Fermionic spectrum of superfluid phases of 3 He under strong confinement

B. Fåk, H. R. Glyde

Cesar R. Cabrera, René Henke, Lukas Broers +5 more

In phase transitions, spontaneous symmetry breaking results in a nonzero order parameter and two collective excitations: the Goldstone and the amplitude mode. These modes, which define key properties of superconductors and fermionic superfluids, are well understood in homogeneous systems. However, their behavior under strong confinement remains largely unexplored, particularly when their excitation energy becomes comparable to the imposed discrete level spacing. In this scenario, hybridization between different collective modes is expected to take place. Here, we show how the amplitude mode hybridizes with a spatial mode in a confined fermionic superfluid. Using lattice modulation spectroscopy, we observe the evolution of the mode throughout the entire crossover from the Bardeen-Cooper-Schrieffer (BCS) state to Bose-Einstein condensation (BEC) of molecules. In the BCS regime, the excitation energy is located at twice the pairing gap, then gradually becomes an in-gap excitation in the strongly correlated regime. Further to the BEC limit, the excitation energy approaches twice the level spacing. The spectral weight of this mode vanishes when approaching the superfluid critical temperature. Our experimental results are in excellent agreement with an effective field theory, providing strong evidence that amplitude oscillations hybridize with and eventually transform into breathing oscillations of the order parameter. The strong modification of the excitation spectrum reveals how confinement and finite-size effects impact fundamental modes of symmetry-broken states.

Matthew Case

In this thesis, we study various issues arising from the QED theory of underdoped, high temperature superconductors in 2+1 dimensions. The theory breaks up roughly into two sectors: fermionic and bosonic. With regard to the fermionic sector, we consider confinement of the emergent gauge field which we take to be compact. In the absence of fermions, the interaction between monopoles is Coulombic and the well known result is that the pure gauge theory is permanently confining. With the addition of fermions, the interaction becomes logarithmic, and an analogy with the usual Kosterlitz-Thouless transition suggests a deconfinement transition for the fermions. We show, however, that, when screening is taken into account, the deconfined phase is destabilized and fermions remain permanently confined. The bosonic sector models Cooper pair phase fluctuations, whose effect on the depletion of the superfluid density we examine in two separate studies. In the first of these, we study the quantum XY model, and show that the quasi-two dimensionality, low critical temperatures and large d-wave gap characteristic of underdoped cuprates severely constrain the form of the superfluid density. Under these assumptions, we find that phase fluctuations alone are insufficient to account for recent observations of deviations from Uemura scaling, and that the quasiparticle contribution is a necessity. We use our results to satisfactorily fit the recent data. In the second study, we model the cuprates by a layered system of interacting bosons and examine the collective excitations in this system. Depending on the anisotropy and the interaction strength, we find find four different regimes of temperature dependence of the superfluid density. We argue that interactions in the underdoped cuprates are effectively short-ranged and weak. Finally, we study the related issue of disordered, interacting bosons in the large-N limit and 2 strong commensuration. Perturbatively at weak disorder and numerically at strong, we show that th screening of the random potential due to interactions is insufficient to delocalize the single-particl states so that no superfluid transition occurs from the Mott insulator.

J. M. Parpia, Nikolay Zhelev, T. S. Abhilash +5 more

L. V. Levitin

T. Domański, J. Ranninger

The signature of superfluidity in bosonic systems is a sound-wave-like spectrum of the single particle excitations which in the case of strong interactions is roughly temperature independent. In Fermionic systems, where Fermion pairing arises as a resonance phenomenon between free Fermions and paired Fermionic states (examples are: the atomic gases of $^{6}\mathrm{Li}$ or $^{40}\mathrm{K}$ controlled by a Feshbach resonance, polaronic systems in the intermediary coupling regime, $d$-wave hole pairing in the strongly correlated Hubbard system), remnants of such superfluid characteristics are expected to be visible in the normal state. The single particle excitations maintain a sound-wave-like structure for wave vectors above a certain ${q}_{\mathrm{min}}(T)$ where they practically coincide there with the spectrum of the superfluid phase for $T<{T}_{c}$. Upon approaching the transition from above this region in $q$ space extends down to small momenta, except for a narrow region around $q=0$ where such modes change into damped free particle like excitations.