kind of strongly dipolar quantum gases became available in\nthe last several years. These are weakly bound polar molecules produced from atoms\nwith large magnetic dipole moments, such as erbium. Only very recently a quantum\ndegenerate dipolar Fermi gas of potassium-rubidium molecules has been experimentally realized. Unlike previously considered magnetic systems, heteronuclear molecules\nsuch as potassium-rubidium possess large electric dipole moments. The next natural\nstep is to polarize this system in a preferential direction by an external electric field,\nsuch that the DDI dominates the behavior of the system, which would open up the\nrealm for experimental investigation of strong dipolar Fermi gases...