Few-Body Precursor of the Higgs Mode in a Fermi Gas

Abstract

We demonstrate that an undamped few-body precursor of the Higgs mode can be investigated in a harmonically trapped Fermi gas. Using exact diagonalisation, the lowest monopole mode frequency is shown to depend non-monotonically on the interaction strength, having a minimum in a crossover region. The minimum deepens with increasing particle number, reflecting that the mode is the fewbody analogue of a many-body Higgs mode in the superfluid phase, which has a vanishing frequency at the quantum phase transition point to the normal phase. We show that this mode mainly consists of coherent excitations of time-reversed pairs, and that it can be selectively excited by modulating the interaction strength, using for instance a Feshbach resonance in cold atomic gases.The transition from few-body quantum physics to the thermodynamic limit with increasing particle number is a fundamental problem in science. A systematic investigation of this question is complicated by the fact that the few-body systems existing in nature, such as atoms and nuclei, have limited tunability. Artificially created clusters [1,2] or semiconductor quantum dots [3] offer more flexibility, but they are often strongly coupled to their surroundings making a study of pure quantum states difficult. The creation of highly controllable fewfermion systems using cold atoms in microtraps [4,5], however, has opened new perspectives. Tunneling experiments in the few-body limit demonstrated single-atom control [6,7]. One has already observed the formation of a Fermi sea [8], as well as pair correlations in onedimensional (1D) few-body atomic gases [5] that have also been studied extensively theoretically [9][10][11][12][13]. The few-to many-body transition is arguably even more interesting in higher dimensions, where quantum phase transitions with varying degrees of broken symmetry are ubiquitous [14]. A key question concerns the few-body fate of the order parameter, which describes a broken symmetry phase in the thermodynamic limit.Another fundamental problem concerns the properties of the Higgs mode, which corresponds to oscillations in the size of the order parameter for a given broken symmetry phase [15,16]. Elementary particles acquire their mass from the presence of a Higgs mode [17], which was famously observed at CERN [18,19]. The Higgs mode also leads to collective modes in condensed matter and nuclear systems [14,20]. Despite its fundamental importance, the list of table top systems where it has been observed is short, mainly because it is typically strongly damped, and because it couples only weakly to experimental probes [21][22][23]. Experimental evidence for the existence of a Higgs mode has been reported in disordered and niobium selenide superconductors [24][25][26][27]. Also, neutron scattering experiments for a quantum antiferromagnet [28] are consistent with the presence of a broad Higgs mode, and lattice experiments combined with theoretical models for bosonic atoms in an optical lattice, indicate that a threshold feature can be interpreted i...

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