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arXiv:1510.00987 · Physical Review Letters

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

J. Bjerlin, S. M. Reimann, Georg M. Bruun

Published Apr 13, 2016• 35 citations
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Abstract

We demonstrate that an undamped few-body precursor of the Higgs mode can be investigated in a harmonically trapped Fermi gas. Using exact diagonalization, the lowest monopole mode frequency is shown to depend nonmonotonically on the interaction strength, having a minimum in a crossover region. The minimum deepens with increasing particle number, reflecting that the mode is the few-body 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.

DOI
10.1103/physrevlett.116.155302

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We demonstrate that an undamped few-body precursor of the Higgs mode can be investigated in a harmonically trapped Fermi gas. Using exact diagonalization, the lowest monopole mode frequency is shown to depend nonmonotonically on the interaction strength, having a minimum in a crossover region. The minimum deepens with increasing particle number, reflecting that the mode is the few-body 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.
Many-body physics describes phenomena that cannot be understood by looking only at the constituents of a system1. Striking examples are broken symmetry, phase transitions and collective excitations2. To understand how such collective behaviour emerges as a system is gradually assembled from individual particles has been a goal in atomic, nuclear and solid-state physics for decades3–6. Here we observe the few-body precursor of a quantum phase transition from a normal to a superfluid phase. The transition is signalled by the softening of the mode associated with amplitude vibrations of the order parameter, usually referred to as a Higgs mode7. We achieve fine control over ultracold fermions confined to two-dimensional harmonic potentials and prepare closed-shell configurations of 2, 6 and 12 fermionic atoms in the ground state with high fidelity. Spectroscopy is then performed on our mesoscopic system while tuning the pair energy from zero to a value larger than the shell spacing. Using full atom counting statistics, we find the lowest resonance to consist of coherently excited pairs only. The distinct non-monotonic interaction dependence of this many-body excitation, combined with comparison with numerical calculations allows us to identify it as the precursor of the Higgs mode. Our atomic simulator provides a way to study the emergence of collective phenomena and the thermodynamic limit, particle by particle. An atomic simulator formed of a few ultracold fermionic atoms trapped in a two-dimensional harmonic potential exhibits precursors of a quantum phase transition, revealing the onset of collective quantum many-body phenomena in a few-body system.
We study the Higgs mode of a strongly interacting Fermi gas in the crossover regime between a fermionic and bosonic superfluid. By periodically modulating the interaction strength of the gas, we parametrically excite the Higgs mode and study its resonance frequency and line width as a function of both interaction strength and temperature. We find that the resonance frequency at low temperature agrees with a local-density approximation of the pairing gap. Both frequency and line width do not exhibit a pronounced variation with temperature, which is theoretically unexpected, however, in qualitative agreement with a different recent study.
This thesis reports on experiments investigating the emergence of many-body physics in mesoscopic two-dimensional (2D) few-fermion systems. \nThe starting point are low-entropy samples of ultracold 6Li atoms in a quasi-2D geometry. When scanning the depth of the trapping potential, we observe an enhanced stability of closed-shell configurations of the 2D harmonic oscillator. This enables us to deterministically initialize closed-shell configurations of 2, 6 and 12 atoms in the ground state. \nBy modulating the interaction strength we probe the excitation spectrum arising from the interplay of the finite single-particle gap in closed-shell configurations with the tunable attractive interactions. The full atom-counting statistics reveal pair excitations with a non-monotonous interaction dependence. These modes can be identified as the few-body precursors of a Higgs mode associated with a normal to superfluid phase transition in the thermodynamic limit. \nAdditionally, we can access the momentum distribution with single-particle resolution. This is demonstrated by measuring the momentum distribution of up to six non-interacting fermions in the ground state of the 2D trap. We observe strong density correlations that arise from fermionic quantum statistics. In the future, extending the imaging scheme to interacting systems will allow us to observe the emergence of fermionic many-body paring directly in momentum space.
Experimental evidence of the Higgs mode in strongly interacting superfluid Fermi gases had not been observed until recently [Behrle et al., Nat. Phys. 14, 781 (2018).]. Due to the coupling with other collective modes and quasiparticle excitations, generating stable Higgs-mode oscillations is challenging. We study how to excite long-lived Higgs-mode oscillations in a homogeneous superfluid Fermi gas in the BCS-BEC crossover. We find that the Higgs mode can be excited by time-periodically modulating the scattering length at an appropriate amplitude and frequency. However, even for a modulation frequency below twice the pairing-gap energy, quasiparticles are still excited through the generation of higher harmonics due to nonlinearity in the superfluid. More importantly, we find that persistent Higgs-mode oscillations with almost constant amplitude can be produced by removing particles at an appropriate momentum, and the oscillation amplitude can be controlled by the number of removed particles. Finally, we propose two ways to experimentally realize particle removal.
We study collective excitations of a trapped Fermi gas at finite temperature using the Bogoliubov--de Gennes mean-field theory in conjunction with the generalized random-phase approximation. The collective excitations are analyzed through the density response of a monopole excitation. We show the appearance of several modes at the normal-fluid--superfluid phase-transition temperature: Higgs mode--like pairing amplitude modulations, analogues of the second sound in the trapped gas, and an edge mode that is also the strongest mode in the response.
The Higgs mode corresponds to the collective motion of particles due to the vibrations of an invisible field. It plays a fundamental role in our understanding of both low- and high-energy physics, giving elementary particles their mass and leading to collective modes in condensed-matter and nuclear systems. The Higgs mode has been observed in a limited number of table-top systems, where it however is characterized by a short lifetime due to decay into a continuum of modes. A major goal which has remained elusive so far is, therefore, to realize a long-lived Higgs mode in a controllable system. Here, we show how an undamped Higgs mode can be observed unambiguously in a Fermi gas in a two-dimensional trap, close to a quantum phase transition between a normal and a superfluid phase. We develop a first-principles theory of the pairing and the associated collective modes, which is quantitatively reliable when the pairing energy is much smaller than the trap level spacing, yet simple enough to allow the derivation of analytical results. The theory includes the trapping potential exactly, which is demonstrated to stabilize the Higgs mode by making its decay channels discrete. It is shown to be realistic to realize the proposed system using atoms in microtraps. The unrivaled flexibility of atomic gases combined with the quantitatively accurate theory opens the door to a systematic study of the Higgs mode, including the role of confinement and finite-size effects.