The `Higgs' Amplitude Mode at the Two-Dimensional Superfluid-Mott Insulator Transition (1204.5183v2)

Abstract: Spontaneous symmetry breaking plays a key role in our understanding of nature. In a relativistic field theory, a broken continuous symmetry leads to the emergence of two types of fundamental excitations: massless Nambu-Goldstone modes and a massive `Higgs' amplitude mode. An excitation of Higgs type is of crucial importance in the standard model of elementary particles and also appears as a fundamental collective mode in quantum many-body systems. Whether such a mode exists in low-dimensional systems as a resonance-like feature or becomes over-damped through coupling to Nambu-Goldstone modes has been a subject of theoretical debate. Here we reveal and study a Higgs mode in a two-dimensional neutral superfluid close to the transition to a Mott insulating phase. We unambiguously identify the mode by observing the expected softening of the onset of spectral response when approaching the quantum critical point. In this regime, our system is described by an effective relativistic field theory with a two-component quantum-field, constituting a minimal model for spontaneous breaking of a continuous symmetry. Additionally, all microscopic parameters of our system are known from first principles and the resolution of our measurement allows us to detect excited states of the many-body system at the level of individual quasiparticles. This allows for an in-depth study of Higgs excitations, which also addresses the consequences of reduced dimensionality and confinement of the system. Our work constitutes a first step in exploring emergent relativistic models with ultracold atomic gases.

• The paper experimentally detects the Higgs amplitude mode in a 2D superfluid-Mott insulator transition using ultracold bosonic atoms in optical lattices.
• Key findings include the observed softening and distinct spectral response of the Higgs mode near the quantum critical point.
• This research provides experimental evidence supporting theoretical predictions of the Higgs mode's behavior in 2D systems and opens new avenues for studying quantum phase transitions.

An Analysis of the Higgs Amplitude Mode at the 2D Superfluid-Mott Insulator Transition

The paper "The `Higgs' Amplitude Mode at the Two-Dimensional Superfluid-Mott Insulator Transition" introduces a nuanced investigation into the presence of the Higgs amplitude mode within a two-dimensional (2D) superfluid transitioning to a Mott insulating phase. The experiment delineated in this paper integrates extensive measurement precision with ultracold atomic systems to explore the interaction between quantum phase transitions and emergent relativistic models.

Key Focus and Methodology

The paper centers on experimental detection and analysis of the Higgs mode in 2D systems. The authors aim to resolve debates over whether this mode manifests as a damped feature or if it remains distinct due to phase mode decay interactions. Their method employs ultracold bosonic atoms trapped in optical lattices, representing an ideal setup to model Bose-Hubbard dynamics. These systems allow meticulous alteration of parameters like tunneling amplitude $J$ and onsite interaction energy $U$, providing an adjustable paper of the coupling $j = J/U$.

Experimental Findings

The experimental approach involved tuning the lattice depth and employing lattice modulation spectroscopy to probe excitation spectra. The paper reports a distinct softening of the Higgs mode near the quantum critical point where the superfluid-Mott transition occurs. Notably, reduced dimensionality in this experiment allows for discrete analysis of individual quasiparticles, unveiling insights into amplitude vibrations and their transitions in spectral behavior.

A significant outcome is the observed softening of the spectral response as the critical point is approached from the superfluid side, supporting its identification as the Higgs mode. Utilizing high-resolution data acquisition, the authors attained almost single-quasiparticle resolution, affirming theoretical predictions at critical coupling values.

Theoretical and Analytical Context

From a theoretical standpoint, the investigation draws on effective field theories, particularly relating to $O(2)$ relativistic models. The analysis distinguishes two excitation modes: amplitude (Higgs) and phase (Nambu-Goldstone), with the amplitude mode exhibiting a finite excitation gap that diminishes when nearing the Mott transition.

The authors perform both Gutzwiller approximations and cluster mean-field simulations to validate experimental outcomes. These theoretical supports offer descriptive frequencies and aggregations consistent with observed modulation responses, further buttressing experimental claims with a stable theoretical framework.

Implications and Future Directions

These findings influence both theoretical and practical domains. At the theoretical level, they contribute to the foundational understanding of quantum many-body systems under symmetry-breaking paradigms. Practically, the techniques establish platforms for exploring novel quantum phases and properties of matter. Experimentally observing the Higgs mode in two dimensions initiates new discourse on its manifestations across various condensed matter systems and potentially bridges gaps to particle physics by paralleling confined framework behaviors with conjectured scenarios in high-energy physics.

Future developments may involve deepening exploration into broader dimensional systems, extending these methodologies to different quantum phase transitions, or refining theories regarding amplitude decay in reduced dimensionalities. The paper paves pathways for engaged interdisciplinary research that spans quantum simulation, atomic physics, and condensed matter theory. This paper’s experimental and analytical contributions mark a critical step in advancing the scope and application of quantum critical phenomena.